Download PERBANDINGAN KURIKULUM

PEMETAAN KURIKULUM
CAMBRIDGE INT. EXAMINATION (CIE) 2008 & NASIONAL (KTSP 2006)
MATEMATIKA
Catatan:
- pemetaan kurikulum berikut belum disusun dengan urut, karena perbedaan urutan antara kurikulum nasional & internasional
- IGCSE setara dengan kelas X-XI, A level setara dengan kelas XI-XII
Gambaran umum
No.
Topik
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Introduction to Mathematics
Graph
Two & Three Dimensional Space
Trigonometry
Logarithmic & Exponential function, radicals
Quadratics
Linear functions and equations
Algebra – introduction
Algebra – functions & inverse
Algebra – Matrices, vector & transformation
Algebra: Sigma Notations, Sequences and
Series, and Mathematical Induction
Inequalities
Mathematical Logic
Calculus – Limit function
Calculus – Integral
L.
M.
N.
O.
Differential
Numerical solution & equation
Complex number
Statistics & Probability
Mechanics
Algorithm – Suku Banyak
Keterangan:
Level di kurikulum CIE
A level
IGCSE
P1 P3 S1 S2 M1
V
V
v
v
V
V V
V
V
V
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V
V
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V
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V
V
V
v
M2
Level di kurikulum nasional
XI
XII
X
IA IS IA IS
v
v
V
V
V
v
v
V
v
v
v
V
v
v
v
v
v
V
v
v
V
v
V
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v
v
v
v
v
v
v
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V
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Level di kurikulum SNBI
XI
XII
X
IA IS IA IS
P : pure math
S : statistic
M : mechanics
IA : program IPA
IS : program IPS
Untuk mengambil A level, siswa perlu mengikuti ujian sebanyak 4 paper dengan kombinasi pilihan sebagai berikut:
Pilihan 1 : P1, P3, S1 dan S2
Pilihan 2 : P1, P3, M1 dan M2
Pilihan 3 : P1, P3, S1 dan M1
Untuk mengambil AS level, yang berbobot setengah dari sertifikat A level, siswa perlu mengikuti ujian sebanyak 3 paper dengan kombinasi pilihan sebagai berikut:
Pilihan 1 : P1, P2 dan S1
Pilihan 2 : P1, P2 dan M1
Detail
A. INTRODUCTION TO MATHEMATICS
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Number, set notation and language
- identify and use natural numbers, integers (positive, negative and zero), prime numbers, square numbers, common factors
and common multiples, rational and irrational numbers (e.g. π , 2 ), real numbers; continue a given number sequence;
recognise patterns in sequences and relationships between different sequences, generalise to simple algebraic statements
(including expressions for the nth term) relating to such sequences
- use language, notation and Venn diagrams to describe sets and represent relationships between sets as follows:
Level
X-1
Nasional 2006
Indikator
2. Squares, square roots and cubes
- calculate squares, square roots, cubes and cube roots of numbers
3. Directed numbers
- use directed numbers in practical situations (e.g. temperature change, flood levels)
4. Vulgar and decimal fractions and percentages
- use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts;
recognise equivalence and convert between these forms
5. Ordering
- order quantities by magnitude and demonstrate familiarity with the symbols =, ╪, >, <, [,Y
6. Standard form
- use the standard form A x 10n where n is a positive or negative integer, and 1 YA< 10
7. The four rules
- use the four rules for calculations with whole numbers, decimal fractions and vulgar (and mixed) fractions, including correct
ordering of operations and use of brackets
8. Estimation
- make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and
decimal places and round off answers to reasonable accuracy in the context of a given problem
9. Limits of accuracy
- give appropriate upper and lower bounds for data given to a specified accuracy (e.g. measured lengths)
- obtain appropriate upper and lower bounds to solutions of simple problems (e.g. the calculation of the perimeter or the area
of a rectangle) given data to a specified accuracy
10. Ratio, proportion, rate
- demonstrate an understanding of the elementary ideas and notation of ratio, direct and inverse proportion and common
measures of rate; divide a quantity in a given ratio; use scales in practical situations; calculate average speed
- express direct and inverse variation in algebraic terms and use this form of expression to find unknown quantities; increase
and decrease a quantity by a given ratio
11. Percentages
- calculate a given percentage of a quantity; express one quantity as a percentage of another; calculate percentage increase or
decrease
- carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage
profit
12. Use of an electronic calculator
- use an electronic calculator efficiently; apply appropriate checks of accuracy
13. Measures
- use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger
or smaller units
14. Time
- calculate times in terms of the 24-hour and 12-hour clock; read clocks, dials and timetables
15. Money
- calculate using money and convert from one currency to another
16. Personal and household finance
- use given data to solve problems on personal and household finance involving earnings, simple interest and compound
interest (knowledge of compound interest formula is not required), discount, profit and loss; extract data from tables and
charts
23. Indices
- use and interpret positive, negative and zero indices
- use and interpret fractional indices, e.g. solve 32x = 2
B. GRAPHS
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Graphs in practical situations
- demonstrate familiarity with cartesian coordinates in two dimensions, interpret and use graphs in practical situations including
travel graphs and conversion graphs, draw graphs from given data
- apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and
deceleration; calculate distance travelled as area under a linear speed-time graph
Level
Nasional 2006
Indikator

2. Graphs of functions
- construct tables of values for functions of the form ax + b, ± x2 + ax + b, a/x (x ╪ 0) where a and b are integral constants;
draw and interpret such graphs; find the gradient of a straight line graph; solve linear and quadratic equations approximately by
graphical methods
- construct tables of values and draw graphs for functions of the form axn where a is a rational constant and n = − 2, − 1, 0, 1, 2,
3 and simple sums of not more than three of these and for functions of the form ax where a is a positive integer; estimate
gradients of curves by drawing tangents; solve associated equations approximately by graphical methods
3. Straight line graphs
- interpret and obtain the equation of a straight line graph in the form y = mx + c;
determine the equation of a straight line parallel to a given line
- calculate the gradient of a straight line from the co-ordinates of two points on it;
calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
C. TWO &THREE DIMENSIONAL SPACE
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Geometrical terms and relationships
- use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex
angles, perpendicular, similarity, congruence; use and interpret vocabulary of triangles, quadrilaterals, circles,
polygons and simple solid figures including nets
- use the relationships between areas of similar triangles, with corresponding results for similar figures and
extension to volumes and surface areas of similar solids
2. Geometrical constructions
- measure lines and angles; construct a triangle given the three sides using ruler and compasses only; construct
Level
X-2
Nasional 2006
Indikator
 Menentukan kedudukan titik dan
garis dalam ruang
 Menentukan kedudukan titik dan
bidang dalam ruang
 Menentukan kedudukan antara dua
garis dalam ruang
 Menentukan kedudukan garis dan
bidang dalam ruang
other simple geometrical figures from given data using protractors and set squares as necessary; construct angle
bisectors and perpendicular bisectors using straight edges and compasses only; read and make scale drawings
 Menentukan kedudukan antara dua
bidang dalam ruang
3. Symmetry
- recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions and
properties of triangles, quadrilaterals and circles directly related to their symmetries
- recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone); use the
following symmetry properties of circles:
(a) equal chords are equidistant from the centre
(b) the perpendicular bisector of a chord passes through the centre
(c) tangents from an external point are equal in length
 Menentukan jarak titik dan garis
dalam ruang
4. Angle properties
- calculate unknown angles using the following geometrical properties:
(a) angles at a point
(b) angles on a straight line and intersecting straight lines
(c) angles formed within parallel lines
(d) angle properties of triangles and quadrilaterals
(e) angle properties of regular polygons
(f) angle in a semi-circle
(g) angle between tangent and radius of a circle
- use in addition the following geometrical properties:
(a) angle properties of irregular polygons
(b) angle at the centre of a circle is twice the angle at the circumference
(c) angles in the same segment are equal
(d) angles in opposite segments are supplementary; cyclic quadrilaterals
5. Locus
- use the following loci and the method of intersecting loci for sets of points in two dimensions:
(a) which are at a given distance from a given point
(b) which are at a given distance from a given straight line
(c) which are equidistant from two given points
(d) which are equidistant from two given intersecting straight lines
6. Mensuration
- carry out calculations involving the perimeter and area of a rectangle and triangle, the circumference and area
of a circle, the area of a parallelogram and a trapezium, the volume of a cuboid, prism and cylinder and the
surface area of a cuboid and a cylinder
- solve problems involving the arc length and sector area as fractions of the circumference and area of a circle,
the surface area and volume of a sphere, pyramid and cone (given formulae for the sphere, pyramid and cone)
 Menentukan jarak titik dan bidang
dalam ruang
 Menentukan jarak antara dua garis
dalam ruang
 Menentukan besar sudut antara
dua garis dalam ruang
 Menentukan besar sudut antara
garis dan bidang dalam ruang
 Menentukan besar sudut antara dua
bidang dalam ruang
A
level
A
level
P1
- determine the locus of points, lines and planes in three dimensional space,
- find the volumes of solid figures,
- draw solid figures,
- find the distances from a point to a line and from a point to a plane,
- find the distance of two non parallel lines in a solid figure,
- find the distance of two parallel planes in a solid figure,
- draw and calculate the angle between a line and a plane,
- draw and calculate the angle between two planes,
- draw the intersection of a plane and a solid figure
XI-1
 Menentukan pusat dan jari-jari
lingkaran yang persamaannya
diketahui.
 Menentukan persamaan lingkaran
yang memenuhi kriteria tertentu.
– find the length, gradient and mid-point of a line segment, given the coordinates of the end-points;
– find the equation of a straight line given sufficient information (e.g. the coordinates of two points on it, or
one point on it and its gradient);
– understand and use the relationships between the gradients of parallel and perpendicular lines;
– interpret and use linear equations, particularly the forms y = mx + c and y − y1 = m(x − x1) ;
– understand the relationship between a graph and its associated algebraic equation, and use the relationship
between points of intersection of graphs and solutions of equations (including, in simple cases, the
correspondence between a line being tangent to a curve and a repeated root of an equation).
Measuring circular
– understand the definition of a radian, and use the relationship between radians and degrees;
– use the formulae s = rθ and
circle.
 Merumuskan persamaan lingkaran
berpusat di (0,0) dan (a,b).
 Merumuskan persamaan lingkaran
berpusat di (0,0) dan (a,b).
 Menentukan pusat dan jari-jari
lingkaran yang persamaannya
diketahui.
 Menentukan persamaan lingkaran
yang memenuhi kriteria tertentu.
in solving problems concerning the arc length and sector area of a
D. TRIGONOMETRY
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE - interpret and use three-figure bearings measured clockwise from the North (i.e. 000°-360°)
- apply Pythagoras' theorem and the sine, cosine and tangent ratios for acute angles to the
calculation of a side or of an angle of a right-angled triangle (angles will be quoted in, and
answers required in, degrees and decimals to one decimal place)
- solve trigonometrical problems in two dimensions involving angles of elevation and
depression, extend sine and cosine values to angles between 90° and 180°, solve problems
using the sine and cosine rules for any triangle and the formula area of triangle =
,
solve simple trigonometrical problems in three dimensions including angle between a line
and a plane
Level
X-2
Nasional 2006
Indikator
 Menentukan nilai perbandingan trigonometri pada
segitiga siku-siku
 Menentukan nilai perbandingan trigonometri dari
sudut khusus.
 Menentukan nilai perbandingan trigonometri dari
sudut di semua kuadran
 Menggambar grafik fungsi trigonometri sederhana.
 Menyelesaikan persamaan trigonometri sederhana.
 Membuktikan identitas trigonometri sederhana.
A
level
A
level
P1
- explain the meaning of degree and radian,
- change the angle unit, degrees to radians and vice versa,
- determine sine, cosine and tangent of an angle of a right triangle,
- determine sine, cosine and tangent of special angles,
- determine sine, cosine and tangent of angles in all quadrants,
- find the angles with the value of sine, cosine or tangent is given,
- use calculator to find approximation values of trigonometric functions and angles,
- apply trigonometry formulas to solve problems,
- sketch and use graphs of sine, cosine and tangent functions,
- apply trigonometric identities to solve problems,
- prove elementary trigonometric identities,
- prove sine and cosine laws,
- calculate areas of triangles,
- construct mathematical models of problems involving trigonometric functions, sine and
cosine laws, solve the models, and interpret the solutions,
- find all the solutions of simple trigonometrycal equations lying in a specified interval.
– sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and
using either degrees or radians);
– use the exact values of the sine, cosine and tangent of 30º, 45º, 60º, and related angles, e.g.
– use the notations sin−1 x, cos−1 x, tan−1 x to denote the principal values of the inverse
trigonometric relations;
– use the identities
– find all the solutions of simple trigonometrical equations lying in a specified interval
(general forms of solution are not included).
 Menyelesaikan perhitungan soal menggunakan
aturan sinus dan aturan cosinus.
 Menghitung luas segitiga yang komponennya
diketahui
XI-1

Mengidentifikasi masalah yang berhubungan
dengan perbandingan, fungsi, persamaan dan
identitas trigonometri

Membuat model matematika yang berhubungan
dengan perbandingan, fungsi, persamaan dan
identitas trigonometri

Menentukan penyelesaian model matematika dari
masalah yang berkaitan dengan perbandingan,
fungsi, persamaan dan identitas trigonometri

Menafsirkan hasil penyesaian masalah yang
berkaitan dengan perbandingan, fungsi, persamaan
dan identitas trigonometri
 Menggunakan rumus sinus jumlah dan selisih dua
sudut.
 Menggunakan rumus kosinus jumlah dan selisih dua
sudut
 Menyatakan perkalian sinus dan cosinus dalam
jumlah atau selisih sinus atau cosinus.
A
level
P3
– understand the relationship of the secant, cosecant and cotangent functions to
cosine, sine and tangent, and use properties and graphs of all six trigonometric
functions for angles of any magnitude;
– use trigonometrical identities for the simplification and exact evaluation of expressions and
in the course of solving equations, and select an identity or identities appropriate to the
context, showing familiarity in particular with the use of θ θ sec2 ≡ 1+ tan2 and θ θ cosec2 ≡
1+ cot2 , the expansions of sin(A ± B) , cos(A ± B) and tan(A ± B) , the formulae for sin2A ,
cos2A and tan2A , the expressions of asinθ + b cosθ in the forms Rsin(θ ± α) and Rcos(θ ± α)
 Menggunakan rumus trigonometri jumlah dan selisih
dua sudut dalam pemecahan masalah.
 Membuktikan rumus trigonometri jumlah dan selisih
dua sudut.
 Membuktikan rumus trigonometri jumlah dan selisih
dari sinus dan cosinus dua sudut.
 Merancang dan membuktikan identitas trigonometri
 Menyelesaiakan masalah yang melibatkan rumus
jumlah dan selisih dua sudut
E. EXPONENTS, RADICALS, AND LOGARITHMS
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Squares, square roots and cubes
- calculate squares, square roots, cubes and cube roots of numbers Algebraic
representation and formulae
- use letters to express generalized numbers and express basic arithmetic
processes algebraically, substitute numbers for words and letters in formulae;
transform simple formulae; construct simple expressions and set up simple equations
- construct and transform more complicated formulae and equations
Level
X-1
2. Algebraic manipulation
- manipulate directed numbers; use brackets and extract common factors
- expand products of algebraic expressions; factorise where possible expressions of the
form ax + bx+ kay+ kby, a2x2 – b2 y2; a2 + 2ab + b2; ax2 + bx+ c; manipulate
algebraic fractions, factorise and simplify expressions
Nasional 2006
Indikator
 Mengubah bentuk pangkat negatif ke pangkat positif dan
sebaliknya.
 Mengubah bentuk akar ke bentuk pangkat dan sebaliknya.
 Melakukan operasi aljabar pada bentuk pangkat, dan akar
 Menyederhanakan bentuk aljabar yang memuat pangkat
rasional
 Merasionalkan bentuk akar
 Mengubah bentuk pangkat ke bentuk logaritma dan
sebaliknya.
 Melakukan operasi aljabar dalam bentuk logaritma.
 Menyederhanakan bentuk aljabar yang memuat bentuk
pangkat, akar, dan logaritma
 Membuktikan sifat-sifat sederhana tentang bentuk pangkat,
akar, dan logaritma

A
level
- change expressions involving negative exponents to the expressions involving
positive exponents, and vice versa,
- change expressions involving radicals to the expressions involving exponents, and
vice versa,
- change expressions involving exponents to the expressions involving logarithms,
and vice versa,
XII-2
 Menghitung nilai fungsi eksponen dan logaritma
 Menentukan sifat-sifat fungsi eksponen dan logaritma
 Menyelesiakan masalah yang berkaitan dengan fungsi
eksponen dan logaritma
A
level
P3
- simplify expressions involving rational exponents,
- simplify expressions involving logarithms,
- rationalize denominators involving radicals,
- prove elementary laws of exponents, radicals, and logarithms.
- understand the relationship between logarithms and indices, and use the laws of
logarithms (excluding change of base);
– understand the definition and properties of x e and lnx , including their relationship
as inverse functions and their graphs;
- use logarithms to solve equations of the form ax b = , and similar inequalities;
- use logarithms to transform a given relationship to linear form, and hence determine
unknown constants by considering the gradient and/or intercept.
 Menentukan nilai fungsi eksponen dan logaritma untuk
menggambar grafik
 Menemukan sifat-sifat grafk fungsi eksponen dan logaritma
 Menentukan penyelesaian pertidaksamaan eksponen dan
syaratnya
 Menentukan penyelesaian pertidaksamaan logaritma dan
syaratnya
F. QUADRATICS
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE Graphs of functions – construct tables of values for functions of the form ax + b, ± x2 + ax
+ b, a/x (x ╪ 0) where a and b are integral constants; draw and interpret such graphs; find
the gradient of a straight line graph; solve linear and
quadratic equations approximately by graphical methods
- construct tables of values and draw graphs for functions of the form axn where a is a
rational constant and n = − 2, − 1, 0, 1, 2, 3 and simple sums of not more than three of
these and for functions of the form ax where a is a positive integer; estimate gradients of
curves by drawing tangents; solve associated equations approximately by graphical
methods
- use function notation, e.g. f (x) = 3x- 5, f:xa 3x- 5 to describe simple functions, and the
notation f
-1(x) to describe their inverses; form composite functions as defined by gf(x) = g(f(x))
Level
X-1
Nasional 2006
Indikator
 Membedakan relasi yang merupakan fungsi dan yang
bukan fungsi
 Mengidentifikasi jenis-jenis dan sifat-sifat fungsi
 Menyelidiki karakteristik grafik fungsi kuadrat dari
bentuk aljabarnya.
 Menggambar grafik fungsi kuadrat
 Menentukan definit positif dan definit negatif
 Membuat grafik fungsi aljabar sederhana
A
level
- solve quadratic equations by factoring, by completing the square, and by quadratic
formula,
- use the discriminant of quadratic polynomials to solve the quadratic equation roots
problems,
- calculate the sum and the product of the root of a quadratic equation,
- determine a quadratic equation with its roots satisfy given conditions,
- recognize and solve equations in x which are quadratic in some function of x,
- determine the symmetric axe and a maximum or a minimum point of the graph of a
quadratic function,
- sketch a graph of a quadratic function,
- determine whether a quadratic function is definitely positive or negative,
- explain the relations between quadratic equations and quadratic functions,
- determine a quadratic function where its graph contains three given nonlinear points,
- construct mathematical models of problems involving quadratic equations and quadratic
functions, solve the models, and interpret the solutions.
A
level
P1
– carry out the process of completing the square for a quadratic polynomial
,
and use this form, e.g. to locate the vertex of the graph of
or to sketch the
graph;
- find the discriminant of a quadratic polynomial ax + bx + c 2 and use the discriminant,
e.g. to determine the number of real roots of the equation 2 0 ax + bx + c = ;
- solve quadratic equations, and linear and quadratic inequalities, in one unknown;
- solve by substitution a pair of simultaneous equations of which one is linear and
one is quadratic;
- recognize and solve equations in x which are quadratic in some function of x, e.g.
 Menentukan akar-akar persamaan kuadrat.
 Menentukan himpunan penyelesaian pertidaksamaan
kuadrat
 Menggunakan rumus jumlah dan hasil kali akar-akar
persamaan kuadrat
 Membedakan jenis-jenis akar persamaan kuadrat
 Menyusun persamaan kuadrat yang akar-akarnya
diketahui.
 Menentukan penyelesaian persamaan yang dapat
dinyatakan ke bentuk persamaan
kuadrat/pertidaksamaan kuadrat

Membuat model matematika dari suatu masalah dalam
matematika, mata pelajaran lain atau kehidupan seharihari yang berkaitan dengan persamaan atau fungsi
kuadrat

Menyelesaikan model matematika dari suatu masalah
dalam matematika, mata pelajaran lain atau kehidupan
sehari-hari yang berkaitan dengan persamaan atau
fungsi kuadrat
 Menafsirkan penyelesaian masalah dalam matematika,
mata pelajaran lain atau kehidupan sehari-hari yang
berkaitan dengan persamaan atau fungsi kuadrat
G. LINEAR FUNCTIONS & EQUATIONS
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Solutions of equations and inequalities
- solve simple linear equations in one unknown; solve
simultaneous linear equations in two unknowns
- solve quadratic equations by factorization and either by use of
the formula or by completing the square; solve simple linear
inequalities
Level
X-1
Nasional 2006
Indikator
 Menentukan penyelesaian sistem persamaan linear dua variabel
 Menentukan penyelesaian sistem persamaan linear tiga variabel
 Menentukan penyelesaian sistem persamaan campuran linear dan kuadrat dalam
dua variabel
A
level
2. Linear programming
- represent inequalities graphically and use this representation in
the solution of simple
linear programming problems (the conventions of using broken
lines for strict inequalities and shading unwanted regions will be
expected)
- explain what the solution of a linear equation system means,
- solve linear equation systems in two variables,
- give a geometrical interpretation of a solution of linear equation
system in two variables,
- solve linear equation systems in three variables,
- solve linear and quadratic equation systems in two variables,
- solve quadratic equation systems in two variables,
- construct a mathematical model of a problem involving linear
equation system in three variables, solve the model, and interpret
the solution.
 Mengidentifikasi masalah yang berhubungan dengan sistem persamaan linear
 Membuat model matematika yang berhubungan dengan sistem persamaan linear
 Menentukan penyelesaian model matematika dari masalah yang berhubungan
dengan sistem persamaan linear
 Menafsirkan hasil penyelesaian masalah yang berkaitan dengan sistem
persamaan linear
 Menentukan syarat penyelesaian pertidaksamaan yang melibatkan bentuk
pecahan aljabar
 Menentukan penyelesaian pertidaksamaan satu variabel yang melibatkan bentuk
pecahan aljabar
 Mengidentifikasi masalah yang berhubungan dengan pertidaksamaan satu
variabel bentuk pecahan aljabar
 Membuat model matematika yang berhubungan dengan pertidaksamaan satu
variabel bentuk pecahan aljabar
 Menentukan penyelesaian model matematika dari masalah yang berkaitan dengan
pertidaksamaan satu variabel berbentuk pecahan aljabar
 Menafsirkan hasil penyelesaian masalah yang berkaitan dengan pertidaksamaan
satu variabel berbentuk pecahan aljabar
XII-1
 Mengenal arti sistem pertidaksamaan linear dua variabel
 Menentukan penyelesaian sistem pertidaksamaan linear dua variable
 Mengenal masalah yang merupakan program linier
 Menentukan fungsi objektif dan kendala dari program linier
 Menggambar daerah fisibel dari program linier
 Merumuskan model matematika dari masalah program linear

Menentukan nilai optimum dari fungsi objektif
 Menafsirkan solusi dari masalah program linear
H. ALGEBRA - INTRODUCTION
International (CIE) 2008
Nasional 2006
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Algebraic representation and formulae
- use letters to express generalized numbers and express basic arithmetic processes algebraically, substitute numbers for ords
and letters in formulae; transform simple formulae; construct simple expressions and set up simple equations
- construct and transform more complicated formulae and equations
2. Algebraic manipulation
- manipulate directed numbers; use brackets and extract common factors
- expand products of algebraic expressions; factorise where possible expressions of the form ax + bx+ kay+ kby, a2x2 - b2
y2; a2 + 2ab + b2; ax2 + bx+ c; manipulate algebraic fractions, e.g.
A
level
P3
,
Factorize & simplify expressions, such as
– understand the meaning of x , and use relations such as a = b ⇔a2 = b2 and x − a < b ⇔a − b < x < a + b in the course of
solving equations and inequalities;
– divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial,
and identify the quotient and remainder (which may be zero);
– use the factor theorem and the remainder theorem, e.g. to find factors, solve
polynomial equations or evaluate unknown coefficients;
– recall an appropriate form for expressing rational functions in partial fractions, and
carry out the decomposition, in cases where the denominator is no more complicated than
and where the degree of the numerator does not exceed that of the denominator;
– use the expansion of n (1+ x) , where n is a rational number and x < 1 (finding a general term is not included, but adapting
the standard series to expand e.g.
is included).
I. ALGEBRA – FUNCTIONS & INVERSE
International (CIE) 2008
Nasional 2006
Level
Indikator

Level
Learning Outcomes (students should be able to …)
IGCSE 1. Functions
- use function notation, e.g. f (x) = 3x- 5, f:xa 3x- 5 to
describe simple functions,
and the notation f -1(x) to describe their inverses;
form composite functions as defined by gf(x) =
g(f(x))
Level
X-1
Indikator
 Menentukan syarat dan aturan fungsi yang dapat dikomposisikan
 Menentukan fungsi komposisi dari beberapa fungsi.
 Menyebutkan sifat-sifat komposisi fungsi.
 Menentukan komponen pembentuk fungsi komposisi apabila fungsi komposisi dan komponen
lainnya diketahui.
 Menjelaskan syarat agar suatu fungsi mempunyai invers.
 Menggambarkan grafik fungsi invers dari grafik fungsi asalnya
 Menentukan fungsi invers dari suatu fungsi.
 mengidentifikasi sifat-sifat fungsi invers.
XI-2
A
level
- understand the terms function, domain range, oneone function, inverse function, and composition
functions,
- identify the range of given function,
- determine the value of the composition of
functions,
- determine a component of a given composition
function with given another component,
- explain the characteristics of composition of
functions,
- explain the conditions such that a function has an
inverse function,
- find the inverse of a function,
- illustrate in graphical terms the relation between a
one-one function and its inverse,
- describe the inverse function in term of
composition of functions.
 Menjelaskan arti limit fungsi di satu titik melalui perhitungan nilai-nilai disekitar titik tersebut
 Menjelaskan arti limit fungsi di tak berhingga melalui grafik dan perhitungan.
 Menghitung limit fungsi aljabar dan trigonometri di satu titik.
 Menjelaskan sifat-sifat yang digunakan dalam perhitungan limit.
 Menjelaskan arti bentuk tak tentu dari limit fungsi.
 Menghitung limit fungsi aljabar dan trigonometri dengan menggunakan sifat-sifat limit
 Menghitung limit fungsi yang mengarah ke konsep turunan.
 Menjelaskan arti fisis (sebagai laju perubahan) dan arti geometri turunan di satu titik
 Menghitung turunan fungsi yang sederhana dengan menggunakan definisi turunan
 Menentukan sifat-sifat turunan fungsi
 Menentukan turunan fungsi aljabar dan trigonometri dengan menggunakan sifat-sifat turunan
 Menentukan turunan fungsi komposisi dengan aturan rantai.
 Menentukan fungsi monoton naik dan turun dengan menggunakan konsep turunan pertama
 Menggambar sketsa grafik fungsi dengan menggunakan sifat-sifat turunan
 Menentukan titik ekstrim grafik fungsi
 Menentukan persamaan garis singgung dari sebuah fungsi
 Mengidentifikasi masalah-masalah yang bisa diselesaikan dengan konsep ekstrim fungsi
 Merumuskan model matematika dari masalah ekstrim fungsi
 Menyelesaiakan model matematika dari masalah ekstrim fungsi
 Menafsirkan solusi dari masalah nilai ekstrim
J. ALGEBRA – MATRICES, VECTOR & TRANSFORMATION
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE 1. Vectors in two dimensions
- describe a translation by using a vector represented by
subtract vectors; multiply a vector by a scalar
- calculate the magnitude of a vector
as
or a; add and
. (Vectors will be printed as
or a and their magnitudes denoted by modulus signs, e.g.
. In their
answers to questions candidates are expected to indicate a in some definite way, e.g.
by an arrow or by underlining, thus
or a)
- represent vectors by directed line segments; use the sum and difference of two
vectors to express given vectors in terms of two coplanar vectors; use position vectors
2. Matrices
- display information in the form of a matrix of any order; calculate the sum and
product (where appropriate) of two matrices; calculate the product of a matrix and a
scalar quantity; use the algebra of 2 x 2 matrices including the zero and identity 2 x 2
matrices; calculate the determinant and inverse A-1 of a non-singular matrix A
3. Transformations
- reflect simple plane figures in horizontal or vertical lines; rotate simple plane figures
about the origin, vertices or mid points of edges of the figures, through multiples of
90°; construct given translations and enlargements of simple plane figures; recognise
and describe reflections, rotations, translations and enlargements
- use the following transformations of the plane: reflection (M); rotation (R);
translation (T); enlargement (E); shear (H); stretching (S) and their combinations (if
M(a) = b and R(b) = c the notation RM(a) = c will be used; invariants under these
transformations may be assumed.)
- identify and give precise descriptions of transformations connecting given figures;
describe transformations using co-ordinates and matrices (singular matrices are
Level
XII-1
Nasional 2006
Indikator
 Mengenal matriks persegi
 Melakukan operasi aljabar atas dua matriks
 Menurunkan sifat-sifat operasi matriks persegi melalui
contoh
 Mengenal invers matriks persegi
 Menentukan determinan matriks 2x2
 Menentukan invers dari matrks 2x2
 Menentukan persamaan matriks dari sistem persamaan
linier
 Menyelesaian sistem persamaan linear dua variabel
dengan matriks invers
 Menjelaskan vektor sebagai besaran yang memilki besar
dan arah
 Mengenal vektor satuan
 Menentukan operasi aljabar vektor : jumlah, selisih, hasil
kali vektor dengan skalar, dan lawan suatu vektor
 Menjelaskan sifat-sifat vektor secara aljabar dan geometri
 Menggunakan rumus perbandingan vektor
 Menentukan hasilkali skalar dua vektor di bidang dan
ruang
 Menjelaskan sifat-sifat perkalian skalar dua vektor
 Menjelaskan arti geometri dari suatu transformasi bidang
A
level
P1
A
level
P3
excluded)
– use standard notations for vectors, i.e.
 Melakukan operasi berbagai jenis transformasi: translasi
refleksi, dilatasi, dan rotasi.
 Menentukan persamaan matriks dari transformasi pada
bidang.
– carry out addition and subtraction of vectors and multiplication of a vector by a
scalar, and interpret these operations in geometrical terms;
– use unit vectors, displacement vectors and position vectors;
– calculate the magnitude of a vector and the scalar product of two vectors;
– use the scalar product to determine the angle between two directions and to solve
problems concerning perpendicularity of vectors.
– understand the significance of all the symbols used when the equation of a straight
line is expressed in the form r = a + tb ;
– determine whether two lines are parallel, intersect or are skew;
– find the angle between two lines, and the point of intersection of two lines when it
exists;
– understand the significance of all the symbols used when the equation of a plane is
expressed in either of the forms ax + by + cz = d or (r − a).n = 0 ;
– use equations of lines and planes to solve problems concerning distances, angles
and intersections, and in particular
find the equation of a line or a plane, given sufficient information,
determine whether a line lies in a plane, is parallel to a plane, or intersects a
plane, and find the point of intersection of a line and a plane when it exists,
find the line of intersection of two non-parallel planes,
find the perpendicular distance from a point to a plane, and from a point to a
line, find the angle between two planes, and the angle between a line and a plane.
 Menentukan aturan transformasi dari komposisi beberapa
transformasi
 Menentukan persamaan matriks dari komposisi
transformasi pada bidang.

K. ALGEBRA : SIGMA NOTATIONS, SEQUENCES AND SERIES, AND MATHEMATICAL INDUCTION
Level
International (CIE) 2008
Learning Outcomes (students should be able to …)
Level
Nasional 2006
Indikator
A
level
P1
1. Sequences
- explain the characteristics of arithmetic sequences and geometric sequences,
- determine the formula of the nth term and the sum of n terms of an
arithmetic sequence and a geometric sequence,
- determine the nth term and the sum of n terms of an arithmetic sequence and
a geometric sequence,
- explain the characteristics of an infinite geometric series which has a sum,
- calculate the sum of an infinite geometric series which has a sum,
- represent arithmetic series and geometric series in the sigma notations,
- represent series in the sigma notations,
- explain the characteristics of a formula that can be prove by mathematical
induction,
- use mathematical induction to prove formulas,
- explain the characteristics of a problems which its mathematical model is an
arithmetic series or a geometric series,
- determine a series which is a mathematical model of a problem, solve the
model, and interpret the solution,
- describe formulas of mathematical finance using arithmetic series or a
geometric series,
- determine simple interest, compound interest, and annuity.
2. series
– use the expansion of (a + b)n , where n is a positive integer (knowledge of
the
greatest term and properties of the coefficients are not required, but the
notations
and n! should be known);
–
ecognize arithmetic and geometric progressions;
– use the formulae for the nth term and for the sum of
the first n terms to solve
problems involving arithmetic or geometric progressions;
– use the condition for the convergence of a geometric
progression, and the formula
for the sum to infinity of a convergent geometric progression.
XII-2
 Menjelaskan arti barisan dan deret
 Menemukan rumus barisan dan deret aritmatika
 Menemukan rumus barisan dan deret geometri
 Menghitung suku ke-n dan jumlah n suku deret aritmetika dan deret
geometri.
 Menuliskan suatu deret dengan notasi sigma.
 Menggunakan induksi matematika dalam pembuktian
 Mengidentifikasi masalah yang berkaitan dengan deret.
 Merumuskan model matematika dari masalah deret
 Menentukan penyelesaian model matematika yang berkaitan dengan
deret
 Memberikan tafsiran terhadap hasil penyelesaian yang diperoleh

L. INEQUALITIES
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE Solutions of equations and inequalities
- solve simple linear equations in one unknown; solve simultaneous linear equations in two unknowns
- solve quadratic equations by factorization and either by use of the formula or by completing the square; solve simple
linear inequalities
A
- Explain what one variable inequalities solutions mean,
level
- solve inequalities involving linear and quadratic equations in one variable,
- solve fraction inequalities involving linear or quadratic equations,
- solve inequalities involving radicals,
- explain the laws and properties used in solving the qualities,
- solve inequalities involving absolute value,
- construct a mathematical model of a problem involving inequalities, solve the model, and interpret the solution.
Level
Nasional 2006
Indikator


M. MATHEMATICAL LOGIC
Level
A
level
International (CIE) 2008
Learning Outcomes (students should be able to …)
Level
- determine the truth values and the negations of statements,
X-2
- determine the truth values of disjunction, conjunction, and their negation,
- determine the truth values of conditional statements, their converse, inverse,
and contra positives,
- determine the negations of conditional statements,
- explain the meaning of universal quantifier and existential quantifier,
- determine the negations of universal statements and existential statements,
- use syllogisms, modes ponens and modes tollens, to make conclusions,
- prove principles of mathematics using direct proof,
- prove principles of mathematics using indirect proof (contradiction and
contraposition).
Nasional 2006
Indikator

Menentukan nilai kebenaran dari suatu pernyataan berkuantor

Menentukan ingkaran dari suatu pernyataan berkuantor

Menentukan nilai kebenaran dari suatu pernyataan majemuk

Menentukan ingkaran dari suatu pernyataan majemuk

Memeriksa kesetaraan antara dua pernyataan majemuk

Membuktikan kesetaraan antara dua pernyataan majemuk

Membuat pernyataan yang setara dengan pernyataan majemuk

Memeriksa keabsahan penarikan kesimpulan menggunakan prinsip
logika matematika

Menentukan kesimpulan dari beberapa premis yang diberikan
N. STATISTICS & PROBABILITY
International (CIE) 2008
Level
Learning Outcomes (students should be able to …)
IGCSE - collect, classify and tabulate statistical data; read, interpret and draw simple inferences from
tables and statistical diagrams; construct and use bar charts, pie charts, pictograms, simple
frequency distributions, histograms with equal intervals and scatter diagrams (including drawing
a line of best fit by eye); understand what is meant by positive, negative and zero correlation;
calculate the mean, median and mode for individual and discrete data and distinguish between
the purposes for which they are used; calculate the range
- construct and read histograms with equal and unequal intervals (areas proportional to
frequencies and vertical axis labeled 'frequency density'); construct and use cumulative
frequency diagrams; estimate and interpret the median, percentiles, quartiles and inter-quartile
range; calculate an estimate of the mean for grouped and continuous data; identify the modal
class from a grouped frequency distribution
A
level
S1
Probability
- calculate the probability of a single event as either a fraction or a decimal (not a ratio);
understand and use the probability scale from 0 to 1; understand that: the probability of an event
occurring = 1 – the probability of the event not occurring; understand probability in practice, e.g.
relative frequency
- calculate the probability of simple combined events, using possibility diagrams and tree
diagrams where appropriate (in possibility diagrams outcomes will be represented by points on a
grid and in tree diagrams outcomes will be written at the end of branches and probabilities by the
side of the branches)
1. Representation of Data
– select a suitable way of presenting raw statistical data, and discuss advantages and/or
disadvantages that particular representations may have;
– construct and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms
and cumulative frequency graphs;
– understand and use different measures of central tendency (mean, median, mode) and variation
(range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data;
– use a cumulative frequency graph to estimate the median value, the quartiles and
the interquartile range of a set of data;
– calculate the mean and standard deviation of a set of data (including grouped data) either from
the data itself or from given totals such as Σx and 2 Σx , or Σ(x − a) and 2 Σ(x − a) .
2. Permutations & Combinations
– understand the terms permutation and combination, and solve simple problems involving
selections;
– solve problems about arrangements of objects in a line, including those involving repetition
Level
XI-1
Nasional 2006
Indikator
 Membaca sajian data dalam bentuk diagram garis,
diagram lingkaran dan diagram batang.
 Mengidentifikasi nilai suatu data yang ditampilkan
pada tabel dan diagram
 Menyajikan data dalam bentuk diagram batang,
garis, lingkaran, dan ogive serta penafsirannya
 Menafsirkan data dalam bentuk diagram batang,
garis, lingkaran, dan ogive
 Membaca sajian data dalam bentuk tabel distribusi
frekuensi dan histogram.
 Menyajikan data dalam bentuk tabel distribusi
frekuensi dan histogram.
 Menentukan rataan, median, dan modus.
 Memberikan tafsiran terhadap ukuran pemusatan.
 Menentukan simpangan rata-rata dan simpangan
baku
 Menyusun aturan perkalian, permutasi dan
kombinasi
 Menggunakan aturan perkalian, permutasi dan
kombinasi
 Menentukan banyak kemungkinan kejadian dari
berbagai situasi
 Menuliskan himpunan kejadian dari suatu
percobaan
 Menentukan peluang kejadian melalui percobaan
 Menentukan peluang suatu kejadian secara teoritis
(e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’), restriction (e.g. the
number of ways several people can stand in a line if 2 particular people must — or must not —
stand next to each other).
3. Probability
– evaluate probabilities in simple cases by means of enumeration of equiprobable elementary
events (e.g. for the total score when two fair dice are thrown), or by calculation using
permutations or combinations;
– use addition and multiplication of probabilities, as appropriate, in simple cases;
– understand the meaning of exclusive and independent events, and calculate and use conditional
probabilities in simple cases, e.g. situations that can be represented by means of a tree diagram.
4. Discrete Random Variables
– construct a probability distribution table relating to a given situation involving a discrete
random variable X, and calculate E(X) and Var(X) ;
– use formulae for probabilities for the binomial distribution, and recognise practical situations
where the binomial distribution is a suitable model (the notation B(n, p) is included);
– use formulae for the expectation and variance of the binomial distribution.
5. The normal distribution
– understand the use of a normal distribution to model a continuous random variable,
and use normal distribution tables;
A
level
S2
– solve problems concerning a variable X,
, including finding the value of P(X > x1)
, or a related probability, given the values of
finding a relationship between μ , x1 and σ
given the value of P(X > x1) or a related probability;
– recall conditions under which the normal distribution can be used as an approximation to the
binomial distribution (n large enough to ensure that np > 5 and nq > 5 ), and use this
approximation, with a continuity correction, in solving problems.
1. The Poisson Distribution
– calculate probabilities for the distribution Po(μ) ;
– use the fact that if X ~ Po(μ) then the mean and variance of X are each equal to μ ;
– understand the relevance of the Poisson distribution to the distribution of random events, and
use the Poisson distribution as a model;
– use the Poisson distribution as an approximation to the binomial distribution where appropriate
( n > 50 and np < 5 , approximately);
– use the normal distribution, with continuity correction, as an approximation to the Poisson
distribution where appropriate ( μ > 15 , approximately).
2. Linier Combination of Random Variables
– use, in the course of solving problems, the results that

for independent X and Y,
if X has a normal distribution then so does aX + b ,
if X and Y have independent normal distributions then aX + bY has a normal distribution,
if X and Y have independent Poisson distributions then X +Y has a Poisson distribution.
3. Continuous Random Variables
– understand the concept of a continuous random variable, and recall and use properties of a
probability density function (restricted to functions defined over a single interval);
– use a probability density function to solve problems involving probabilities, and to calculate
the mean and variance of a distribution (explicit knowledge of the cumulative distribution
function is not included, but location of the median, for example, in simple cases by direct
consideration of an area may be required).
4. Sampling & Estimation
– understand the distinction between a sample and a population, and appreciate the necessity for
randomness in choosing samples;
– explain in simple terms why a given sampling method may be unsatisfactory (knowledge of
particular sampling methods, such as quota or stratified sampling, is not required, but candidates
should have an elementary understanding of the use of random numbers in producing random
samples);
– recognise that a sample mean can be regarded as a random variable, and use the
facts that
– use the fact that X has a normal distribution if X has a normal distribution;
– use the Central Limit theorem where appropriate;
– calculate unbiased estimates of the population mean and variance from a sample, using either
raw or summarised data (only a simple understanding of the term ‘unbiased’ is required);
– determine a confidence interval for a population mean in cases where the population is
normally distributed with known variance or where a large sample is used;
– determine, from a large sample, an approximate confidence interval for a population
proportion.
5. Hypothesis Test
– understand the nature of a hypothesis test, the difference between one-tail and two-tail tests,
and the terms null hypothesis, alternative hypothesis, significance level, rejection region (or
critical region), acceptance region and test statistic;
– formulate hypotheses and carry out a hypothesis test in the context of a single observation from
a population which has a binomial or Poisson distribution, using either direct evaluation of
probabilities or a normal approximation, as appropriate; – formulate hypotheses and carry out a
hypothesis test concerning the population mean in cases where the population is normally
distributed with known variance or where a large sample is used;
– understand the terms Type I error and Type II error in relation to hypothesis tests;
– calculate the probabilities of making Type I and Type II errors in specific situations involving
tests based on a normal distribution or direct evaluation of binomial or Poisson probabilities.
O. CALCULUS - INTEGRAL
Level
A
level
P1
International (CIE) 2008
Learning Outcomes (students should be able to …)
– understand integration as the reverse process of differentiation, and integrate (ax + b)n
(for any rational n except −1), together with constant multiples, sums and differences;
– solve problems involving the evaluation of a constant of integration, e.g. to find the
equation of the curve through (1, − 2) for which
– evaluate definite integrals (including simple cases of ‘improper’ integrals, such as
Level
XII-1
Nasional 2006
Indikator
 Mengenal arti Integral tak tentu
 Menurunkan sifat-sifat integral tak tentu dari turunan
 Menentukan integral tak tentu fungsi aljabar dan
trigonometri
 Mengenal arti integral tentu
– use definite integration to find the area of a region bounded by a curve and lines parallel
to the axes, or between two curves, a volume of revolution about one of the axes.
A
level
P3
– extend the idea of ‘reverse differentiation’ to include the integration of
– use trigonometrical relationships (such as double-angle formulae) to facilitate the
 Menentukan integral tentu dengan menggunakan sifatsifat integral
 Menyelesaikan masalah sederhana yang melibatkan
integral tentu dan tak tentu
 Menentukan integral dengan dengan cara substitusi
 Menetukan integral dengan dengan cara parsial
integration of functions such as
;
– integrate rational functions by means of decomposition into partial fractions (restricted to
the types of partial fractions specified in paragraph 1 above);
 Menentukan integral dengan dengan cara substitusi
trigonometri
– recognise an integrand of the form
 Menghitung luas suatu daerah yang dibatasi oleh kurva
dan sumbu-sumbu pada koordinat.
, and integrate, for example,
 Menghitung volume benda putar
or tanx ;
– recognise when an integrand can usefully be regarded as a product, and use integration
by parts to integrate, for example,
– use a given substitution to simplify and evaluate either a definite or an indefinite integral;
– use the trapezium rule to estimate the value of a definite integral, and use sketch graphs
in simple cases to determine whether the trapezium rule gives an overestimate or an underestimate.
P. DIFFERENTIAL & DIFFERENTIAL EQUATION
Level
A
level
P1
A
level
P3
International (CIE) 2008
Learning Outcomes (students should be able to …)
Level
Nasional 2006
Indikator
– understand the idea of the gradient of a curve, and use the notations f′(x) , f′′(x) ,
(the technique of
differentiation from first principles is not required);
– use the derivative of n x (for any rational n), together with constant multiples, sums, differences of functions, and of
composite functions using the chain rule;
– apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (including
connected rates of change);
– locate stationary points, and use information about stationary points in sketching graphs (the ability to distinguish between
maximum points and minimum points is required, but identification of points of inflexion is not included).
– use the derivatives of x e , lnx , sin x , cos x , tanx , together with constant multiples, sums, differences and composites;
– differentiate products and quotients;
– find and use the first derivative of a function which is defined parametrically or implicitly.
– formulate a simple statement involving a rate of change as a differential equation, including the introduction if necessary of
a constant of proportionality;
– find by integration a general form of solution for a first order differential equation in which the variables are separable;
– use an initial condition to find a particular solution;
– interpret the solution of a differential equation in the context of a problem being modelled by the equation.
Q. NUMERICAL SOLUTION & EQUATION
Level
A
level
P3
International (CIE) 2008
Learning Outcomes (students should be able to …)
– locate approximately a root of an equation, by means of graphical considerations and/or searching for a sign change;
– understand the idea of, and use the notation for, a sequence of approximations which converges to a root of an equation;
– understand how a given simple iterative formula of the form
relates to the equation being solved, and use a given
iteration, or an iteration based on a given rearrangement of an equation, to determine a root to a prescribed degree of accuracy
(knowledge of the condition for convergence is not included, but candidates should understand that an iteration may fail to converge).
Nasional 2006
Level
Indikator
R. COMPLEX NUMBER
Level
A
level
P3
International (CIE) 2008
Learning Outcomes (students should be able to …)
– understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument,
conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal;
– carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in cartesian form x +
iy ;
– use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs;
– represent complex numbers geometrically by means of an Argand diagram;
– carry out operations of multiplication and division of two complex numbers expressed in polar form θ θ θ i r(cos + isin ) ≡ r e ;
– find the two square roots of a complex number;
– understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and
dividing two complex numbers;
– illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram, e.g. z − a < k , z −
a = z − b , arg(z − a) = α .
Nasional 2006
Level
Indikator

S. MECHANICS
Level
A
level
M1
International (CIE) 2008
Learning Outcomes (students should be able to …)
1. Forces and equilibrium
– identify the forces acting in a given situation;
– understand the vector nature of force, and find and use components and resultants;
– use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of
the components in any direction is zero;
– understand that a contact force between two surfaces can be represented by two components, the normal component and the
frictional component;
– use the model of a ‘smooth’ contact, and understand the limitations of this model;
– understand the concepts of limiting friction and limiting equilibrium; recall the definition of coefficient of friction, and use the
relationship F = μR or F ≤ μR , as appropriate;
– use Newton’s third law.
2. Kinematics of motion in a straight line
– understand the concepts of distance and speed as scalar quantities, and of displacement, velocity and acceleration as vector
quantities (in one dimension only);
– sketch and interpret displacement-time graphs and velocity-time graphs, and in particular appreciate that the area under a
Nasional 2006
Level
Indikator

velocity-time graph represents displacement, the gradient of a displacement-time graph represents velocity, the gradient of a
velocity-time graph represents acceleration;
– use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and
acceleration (restricted to calculus within the scope of unit P1);
– use appropriate formulae for motion with constant acceleration in a straight line.
3. Newton’s laws of motion
– apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces,
which may include friction;
– use the relationship between mass and weight;
– solve simple problems which may be modelled as the motion of a particle moving vertically or on an inclined plane with constant
acceleration;
– solve simple problems which may be modelled as the motion of two particles, connected by a light inextensible string which may
pass over a fixed smooth peg or light pulley.
A
level
M2
4. Energy, work and power
– understand the concept of the work done by a force, and calculate the work done by a constant force when its point of application
undergoes a displacement not necessarily parallel to the force (use of the scalar product is not required);
– understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae;
– understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in
appropriate cases the principle of conservation of energy;
– use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for
a force acting in the direction of motion;
– solve problems involving, for example, the instantaneous acceleration of a car moving on a hill with resistance.
1. Motion of a projectile
– model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of the model;
– use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude
and direction of the velocity at a given time of position, the range on a horizontal plane and the greatest height reached;
– derive and use the cartesian equations of the trajectory of a projectile, including problems in which the initial speed and/or angle
of projection may be unknown.
2. Equilibrium of a rigid body
– calculate the moment of a force about a point, in two dimensional situations only (understanding of the vector nature of moments
is not required);
– use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and
identify the position of the centre of mass of a uniform body using considerations of symmetry;
– use given information about the position of the centre of mass of a triangular lamina and other simple shapes;
– determine the position of the centre of mass of a composite body by considering an equivalent system of particles (in simple cases
only, e.g. a uniform L-shaped lamina);
– use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero
and the sum of the moments of the forces about any point is zero, and the converse of this;

– solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving
toppling or sliding (problems set will not involve complicated trigonometry).
3. Uniform motion in a circle
– understand the concept of angular speed for a particle moving in a circle, and use the relation v = rω ;
– understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle,
and use the formulae
– solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed.
4. Hooke’s law
– use Hooke’s law as a model relating the force in an elastic string or spring to the extension or compression, and understand the
term modulus of elasticity;
– use the formula for the elastic potential energy stored in a string or spring;
– solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are
needed
5. Linear motion under a variable force
– use
for velocity, and
for acceleration, as appropriate;
– solve problems which can be modelled as the linear motion of a particle under the action of a variable force, by setting up and
solving an appropriate differential equation (restricted to equations in which the variables are separable).
T. ALGORITHM – SUKU BANYAK
Level
IGCSE
A
level
International (CIE) 2008
Learning Outcomes (students should be able to …)
Level
XI-2
Nasional 2006
Indikator
 Menjelaskan algoritma pembagian sukubanyak.
 Menentukan derajat sukubanyak hasil bagi dan sisa pembagian dalam algoritma pembagian.
 Menentukan hasil bagi dan sisa pembagian sukubanyak oleh bentuk linear atau kuadrat.
 Menentukan sisa pembagian suku-banyak oleh bentuk linear dan kuadrat dengan teorema sisa.
 Menentukan faktor linear dari suku-banyak dengan teorema faktor.
 Menyelesaikan persamaan suku-banyak dengan menggunakan teorema faktor
Pertanyaan:
1. Bagaimana perbandingan antara kurikulum nasional dan CIE secara umum?
2. Bagaimana perbandingan antara level IGCSE & A level pada kurikulum CIE?
3. Sub topic apa yang tercantum dalam kurikulum nasional tetapi tidak dalam kurikulum CIE?
4. Sub topic apa yang tercantum dalam kurikulum CIE tetapi tidak dalam kurikulum nasional?
5. Topik-topik mana yang dapat dipelajari secara independent oleh siswa?
6. Topik-topik mana yang sangat berkaitan antara yang satu dengan yang lain, sehingga dalam pengajarannya dapat digabungkan?
7. Topik-topik mana yang berkaitan dengan mata pelajaran lain (biologi, fisika, matematika, bahasa)?
8. Desain beberapa project untuk siswa yang menggabungkan pengajaran kimia dan bidang ilmu lainnya dalam suatu rangkaian yang sistematis.
9. Bagaimana urutan topic pengajaran yang paling sesuai menurut anda? Dengan pertimbangan bahwa siswa akan mengikuti ujian IGCSE pada akhir kelas XI semester 1,
ujian nasional (UAS & UAN) serta ujian A level pada akhir kelas XII semester 2.