Lesson-2.1.1- Know that letters can be used to represent generalized numbers.

Lesson-2.1.2- Substitute numbers into expressions and formulas.

Lesson-2.1.3- Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g. 2a^2 + 3ab – 1 + 5a^2 – 9ab + 4 = 7a^2 – 6ab + 3.

Lesson-2.1.4- Expand products of algebraic expressions. e.g. expand 3x(2x – 4y), (3x + y)(x – 4y). Includes products of more than two brackets, e.g. expand (x – 2)(x + 3)(2x + 1).

Lesson-2.1.5- Factorize by extracting common factors. Factorise means factorise fully, e.g. 9x^2 + 15xy = 3x(3x + 5y).

Lesson-2.1.6- Factorise expressions of the form: • ax + bx + kay + kby • a^2 x^2 − b^2 y^2 • a^2 + 2ab + b2 • ax^2 + bx + c • ax^3 + bx2 + cx .

Lesson-2.1.7- Manipulate algebraic fractions.

Lesson-2.1.8- Factorize and simplify rational expressions.

Lesson-2.1.9- Understand and use indices (positive, zero, negative and fractional). e.g. solve: • 32^x = 2 , 5^(x + 1) = 25^x .

Lesson-2.1.10- Understand and use the rules of indices.

Lesson-2.1.11- Construct expressions, equations and formulas. e.g. write an expression for the product of two consecutive even numbers. Includes constructing simultaneous equations.

Lesson-2.1.12- Solve linear equations in one unknown. Examples include: • 3x + 4 = 10 , 5 – 2x = 3(x + 7).

Lesson-2.1.13- Solve simultaneous linear equations in two unknowns.

Lesson-2.1.14- Solve quadratic equations by factorization, completing the square and by use of the quadratic formula. Includes writing a quadratic expression in completed square form. Candidates may be expected to give solutions in surd form. The quadrati

Lesson-2.1.15- Change the subject of formulas. e.g. change the subject of a formula where: • the subject appears twice • there is a power or root of the subject.

Lesson-2.1.16- Represent and interpret inequalities, including on a number line. When representing and interpreting inequalities on a number line: • open circles should be used to represent strict inequalities () • closed circles should be used to rep

Lesson-2.1.17- Construct, solve and interpret linear inequalities. Examples include: • 3x < 2x + 4 • –3 ⩽ 3x – 2 < 7 .

Lesson-2.1.18- Represent and interpret linear inequalities in two variables graphically. The following conventions should be used: • broken lines should be used to represent strict inequalities () • solid lines should be used to represent inclusive in

Lesson-2.1.19- List inequalities that define a given region. Linear programming problems are not included.

Lesson-2.1.19- Continue a given number sequence or pattern. Subscript notation may be used, e.g. Tn is the nth term of sequence T

Lesson-2.1.20 -Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences. Includes linear, quadratic, cubic and exponential sequences and simple combinations of these.

Lesson-2.1.21- Find and use the nth term of sequences.

Lesson-2.1.22- Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities. Includes linear, square, square root, cube and cube root proportion. Knowledge of proportional symbol (∞) is required.

Lesson-2.1.23- Use and interpret graphs in practical situations including travel graphs and conversion graphs. Includes estimation and interpretation of the gradient of a tangent at a point.

Lesson-2.1.24- Draw graphs from given data.

Lesson-2.1.25- Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.

Lesson-2.1.26- Calculate distance travelled as area under a speed–time graph. Areas will involve linear sections only.

Lesson-2.1.27- Construct tables of values, and draw, recognize and interpret graphs for functions

Lesson-2.1.28- Solve associated equations graphically, including finding and interpreting roots by graphical methods. e.g. finding the intersection of a line and a curve.

Lesson-2.1.29- Draw and interpret graphs representing exponential growth and decay problems.

Lesson-2.1.30 -Estimate gradients of curves by drawing tangents.

Lesson-2.1.31- Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic

Lesson-2.1.32- Recognize, sketch and interpret graphs of the following functions: (c) cubic (d) reciprocal (e) exponential.

Lesson-2.1.33- Understand functions, domain and range, and use function notation.

Lesson-2.1.34- Understand and find inverse functions f^–1(x).

Lesson-2.1.35- Form composite functions as defined by gf(x) = g(f(x)).

Lesson-3.1.1- Use and interpret Cartesian coordinates in two dimensions.

Lesson-3.1.2- Draw straight-line graphs for linear equations. Examples include: • y = –2x + 5 • y = 7 – 4x • 3x + 2y = 5 .

Lesson-3.1.3- Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.

Lesson-3.1.4- Calculate the length of a line segment. Find the coordinates of the midpoint of a line segment.

Lesson-3.1.5- Interpret and obtain the equation of a straight-line graph. Questions may: • use and request lines in different forms, e.g. ax + by = c y = mx + c x = k • involve finding the equation when the graph is given • ask for the gradient or y

Lesson-3.1.6- Find the gradient and equation of a straight line parallel to a given line. e.g. Find the equation of the line parallel to y = 4x – 1 that passes through (1, –3).

Lesson-3.1.7- Find the gradient and equation of a straight line perpendicular to a given line. Examples include: • Find the gradient of a line perpendicular to 2y = 3x + 1 . • Find the equation of the perpendicular bisector of the line joining the poi

Lesson-4.1.1- Use and interpret the following geometrical terms: • point • vertex • line • plane • parallel • perpendicular • perpendicular bisector • bearing • right angle • acute, obtuse and reflex angles • interior and exterior an

Lesson-4.1.2- Use and interpret the vocabulary of: • triangles • special quadrilaterals • polygons • nets • solids. Includes the following terms. Triangles: • equilateral • isosceles • scalene • right-angled. Quadrilaterals: • square ?

Lesson-4.1.3- Use and interpret the vocabulary of a circle. Includes the following terms: • centre • radius (plural radii) • diameter • circumference • semicircle • chord • tangent • major and minor arc • sector • segment.

Lesson-4.1.4- Measure and draw lines and angles. A ruler should be used for all straight edges. Constructions of perpendicular bisectors and angle bisectors are not required.

Lesson-4.1.5- Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only. e.g. construct a rhombus by drawing two triangles. Construction arcs must be shown.

Lesson-4.1.6- Draw, use and interpret nets. Examples include: • draw nets of cubes, cuboids, prisms and pyramids • use measurements from nets to calculate volumes and surface areas.

Lesson-4.1.7- Draw and interpret scale drawings. A ruler must be used for all straight edges.

Lesson-4.1.8- Use and interpret three-figure bearings. Bearings are measured clockwise from north (000° to 360°), e.g. Find the bearing of A from B if the bearing of B from A is 025°. Includes an understanding of the terms north, east, south and west,

Lesson-4.1.9- Calculate lengths of similar shapes. 2 Use the relationships between lengths and areas of similar shapes and lengths, surface areas and volumes of similar solids.

Lesson-4.1.10- Solve problems and give simple explanations involving similarity. Includes showing that two triangles are similar using geometric reasons.

Lesson-4.1.11- Recognize line symmetry and order of rotational symmetry in two dimensions. Includes properties of triangles, quadrilaterals and polygons directly related to their symmetries.

Lesson-4.1.12- Calculate unknown angles and give simple explanations using the following geometrical properties: • sum of angles at a point = 360° • sum of angles at a point on a straight line = 180° • vertically opposite angles are equal • angl

Lesson-4.1.13 - Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior (supplementary) angles sum to 180°.

Lesson-4.1.14- Know and use angle properties of regular and irregular polygons. Includes exterior and interior angles, and angle sum.

Lesson-4.1.15- alculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90° • angle at the centre is twice the angle at the circumferenc

Lesson-4.1.16- Use the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the Centre • tangents from an external point are equal in length.

Lesson-5.1.1- Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units. Units include: • mm, cm, m, km • mm^2 , cm^2 , m^2 , km^2 • mm^3 , cm^3 , m^3 • ml, l • g, kg

Lesson-5.1.2- Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium. Except for the area of a triangle, formulas are not given.

Lesson-5.1.3- Carry out calculations involving the circumference and area of a circle. Answers may be asked for in terms of π. Formulas are given in the List of formulas.

Lesson-5.1.4- Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle. Includes minor and major sectors.

Lesson-5.1.5- Carry out calculations and solve problems involving the surface area and volume of a: • cuboid • prism • cylinder • sphere • pyramid • cone. Answers may be asked for in terms of π. The following formulas are given in the List of

Lesson-5.1.6- Carry out calculations and solve problems involving perimeters and areas of: • compound shapes • parts of shapes. Answers may be asked for in terms of π.

Lesson-5.1.7- Carry out calculations and solve problems involving surface areas and volumes of: • compound solids • parts of solids. e.g. find the surface area and volume of a frustum

Lesson-6.1.1- Know and use Pythagoras’ theorem.

Lesson-6.1.2- Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. Angles will be given in degrees and answers should be written in degrees, with decimals correct to one d

Lesson-6.1.3- Solve problems in two dimensions using Pythagoras’ theorem and trigonometry. Knowledge of bearings may be required.

Lesson-6.1.4- Know that the perpendicular distance from a point to a line is the shortest distance to the line.

Lesson-6.1.5- Carry out calculations involving angles of elevation and depression.

Lesson-6.1.6- Use the sine and cosine rules in calculations involving lengths and angles for any triangle. Includes problems involving obtuse angles and the ambiguous case.

Lesson-6.1.7- Use the formula area of triangle = 1/2 ab sinC . The sine and cosine rules and the formula for area of a triangle are given in the List of formulas.

Lesson-6.1.8- Carry out calculations and solve problems in three dimensions using Pythagoras’ theorem and trigonometry, including calculating the angle between a line and a plane.

Lesson-7.1.1- Recognize, describe and draw the following transformations: 1 Reflection of a shape in a straight line. 2 Rotation of a shape about a Centre through multiples of 90°.

Lesson-7.1.2- Recognize, describe and draw the following transformations: Enlargement of a shape from a centre by a scale factor. 4 Translation of a shape by a vector (x y)

Lesson-7.1.3- Describe a translation using a vector represented by (x y), AB or a.

Lesson-7.1.4- Add and subtract vectors. Multiply a vector by a scalar.

Lesson-7.1.5- Calculate the magnitude of a vector (x y) as √x²+y²

Lesson-7.1.6- Represent vectors by directed line segments. 2 Use position vectors. 3 Use the sum and difference of two or more vectors to express given vectors in terms of two coplanar vectors.

Lesson-7.1.7- Use vectors to reason and to solve geometric problems. Examples include: • show that vectors are parallel • show that 3 points are collinear • solve vector problems involving ratio and similarity.

Lesson-8.1.1- Understand and use the probability scale from 0 to 1.

Lesson-8.1.2- Understand and use probability notation. P(A) is the probability of A. P(A′) is the probability of not A.

Lesson-8.1.3-Calculate the probability of a single event. Probabilities should be given as a fraction, decimal or percentage. Problems may require using information from tables, graphs or Venn diagrams.

Lesson-8.1.4- Understand that the probability of an event not occurring = 1 – the probability of the event occurring. e.g. P(B) = 0.8, find P(B′) .

Lesson-8.1.5- Understand relative frequency as an estimate of probability. e.g. use results of experiments with a spinner to estimate the probability of a given outcome.

Lesson- 8.1.6- Calculate expected frequencies. e.g. use probability to estimate an expected value from a population. Includes understanding what is meant by fair and bias.

Lesson- 8.1.7- Calculate the probability of combined events using, where appropriate: • sample space diagrams.

Lesson-8.1.8- Calculate the probability of combined events using, where appropriate: Venn diagrams • tree diagrams. The notation P(A ∩ B) and P(A ∪ B) may be used in the context of Venn diagrams. On tree diagrams outcomes will be written at the end

Lesson-9.1.1- Classify and tabulate statistical data. e.g. tally tables, two-way tables.

Lesson-9.1.2- Read, interpret and draw inferences from tables and statistical diagrams.

Lesson-9.1.3- Compare sets of data using tables, graphs and statistical measures. e.g. compare averages and measures of spread between two data sets.

Lesson-9.1.4- Appreciate restrictions on drawing conclusions from given data.

Lesson-9.1.5- Calculate the mean, median, mode and range for individual data and distinguish between the purposes for which these are used.

Lesson-9.1.6- 2 Calculate an estimate of the mean for grouped discrete or grouped continuous data.

Lesson-9.1.7- Identify the modal class from a grouped frequency distribution.

Lesson-9.1.8- Draw and interpret: (a) bar charts (b) pie charts (c) pictograms (d) simple frequency distributions.

Lesson-9.1.9- Draw and interpret scatter diagrams. Plotted points should be clearly marked, for example as small crosses (×).

Lesson-9.1.10-Understand what is meant by positive, negative and zero correlation.

Lesson-9.1.11- Draw by eye, interpret and use a straight line of best fit. A line of best fit: • should be a single ruled line drawn by inspection • should extend across the full data set • does not need to coincide exactly with any of the points bu

Lesson-9.1.12- Draw and interpret cumulative frequency tables and diagrams. Plotted points on a cumulative frequency diagram should be clearly marked, for example as small crosses (×), and be joined with a smooth curve.

Lesson-9.1.13- Estimate and interpret the median, percentiles, quartiles and interquartile range from cumulative frequency diagrams.

Lesson-9.1.14- Draw and interpret histograms. On histograms, the vertical axis is labelled ‘Frequency density’.

Lesson-9.1.15- Calculate with frequency density. Frequency density is defined as frequency density = frequency ÷ class width .