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Course entry requirements: 5 A* - C grades including at least B grade in Mathematics. During the summer break you are required to complete all of the work in this pack. This will give you the chance to demonstrate your commitment and enthusiasm for this subject. You will still need to achieve the entry requirements to study this course. Transition classes will be run on Monday 11th, Tuesday 12th and Wednesday 13th of July. Attending these classes will give you an insight into the subject and help you complete your transition pack. NOTE: There are many examples online to the concepts examined in this booklet. Chapter 1: REMOVING BRACKETS EXERCISE A Multiply out the following brackets and simplify. 1. 7(4x + 5) 2. -3(5x - 7) 3. 5a – 4(3a - 1) 4. 4y + y(2 + 3y) 5. -3x – (x + 4) 6. 5(2x - 1) – (3x - 4) 7. (x + 2)(x + 3) 8. (t - 5)(t - 2) 9. (2x + 3y)(3x – 4y) 10. 4(x - 2)(x + 3) 11. (2y - 1)(2y + 1) 12. (3 + 5x)(4 – x) EXERCISE B Multiply out 1. (x - 1)2 2. (3x + 5)2 3. (7x - 2)2 4. (x + 2)(x - 2) 5. (3x + 1)(3x - 1) 6. (5y - 3)(5y + 3) Chapter 2: LINEAR EQUATIONS Exercise C: Solve these equations 1) 1 ( x 3) 5 2 3) y y 3 5 4 3 2) 2x x 1 4 3 3 4) x2 3 x 2 7 14 6) y 1 y 1 2y 5 2 3 6 Exercise C (continued) 5) 7x 1 13 x 2 2x 7) x 1 5x 3 2 3 2 8) 5 10 1 x x Forming equations Example 8: Find three consecutive numbers so that their sum is 96. Solution: Let the first number be n, then the second is n + 1 and the third is n + 2. Therefore n + (n + 1) + (n + 2) = 96 3n + 3 = 96 3n = 93 n = 31 So the numbers are 31, 32 and 33. Exercise D: 1) Find 3 consecutive even numbers so that their sum is 108. 2) The perimeter of a rectangle is 79 cm. One side is three times the length of the other. Form an equation and hence find the length of each side. 3) Two girls have 72 photographs of celebrities between them. One gives 11 to the other and finds that she now has half the number her friend has. Form an equation, letting n be the number of photographs one girl had at the beginning. Hence find how many each has now. Chapter 3: SIMULTANEOUS EQUATIONS Exercise: Solve the pairs of simultaneous equations in the following questions: 1) x + 2y = 7 2) 3x + 2y = 9 3) 3x – 2y = 4 3x + 2y = -7 4) 2x + 3y = -6 5) 4a + 3b = 22 5a – 4b = 43 Chapter 4: FACTORISING x + 3y = 0 9x – 2y = 25 4x – 5y = 7 6) 3p + 3q = 15 2p + 5q = 14 Exercise A Factorise each of the following 1) 3x + xy 2) 4x2 – 2xy 3) pq2 – p2q 4) 3pq - 9q2 5) 2x3 – 6x2 6) 8a5b2 – 12a3b4 7) 5y(y – 1) + 3(y – 1) Factorising quadratics Exercise B Factorise 1) x2 x 6 2) x2 6 x 16 3) 2 x2 5x 2 4) 2 x 2 3x 5) 3x 2 5 x 2 6) 2 y 2 17 y 21 7) 7 y 2 10 y 3 8) 10 x2 5x 30 (factorise by taking out a common factor) 9) 4 x 2 25 10) x2 3x xy 3 y 2 11) 4 x2 12 x 8 12) 16m2 81n2 13) 4 y3 9a 2 y 14) 8( x 1)2 2( x 1) 10 Chapter 5: CHANGING THE SUBJECT OF A FORMULA Exercise A Make x the subject of each of these formulae: 1) y = 7x – 1 4y 3) x 2 3 y x5 4 y 4(3x 5) 9 P wt 2 32r P 2t g 2) 4) Exercise B: Make t the subject of each of the following P 1) 3) wt 32r 1 V t2h 3 Pa 5) w(v t ) g 2) 4) 6) r a bt 2 2) 3( x a) k ( x 2) 4) x x 1 a b Exercise C Make x the subject of these formulae: 1) ax 3 bx c y 3) 2x 3 5x 2 Chapter 6: SOLVING QUADRATIC EQUATIONS EXERCISE 1) Use factorisation to solve the following equations: a) x2 + 3x + 2 = 0 c) x2 = 15 – 2x b) x2 – 3x – 4 = 0 b) x2 – 4x = 0 2) Find the roots of the following equations: a) x2 + 3x = 0 c) 4 – x2 = 0 3) Solve the following equations either by factorising or by using the formula: a) 6x2 - 5x – 4 = 0 b) 8x2 – 24x + 10 = 0 4) Use the formula to solve the following equations to 3 significant figures. Some of the equations can’t be solved. a) x2 +7x +9 = 0 b) 6 + 3x = 8x2 c) 4x2 – x – 7 = 0 d) x2 – 3x + 18 = 0 e) 3x2 + 4x + 4 = 0 f) 3x2 = 13x – 16 Chapter 7: INDICES Exercise A Simplify the following: 1) b 5b5 = 2) 3c 2 2c5 = 3) b2 c bc3 = 4) 2n6 (6n2 ) = 5) 8n8 2n3 = 6) d 11 d 9 = 7) a 3 2 = (Remember that b = b1) d 4 3 8) = Exercise B: Find the value of: 1) 41/ 2 2) 271/ 3 3) 19 4) 52 5) 180 1/ 2