Name: Date: Time: Total marks available: Total marks achieved: Question 1-11 Non Calc Questions 12-21 Calculator
Questions Q1. (a) Factorise fully 6ab + 10ac... (2) (b) Expand and simplify (x 5)(x + 7)... (2) (c) Simplify Give your answer in its simplest form.... (2) (d) Factorise y 2 16... (1) (e) Simplify (h 2 ) 3... (1) (Total for Question is 8 marks)
Q2. The point A has coordinates (3, 8). The point B has coordinates (7, 5). M is the midpoint of the line segment AB. Find the coordinates of M. (Total for Question is 2 marks) Q3. Simplify fully (Total for Question is 3 marks)
Q4. * The diagram shows a pentagon. All measurements are in centimetres. Show that the area of this pentagon can be written as 5x 2 + x 6 (Total for Question is 4 marks) 5. Solve the simultaneous equations 5x + 2y = 11 4x 3y = 18 x =...................... y =...................... (Total for Question is 4 marks)
Q6. On the grid, draw the graph of y = 2x 3 for values of x from 2 to 2 (Total for Question is 3 marks)
Q7. Make t the subject of the formula (Total for Question is 4 marks) Q8. *This formula is used to work out the body mass index, B, for a person of mass M kg and height H metres. A person with a body mass index between 25 and 30 is overweight. Arthur has a mass of 96 kg. He has a height of 2 metres. Is Arthur overweight? You must show all your working. (Total for Question is 3 marks)
Q9. You can use the graph opposite to find out how much Lethna has to pay for the units of electricity she has used. Lethna pays at one rate for the first 100 units of electricity she uses. She pays at a different rate for all the other units of electricity she uses. Lethna uses a total of 900 units of electricity. Work out how much she must pay. (Total for Question is 3 marks)
Q10. ABC is a triangle. Angle ABC = angle BCA. The length of side AB is (3x 5) cm. The length of side AC is (19 x) cm. The length of side BC is 2x cm. Work out the perimeter of the triangle. Give your answer as a number of centimetres.... cm (Total for Question is 5 marks)
Q11. (a) Expand and simplify (p + 9)(p 4) (2) (b) Solve = 4w + 2 w =...................... (3) (c) Factorise x 2 49 (1) (d) Simplify (9x 8 y 3 ) ½ (2) (Total for Question is 8 marks)
Q12. k = 3e + 5 (a) Work out the value of k when e = 2 (b) Solve 4y + 3 = 2y + 14 (2) (c) Solve 3(x 5) = 21 y =..................... (2) 3 < n < 4 n is an integer. x =..................... (2) (d) Write down all the possible values of n. (2) (Total for Question is 8 marks)
Q13. The straight line P has been drawn on a grid. Find the gradient of the line P. (Total for Question is 2 marks) Q14. T is inversely proportional to d 2 T = 160 when d = 8 Find the value of T when d = 0.5 (Total for Question is 3 marks)
Q15. Here are the first five terms of an arithmetic sequence. 4 9 14 19 24 (a) Find, in terms of n, an expression for the nth term of this sequence. Here are the first five terms of a different sequence.... (2) 2 2 0 4 10 An expression for the nth term of this sequence is 3n n 2 (b) Write down, in terms of n, an expression for the nth term of a sequence whose first five terms are 4 4 0 8 20... (1) (Total for Question is 3 marks)
Q16. The points A, B and C lie on a straight line. The coordinates of A are (9, 0). The coordinates of B are (7, 4). The coordinates of C are (1, q). Work out the value of q.... (Total for Question is 3 marks)
Q17. Stephanie is x years old. Tobi is twice as old as Stephanie. Ulrika is 3 years younger than Tobi. The sum of all their ages is 52 years. (a) Show that 5x 3 = 52 (b) Work out the value of x. (3) x =... (2) (Total for Question is 5 marks) Q18. * Vicky makes 8 purses and 9 key rings to sell for charity. The price of a purse will be twice as much as the price of a key ring. Vicky wants to get a total of exactly 40 when she sells all the purses and all the key rings. Work out the price Vicky needs to charge for each purse and for each key ring. (Total for Question is 4 marks) Q19.
Julie is x years old. Kevin is x + 3 years old. Omar is 2x years old. Write an expression, in terms of x, for the mean of their ages.... (Total for Question is 2 marks) Q20. (a) Factorise x 2 + 7x (b) Factorise y 2 10y + 16 (1) *(c) (i) Factorise 2t 2 + 5t + 2 (2) (ii) t is a positive whole number. The expression 2t 2 + 5t + 2 can never have a value that is a prime number. Explain why. (3) (Total for Question is 6 marks)
Mark Scheme Q1. Q2. Q3.
Q4. * Question Working Answer Mark Notes (2x 2)(2x +1) + ½ (2x 2)((3x + 5) (2x +1)) 4x 2 2x 2 + x 2 + 4x x - 4 = 5x 2 + x 6 Or (2x 2)(3x + 5) ½ (2x 2)((3x + 5) (2x +1)) = 6x 2 6x + 10x - 10 - x 2-4x + x + 4 = 5x 2 + x 6 Show 4 M1 for correct expression for a single rectangle area (2x 2)(2x +1) or (2x 2)(3x + 5) M1 for correct expression for triangle area ½ (2x 2)((3x + 5) (2x +1)) M1 for all 4 terms correct with or without signs or 3 out of no more than four terms correct with signs in expansion of any two linear expressions. C1 for 5x 2 + x 6 and all steps clearly shown in a logical progression QWC: All steps need to be clearly laid out showing a logical progression Q5.
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Q17. Q18. Q19. Q20.