Download File - Mr.England`s Maths Resources

`MATHEMATICS CURRICULM
Key Stage 4 – Higher IGCSE Edexcel 2016-17
Unless stated otherwise all chapter/page numbers refer to the following text:
Collins Edexcel IGCSE Maths Student Book
978-0-00-741015-6
Lesson Plans and Homework for all lessons taught using the above text can be set using:
Collins Edexcel IGCSE Maths Teachers Pack
978-0-00-741017-0
All numbered units are in reference to the CIE book that students have been asked to buy in case you wish to use this in class.
Topic/Unit
Number
Symmetry
Directed Numbers
Sub Topic(s)
TERM 1 – YEAR 10
 Multiples of whole numbers - Use the terms odd and even numbers, multiples. Identify
common multiples.
 Factors of Whole Numbers - Use the term factor. Identify common factors.
 Prime Numbers - Use the term prime number.
 Square Numbers and Cube Numbers - Identify square numbers and cube numbers.
Calculate squares and cubes.
 Products of Prime Numbers - Identify prime factors. Express integers as the product of
powers of prime factors.
 HCF and LCM - Evaluate Highest Common Factors (HCF) and Lowest Common
Multiples (LCM).
 Lines of Symmetry - Recognise line symmetry.
 Rotational Symmetry - Recognise rotational symmetry.
 Symmetry of special two-dimensional shapes - Identify any lines of symmetry and the
order of rotational symmetry of a given two-dimensional figure.
 In addition check students know the names of common 3D shapes, can sketch/identify
nets, understand faces/edges/vertices, drawing planes of symmetry.
 Introduction to and everyday use of directed numbers - Use directed numbers in
practical situations
 The number line - Understand and use integers (positive, negative and zero) as positions
on a number line. Use directed numbers in practical situations.
 Adding and Subtracting directed numbers - Understand and use integers (positive,
negative and zero) both as positions and translations on a number line. Use directed
numbers in practical situations. Use the four rules of addition, subtraction,
multiplication and division.
 Multiplying and Dividing directed numbers - Use the four rules of addition, subtraction,
multiplication and division.
Resources
Chapter 1
1.2
Chapter 28
4.3
Chapter 4
2.2
Squares, cubes and
roots
Algebra and Formulae






Integer Sequences



Statistical
Representation



Squares and square roots - Identify square numbers. Calculate squares and square roots.
Cubes and cube roots - Identify cube numbers. Calculate cubes and cube roots.
Surds - Understand the meaning of surds. Manipulate surds, including rationalising the
denominator where the denominator is a pure surd. NOTE: Edexcel have used more
challenging surds questions than are covered in the book in past papers – use past paper
questions as guidance.
The language of algebra - Understand that symbols may be used to represent numbers
in equations or variables in expressions and formulae. Understand that a letter may
represent an unknown number or a variable. Use correct notational conventions for
algebraic expressions and formulae. Use formulae from mathematics and other real-life
contexts expressed initially in words or diagrammatic form and convert to letters and
symbols.
Substitution into formulae - Understand that algebraic expressions follow the
generalised rules of arithmetic. Evaluate expressions by substituting numerical values
for letters. Substitute positive and negative integers, decimals and fractions for words
and letters in expressions and formulae.
Rearranging formulae - Understand the process of manipulating formulae to change the
subject, to include cases where the subject may appear twice or a power of the subject
occurs.
Number sequences - Find subsequent terms of an integer sequence and the rule for
generating it.
The nth term of a sequence - Generate terms of a sequence using term-to-term and
position-to-term definitions of the sequence.
Finding the nth term of a linear sequence - Use linear expressions to describe the nth
term of an arithmetic sequence.
Frequency tables - Use appropriate methods of tabulation to enable the construction of
statistical diagrams.
Pictograms, Bar Charts and Pie Charts - Use different methods of presenting data.
Interpret statistical diagrams
Histograms - Construct and interpret histograms.
Chapter 5
1.2
Chapter 11
2.3
2.4
5.2
Chapter 17
1.2
Chapter 31
10.1
Fractions and
Percentages










Ratio, proportion and
speed




Algebraic Manipulation







Equivalent fractions - Understand and use equivalent fractions, simplifying a fraction
by cancelling common factors. Identify and apply common denominators. Apply
common denominators to order fractions. Express a given number as a fraction of
another number.
Fractions and decimals - Convert a fraction to a decimal. Use decimal notation. Order
decimals. Convert a decimal to a fraction. Recognise that a terminating decimal is a
fraction.
Recurring Decimals - Convert recurring decimals into fractions.
Percentages, fractions and decimals - Convert a fraction to a decimal or a percentage.
Convert a decimal to a fraction or a percentage. Express a percentage as a fraction and
as a decimal.
Calculating a percentage - Understand that ‘percentage’ means ‘number of parts per
100’. Understand the multiplicative nature of percentages as operators. Solve simple
percentage problems.
Increasing or decreasing quantities by a percentage - Solve simple percentage problems,
including percentage increase and decrease.
Expressing one quantity as a percentage of another - Express a given number as a
percentage of another number. Solve simple percentage problems, including percentage
increase and decrease.
Compound interest - Solve compound interest problems.
Repeated percentage change - Repeated percentage change.
Reverse percentage - Use reverse percentages.
TERM 2 – YEAR 10
Chapter 2
Ratio - Use ratio notation, including reduction to its simplest form and its various links
to fraction notation. Divide a quantity in a given ratio or ratios. Solve word problems
about ratio and proportion.
Speed - Understand and use the relationship between average speed, distance and time.
Direct Proportion - Calculate an unknown quantity from quantities that vary in direct
proportion.
Proportional Variables - Use the process of proportionality to evaluate unknown
quantities.
Simplifying expressions - Collect like terms.
Expanding Brackets - Multiply a single term over a bracket.
Factorisation - Take out single common factors.
Expanding two brackets - Expand the product of two simple linear expressions.
Multiplying more complex expressions - Expand the product of two linear expressions.
Quadratic factorsation - Understand the concept of a quadratic expression and be able to
factorise such expressions.
Algebraic Fractions - Manipulate algebraic fractions where the numerator and/or the
denominator can be numeric, linear or quadratic.
Chapter 7
1.1
1.6
1.5
Chapter 12
2.9
5.1
Angle Properties –











The Four Rules





Angle facts - Use angle properties of intersecting lines and angles on a straight line.
Parallel Lines - Use angle properties of intersecting lines, parallel lines and angles on a
straight line.
Angles in a triangle - Understand the exterior angle of a triangle property and the angle
sum of a triangle property. Understand the terms isosceles, equilateral and right-angled
triangles and the angle properties of these triangles
Angles in a quadrilateral - Recognise and give the names of polygons. Understand and
use the term quadrilateral and the angle sum property of quadrilaterals. Understand and
use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite.
Regular Polygons - Recognise and give the names of polygons. Understand the term
regular polygon and calculate interior and exterior angles of regular polygons.
Irregular Polygons - Understand and use the angle sum of polygons.
Tangents and Chords - Understand chord and tangent properties of circles.
Angles in a circle - Understand and use angle properties of the circle including:
o angle subtended by an arc at the centre of a circle is twice the angle subtended
at any point on the remaining part of the circumference
o angle subtended at the circumference by a diameter is a right angle
o angles in the same segment are equal.
Cyclic Quadrilaterals - Recognise the term cyclic quadrilateral. Understand and use
angle properties of the circle including: the sum of the opposite angles of a cyclic
quadrilateral is 180°.
Alternate Segment Theroem - Understand and use angle properties of the circle
including: the alternate segment theorem.
Intersecting Chords - Understand and use the internal and external intersecting chord
properties.
Order of operations - Use brackets and the hierarchy of operations.
Choosing the correct operation - Use the four rules of addition, subtraction,
multiplication and division.
Finding a fraction of a quantity - Calculate a given fraction of a given quantity,
expressing the answer as a fraction.
Adding and subtracting fractions - Use common denominators to add and subtract
fractions. Understand and use mixed numbers and vulgar fractions.
Multiplying and dividing fractions - Multiply and divide a given fraction by a unit
fraction and by a general fraction. Understand and use unit fractions as multiplicative
inverses.
Chapter 23
4.1
4.5
Chapter 3
1.1
Estimation and limits of
accuracy






Solutions of equations







Statistical measures









Rounding whole numbers - Round integers to a given power of 10.
Rounding decimals - Round to a given number of decimal places.
Rounding to significant figures - Round to a given number of significant figures.
Approximations of calculations - Use estimation to evaluate approximations to
numerical calculations.
Upper and lower bounds - Identify upper and lower bounds where values are given to a
degree of accuracy.
Upper and lower bounds for calculations - Solve problems using upper and lower
bounds where values are given to a degree of accuracy.
Solving linear equations - Solve linear equations, with integer or fractional coefficients,
in one unknown in which the unknown appears on either side or both sides of the
equation.
Setting up equations - Set up simple linear equations from given data.
More complex equations - Solve more complex linear equations.
Solving quadratic equations by factorization - Solve quadratic equations by
factorisation. Form and solve quadratic equations from data given in a context.
Solving quadratic equations by the quadratic formula - Solve quadratic equations by
using the quadratic formula.
Simple simultaneous equations - Calculate the exact solution of two simultaneous
equations in two unknowns.
Linear and non-linear equations - Solve simultaneous equations in two unknowns, one
equation being linear and the other being quadratic.
TERM 3 – YEAR 10
Chapter 8
The mode - Understand the concept of average. Calculate the mode for a discrete data
set.
The median - Calculate the median for a discrete data set.
The mean - Calculate the mean for a discrete data set.
The range - Calculate the range for a discrete data set.
Which average to use - Understand the concept of average. Calculate the mean, median,
mode and range for a discrete data set.
Using frequency tables - Understand the concept of average. Calculate the mean,
median, mode and range for a discrete data set.
Grouped data - Calculate an estimate for the mean for grouped data. Identify the modal
class for grouped data.
Measuring spread - Understand the concept of a measure of spread. Find the
interquartile range from a discrete data set.
Cumulative frequency diagrams - Construct cumulative frequency diagrams from
tabulated data. Use cumulative frequency diagrams. Estimate the median from a
cumulative frequency diagram. Estimate the interquartile range from a cumulative
frequency diagram.
Chapter 32
1.3
Chapter 13
2.5
2.6
2.10
2.11
2.7
2.8
10.2
10.3
Set language and
notation



Transformations







Graphs in practical
situations



Inequalities - Understand and use the symbols >, <, ≥ and ≤.
Sets - Understand the definition of a set. Use the set notation ,  and ∈ and ∉.
Understand the concept of the universal set and the empty set and the symbols for these
sets.
Venn diagrams - Understand sets defined in algebraic terms. Understand and use
subsets. Understand and use the complement of a set. Use Venn diagrams to represent
sets and the number of elements in sets. Use the notation n(A) for the number of
elements in the set A Universal set.
Practical Problems - Use sets in practical situations.
Translations - Understand that translations are specified by a distance and direction.
Translate a shape. Understand that translations preserve length and angle so that a
transformed shape remains congruent to the original shape.
Reflections - Understand that reflections are specified by a mirror line. Construct a
mirror line given an object. Understand that reflections preserve length and angle so
that a transformed shape remains congruent to the original shape.
Further Reflections - Reflect a shape given a mirror line.
Rotations - Understand that rotations are specified by a centre and an angle. Recognise
that an anti-clockwise rotation is a positive angle of rotation and a clockwise rotation is
a negative angle of rotation. Rotate a shape about a point through a given angle.
Understand that rotations preserve length and angle so that a transformed shape remains
congruent to the original shape.
Further Rotations - Rotate a shape about a point through a given angle.
Enlargements - Understand that enlargements are specified by a centre and a scale
factor. Understand that enlargements preserve angles and not lengths. Enlarge a shape
given the scale factor.
Conversion graphs - Draw and interpret straight line conversion graphs.
Travel graphs - Interpret information presented in a range of linear and non-linear
graphs.
Speed-time graphs - Interpret information presented in a range of linear and non-linear
graphs.
Chapter 6
8.1
8.2
Chapter 30
9.3
9.4
Chapter 14
7.5
1.7
7.7
7.8
Applying number and
using calculators






Probability








Units of measurement - Make sensible estimates of a range of measures.
Converting between metric units - Carry out calculations using standard units of mass,
length, area, volume and capacity. Convert measurements within the metric system to
include linear and area units. Convert between units of volume within the metric
system.
Reading scales - Interpret scales on a range of measuring instruments.
Time - Understand and carry out calculations using time. Calculate time intervals in
terms of the 24-hour and 12-hour clock.
Currency conversions - Carry out calculations using money, including converting
between currencies.
Using a calculator efficiently - Use a scientific electronic calculator to determine
numerical results.
The probability scale - Understand the language of probability. Understand and use the
probability scale.
Calculating probability - Understand and use estimates or measures of probability from
theoretical models.
Probability that an event will not happen - Calculate the probability of the complement
of an event happening.
Addition rule for probabilities - Use the addition rule of probability for mutually
exclusive events.
Probability from data - Estimate probabilities from previously collected data.
Expected frequency - Understand and use the term expected frequency.
Combined events - Understand the concepts of a sample space and an event, and how
the probability of an event happening can be determined from the sample space. List all
the outcomes for single events and for two successive events in a systematic way.
Tree diagrams - Draw and use tree diagrams. Determine the probability that two or
more independent events will both occur. Use simple conditional probability when
combining events. Apply probability to simple problems.
Chapter 10
1.8
Chapter 33
10.4
10.5
10.6
Revision 10A
TERM 1 – YEAR 11
Straight Line Graphs







Geometrical
Constructions


Standard Form


Using coordinates - Understand and use the conventions for rectangular Cartesian
coordinates. Plot points (x, y) in any of the four quadrants. Determine the coordinates of
the midpoint of a line segment.
Drawing straight line graphs - Recognise that equations of the form y = mx + c are
straight line graphs. Generate points and plot graphs of linear functions.
More straight lines - Generate points and plot graphs of linear functions. Find the
gradient of a straight line. Locate points with given coordinates. Determine the
coordinates of points identified by geometrical information.
The equation y = mx + c - Recognise that equations of the form y = mx + c are straight
line graphs with gradient m and intercept on the y axis at the point (0, c).
Parallel lines - Find the equation of a straight line parallel to a given line.
Finding equations - Calculate the gradient of a straight line given the coordinates of two
points.
Graphs and simultaneous equations - Interpret the equations as lines and the common
solution as the point of intersection.
Constructing shapes - Measure and draw lines to the nearest millimetre. Construct
triangles and other two-dimensional shapes using a combination of a ruler, protractor
and compasses.
Bisectors - Use straight edge and compasses to:
o construct the perpendicular bisector of a line segment
o construct the bisector of an angle.
o Scale Drawings - Solve problems using scale drawings. Use and interpret maps
and scale drawings.
Standard form - Express numbers in form a × 10n when n is an integer and 1 ≤ a < 10.
Calculating with standard form - Express numbers in form a × 10n when n is an integer
and 1 ≤ a < 10. Solve problems involving standard form.
Chapter 15
7.1
7.2
7.3
Chapter 25
4.6
Chapter 9
1.4
Mensuration











Indices




Perimeter and area of a rectangle - Find the perimeter of shapes made from rectangles.
Find the area of simple shapes using the formulae for the area of rectangles.
Area of a triangle - Find the perimeter of shapes made from triangles and rectangles.
Find the area of simple shapes using the formulae for the areas of triangles and
rectangles
Area of a parallelogram - Find the area of parallelograms
Area of a trapezium - Find the area of trapezia.
Circumference and area of a circle - Find circumferences and areas of circles using
relevant formulae.
Surface area and volume of a cuboid - Find the surface area of simple shapes using the
area formulae for rectangles. Find the volume of cuboids, using an appropriate formula.
Volume of a prism - Find the surface area of simple shapes using the area formulae for
triangles and rectangles. Find the volume of right prisms, using an appropriate formula.
Volume and surface area of a cylinder - Find the surface area of a cylinder. Find the
volume of cylinders, using an appropriate formula.
Arcs and sectors - Find perimeters and areas of sectors of circles.
Volume and surface area of a cone - Find the surface area and volume of a right circular
cone using relevant formulae.
Volume and surface area of a sphere - Find the surface area and volume of a sphere
using relevant formulae.
Using indices - Use index notation. Use index notation for positive integer powers.
Multiplying and dividing with indices - Use index notation and index laws for
multiplication and division of positive integer powers. Use index laws in simple cases.
Negative indices - Use index laws to simplify and evaluate numerical expressions
involving integer and negative powers. Use index notation involving negative and zero
powers.
Fractional indices - Use index laws to simplify and evaluate numerical expressions
involving integer, fractional and negative powers. Use index notation involving
fractional powers.
Chapter 27
3.1
3.2
3.3
3.5
3.6
Revision 3A
Chapter 18
5.4
Geometrical terms and
relationships






Graphs of functions




Direct and inverse
proportion



Measuring and drawing angles - Distinguish between acute, obtuse, reflex and right
angles. Measure an angle to the nearest degree.
Bearings - Understand angle measure including three-figure bearings.
Congruent shapes - Understand congruence as meaning the same shape and size.
Understand that two or more polygons with the same size and shape are said to be
congruent to each other.
Similar shapes - Understand and use the geometrical properties that similar figures have
corresponding lengths in the same ratio but corresponding angles remain unchanged.
Areas of similar triangles - Understand that areas of similar figures are in the ratio of
the square of corresponding sides.
Areas and volumes of similar shapes - Understand that areas of similar figures are in the
ratio of the square of corresponding sides. Understand that volumes of similar figures
are in the ratio of the cube of corresponding sides. Use areas and volumes of similar
figures in solving problems.
Quadratic graphs - Generate points and plot graphs of linear and quadratic functions.
Solving equations with quadratic graphs - Find the intersection points of two graphs,
one linear (y1) and one non-linear (y2), and recognise that the solutions correspond to
the solutions of y2 – y1 = 0.
Other graphs - Plot and draw graphs with equation:y = Ax3 + Bx2 + Cx + D in which:
o the constants are integers and some could be zero
o the letters x and y can be replaced with any other two letters
or: y = Ax3 + Bx2 + Cx + D + E/x + F/x2 in which:
o the constants are numerical and at least three of them are zero
o the letters x and y can be replaced with any other two letters.
Estimating gradients - Find the gradients of non-linear graphs.
Direct proportion - Set up problems involving direct proportion and relate algebraic
solutions to graphical representation of the equations.
Inverse proportion - Set up problems involving inverse proportion and relate algebraic
solutions to graphical representation of the equations.
Chapter 24
End of 6.1
4.4
Chapter 16
7.4
7.6
Chapter 19
5.3
TERM 2 – YEAR 11
Trigonometry











Chapter 26
6.1
6.3
6.5
6.6
Revision Ex 6A
Problems in three dimensions - Use Pythagoras’ Theorem in 3 dimensions. Apply
trigonometrical methods to solve problems in 3 dimensions, including finding the angle
between a line and a plane.
Sine, cosine and tangent of obtuse angles - Understand and use sine, cosine and tangent
of obtuse angles.
The sine rule and the cosine rule - Understand and use the sine rule and cosine rule for
any triangle.
Using sine to find the area of a triangle - Understand and use the formula
1
2
ab sin C for
the area of a triangle.
Paper 3H and 4H – remove any questions not yet covered from the final grade
Mock Exams
Inequalities and regions
– 6 lessons
Pythagoras’ theorem - Understand and use Pythagoras’ theorem in two dimensions.
Link to coordinates and find the length of a line segment.
Trigonometric ratios - Understand and use sine, cosine and tangent of acute angles to
determine lengths and angles of a right-angled triangle.
Calculating angles - Understand and use sine, cosine and tangent of acute angles to
determine lengths and angles of a right-angled triangle.
Using sine, cosine and tangent functions - Understand and use sine, cosine and tangent
of acute angles to determine lengths and angles of a right-angled triangle.
Which ratio to use - Understand and use sine, cosine and tangent of acute angles to
determine lengths and angles of a right-angled triangle.
Solving problems using trigonometry - Apply trigonometrical methods to solve
problems in two dimensions.
Angles of elevation and depression - Understand and use angles of elevation and
depression.





Linear inequalities - Understand and use the convention for open and closed intervals
on a number line. Solve simple linear inequalities in one variable and represent the
solution set on a number line.
Quadratic inequalities - Solve quadratic inequalities in one unknown and represent the
solution set on a number line.
Graphical inequalities - Represent simple linear inequalities on rectangular Cartesian
graphs.
More than one inequality - Identify regions on rectangular Cartesian graphs defined by
simple linear inequalities.
More complex inequalities - Identify harder examples of regions defined by linear
inequalities.
Chapter 20
5.5
5.6
Functions


Calculus





Vectors



Final Revision




Function notation - Understand the concept that a function is a mapping between
elements of two sets. Use function notations of the form f(x) = … and f : x → …
Domain and range - Understand the terms domain and range and which values may
need to be excluded from the domain.
Inverse functions - Understand and find the inverse function f −1
Composite functions - Understand and find the composite function fg
The gradient of a curve - Determine gradients and rates of change by differentiation and
relate these to graphs.
More complex curves - Understand the concept of a variable rate of change.
Differentiate integer powers of x.
Turning points - Determine turning points (maxima and minima) and relate these to
graphs. Distinguish between maxima and minima by considering the general shape of
the graph. Apply calculus to simple practical problems.
Motion of a particle - Apply calculus to linear kinematics.
Introduction to vectors - Understand that a vector has both magnitude and direction.
Understand and use vector notation. Multiply vectors by scalar quantities. Add and
subtract vectors.
Using vectors - Find the resultant of two or more vectors. Apply vector methods for
simple geometrical proofs.
The magnitude of a vector - Calculate the modulus (magnitude) of a vector
Revision of more difficult topics – aiming for A/A* book (see H.Dixon) is good for
extra practice of most difficult topics where students lose most marks.
Focused exam practice on particular topics.
Timed practice of past papers
Chapter 21
8.6
Chapter 22
Not in CIE Book
Chapter 29
8.3
8.4
8.5
Aiming for A/A* Book
Examwizard/H.Dixon
Past Papers