CURRICULUM SUMMARY – September to December 2015
SUBJECT: Mathematics Core/Extended
YEAR GROUP: Y11
TEACHER:
Agata Piskorz
Week
Learning objectives:
Activities (in brief)
1
GRAPHS
 Draw and interpret quadratic graphs.
 Know vertex and axis of symmetry of a
parabola.
 Use graphs to find approximate solution of
equations
 Draw and interpret graphs representing
exponential growth and decay problems.
 Construct tables of values and draw graphs
for functions of the form 𝑦 = 𝑎𝑥 𝑛 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 𝑦 = 𝑎 𝑥
where a is a positive integer
 Solve quadratic equations by factorisation
 Solve quadratic equations by completing the
square
 Solve quadratic equations by use of the
quadratic formula
 Know gradient and y – intercept of a line.
 Understand and use gradient of a straight
line.
 Understand and estimate gradient of a curve
Constructing tables of values for functions of the form 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, 𝑦 = 𝑥 and drawing
their graphs
Solving linear and quadratic equations approximately by graphical methods.
2
3
4
5
6
TRIGONOMETRY
 Know and understand the sine, cosine and
tangent ratios for an acute angle of a rightangled triangle.
 Know and use the concept of an angle of
elevation and an angle of depression.
𝑎
Graphing by hand or by using technology
Using GEOGEBRA software.
Solving different equations approximately by graphical methods.
Using different methods to solve quadratic equations - REVISION
Revising how to find the gradient of a straight line passing through two given points.
Revising how to find gradient of a line when its equation is given.
Writing equations of parallel and perpendicular lines.
Estimating gradients of curves by drawing tangents.
Revising.
Writing a test
Feedback of a test.
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 right-angled triangle.
Solving trigonometrical problems in two dimensions involving angles of elevation and depression.
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7
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Extend sine and cosine values to angles
between 90° and 180°.
Know and use sine and cosine rules
Know and use formula for an area of a
1
triangle 𝐴 = 2 𝑎𝑏𝑠𝑖𝑛(∡𝐶)
8
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9
MATRICES AND TRANSFORMATIONS
 Understand coordinates of a vector as a
movement of x units in the x-direction and yunits in the y-direction.
 Understand equal vectors and zero vector
 Add and subtract vectors
 Multiply a vector by a scalar.
 Know how to find an image of a point and a
simple figure
 Recognise and describe different
transformations and their combinations.
 Represent vectors by directed line segments
 Know different notation for a vector
 Know the magnitude of a vector
10
11
Know how to find an angle between a line
and a plane
Solving trigonometrical problems involving sine and cosine rules.
Calculating areas of triangles.
Finding sides and angles of different triangles.
Solve simple trigonometrical problems in three dimensions including angle between a line and a
plane
Revising.
Writing 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 positive, fractional and negative scale factors for enlargements
Reflecting simple plane figures in horizontal or vertical lines.
Rotating simple plane figures about the origin, through multiples of 90°.
Describing reflections, rotations, translations and enlargements
Using different notations of a vector.
Finding coordinates of a vector given two points.
Calculating the magnitude of a vector
12

Know and use position vectors and their
linear combination
Use the sum and difference of two vectors to express given vectors in terms of two coplanar
vectors
Revising
Writing a test
13

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
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.
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14

Calculating the determinant IAI and inverse 𝐴−1of a non-singular matrix A.
15


Know how to find an inverse matrix
Describe transformations using co-ordinates
and matrices (singular matrices are
excluded).
Using matrices to describe translations, reflections, rotations, enlargements, stretches.
Revising
Writing a test