Module 14  Proof  
Teacher Guide  Lesson Resources  Lesson Plans  Exam Questions 
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Module  Grade  Topic 
Description 

14 
2 
1 
Understand the concepts and vocabulary of factor (divisor), multiple and common factor and prime number. Recognise primes (less than 100); use simple tests of divisibility. 











14 
2 
2 
Recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles at a vertex; use angle properties of equilateral, isosceles and rightangled triangles. 











14 
3 
3 
Use the term cube; recall the squares and cubes of 2, 3, 4, 5, and 10; use index notation for simple integer powers. 











14 
3 
4 
Manipulate algebraic expressions by collecting like terms, including expanding brackets such as 3(x+2) 











14 
3 
5 
Use axes and coordinates to specify or locate points in all four quadrants; find the coordinates of points identified by geometrical information. 











14 
3 
6 
Find the area and perimeter of a rectangle. 











14 
3 
7 
Calculate, use and interpret the statistical measures mode, median, mean and range for discrete data, including comparing distributions. 











14 
4 
8 
Generate terms of a sequence using termtoterm and positionto term definitions of the sequence, on paper and using ICT. Generate sequences from practical contexts and write an expression to describe the nth term of an arithmetic sequence. 











14 
4 
9 
Use parallel lines, alternate angles and corresponding angles; calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons. Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. 




Angle Proofs 





14 
4 
10 
Solve angle problems involving intersecting and parallel lines, and polygons; understand that the tangent at any point on a circle is perpendicular to the radius at that point. 











14 
4 
11 
Identify different mutuallyexclusive outcomes and know that the sum of the probabilities of all these outcomes is one. 











14 
5 
12 
Expand the product of two linear expressions and simplify (x+2)(x5). Factorise simple quadratics. 











14 
5 
13 
Use and justify simple quadratic sequences to generate the nth term of a quadratic sequence, including triangular numbers 











14 
5 
14 
Understand, recall and use Pythagoras’ theorem. Find the length AB given the points A and B in 2D 











14 
5 
15 
Multiply expressions of the form (2x + 3)(3x – 7) and simplify the resulting expression 











14 
6 
16 
Solve quadratic equations of the form x^{2} +/– … by factorisation, including the difference of two squares. 











14 
7 
17 
Use and understand terminating and recurring decimals including exact fraction equivalents 











14 
8 
18 
Solve quadratic equations by completing the square and using the quadratic formula. 











14 
8 
19 
Solving Algebraic problems, e.g. explain why (n+1)(n+20) is an even number. 




Basic Proofs and Proof Techniques 


14 
8 
20 
Understand and use SSS, SAS, ASA and RHS condition to prove the congruence of triangles; verify standard ruler and compass constructions; use congruence to show that translations, reflections and rotations preserve length and angle. 











14 
8 
21 
Understand and use vector notation; calculate, and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector; calculate the resultant of two vectors; understand and use the commutative and associative properties of vector addition; solve simple geometrical problems in 2D using vector methods. 




Vector Proofs 





14 
8 
22 
Using the Circle Theorems and knowing the proofs [INCLUDING alternate segment theorem, and problems involving tangents meeting] 




Circle Theorem Proofs 



