non- calculator paper 1 compare fractions; equivalent fractions; factorise an expression

1. non- calculator paper 1 compare fractions; equivalent fractions; factorise an expression 2 draw plan and elevations of 3D shape made from cuboids 3 circumference of circle; area of circle; area of compound shape 4 algebraic expressions; make and solve an equation 5 multiply out an expression; evaluate an expression 6 square numbers 7 multiply out and simplify expressions involving brackets 8 solve a factorised quadratic equation 9 calculate the length of a side in a right-angled triangle; similar triangles 10 change the subject of a formula; evaluate an expression; negative numbers 11 inequality on a number line; solve an inequality; find a non-integer solution 12 use circle theorems 13 sector of a circle; perimeter; answer “in terms of π” 14 volume of compound shape; density and mass 15 add algebraic fractions grade boundaries for this paper

2. 1. Here is a multiplication table (a) Emma says that is greater than Is she correct? Explain your answer. Yes! Three quarters of 48 is 36. 37 is greater than 36 2 marks (b) Complete the following (c) Factorise 33x +44 66 11 ( 3x + 4 ) 87 1 mark 1 mark 1 mark

3. 2. The diagram shows a solid made from two cuboids The large cuboid is 5cm by 4cm by 3cm The small cuboid is 3cm by 1cm by 1cm On the centimetre grids draw the plan view, side elevation and front elevation Plan view Front elevation 3 marks Side elevation

4. 3 (a) Use π = 3 to work out an estimate for the circumference of a circle with diameter 15 cm circumference = π × diameter = 3 × 15 Answer = 45 cm 2 marks 3 (b) (i) Use π = 3.14 to work out the area of a circle with radius 10 cm area of circle = π × radius2 = 3.14 × 102 Answer = 314 cm2 2 marks

5. 3 (b) (ii) The diagram shows a shape made of two semicircles and a rectangle Use your answer to part (b) (i) to work out the area of the shape area rectangle = 20 × 30 = 600 area shape = 600 + 314 = 914 cm2 3 marks

6. 4 Matias is x years old Kaz is three years younger than Matias 4 (a) Write down an expression, in terms of x, for Kaz’s age Matias’ age = x Kaz’s age = x − 3 1 mark (b) The sum of the ages of Matias and Kaz is 91 Use this information to write down an equation in terms of x x + x− 3 = 91 2x − 3 = 91 2 marks (c) Solve your equation formed in part (b) to work out the age of Matias 2x = 94 Matias is 47 years old 2 marks

7. 5 (a) Multiply out a(b + c) = ab + ac 1 mark (b) Work out the value of xy +xz when x = 27, y = 3 and z = 7 xy + xz = x(y + z) = 27 ( 3 + 7 ) = 27 × 10 = 270 3 marks

8. 6 (a) write down the value of 132 Answer = 169 1 mark (b) explain how you know that 142 is not equal to 192 42 ends in a 6 not a 2 Or 10 × 14 = 140 4 × 14 = 56 Therefore 14 × 14 = 196 which is not 192 1 mark

9. 7(a) Multiply out −2(3a − b + 5) = −6a + 2b − 10 2 marks (b) Multiply out and simplify 4(8e − 9) + 2e = 32e − 36 + 2e = 34e − 36 2 marks

10. 8 Solve (x − 13)(x + 1) = 0 when two expressions are multiplied together and the answer is zero, then one of the expressions must be zero either x − 13 = 0 or x + 1 = 0 so x = 13 or x = -1 2 marks

11. 9 (a) The diagram shows a right-angled triangle ABC AC = 10cm and BC = 3cm Calculate the length of AB Leave your answer as a square root h y x Think – PYTHAGORAS h2 = x2 + y2 102 = x2 + 32 x2 = 100 – 9 AB2 = 91 3 marks AB =√91

12. 9 (b) Triangles ABC and DEF are similar Work out the length of EF marked x on the diagram DEF is an enlargement of ABC with scale factor 15÷10 = 1.5 DF = 1.5 × AC x = 1.5 × 3 EF = 4.5 cm 3 marks

13. 10 You are given the formula (a) Make x the subject of the formula Must have ± sign to score full marks 5y = x2 - 49 x2 - 49 = 5y x2 = 5y + 49 x = ± √( 5y + 49 ) 3 marks (b) Work out the values of x when y = −9 x = ± √( 5 × −9 + 49 ) x = ± √( −45 + 49 ) x = ± √( 4 ) x = 2 and −2 3 marks

14. 11 (a) Write down the integers that satisfy this inequality diagram -2 ≤ x < 2 integers -2, -1, 0, 1 2 marks (b) Solve the inequality 14 + x ≤ 12 + 3x 14 – 12 ≤ 3x - x 2 ≤ 2x x ≥ 1 2 marks (c) Write down a non-integer value that satisfies both the inequality diagram and part (b) 1 < answer < 2 x = 1.5 for example 1 mark

15. 12 ABCD is a cyclic quadrilateral PCQ is a tangent at C O is the centre of the circle Triangle ABC is isosceles (a) work out the value of x 0pposite angles of a cyclic quadrilateral add up to 180 x = 180 – 86 = 94⁰ 2 marks (b) (i) Work out the value of y angle BAC is equal to y ** triangle BAC is isosceles 180 – 86 = 94 angle BAC = 94 ÷ 2 = 47⁰ y = 47⁰ 3 marks (b) (ii) Write down the name of the circle theorem used in part (b)(i) ** Alternate Segment Theorem 1 mark

16. 13 The diagram shows a major sector of a circle The radius of the sector is 18 cm The angle of the minor sector is 120° Work out the perimeter of the major sector Leave your answer in terms of π Simplify your answer as fully as possible 240⁰ Perimeter = 24π + 18 + 18 = 24π + 36 cm 4 marks

17. 14 The diagram shows a solid metal object made from two cubes and a square-based pyramid The area of the base of each cube is 25cm2 The height of the pyramid is equal to the height of each cube The density of the metal is 9g/cm3 You are given the formula Volume of pyramid = ⅓ × area of base × height Work out the mass of the solid metal object Area of square base = 25cm2 means length of each edge is 5cm volume of each cube = 125cm3 volume of pyramid = ⅓ × 25 × 5 = 41⅔ cm3 volume of solid metal object = 125 + 125 + 41⅔ = 291⅔ cm3 mass = density × volume = 9 × 291⅔ = 2625g 7 marks

18. 4 marks

19. Total: out of 70 19