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Applications

Applications. Marking Scheme. 1.1. 1.1. 1 Calculate the area of this triangle. 9cm. C. B. 72 °. Area = ½ abSinC = ½ X 9 X 14 X Sin72 0 = 59.9cm 2. 14cm. A. 40cm. 1.1. 1.1. 1.1. 1.1. C. A. 12°. 35cm. B. 2 Calculate the length of side AB.

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Applications

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  1. Applications Marking Scheme

  2. 1.1 1.1 1 Calculate the area of this triangle 9cm C B 72° Area = ½ abSinC = ½ X 9 X 14 X Sin720 = 59.9cm2 14cm A

  3. 40cm 1.1 1.1 1.1 1.1 C A 12° 35cm B 2 Calculate the length of side AB. c2 = a2 + b2 – 2ab Cos C = 352 + 402 – 2 X 35 X 40 X Cos120 = 86.1867 c = √86.1867 = 9.3cm

  4. 1.1 1.1 N A 22Km 1100 B 18Km C 3 The positions of boats Amiable Archie (A), Buoyant Bertie (B) and Cheerie Charlie (C) are shown below. Charlie is 22Km from Archie. Bertie is 18Km from Charlie. Charlie is on a bearing of 110° from Bertie Calculate the bearing of Charlie from Archie. Give your answer to the nearest degree. a b = sinA sinB 18 22 = sinA sin110o 1300 18 X sin1100 22 X sinA = 500 sinA = 18 X sin1100 # 2.1 22 sinA = 0.7688 A = 500 1.1 Out of 8

  5. 1.2 1.2 1.2 4. The diagrams show 2 directed line segments u and v. v u Draw the resultant of u +2v. v v u + 2v u

  6. z D y C B x O A (6, 0, 0) 1.2 5 The diagram below shows a square based model of a glass pyramid of height 8 cm. Square OABC has a side length of 6 cm. The coordinates of A are (6, 0, 0). C lies on the y-axis. Write down the coordinates of D. D(3 , 3 , 8) 8 3 3

  7. 1.2 1.2 ( ) ( ) ( ) 2.53.5 -7 4.5 1.5- 1 4 -2 5 6 The forces acting on a body are represented by three vectors a, b and c as given below. Find the resultant force. ( ) ( ) ( ) ( ) 2.53.5 -7 4.5 1.5- 1 11 3 -3 4 -2 5 = + +

  8. 1.2 1.2 1.2 ( ) ( ) 3 1 4 -2 7. Vector g = Vector h = Calculate | 2g + h | | 2g + h | = √ 112 + (-3)2 = √130 ( ) ( ) ( ) 3 1 4 -2 11-3 2 + = 1.2 Out of 9

  9. 1.3 1.3 1.3 1.3 1.3 1.3 8 Brendan bought a new van for £22 000. Its value decreased by 12% each year. Find the value of the van after 3 years. 12% decrease → 88% remaining. After 1 year: 0.88 X 22000 = 19360 After 2 years: 0.88 X 19360 = 17036.80 After 3 year3: 0.88 X 17036.80 = £14992.38 (or 0.883 X 22000 = £14992.38) OR

  10. 1.3 1.3 9 The dimensions of a sign are shown below. Calculate the exact area of the sign (in m2). 5 3 1 2 X 7 5 156 12 13 = X 35 7 5 16 m2 4 = 35

  11. 1.2 10. Siobhan is delighted to receive a pay rise of 5%. Her new pay is £19530 What was her pay before her rise? Pay Rise 5% → Multiplier 1.05 Previous Pay = 19350 ÷ 1.05 = £18600 OR 105% → 19530 1% → 186 100% → £18600 # 2.1 OR 1.3 Out of 6 # 2.1 2.1 Out of 2

  12. 11. The times (secs) for Hopeful Harriers athletes to run 400m are shown below. 48 52 45 57 61 55 a) Calculate the mean and the standard deviation 1.4 1.4 1.4 1.4 2 2 318 (∑x)/n ∑x2 – s = 17028 / – 6 s = n – 1 5 n = 6 174 x = x2 5 485245576155 230427042025324937213025 √ = 34.8 = 5.9 Mean = 318 ÷ 6 = 53 ∑x ∑x2 318 17028

  13. b) Results for rival club Resilient Runners are as follows: Mean: 57 secs Standard Deviation: 3 secs Compare the data of the two clubs making two valid comparisons. Runners have a higher mean, so on average their athletes take longer (are slower) Runners have a lower standard deviation, meaning that their athletes’ times do not vary as much. #2.2

  14. 1.4 1.4 1.4 12 A football team was analysed by recording the amount of goals they scored and how many shots at goal they had in a series of matches The results were plotted in the scatter graph below. 20 (a) Determine the gradient and the y-intercept of the line of best fit shown. 18 16 (6 , 16) 14 12 Using (2 , 7) and (6 , 16) Gradient = 16 – 7 Extending Line Y Intercept = 3 10 = 9 = 2.25 8 6 – 2 4 (2 , 7) 6 Shots (s) 4 2 0 0 1 2 3 4 5 6 7 Goals (G)

  15. 1.4 (b) Using these values for the gradient and the y- intercept, write down the equation of the line. y = 2.25x + 3 → S = 2.25G + 3 (c) Estimate how many shots Rovers would have to take to score 8 goals. G = 8 Using equation, S = 2.25 X 8 + 3 = 21 shots 1.4 Out of 8 #2.2 2.2 Out of 2

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