Year 8 Year 9 Year 10 Year 10A Number and place value Investigate index notation and represent whole numbers as products of powers of prime numbers Investigate and use square roots of perfect square numbers Apply the associative, commutative and distributive laws to aid mental and written computation Compare, order, add and subtract integers. Use index notation with numbers to establish the index laws with positive integral indices and the zero index Carry out the four operations with integers, using efficient mental and written strategies and appropriate digital technologies . Real numbers Investigate terminating and recurring decimals Investigate the concept of irrational numbers, including π Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies Solve a range of problems involving rates and ratios, with and without digital technologies Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems Apply index laws to numerical expressions with integer indices Express numbers in scientific notation Define rational and irrational numbers and perform operations with surds and fractional indices Use the definition of a logarithm to establish and apply the laws of logarithms Money and financial mathematics Solve problems involving profit and loss, with and without digital technologies Solve problems involving simple interest Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies Patterns and algebra Extend and apply the distributive law to the expansion of algebraic expressions Factorise algebraic expressions by identifying numerical factors Simplify algebraic expressions involving the four operations Extend and apply the index laws to variables, using positive integral indices and the zero index Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate Factorise algebraic expressions by taking out a common algebraic factor Simplify algebraic products and quotients using index laws Apply the four operations to simple algebraic fractions with numerical denominators Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems
such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume Solve problems involving duration, including using 12- and 24-hour time within a single time zone very large time scales and intervals Geometric reasoning Define congruence of plane shapes using transformations Develop the conditions for congruence of triangles Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar Solve problems using ratio and scale factors in similar figures Formulate proofs involving congruent triangles and angle properties Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes Prove and apply angle and chord properties of circles Pythagoras and trigonometry Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles Apply trigonometry to solve right-angled triangle problems Solve right-angled triangle problems including those involving direction and angles of elevation and depression Establish the sine, cosine and area rules for any triangle and solve related problems Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies Solve simple trigonometric equations Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles Year 8 Year 9 Year 10 Year 10A