## Unit 1:Numbers and Algebra

Numbers and the four operations Practise Now

Primes and prime factorisation.

Finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation.

Negative numbers, integers, rational numbers, real numbers and their four operations.

calculations with the use of a calculator.

Representation and ordering of numbers on the number line.

Use of the symbols <,>, ≤, ≥ .

Approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors).

Ratio, rate and proportion Practise Now

Writing a ratio in its simplest form.

Average rate.

Problems involving ratio and rate.

Percentage Practise Now

Expressing one quantity as a percentage of other.

algebraic expressions.

Recognising and representing number patterns (including finding an algebraic expression for the nth term).

Algebraic manipulation

Addition and subtraction of linear algebraic expressions

Simplification of linear algebraic expressions, e.g.

-2(3x . 5) + 4x

(2x/3)-3(x-5)/2.

Factorisation of linear algebraic expressions of the form:

ax + ay (where a is a constant)

ax + bx + kay + kby (where a, b and k are constants).

Functions and graphs

Cartesian coordinates in two dimensions.

Graph of a set of ordered pairs.

Linear relationships between two variables (linear functions).

The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients).

Classifying special quadrilaterals on the basis of their properties.

Angle sum of interior and exterior angles of any convex polygon.

Properties of regular pentagon, hexagon, octagon and decagon.

Properties of perpendicular bisectors of line segments and angle bisectors.

Construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate.

MensurationPractise Now

Area of parallelogram and trapezium.

Problems involving perimeter and area of composite plane figures (including triangle and circle).

Volume and surface area of cube, cuboid, prism and cylinder.

Conversion between cm^{2} and m^{2} , and between cm^{3} and m^{3}.

Problems involving volume and surface area of composite solids.