Haringey Sixth Form Mathematics Department Algebra Revision SHOW ALL WORKING OUT Forming Equations 1. A shop sells doughnuts and muffins. Doughnuts cost d pence each. Muffins cost m pence each. Daniel buys 4 doughnuts and 3 muffins. The total cost is C pence. Write down a formula for C in terms of d and m..... 2. The cost, in pounds, of hiring a car can be worked out using this rule. Add 3 to the number of days hire Multiply your answer by 10 The cost of hiring a car for n days is C pounds. Write down a formula for C in terms of n.. Haringey Sixth Form Mathematics Department 1
3. Mr Smith owns minibuses and coaches. Each minibus has 12 seats. (a) Write an expression, in terms of m, for the number of seats in m minibuses. Each coach has 48 seats Write an expression, in terms of m and c, for the number of seats in m minibuses and c coaches. Mr Smith is going to sell drinks on his coaches. He wants to know what type of drinks people like. He designs a questionnaire. (c) Design a suitable questionnaire he could use to find out what type of drink people like. (Total 5 marks) 4. Jessica is paid 7 for each hour that she works. She works for y hours. (a) Write down an expression, in terms of y, for the amount, in pounds ( ), that Jessica is paid.. Haringey Sixth Form Mathematics Department 2
(Question 4 continued) Lucy is also paid 7 for each hour that she works. She works for three times as many hours as Jessica. Write down an expression, in terms of y, for the amount, in pounds ( ), that Lucy is paid. Give your answer as simply as possible. 5.. A 2x 2x B 10 C Diagram NOT accurately drawn In the diagram, all measurements are in centimetres. ABC is an isosceles triangle. AB = 2x AC = 2x BC = 10 (a) Find an expression, in terms of x, for the perimeter of the triangle. Simplify your expression. The perimeter of the triangle is 34 cm. Find the value of x. x = (Total 4 marks) Haringey Sixth Form Mathematics Department 3
Solving Linear Equations 6. x + 90 x + 20 x + 10 Diagram NOT accurately drawn 2x The sizes of the angles, in degrees, of the quadrilateral are x + 10 2x x + 90 x + 20 (a) Use this information to write down an equation in terms of x.... Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral.... (3) (Total 5 marks) Haringey Sixth Form Mathematics Department 4
7. (a) Solve 6x = 18 x = Solve 2y + 3 = 8 y = 8. Solve 2x + 5 = 3 x =... (Total 2 marks) 9. Solve 4x + 3 = 19 x = (Total 2 marks) 10. (a) Solve 7p + 2 = 5p + 8 p =... Haringey Sixth Form Mathematics Department 5
Solve 7r + 2 = 5(r 4) r =... (Total 4 marks) 11. Solve 4 x = 2(3x 1) x =... 12. (a) Solve 4y + 1 = 2y + 8 y = Simplify 2(t + 5) + 13 (Total 4 marks) 13. (a) Solve 5 3x = 2(x + 1) x =. (3) Haringey Sixth Form Mathematics Department 6
(Question 13 continued) 3 y < 3 y is an integer. Write down all the possible values of y.. (Total 5 marks) Factorising Quadratic Equations & Solving Quadratic Equations 14. (a) Solve 6x + 2 = 4(x 7) x =.. 15 2x Solve 4 3 x =.. (3) (c) (i) Factorise x 2 23x 42.... Haringey Sixth Form Mathematics Department 7
(ii) Hence solve x 2 23x 42 = 0 (3) (d) Factorise (x y) 2 3(x y).... (Total 9 marks) 15. (a) Factorise x 2 2x 15 Hence, or otherwise, solve x 2 2x 15 = 0 x = or x =.. 16. (i) Factorise x 2 7x + 12... Haringey Sixth Form Mathematics Department 8
(ii) Solve the equation x 2 7x + 12 = 0... Substition into Equations 17. (a) Work out the value of 2a + ay when a = 5 and y = 3. Work out the value of 5t 2 7 when t = 4 18. T, x and y are connected by the formula. (3) (Total 5 marks) T = 5x + 2y x = 3 and y = 4 (a) Work out the value of T. T = Haringey Sixth Form Mathematics Department 9
(Question 18 continued) T = 16 and x = 7 Work out the value of y. y = (3) (Total 5 marks) Transposing Formulae 19. (a) Solve the inequality x 2 5... Make y the subject of the formula 3x + 2y = 6 y =. 20. Make t the subject of the formula u = 7t + 30 t =... (Total 2 marks) Haringey Sixth Form Mathematics Department 10
Sequences 21. Here are the first 4 terms of an arithmetic sequence 3 7 11 15 Find an expression, in terms of n, for the nth term of the sequence. (Total 2 marks) 22. Here are the first 5 terms of an arithmetic sequence. 6, 11, 16, 21, 26 Find an expression, in terms of n, for the nth term of the sequence.... (Total 2 marks) 23. The first five terms of an arithmetic sequence are 2 7 12 17 22 Write down, in terms of n, an expression for the nth term of this sequence.... (Total 2 marks) Haringey Sixth Form Mathematics Department 11
24. Here are the first four terms of an arithmetic sequence. 3 7 11 15 Write down, in terms of n, an expression for the nth term of the sequence. Simplifying Equations... (Total 2 marks) 25. (a) Simplify (i) 3a + 4b 2a b... (ii) 5x 2 + 2x 3x 2 x... (4) Expand the brackets (i) 4(2x 3)... (ii) p(q p 2 )... Haringey Sixth Form Mathematics Department 12
(c) Expand and simplify 5(3p + 2) 2(5p 3)... (Total 8 marks) 26. (a) Solve the inequality 5x + 12 > 2 Expand and simplify (x 6)(x + 4) (Total 4 marks) 27. (a) Solve the inequality 6x < 7 + 4x... Expand and simplify (y + 3)(y + 4)... (Total 4 marks) Haringey Sixth Form Mathematics Department 13
28. (a) Expand the brackets p(q p 2 )... Expand and simplify 5(3p + 2) 2(5p 3)... 29. (a) Simplify p 3 p 2... Simplify q 3 q q 2 4 q... (Total 2 marks) Haringey Sixth Form Mathematics Department 14
Index Notation (Powers) 30. (a) Expand and simplify (x 6)(x + 4) Factorise completely 12x 2 18xy (Total 4 marks) 31. (a) Simplify (i) p 2 p 7 (ii) x 8 x 3 (iii) 4 y y y 5 3 (3) Expand t(3t 2 + 4) (Total 5 marks) Haringey Sixth Form Mathematics Department 15
32. (a) Simplify 6 x (i) 2 x... (ii) (y 4 ) 3 Expand and simplify (t + 4)(t 2)...... (c) Write down the integer values of x that satisfy the inequality 2 x < 4... (Total 6 marks) 33. (a) Simplify x 5 x 2 Simplify 2w 4 y 3w 3 y 2 15a b 34. Simplify 2 3 3a b 3 7.. (Total 2 marks) Haringey Sixth Form Mathematics Department 16
35. (a) Expand and simplify (x + 7)(x 4). Expand y(y 3 + 2y). (c) Factorise p 2 + 6p. (d) Factorise completely 6x 2 9xy. (Total 8 marks) 36. (a) Simplify 8 p p 2... Simplify (w 4 ) 3... (c) Simplify 5e 3 f e 2 f 2... (Total 4 marks) Haringey Sixth Form Mathematics Department 17
37. Simplify fully (i) (p 3 ) 3... (ii) 4 3q 2q q 3 5... Haringey Sixth Form Mathematics Department 18