Exam: Friday 4 th May How to Revise. What to use to revise:

Transcription

1 National 5 Mathematics Exam Revision Questions Exam: Friday 4 th May 2018 How to Revise Use this booklet for homework Come to after school revision classes Come to the Easter holiday revision class There will be an immersion revision day before the exam Also revise AT HOME. A lot. What to use to revise: All the questions from this booklet Past Papers (on website or buy from your teacher) The revision notes (on website or buy from your teacher) How to use these questions: Use these questions along with the revision notes. 1. Try all the questions in this booklet once and check the answers. Ask for help as required: If you are aiming for an A, you should focus mostly on questions marked. If you are aiming for a C, you should mostly avoid the questions marked. 2. Put a star next to all the questions you got wrong or required help (from teachers, friends or the notes) with. 3. Wait a few days and then try the starred questions a second time to see if you can manage them now. 4. If you cannot do them, ask for help again, wait a day or two and then try them again. 5. Repeat until you can do all the questions without needing help.

2 FORMULAE LIST b ± (b2 4 ac) 2a The roots of ax 2 + bx + c = 0 are x = Sine rule: a b c = = sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 2bc cos A or cos A = Area of a triangle: A = 21 ab sin C Volume of a sphere: V = 43 π r 3 Volume of a cone: V = 31 π r 2 h Volume of a pyramid: V = 31 Ah Standard deviation: s= or s = b2 + c2 a 2 2bc Σ( x x )2 n 1 ( Σ x) 2 n, where n is the sample size. n 1 Σx2 Page 1

3 NON CALCULATOR Section A: Non-Calculator Page 2

4 NON CALCULATOR 7. Find the equation of each of these straight lines: (b) (a) (c) (d) Page 3

5 NON CALCULATOR Page 4

6 NON CALCULATOR (j) (i) (a) (b) (c) (d) (e) (f) State the nature of the roots of the equation 3x² 6x + 2 = State the nature of the roots of the equation 2x² x + 6 = Page 5

7 NON CALCULATOR Page 6

8 NON CALCULATOR Page 7

9 NON CALCULATOR Page 8

10 NON CALCULATOR Page 9

11 NON CALCULATOR Page 10

12 NON CALCULATOR Page 11

13 NON CALCULATOR Page 12

14 NON CALCULATOR Page 13

15 NON CALCULATOR Page 14

16 NON CALCULATOR NOT PRELIM 52. Page 15

17 NON CALCULATOR a) b) c). d) e). Page 16

18 NON CALCULATOR Divide Page 17

19 NON CALCULATOR 64., using simultaneous equations. 65. (the first symbol is add, the second is divide) Divide: 72. Page 18

20 NON CALCULATOR Page 19

21 NON CALCULATOR Page 20

22 NON CALCULATOR Page 21

23 NON CALCULATOR Page 22

24 NON CALCULATOR ) , x 10 x 3, Page 23 ) ,2 3

25 NON CALCULATOR AB 4 AB Page 24

26 NON CALCULATOR Calculate the gradient and y-intercept of each line: (Hint: you will need to do some rearranging) Page 25

27 NON CALCULATOR Page 26

28 NON CALCULATOR Page 27

29 NON CALCULATOR Page 28

30 NON CALCULATOR Page 29

31 NON CALCULATOR Page 30

32 NON CALCULATOR Page 31

33 NON CALCULATOR Page 32

34 NON CALCULATOR 133. Simplify the fractions: (a) (3 x 1) 2 2(3 x 1) (b) Simplify 135. Write as a single fraction in its simplest form: 136. (c) x2 6x 5 x2 5x ab 4 (b) 2 b2 1 5 (f) y 2y y 4x (a) 8 y2 2 1 (e) 2 a a 3x 8 y (c) 4 x3 3 2 (g) x 1 x 3 3a 2 a (d) b b2 3 6 (h) x 5 x 4 State the nature of the roots of each equation: (a) x 2 6 x x2 8x 4 2 x2 2 (b) x 2 x 6 0 (c) 3 x 2 3 x Simplify 138. (a) Write down expressions for the areas of these two rectangles. (b) The area of rectangle I is greater than the area of rectangle II. By how much is it greater? 139. Evaluate: 140. Simplify 141. a) The equation ax 2 4 x 2 0 has equal roots. Find the value of a b) The equation 3 x 2 2 x c 0 has equal roots. Find the value of c. Page 33

35 NON CALCULATOR a) The equation 2 x 2 bx 8 0 has equal roots. Find the possible values of b. b) The equation kx 2 kx 2 0 has equal roots. Find the possible values of k Page 34

36 Section B (Calculator Allowed) Page 35

37 Page 36

38 Page 37

39 Page 38

40 Page 39

41 Page 40

42 Page 41

43 34. Page 42

44 Page 43

45 Page 44

46 Page 45

47 Page 46

48 48. Page 47

49 49. (b) After training the mean number of sit ups was 38 and the semi-interquartile range was 10. Make two valid comments to compare the performances before and after training Page 48

50 Page 49

51 Page 50

52 Page 51

53 Page 52

54 Page 53

55 (a) Sketch the graph of y = 3cos2x (b) Sketch the graph of y = sin x + 1 (c) Sketch the parabola y = (x + 5)(x 3), showing the intercepts with the x and y axes and the turning point It is estimated that house prices will increase at the rate of 3 15% per annum. A house is valued at If its value increases at the predicted rate, calculate its value after 3 years. Give your answer correct to four significant figures. Page 54

56 Page 55

57 74. Hint: equal lengths in the triangle Page 56

58 77. (a) Calculate the area of paper used to make the cone. (b) Calculate the circumference of the base of the cone Page 57

59 Page 58

60 Page 59

61 Page 60

62 Page 61

63 Page 62

64 Page 63

65 Page 64

66 (a) (b) (c) (d) Page 65

67 Page 66

68 Page 67

69 Page 68

70 Page 69

71 (a) Sketch the graph of y = (x + 4)(x 2), annotating the points where the graph cuts the x and y axes and the turning point. (b) Express x² 8x + 20 in the form (x + a)² + b (c) Hence sketch the graph of y = x² 8x + 20, annotating the point where the graph cuts the y axis and the turning point. Page 70

72 Page 71

73 a) b) c) What is the frequency of the graph of y = 3sin4x? What is the period of the graph of y = 5sin6x? What is the period of the graph of y = 7cos(½x)? 122. (a) Sketch the graph of y = (x + 9)(x 5), annotating the points where the graph cuts the x and y axes and the turning point. (b) Express x² + 6x + 2 in the form (x + a)² + b (c) Hence sketch the graph of y = x² + 6x + 2, annotating the point where the graph cuts the y axis and the turning point Page 72

74 124. Simplify the fraction: 125. E 19.7 m D A 126. Page 731 C B 60 m

75 Page 74