such as circumference, very large time scales and area, radius and diameter. intervals 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 Define congruence of Use the enlargement Formulate proofs involving Prove and apply angle plane shapes using transformation to explain congruent triangles and and chord properties of transformations similarity and develop the angle properties circles Develop the conditions for conditions for triangles to Apply logical reasoning, congruence of triangles be similar including the use of reasoning Establish properties of Solve problems using ratio congruence and similarity, quadrilaterals using and scale factors in similar to proofs and numerical congruent triangles and figures exercises involving plane angle properties, and solve shapes Geometric related numerical problems using reasoning Investigate Pythagoras’ Solve right-angled triangle Establish the sine, cosine Theorem and its problems including those and area rules for any application to solving involving direction and triangle and solve related simple problems involving angles of elevation and problems right angled triangles depression Use the unit circle to Use similarity to define trigonometric investigate the constancy functions, and graph them of the sine, cosine and with and without the use trigonometry tangent ratios for a given of digital technologies angle in right-angled Solve simple trigonometric and triangles equations Apply trigonometry to Apply Pythagoras’ solve right-angled triangle theorem and problems trigonometry to solving Pythagoras three-dimensional problems in right-angled triangles Year 8 Year 9 Year 10 Year 10A
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