2. Non Calculator Tests Fourth Year

3. Non Calculator Tests 123456 789101112 131415161718 192021222324 252627282930 313233343536 Click on a number in the table above to go to the test of your choice. The solutions follow after the test

4. Non Calculator – Test 1

6. QuestionSolutions – Test 1 155 2 8¾8¾ 3 4½4½ 41·8 510·08cm 2 60·35 737.67 84 937·6 10 1¼1¼ 1110√3

7. 1. Find 8% of £24 2.Evaluate ½ of ( 12¼ - 5¾) 3. If a = 5, b = -3 and c = 4 find the value of b 2 – 4ac 4.Evaluate 2.9 + 3.1  2 5. Factorise 9x 2 – 25 6. Solve 5(2x-1) = 7 7. The perimeter is 32, find x 8. Solve 2x 2 = 98 9.If 5% of a number is 12, find the number. 10. Solve the equations x + y = 13 x – y = 4 x 2x+1 Non Calculator – Test 2

8. QuestionSolutions – Test 2 1₤1·92 2 3¼3¼ 3-71 49·1 5(3x-5)(3x+5) 6x = 1·2 7x = 5 8x = 7 or x = -7 9240 10x = 8.5 and y = 4.5

9. 1.Evaluate 2. Evaluate 21.6 – 3.2 + 2.1 3.Find of ( + ) 4. Write  60 as a surd in it’s simplest form. 5. Factorise fully 2x 3 – 8x 6.Simplify 7. Solve 5x – 2(3x-1) > 4 8. Remove the brackets (2x + 3)(x 2 + x + 3) 9. If sinA = ¾ and A is an acute angle, find the exact value of cosA. 10. If y varies directly as the cube of x and x is doubled, find the effect on y ? Non Calculator- Test 3

10. QuestionSolutions – Test 3 1x2x2 220·5 311/36 42√15 52x(x-2)(x+2) 68/3 7x > 0·5 82x 3 + 5x 2 + 9x + 9 9√7/4 10multiplied by a factor of 8

11. 1. If f(x) = 3 – 2x 2, find the value of f(-2) 2. Solve the equation 4x 2 – 7x = 0 3. Factorise fully x 3 – 4x 4. Simplify  45 +  20 5.Simplify the expression 6. The perimeter of a rectangle is 36 and the length is twice the breadth. Find the area of the rectangle. 7.Solve = 8.Find 3% of 480 9. Evaluate  2 10. Evaluate Non Calculator- Test 4

12. QuestionSolutions – Test 4 1-5 2x = 0 or x = 7/4 3x(x-2)(x+2) 45√5 5x9x9 672cm 2 7x = 3·2 814·4 9 7½7½ 108

13. 1. Find 25% of £19 2. If x = -2 and y = 5 find the value of + 3. If the diameter of the larger circle is 20cm and the diameter of the smaller circle is 10cm, find the shaded area. Take as 3. 4. Subtract 6.38 from 13.9 5. How many pencils costing 14p each can you buy for £5 ? 6. Change to a decimal. 7. A pupil scored in an English exam. What was his percentage mark. 8. Find the gradient of the line 2x+y+5 = 0 9. If y varies inversely as x and y=5 when x =2 find a formula connecting x and y. Find y when x = 20. 10. If y = mx + c, change the subject of the formula to m. Non Calculator- Test 5

14. QuestionSolutions – Test 5 1₤4·75 21·5 3225cm 2 47·52 535 pencils 60·6 772% 8m = -2 9y=10/x ; 0·5 10m = (y-c)/x

15. 1.If tanx = find the exact value of cosx. 2.Write the fraction with a rational denominator in its simplest possible form. 3.Find 5% of 42 4.Evaluate of 5. A rectangle has a length 3+  2 and a breadth 3-  2. Find an expression for the area in its simplest form. 6. Factorize 6x 2 – 13x + 6 7. The perimeter of a square is 6cm. Find the area. 8.If x = 4 and y = 25, find the value of 9.If f(x) = 3x + 5 and f(t) = 32 find the value of t 10. Solve the equation 3x 2 = 5x Non Calculator – Test 6

16. QuestionSolutions – Test 6 112/13 2√3 32·1 411/24 57 6(3x-2)(2x-3) 72·25cm 2 82/5 9t = 9 10x = 0 or x = 5/3

17. 1.Simplify 2.Simplify 3.Solve the equation 5 – 2(2x – 3) 13 4.If T =, change the subject of the formula to P 5. If x = 4 and y = 25 find the value of 2 6. If x + y = 17 and x – y = 4, find the value of y. 7. If f(x) = 5x – 4 and f(t) = 11, find t. 8. Simplify  60 +  135 9.If A is an acute angle and sinA =, find the exact value of tanA. 10. Solve the equation 2x 2 – 2x = 0 11. The diagram shows the graph of the function y = x 2 – 4x. Find the coordinates of point P 12. Find the equation of the straight line shown. (0,5) (4,7)  P. Non Calculator – Test 7

18. QuestionSolutions – Test 7 12x 9 2(2x+5)/x 3x less than or equal to -0·5 4P = (7T-124)/4 54/5 6y = 6·5 7t = 3 85√15 94/3 10x = 0 or x = 1

19. 1.Simplify 2.Find x as a surd in its simplest form. 3. If f(x) = 1 – 2x – x 2, find the value of f(-1). 4. If a = -3, b = -2 and c = 5 find the value of b 2 – 4ac. 5. The gradient of the line joining the points (2,5) and (5,t) is 3. Find the value of t. 6. Find the coordinates of point T shown in the diagram 7. If x = 2  3 and y = 3  2 find the value of x 2 y 2 8.The graph shows the relation y varies inversely as x’. Find the equation connecting x and y. 9. If y varies directly as the cube of x and x is doubled, find the effect on y. 10.Solve the equations 3x + 2y = 3 y = 2x – 9 11. Factorize fully 8x 4 – 2x 2 12. Remove the brackets (4x – 3)( x 2 – 2x – 3) 2 6 x T  x – y = 2 x + y =10 y x (3,10). Non Calculator – Test 8

20. QuestionSolutions – Test 8 16x - 3 24√2 32 464 5t = 14 6T(6,4) 7216 8y=30/x 9y is mult by factor of 8 10x = 3, y = -3 112x 2 (2x-1)(2x+1) 124x 3 - 11x 2 – 6x + 9

21. 1. What is the equation of the function shown in the diagram? 2. Factorize fully 15x 2 + x – 6 3. If x = -4, y = 2 and t = -3 find the value of yt – 2x 2 4. Simplify  50 -  18 5. Simplify 6.Evaluate 7. If y varies directly as the square of x and x is multiplied by a factor of 3 find the effect on y. 8Find the equation of the straight line shown. 9Write x as a surd in its simplest form. 10. Write as a single fraction 11.If, change the subject to T and hence find T when P = 40. 12. Solve the inequation -5x –7 11 4 -4 180 360 y  (16,0) (4,6)  x 8 x 12 Non Calculator- Test 9

22. QuestionSolutions – Test 9 14cos2x 2(5x-3)(3x+2) 3-48 42√2 5(x+2)/x 617/24 7y is mult. by a factor of 9 8y = -0.5x + 8 94√5 10(5x-5)/6 11T=(2P-1)/3 ; T = 13 12 x greater than or equal to -3.6

23. 1 Find the equation of the straight line shown in the diagram. 2. If x = -2 find the value of 2x 3. 3. Solve the equation 3x 2 – 9x = 0. 4. y varies inversely as the square of x and y = 1 when x = 2. Find a formula connecting x and y. Find y when x = 4. 5.Evaluate 6. Simplify  75 -  48 7. The perimeter of the rectangle shown is 62cm. Make an equation and find x correct to 1 decimal place. 0 y x (0,3) (6,0)   5 2x+1 Continued on next slide Non Calculator- Test 10

24. 8. Simplify 9. Find 4% of £48 10. Multiply out the brackets (2x – 1) 3 11. Write with a rational denominator 12. Simplify the expression

25. QuestionSolutions – Test 10 1y=-0.5x+3 2-16 3x= 0, 3 4y=4/x 2, y = 0.25 53 6√3 7x = 7.5 81/(x-2) 9₤1·92 108x 3 – 12x 2 + 6x -1 11√3/2 122x 11

26. 1.Write down the equation of the trig. function shown in the diagram. 2.If A is an acute angle and sinA =, find the exact value of cosA giving your answer as a surd with a rational denominator. 3.Simplify the fraction 4.Find the exact value of cosA 5. Remove the brackets (5-3x)(6-4x) 6. If x = 36 and y = 9 find the exact value of Non Calculator - Test 11 -3 3 90º 360º 8 7 5 A

27. 7. Find x if 5x + 2y = 17 and 3x –2y = 7. 8. Find the gradient of the line shown in the diagram. 9. Simplify the expression shown 10. Find 25% of 47 11. Evaluate 12. If f(x) = and f(t) =, find t. y x  (-5,0) (0,-4) 

28. QuestionSolutions – Test 11 13sinx 2√3/2 3 41/7 530 – 38x + 12x 2 618 7x = 3 8m = -0·8 9x – x -1 1011·75 117/12 12 t = ¼

29. 1. Identify the trig. graph shown in the diagram 2. Factorize fully 8x 2 – 2y 2 3.If x = -10 and y = -4 find the exact value of giving your answer as an improper fraction in its simplest form. 4. Write as a single fraction 5. Evaluate 6. If f(x) = 1 - 2x - 4x 2, find the value of f(-3). -3 3 180º 360º Non Calculator – Test 12

30. 7. The area of a square is 300cm 2. Find the perimeter giving your answer as a surd in its simplest form. 8.Find the equation of the straight line shown. 9. y varies directly as the square root of x and y = 5 when x = 16. Find an equation connecting x and y. Find y when x = 9. 10. Evaluate (5x 2 ) 3 11. Solve the equation 7x – 4x 2 = 0. 12. Multiply out the brackets and simplify (3  2 +1)(2  2 – 1) (0,4) 0 (12,0)

31. QuestionSolutions – Test 12 13sin2x 22(2x-y)(2x+y) 3-25/16 4 5 2¼2¼ 6-29 7P = 40√3 8m = -1/3 9y=1.25√x ; y = 3.75 10125x 6 11X = 0, 7/4 1211 - √2

32. Non Calculator - Test 13 1. The rectangle shown has an area of 84 sq.cm Make an equation and find x. 2. Factorize fully 25t 3 – t 3. Find 25% of £350 4. Simplify the expression x(x-3) – (x+2)(x+1) 5. Evaluate 13.8 – 15.6 + 4.7 6. If f(x) = 3x 2 – 2x –1, find the value of f(-2). 7. Write  500 as a surd in its simplest form. 2x+3 3

33. 8.Find the gradient of the straight line shown. 9. y varies directly as the square of x and y = 40 when x = 2. Find an equation connecting x and y. Find y when x = 3. 10. Evaluate (yx 3 ) 4 11. Solve the equation x 2 – 6x - 16 = 0. 12. Multiply out the brackets and simplify (  2 +1)(  2 – 1) (0,5) 0 (10,0)

34. QuestionSolutions – Test 13 1x = 12·5 2t(5t-1)(5t+1) 3₤87·50 4-6x -2 52·9 615 710√5 8 m = - ½ 9y = 10x 2, y = 90 10y 4 x 12 11x = 8, -2 121

35. Non Calculator – Test 14 1. If sinx =, find the exact value of cosx. 2. Write the fraction with a rational denominator in its simplest possible form. 3. Find 9% of 36 4. If f(x) = 3x – 5 and f(t) = 22, find t. 5. A rectangle has a length 5+  6 and a breadth 5-  6. Find an expression for the perimeter in its simplest form. 6. Factorise 9x 2 – 12x + 4 7. The perimeter of a square is 14cm. Find the area. 8. If x + y = 24 and y = 2x, find the value of y 9. Simplify 10. Solve the equation x 2 = 3x

36. QuestionSolutions – Test 14 112/13 2√2 3₤3·24 4t = 9 520 6(3x-2)(3x-2) 712·25 816 99/10 10x = 0, 3

37. Non Calculator – Test 15 1. Simplify 2. Simplify 3. Solve the equation 5x – (2x – 3) 1 4. If W =, change the subject of the formula to M. 5. If x = 9 and y = 16 find the value of 6. Find the V.A.T. on an article costing £400. 7. If f(x) = 5x – 1 and f(t) = -6, find t.

38. 8. Simplify  20 +  45 9. If A is an acute angle and sinA =, find the exact value of tanA. 10. Solve the equation 2x 2 + 5x = 0 11. The diagram shows the graph of the function y = x 2 – 6x. Find the coordinates of point P, the minimum value of the function. 12. Find the equation of the straight line shown. P  (0,1) (10,2) 

39. QuestionSolutions – Test 15 1x8x8 2 3 4M = 2W - 2 5 ¾ 6₤70 7t = -1 85√5 9 10x = 0 or x = -5/2 11(3,-9) 12y = 0.1x + 1 x

40. Non Calculator – Test 16 1. Find 3% of £78 2. Evaluate 3. If a = 2, b = -1 and c = 3 find the value of ab – bc 4. Evaluate 12  4 + 6  2 5. Factorise fully 2x 2 – 3x + 1 6. Simplify the algebraic fraction 7.Write 56% as a fraction in its simplest form. 8. Solve the equation 2x 2 + 5x = 0 9. If 10% of a number is 17, find the number. 10. Find the value of x if x + y = 12 and x – y = 11 11. y varies inversely as x and y = 6 when x = 5. Find y when x = 10.

41. QuestionSolutions – Test 16 1₤2·34 219/30 31 415 5(2x-1)(x-1) 6(x-3)/(x+1) 714/25 8x = 0 or x = -5/2 9170 10x = 11·5 11y = 3

42. Non Calculator – Test 17 1.Evaluate 2. Evaluate 1.6 – 3.2 + 2.1 3.Write as a single fraction 4. Write  80 as a surd in it’s simplest form 5.Factorize fully 6x 2 – 13x + 6 6. Find the gradient of the line which passes through the points (0,4) and (4,0) 7. Solve 6x – (3x+2) < 4 8.Remove the brackets (x + 1)(x 2 + x - 3) 9.If sinA =, and A is an acute angle, find the exact value of tanA. 10. If y varies directly as the square of x and x is trebled, find the effect on y ?

43. QuestionSolutions – Test 17 1x 11 20·5 3(5x+7)/12 44√5 5(3x-2)(2x-3) 6m = -1 7x < 2 8x 3 + 2x 2 – 3x - 3 92/√5 10y is mult. by a factor of 9

44. Non Calculator – Test 18 1. Write the number 32.6904 correct to a) 1 decimal place b) 5 significant figures 2.Write the fraction with a rational denominator in its simplest possible form. 3. Find 50% of 6.42 4.If f(x) = 1-2x and f(t) = 5, find t. 5. Factorize fully 4x 3 – 4x 6.Make x the subject of the formula y = mx + c. 7.The area of a square is 400cm 2. Find the perimeter. 8.If x = 4 and y = 16, find the value of 9. Simplify (x+1)2 – x(x-2) 10. Solve the equation 5 – 2(x-2) = 0

45. QuestionSolutions – Test 18 1a) 32·7 b) 32·690 22√2 33·21 4t = -2 54x(x-1)(x+1) 6x = (y-c)/m 7P = 80 8 ½ 94x + 1 10x = 4·5

46. Non Calculator – Test 19 1.Simplify 2. Find x as a surd in its simplest form. 3.If f(x) = x – x 2, find the value of f(-2). 4. Find 9% of £44 5.The gradient of the line joining the points (0,2) and (2,t) is 4. Find the value of t. 6.Write 40% as a fraction in its simplest form. 7.If x = 4  3 and y = 3  3 find the value of 2xy 8. Solve the inequation 4x – 2(1-2x) > 5 9. If y varies directly as the square of x and x is doubled, find the effect on y 10. Solve the equations 3x + 2y = 16, y = x – 2 11. Factorize fully x 4 – 81 12. Remove the brackets (x – 3)(2x 2 – 2x + 3) 4 8 x

47. QuestionSolutions – Test 19 12x 2 – 4x 24√3 3-6 4₤3·96 5t = 10 62/5 772 8x>7/8 9y is mult. by 4 10x = 2 11(x-3)(x+3)(x 2 +9) 122x 3 – 8x 2 + 9x - 9

48. Non Calculator – Test 20 1. Find the equation of the straight line with a gradient 3 which passes through the origin. 2.If x = -2, find the value of 3x 2. 3.Solve the equation x 2 + x = 0. 4. y varies inversely as the square of x and y = 2 when x = 2. Find a formula connecting x and y. Find y when x = 4. 5.Evaluate 6. Simplify  125 +  75 7. The perimeter of the rectangle shown is 70cm. Make an equation and find x correct to 1 decimal place. 4 x+6

49. 8.Simplify 9.Find 2% of £48.50 10.Multiply out the brackets (x + 2) 3 11. Write in its simplest form with a rational denominator 12. Simplify the expression

50. QuestionSolutions – Test 20 1y = 3x 212 3x = 0 or x = -1 4 y=8/x 2 ; y = ½ 5 65(√5 + √3) 7x = 25 81/(x-2) 9₤0·97 10x 3 + 6x 2 + 12x + 8 11√2/2 125x 11

51. Non Calculator 21 1. Find 10% of £19 2. If x = -1 and y = -2 find the value of + 3.Solve the equation x 2 = 3x. 4. Subtract 4.8 from 7.3 5. Remove the brackets (x + 2) (x 2 + x + 1) 6.Write 8% as a fraction in its simplest form. 7.Simplify 8. Find the gradient of the line 2x+4y+1 = 0 9. If y varies inversely as the square of x and y=2 when x =3 find a formula connecting x and y. Find y when x = 6. 10. If C =, change the subject of the formula to F.

52. QuestionSolutions – Test 21 1₤0·19 21 3x = 0, 3 42·5 5x 3 +3x 2 + 3x + 2 62/25 72/3 8 m = - ½ 9 x = 6 and y = ½ 10

53. Non Calculator – Test 22 1.If sinx = and x is an acute angle, find the exact value of cosx. 2.Write the fraction with a rational denominator in its simplest possible form. 3.Find 2% of 80 4.Evaluate of 5. A rectangle has a length 3  2 and a breadth 5  2 Find an expression for the area in its simplest form. 6. Factorise x 2 – x – 6 7.The perimeter of a square is 10cm. Find the area. 8.If x = 9 and y = 4, find the value of 4 9.If f(x) = 2x + 5 and f(t) = 23, find the value of t. 10. Solve the equation x 2 = 5x + 4

54. QuestionSolutions – Test 22 115/17 2√2 32 43/16 530 6(x-3)(x+2) 76·25cm 2 86 9t = 9 10x = 4, x = 1

55. Non Calculator – Test 23 1.Evaluate 2. Evaluate 11.6 – 13.2 + 2.5 3.Remove the brackets (x + 2)(2x 2 –x -1) 4.Calculate the gradient of the line which passes through the points (5,2) and (-3,2). 5.If f(x) = 3 – x – x 2, find the value of f(-3). 6.Simplify 7. Solve the equation x 2 = 7x 8. Simplify √45 + √20 - √125 9. If P = 4(L + B), change the subject of the formula to B. 10. If y varies inversely as the square of x and x is doubled, find the effect on y?

56. QuestionSolutions – Test 23 12x 2 20·9 32x 3 + 3x 2 – 3x -2 4m = 0 5-3 6x 7x = 0, x = 7 80 9B=(P-4L)/4 10y is divided by a factor of 4

57. Non Calculator – Test 24 1. Write down the equation of the trig. function shown in the diagram. 2. If A is an acute angle and sinA =, find the exact value of tanA, giving your answer as a surd with a rational denominator. 3. Simplify the expression 2x(x+1) – (2x+1)(x-1) 4. Find the exact value of cosA. 5. Solve the equation 6. If x = 25 and y = 4, find the exact value of x -½ y ½ 360º -6 6 90º 4 5 2 A

58. 7.Solve 2x + 3y = 21, y = 3x – 4 8.Find the equation of the line shown in the diagram. 9.Simplify the expression shown 4 10. Find 15% of 20 11. Evaluate 12. Write √120 as a surd in its simplest form. y x  (-2,0) (0,-1) 

59. QuestionSolutions – Test 24 16sinx 22/√5 33x + 1 437/40 5x = -3·8 62/5 7x = 3, y = 5 8y = -0·5x - 1 94 – 4x 103 113/4 122√30

60. Non Calculator – Test 25 1. Find 5% of £60000 2. Evaluate ¼ of ( 10½ - 4) 3. A square has an area of 400 cm 2. Find the perimeter of the square. 4. Evaluate 1.52 + 2.52 5. Factorize fully x 3 – x 6. Solve 4 – 2(x – 1) = 9 7. If f(x) = x 2 + 1 find the value of f(-2) – f(2). 8. Write as a surd with a rational denominator 9. A discount of 40% is offered on a television set in a sale. Find the sale price of the set. 10. State the gradient of the line with equation x + 4y = 1

61. QuestionSolutions – Test 25 1₤3000 2 380cm 48·5 5x(x-1)(x+1) 6x = -1·5 70 84√5/5 9Needs a price for the set. 10 -¼-¼

62. Non Calculator – Test 26 1.Simplify Find the value of this expression when x = 4. 2.Find x as a surd in its simplest form 3. If f(x) = 10 – x – x 3, find the value of f(-1). 4. y varies directly as x and y =6 when x = 4. Find y when x = 10. 5. Solve the equation x 3 – 4x = 0 6. Find the coordinates of point 2 8 x P  x – y = 1 x + y = 8 y x

63. 7.If x = 4  2 and y = 5  2 find the value of x 3 y 8. The graph shows the relation y varies inversely as the square of x Find the equation connecting x and y 9. If x = 4, find the value of √(x 2 + 48) 10. Find the point where the line 2x + 3y -12 = 0 cuts the x axis 11. Factorize fully x 2 – x – 12 12. Remove the brackets (x – 3)( x 2 – 2x + 3) (2,5) 

64. QuestionSolutions – Test 26 14x - 8 22√15 312 4y = 1·5x ; y =15 5x = 0,2,-2 6P(4.5,3.5) 71280 8y=20/x 2 98 10(6,0) 11(x-4)(x+3) 12x 3 - 5x 2 + 9x - 9

65. Non Calculator – Test 27 1. Simplify 2. Simplify 3. Solve the equation 15 – (2x – 3) 1 4. If M =, change the subject of the formula to T 5. Write as a single fraction 6. If 2x + y = 11 and x – y = 4, find the value of y. 7. If f(x) = x 2 – 4 and f(t) = 32, find t.

66. 8. Simplify  242 -  98 9. If A is an acute angle and cosA =, find the exact value of tanA. 10. Solve the equation x 2 – 11x = 0 11. The diagram shows the graph of the function y = x 2 – 6x. Find the coordinates of point P 12. Find the gradient of the straight line shown. P 6 (0,3) (5,9) 

67. QuestionSolutions – Test 27 1x8x8 2 3x 8.5 4 5 6y = 1 7t = 6, -6 84√2 9 10x = 0, 11 11(3,-9) 12

68. Non Calculator – Test 28 1. Find 5% of £1800 2. If x = -2 and y = -4, find the value of + 3. A straight line has equation 4x + 3y = 24. Find the point where the line cuts the y axis. 4. Subtract 4.76 from 12.38 5. Simplify the algebraic fraction 6. Change to a decimal.

69. 7. A pupil scored in a Mathematics exam. What was his percentage mark? 8.If f(x) = ax 2 + 5 and f(2) = 33, find the value of a. 9. If y varies inversely as the cube of x and y = 1 when x =2. Find a formula connecting x and y. Find y when x = 1. 10. If e = mc 2, change the subject of the formula to c.

70. QuestionSolutions – Test 28 190 2-4 3(0,8) 47·62 5 ½ 60·4 770% 8a = 7 9, x = 1, y = 8 10

71. Non Calculator – Test 29 1. Find the equation of the straight line shown in the diagram. 2. If x = -1, find the value of x 3 – x 2 3. Solve the equation 4x 2 – 81 = 0. 4. P varies directly as the square of Q and P = 1 when Q = 2. Find a formula connecting P and Q. Find P when Q = 10. 5. Evaluate 6. Simplify  200 -  128 0 y x (0,4) (8,0)  

72. 7. The perimeter of the rectangle shown is 56cm. Make an equation and find x. 8. Evaluate, when x = 2 9. Evaluate 100 – 25 5 10. Multiply out the brackets (1-3x)(4x+1) 11. Write with a rational denominator 12. Simplify the expression 6 3x+4

73. QuestionSolutions – Test 29 1 m = - ½ 2-2 39/2 and -9/2 4 P= ¼ Q 2, P = 25 56 62√2 7x = 6 81 9-25 101 + x – 12x 2 114(√2 – 1) 12 ½x5½x5

74. Non Calculator – Test 30 1. What is the equation of the function shown in the diagram? 2. If f(x) = 4 + ax 3 and f(-1) = 5, find a formula for f(x) and hence find the value of f(3) 3. If x = 10, y = -2 and t = 3, find the value of 4. Simplify 3x 4 (2x 2 ) 3 5. Simplify 6. Evaluate 7. If x + y = 20 and y = 4x, find the value of y. -12 12 360  180 

75. 8.Find the equation of the straight line shown. 9. Write x as a surd in its simplest form. 10. Evaluate 23.2 – 34.7 + 16.8 11. If, change the subject to M and hence find M when L=10. 12. Solve the inequation -2x +9 5 y  (5,0) (1,3)  x 4 x 6

76. QuestionSolutions – Test 30 112cos2x 2a = -1; f(3)=-23 34 424x 10 5(x-2)/x 65/8 7x = 4, y = 16 8y = -0.75x + 3.75 9x = 2√5 105·3 11M=(2L-15)/9 12 x 2

77. Non Calculator – Test 31 1. The rectangle shown has an area of 72 sq.cm Make an equation and find. 2. Factorize fully 121x 4 – x 2 3. Find 8% of £300. 4. Simplify the expression 2x(x-3) – (x+2)(2x+3) 5. Evaluate 1.4 2 6. A Doctor has been given a pay rise of 25%. He now earns ₤60000 per annum. How much did he earn before the pay rise. 4x 2x

78. 7. Write  800 as a surd in its simplest form. 8.Find the gradient of the straight line shown. 9. If x = √5 + 2 and y = √5 – 2, find the value of x 2 + y 2. 10. Evaluate √(12 2 + 5 2 ) 11. Solve the equation 121 – x 2 = 0 12.Multiply out the brackets and simplify (3  7 +1)(  7 – 1) (0,6) 0 (12,0)

79. QuestionSolutions – Test 31 1x =3 2x 2 (11x-1)(11x+1) 3₤24 4-13x - 6 51·96 648000 720√2 8 m = - ½ 918 1013 11x = 11, -11 1220 - 2√7

80. Non Calculator – Test 32 1. A straight line passes through the points (2,0) and (0,-2). Find its equation. 2.Solve the equation Give your answer correct to 1 decimal place 3. Factorize fully 4x 2 – 15x + 9 4. y varies inversely as the square of x and x is doubled. Find the effect on y. 5. Evaluate 6. Simplify  32 -  18

81. 7. The perimeter of the rectangle shown is 50cm. Make an equation and find x correct to 1 decimal place. 8. Simplify 9 Find 3% of £1000 10. If x = -5, y= 4 and t = -2, find the value of x 2 yt. 11. Write in its simplest form with a rational denominator. 12. Simplify the expression (x+1) 2 – x(x+1) 5 2x+1

82. QuestionSolutions – Test 32 1y = x - 2 2x = 0·9 3(4x-3)(x-3) 4y is divided by 4 5 3½3½ 6√2 7x = 9·5 81/(2x-1) 9₤30 10-200 11√3 12x + 1

83. Non Calculator – Test 33 1Evaluate 2. Simplify the expression -4x(x-1) – 4x(1-x) 3 3. Write as a single fraction 4. Write  72 as a surd in its simplest form. 5. Factorize fully x 2 – 16x + 64 6. The point (t,5) lies on the line x + y - 9 =0. Find the value of t. 7. Solve the inequation 5x – (3x-2) < - 4 8. Remove the brackets (2x + 1)(x 2 - x - 10) 9. A car costs ₤24000. In a sale it is reduced by 20%. Find the sale price of the car. 10 A car travels a distance of 250 km in 2½ hours. Calculate the average speed of the car in km per hour.

84. QuestionSolutions – Test 33 1y8y8 20 3(2x+3)/15 46√2 5(x-8)(x-8) 6t = 4 7x < -3 82x 3 – x 2 – 21x - 10 9₤19200 10100km/hr

85. Non Calculator – Test 34 1. Simplify 2. Find x as a surd in its simplest form. 3. If P = 2(L+B), change the subject to L. 4. Find of 75 5. State the gradient of the line with gradient y = 4. 6. Write 60% as a fraction in its simplest form. 7. If x = 4  3 and y = 3  3 find the value of xy 2 8. Solve the equation x(x+1) = x 2 + 10x + 18 9. The point (4,2) lies on the curve with equation Find the equation of the curve. 10. Evaluate 8.4 – 11.2 – (-7.8) 11. Factorize fully x 4 – 9x 2 12. Remove the brackets (x + 1)(x 2 – x - 3) 5 10 x

86. QuestionSolutions – Test 34 11 – 1/x 25√3 3L=(P-2B)/2 445 5m = 0 63/5 7108√3 8x = -2 9 105 11x 2 (x+3)(x-3) 12x 3 – 4x - 3

87. 1. The rectangle shown has a perimeter of 70 cm. Make an equation and find x. 2. Factorize fully 8x 2 +2x – 15 3. Find 75% of £360 4. Simplify the expression 5. Write as a single fraction 6. If f(x) = x 2 – 5x –6, find the value of f(-3). 7. Write as a surd in its simplest form with a rational denominator. 2x+5 x Non Calculator – Test 35

88. 8.Find the gradient of the straight line shown. 9. y varies directly as the cube of x and y = 64 when x = 4. Find an equation connecting x and y. Find y when x = 6. 10. Simplify (2y 3 x 4 ) 3 11. Solve the equation x 2 = 6x 12. Multiply out the brackets and simplify (3  2 +1)(2  2 + 1) (0,6) 0 (16,0)

89. QuestionSolutions – Test 35 1x = 10 2(4x-5)(2x+3) 3₤270 4 5 618 76√5/5 8-3/8 9y = x 3, y = 216 108y 9 x 12 11x = 0, 6 1213 + 5√2

90. 1. Write down the equation of the trig. function shown in the diagram. 2. If A is an acute angle and tanA =, find the exact value of cosA, giving your answer as a surd with a rational denominator. 3. Simplify the fraction 4. Find the exact value of cosA in the diagram shown. 5. If f(x) = x 3 -7 and f(t) = 57, find t. 6. If x = 49 and y = 9, find the exact value of 360º -1.5 1.5 90º 5 6 4 A Non Calculator – Test 36

91. 7. Find x if x + y = 17 and x – y = 8. 8. Find the equation of the line shown in the diagram. 9.Simplify the expression shown. Hence evaluate this expression when x = 3. 10. Find 125% of 40 11. Evaluate 12. If f(x) = and f(t) =, find t. y x  (-2,0) (0,-1) 

92. QuestionSolutions – Test 36 11.5sinx 23/√10 3x/(x+1) 41/8 5t = 4 6189 7x = 12·5 8y = -0·5x - 1 94x – 2 ; 10 1050 11 12t = 1