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Practice NAB

Practice NAB. Unit 2. represents 1 mark. Outcome 1. 1 A triangular field, PQR, is shown below. PQ = 125 metres, QR = 110 metres and angle PQR = 84°. (a) Calculate the area of the field. (3). Q. 110m. 84 0. R. 125m. P. A = ½ ab sin C = ½ X 125 X 110 X sin 84° = 6837·34m 2.

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Practice NAB

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  1. Practice NAB Unit 2 represents 1 mark

  2. Outcome 1 1 A triangular field, PQR, is shown below. PQ = 125 metres, QR = 110 metres and angle PQR = 84°. (a) Calculate the area of the field. (3) Q 110m 840 R 125m P A = ½ ab sin C = ½ X 125 X 110 X sin 84° = 6837·34m2

  3. Q 110m (b) Calculate the length of PR. (4) 840 R 125m q P q2 = p2 + r2 – 2prcosQ q2 = 1102 + 1252 – 2 X 110 X 125cosQ q2 = 24850·467 q = 157·64m

  4. 2 The diagram shows the positions of an oilrig and two ships. The oilrig at R is 70 kilometres from the ship at A. Angle RAB = 74° and angle RBA = 43°. Calculate how far the ship at B is from the oilrig.. (3) A a 70 70km 740 = sin740 sin430 R 430 a B a 70Xsin740 = sin430 = 98·7km Threshold 7 out of 10

  5. 3 See worksheet. Diagram 1 shows the line 4x + 9y = 48. (a) On the same diagram draw the line y = x + 1 (2) Need any two points Let x = 0 y = 1 (0,1) Let x = 1 y = 2 (1,2) Let x = 2 y = 3 (2,3) Let y = 0 x = -1 (-1,0) etc……

  6. y (b) Use the graph to solve the system of equations 4x + 9y = 48 y = x + 1 (1) 8 6 (3,4) 4 2 12 x 2 4 6 8 10 -2 4x + 9y = 48 -4

  7. 4 Solve, algebraically, the system of equations 3x + 2y = 20 x − y = 5 (3) 3x + 2y = 20 X 2 → 2x – 2y = 10 Add 5x = 30 x = 6 From top equation 18 + 2y = 20 y = 1 Threshold 4 out of 6

  8. 5 See worksheet. The marks obtained in a class test were as follows: 27 28 37 29 14 28 13 25 32 36 19 43 25 24 30 23 32 28 (a) Find the maximum, minimum, median and quartiles of the data set. (4) H 43, L 13 1234 3 4 9 3 4 5 5 7 8 8 8 9 Q2 - 28 0 2 2 6 7 3 Q1 - 24 Q3 - 32 Need to order points

  9. (b) On diagram 2, draw a boxplot to illustrate the data. (2) 13 24 28 32 43

  10. 6 See worksheet. A survey was done amongst ninety pupils who were truanting from school. The table below shows the reasons they gave Reason Number of pupils Dislike teachers 19 Schoolwork too hard 28 School boring 43 (a) Complete the table on the worksheet. (2) Reason Rel. Freq Dislike teachers 19/90 Schoolwork too hard 28/90 School boring 43/90 Angle 760 1120 1720 X 360

  11. (b) On diagram 3, draw a pie chart to illustrate the data. (2) Draw pie chart with correct angles Label Sectors Threshold 7 out of 10

  12. 7 Find the standard deviation of this random sample of digits, showing all the necessary working. 7 8 3 5 10 (4) 7 8 3 5 10 49 64 9 25 100 √ 2 s = 247 – 33/5 4 = √7.3 33 247 = 2.7

  13. (b) State the equation of your line of best fit. (3) Need two points on line m = 20 – 4 30 – 0 m = 16 30 = 0.5 y = 0.5x + 4 c (0,4) (30,20) The scattergraph shows the marks scored in an "algebra" test by a sample of students plotted against the marks scored in a "number" test. (a) Draw your estimate of the line of best fit on the graph. (1) You will have different results – it depends on points on your line

  14. (c) Use your equation to estimate the mark in the "number" test by a student who scored 80 in the algebra test. (2) x = 80 → y = 0.5X80 + 4 = 44 y = 0.5x + 4 You will have different results – it depends on your equation

  15. 9 A Lottery has balls numbered 1 to 34. What is the probability that a ball, selected at random, has a number greater than 30? (2) 4/34 = 2/17 Threshold 8 out of 12

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