Download CURRICULUM SUMMARY – September to October 2008

CURRICULUM SUMMARY – September to December 2016
SUBJECT: Mathematics Extended / Additional
YEAR GROUP: Year 11
TEACHER: Agata Piskorz
Week Date
Learning objectives
Activities (in brief)
1
EXPONENTS
 Revise laws of exponents
 Negative and fractional powers
 Revise factorization methods
Simplifying algebraic expressions with powers.
Finding value of a power with negative or fractional index – more
difficult examples.
Factorising algebraic expression with powers
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Solve exponential equations algebraically
Know and use definition of a logarithm
Use logarithms to solve exponential equations
Know the change – base rule for logarithms
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Revise graphs
Construct tables of values and draw graphs for functions of
the form , where a is a positive integer.
Solve associated equations approximately by graphical
methods.
Draw and interpret graphs representing exponential growth
and decay problems.
Solving exponential equations .
Using calculators to find the value of a logarithm.
Revising.
Writing a test
Feedback of a test.
Construct tables of values and draw graphs for functions of the form
where a is a rational constant, and n = –2, –1, 0, 1, 2, 3, and
simple sums of not more than three of these.
Graphing by hand or by using technology
Using GEOGEBRA software.
Solving different equations approximately by graphical methods.
Finding gradients of a curve.
5-9 Sep
2
12 -16
Sep
3
19-23
Sep
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4
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26-30
Sep
5
3-7 Oct
Use the standard form
n where n is a positive or
negative integer, and
Use the compound interest formula
where P is the
amount invested, r is the percentage rate of interest and n
is the number of years of compound interest.
VECTORS - revision
 Understand coordinates of a vector as a movement of x
units in the x-direction and y-units in the y-direction.
 Understand equal vectors and zero vector
 Add and subtract vectors
 Multiply a vector by a scalar.
 Represent vectors by directed line segments
Calculating using money and converting from one currency to another.
Extracting data from tables and charts.
Using given data to solve problems on personal and household finance
involving earnings, simple interest and compound interest.
Revising.
Writing a test
Feedback of a test.
Writing vectors as number pairs.
Drawing vectors.
Performing some algebraic operations on vectors.
Describe a translation by using a vector.
Constructing given translations and enlargements of simple plane
figures.
Using different notations of a vector.
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6
10-14 Oct
7
17-21 Oct
8
24-28 Oct
MATRICES AND TRANSFORMATIONS
 Know what is a matrix and use it to display information
 Know rows, columns and order of a matrix.
 Calculate the product of a matrix and a scalar quantity.
 Use the algebra of 2 × 2 matrices including the zero and
identity 2 × 2 matrices.
 Know determinant of a matrix
 Know how to find an inverse matrix
 Know how to find an image of a point and a simple figure
 Recognise and describe different transformations and their
combinations.
 Describe transformations using co-ordinates and matrices
31 Oct –
4 Nov
9
7 -11 Nov
10
14 – 18
Nov
Know different notation for a vector
Know the magnitude of a vector
Know and use position vectors and their linear combination
Finding coordinates of a vector given two points.
Calculating the magnitude of a vector
Use the sum and difference of two vectors to express given vectors in
terms of two coplanar vectors
Revising
Writing a test
Displaying information in the form of a matrix of any order.
Adding and subtracting matrices.
Multiplying a matrix by a scalar.
Multiplying two matrices. Multiplication by a unit matrix.
Calculating the determinant IAI and inverse
of a non-singular matrix
Reflecting simple plane figures in horizontal or vertical lines.
Rotating simple plane figures about the origin, through multiples of 90°.
Using positive, fractional and negative scale factors for enlargements
Describing reflections, rotations, translations and enlargements
Revising
Writing a test
Test feedback.
Mid-Term Break
BEARINGS AND TRIGONOMETRY - REVISION
 Know and understand the sine, cosine and tangent ratios
for an acute angle of a right-angled triangle.
 Know and use the concept of an angle of elevation and an
angle of depression.
 Extend sine and cosine values to angles between 90° and
180°.
Applying Pythagoras’ theorem and the sine, cosine and tangent ratios
for acute angles to the calculation of a side or of an angle of a rightangled triangle.
Solving trigonometrical problems in two dimensions involving angles of
elevation and depression.
Solving trigonometrical problems involving sine and cosine rules.
Calculating areas of triangles.
Finding sides and angles of different triangles.
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Know and use sine and cosine rules
Know and use formula for an area of a triangle
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Know how to find an angle between a line and a plane
Solve trigonometrical problems in three dimensions including angle
between a line and a plane
Revising.
Writing a test
Feedback of a test.
11
21 – 25
Nov
ALGEBRA AND GRAPHS
 Represent inequalities graphically.
 Apply the idea of rate of change to easy kinematics.
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12
Understand direct and inverse proportionality
Construct and transform complicated formulae and
equations.
28 Nov –
2 Dec
13
5 Dec – 9
Dec
14
SEQUENCES - REVISION
 Know linear sequences, quadratic and cubic sequences,
exponential sequences and simple combinations of these.
CONSTRUCTIONS AND LOCI
 Revise constructions
 Use the definition of a locus
 Use the method of intersecting loci for sets of points in two
dimensions
12 Dec –
16 Dec
Using graphical representations of inequalities in the solution of simple
linear programming problems.
Solving problems involving distance-time and speed-time graphs,
acceleration and deceleration. Calculate distance travelled as area under
a linear speed-time graph.
Divide a quantity in a given ratio.
Express direct and inverse variation in algebraic terms and use this form
of expression to find unknown quantities.
Transforming formulae where the subject appears twice.
Manipulating algebraic fractions.
Factorising and simplifying rational expressions.
Revising.
Writing a test
Feedback of a test.
Continue a given number sequence.
Recognise patterns in sequences and relationships between different
sequences.
Find the nth term of sequences.
Constructing a triangle given the three sides using ruler and pair of
compasses only.
Constructing other simple geometrical figures from given data using
ruler and protractor as necessary.
Constructing angle bisectors and perpendicular bisectors using straight
edge and pair of compasses only.
Finding sets of points in two dimensions which are:
• at a given distance from a given point
• at a given distance from a given straight line
• equidistant from two given points
• equidistant from two given intersecting straight lines.
Revising.
Writing a test
Feedback of a test.