2. Hosted by Miss Leman (Acknowledgements to Wanganui High School)

3. 100 200 400 300 400 Algebra Probability NumberTriangles 300 200 400 200 100100100100 500 500500500500 100 GraphsMeasurement 200 300 400 100 500 200 300 400 100 500 50 150 250 350

4. Row 1, Col 1 Simplify 4p + 2q – p + 4q ANSWER:3p + 6q

5. 1,2 In a bag, there are 90 blue counters and 25 red counters. What is the probability I pick at random a red counter? ANSWER : P(Red counter) = 25/115 = 5/23

6. 1,3 Write 35 out of 40 as a percentage ANSWER: 35/40 x 100 = 87.5%

7. 1,4 Find cos30 = _____ ANSWER: Cos 30 = 0.866 (3dp)

8. 1,5 The general formula for a Straight line is y = mx +c What does the m stand for and what does the c stand for? ANSWER: m = gradient (rise over run or change in y over change in x) and c = the y intercept (where the line cuts the y axis)

9. 1,6 What is the perimeter of this shape? ANSWER = 12 + 5 + 7 + 5 +5 = 34 cm 5 12 cm 7

10. 2,1 Expand and simplify 3w(w + 5) ANSWER: 3w +15 2

11. 2,2 What is the probability on a random day there will be a)17 cars in the carpark b)Less that 16 cars in the carpark ANSWER : a) 5/34b) (13 + 16) / 34 = 29/34 No. of cars in carpark (x) FrequencyRelative Frequency 1513 16 175 182 TOTAL34

12. 2,3 Complete this table ANSWER: 0.2, 1/5, 20% - 0.5, ½, 50% - 0.625, 5/8, 62.5 – 0.125, 1/8, 12.5% 0.2 50% 5/8 12.5 %

13. 2,4 Find x sin x = 0.6 ANSWER: X = sin^-1 0.6 X = 36.87

14. 2,5 Plot the graph y= 2x +1 ANSWER:

15. 2,6 Convert a)120 cm to meters b) 1.2 L into milliliters c)8500 g into kilograms ANSWER : a) 1.2 m b) 1200 mL c) 8.5 kg

16. 3,1 Solve ANSWER :

17. 3,2 ANSWER: a) 10/32b) 5/12c) 30/32

18. 3,3 a)Find 30 % of $15 b) Find 2/3 of 66 kg ANSWER: a) 30/100 x 15 = $4.50 b) 2/3 x 66 = 44 kg

19. 3,4 ANSWER: Use Pythagoras.

20. 3,5 ANSWER: A parabola that has been shifted up 1 unit. Draw the graph and state the transformation it has gone through.

21. 3,6 What is the area of this shape? ANSWER: ½ base x height = ½ x 6 x 8 = 24 m Please remember your units!!! 6 m 8 m

22. 4,1 ANSWER: x/4 = 3 – 7 x= -4/4 x= -1

23. 4,2 Draw a probability tree that shows all outcomes for tossing 2 coins. What is the probability of getting Heads on both coins? ANSWER : H H H T T HH HT TH TT T P(H,H) = 1/4

24. 4,3 a)Write the number 756000 in standard form b)Write 0.000405 in standard form ANSWER: a) 7.56 x 10^5 b) 4.05 x 10^-4

25. 4,4 ANSWER: Using Trig – Sine rule

26. 4,5 ANSWER: S = 3T Triangles (T)No. of sides (s) 13 26 39 412 Write the rule for this pattern S=

27. 4,6 What is the circumference of this circle? ANSWER: Remember you can also use 2.4 cm

28. 5,1 Factorise ANSWER : 3x(2x-3y)

29. 5,2 If we rolled a dice 300 times – How many times would you expect an even number to show? ANSWER: P(even number) = ½ Therefore expected number = ½ x 300 = 150 times

30. 5,3 Five friends including the Newton twins went for a meal at Pizza Hut. The meal cost $46 and John wanted to pay for himself and his brother. Divide the $46 cost of the meal in the ratio 2:3 to work out the twins share. ANSWER : 2 + 3 = 5 parts. $46 / 5 = $9.20 per part. 2 x 9.20 = $18.403 x 9.20 = 27.60

31. 5,4 ANSWER

32. 5,5 ANSWER: Draw the line y = 3

33. 5,6 What are the limits of accuracy for a)X = 12.4 cm? b)Y = 2 L? ANSWER: Look for the smallest unit given. Then half it, then add and subtract that from the original amount. a)12.35 < x <12.45 cm b)1.5 L < y < 2.5 L

34. 6,1 Calculate m if t = 3 and r = 7 ANSWER : m = 1/2

35. 6,2 ANSWER: a) Hit Hit 3/4 x 4/5 = 3/5 B) Hit Miss or Miss Hit. 3/4 x 1/5 + 1/4 x 4/5 = 7/20 H M M M H H 1 st shot 2 nd shot 3/4 1/4 4/5 1/5 4/5 1/5 a)What is the probability he hits both shots? b)What is the probability that he misses exactly one shot on either his first or second try.

36. 6,3 If I paid $25 for a skirt that was on sale with 30% off, how much was the skirt originally? ANSWER: Therefore $25 / 0.7 = $35.71 Sale PriceOriginal Price x 0.7 Divide by 0.7

37. 6,4 ANSWER: Using Pythagoras to make a right angle triangle. Therefore Calculate the height of this triangle 10 cm 8 cm

38. ANSWER a) 60 m shown by y intercept b) 7 hours c) Every hour it fills 20m (shown by the gradient)

39. 6,6 Calculate the Volume of this shape ANSWER: 3 x 5 x 4 = 60 cm Please remember your correct units! 3

40. 6,1 Simplify ANSWER : 5x

41. 6,2 If I paid $60 for a skirt – how much GST did I pay? Then calculate GST exclusive price. ANSWER : GST is 12.5 %. 0.125 x 60 = $7.50 GST Therefore GST exclusive is $60 - $7.50 = $52.50

42. 4,3 a)Increase $5000 by 20% b) Decrease $80000 by 12% ANSWER: a) 20% of 5000 = $1000 therefore $5000 + $1000 = $6000 b) 12% of $80000 = $9600 therefore $80000 - $9600 = $70,400

43. 4,4 Calculate the height of this triangle ANSWER: 10m 24

44. 4,5 Plot y = - 3x - 2 ANSWER:

45. 4,6 ANSWER: Area of circle = 3.14 x 7 x 7 = 153. 94 cm Volume Area x length = 153.94 x 21 = 3232.7 cm

46. 6,1 ANSWER: (2x -6) = 8 x 4 2x = 32 +6 2x = 38 x = 38 / 2 x = 19 Calculate x

47. Round these numbers a)125589 to 2 s.f b)0.000443 to 1 s.f c)8.987 to 1 d.p 6,2 ANSWER : a) 130000 b) 0.0004 c) 9.0

48. 4,3 The Earth is approximately a sphere of radius 6400 km The surface area of a sphere is given by the formula A = 4πr. Calculate the approximate surface area of the Earth. Give your answer in standard form. ANSWER: 5.147185404 x 10^8 2

49. 4,4 ANSWER: Find angle P then find H

50. 4,5 ANSWERS: a) (0,8) b) -1 c) y= -x + 8 a) (0,1) b) 3 c) y= 3x + 1

51. 4,6 ANSWER: Area of trapezium (6.7 + 4.2)/2 x 3.6 = 50.652 cm Length x Area of trapezium = 165 cm Length = 165/ 50.652 = 3.26 cm

52. 6,1 Gabby is 5 years younger than Rebecca. Together their ages add to 27. Write an algebraic equation and solve to find out Gabby’s age. ANSWER : Rebecca = xGabby = x -5 x + x – 5 = 27 2x = 32 x = 16 years Therefore Gabby is 11 years old

53. I had 7 marbles in a bag. 3 are purple, 4 are green. I will take out 2 marbles without putting the first back into the bag before I take the 2 nd. Draw a probability tree and calculate a)P(both purple) b)P(one of each colour) ANSWER 1 st marble 2 nd marble P P P G G G 3/7 2/6 4/7 3/6 4/6 a)P(both purple = 3/7 x 2/6 = 1/7 b)P(one of each) = 3/7 x 4/6 + 4/7 x 3/6 = 4/7

54. 4,3 During 2005 the average wage earned by some factory workers in New Plymouth rose from $950 to $1025. Calculate the percentage increase. ANSWER: Amount change = 1025 – 950 = $75 Therefore Percentage Change = Change / Original x 100 75/ 950 x 100 = 7.89 % increase in pay

55. 4,4

56. 4,5 Write the rule connecting the plumber cost, C to the hours worked, h. ANSWER: C = 35H + 40

57. 9,6 Calculate the capacity of this cuboid Capacity is the amount of liquid that a container can contain. 1 ml is equivalent to 1 cm, 1 L is equivalent to 1000cm. Therefore the volume of this cuboid is 64cm Therefore its capacity is 64 ml. 2 cm 8 cm 4cm 3 3 3