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National 4

National 4. Expressions and Formulae. 1 (a) Expand the brackets: 5(2x – 2). 10x – 10. 1 (b) Expand the brackets and simplify: 5(3t + 4) + 7t. 15t + 20 + 7t = 22t + 20. 2. Factorise 3g + 18. 3(g + 6). 3. Simplify 6m + 5p + m – 2p. 7m + 3p. 6.

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National 4

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  1. National 4 Expressions and Formulae

  2. 1 (a) Expand the brackets: 5(2x – 2) 10x – 10 1 (b) Expand the brackets and simplify: 5(3t + 4) + 7t 15t + 20 + 7t = 22t + 20 2. Factorise 3g + 18 3(g + 6) 3. Simplify 6m + 5p + m – 2p 7m + 3p 6

  3. 4 (a) When a = 4 and b = 3, find the value of 5a – 4b 5 X 4 – 4 X 3 = 8 (b) Kenny sells bicycles. Her weekly pay is calculated using the formula: P = 6.5H + 2.5B where P is his pay (in pounds), H is the hours he works, and B is the number of bicycles he sells. One week he works 32 hours and sells 24 bicycles. Calculate his pay for that week. P = 6.5 X 32 + 2.5 X 24 = 208 + 60 = £268 4

  4. 5 The diagrams below show a sequence of squares made up of matches 1 Square 2 squares 3 squares (a) Complete the table below. (b) Write down a formula for calculating the number of matches (M) when you know the number of squares (S). M = 3S + 1 (c) A pattern is made up of 31 matches. How many squares were in the pattern? 3 X 10 + 1 = 31 so s = 10 10 13 16 37 Strategy 5

  5. 6 Arthur is designing a wheelchair ramp for access to his shop. Regulations state that the gradient of the ramp must be a maximum of 0.08. The dimensions of the ramp are shown below: 0.23m 2.5m Outcome 1 Threshold 8 out 16 (a) Calculate the gradient of the slope. gradient = 0.23/2.5 = 0.092 (b) Does this ramp meet the regulations? Give a reason for your answer. Does not meet regulations as gradient is over 0.08 1 explain

  6. 42cm 7 The diagram shows a circle with a diameter of 42cm as shown below. (a) Calculate the circumference of the circle. (b) Calculate the area of the circle. C = πD π × 42 131.88cm A = πr2 π × 212 1384.74cm2 4

  7. 110 cm 30 cm 8 A trapezium is made up of a rectangle and two identical right-angled triangles, as shown in the diagram below. Find the area of the trapezium. 80 cm 50 cm Area of Rectangle = 50 X 80 = 4000cm2 Area ofeach triangle = ½ X 30 X 80 = 1200cm2 Total Area = 4000 + 2 X 1200 = 6400cm2 3

  8. 9 A cuboid is 10 centimetres long, 6 centimetres wide and 25 centimetres high, as shown in the diagram below.10 cm6 cm25 cm Find the surface area of the cuboid shown. Area of Front and Back 10 X 25 = 250cm2 Area of Sides 6 x 25 = 150cm2 Area of Top and Bottom 6 X 10 = 60cm2 Total Area = 2 X 250 + 2 X 150 + 2 X 60 = 920cm2 25 cm 6 cm 10 cm 2

  9. 10 A cylinder is shown in the diagram below. The area of the base of the container is 10 square metres. The height of the container is 2·5 metres. Calculate the volume of the cylinder. 2.5 m Outcome 2 Threshold 6 out 11 10 m2 V = Ah = 10 X 2.5 = 25cm3 2

  10. 11 Complete this shape so that it has rotational symmetry of order 4, about 0. Strategy O checking Strategy Threshold 1 out of 2

  11. 12 The number of visitors to a local museum was recorded each day for two weeks. The results are shown below. Complete the frequency table for these results. 3 50 - 59 3 4 60 - 69 70 - 79 3 80 - 89 1 14 2

  12. 13 Eight students were given a Maths Assessment The marks are shown below. (a) Calculate the mean mark. Total = 192 Mean = 192 ÷ 8 = 24 (b) Calculate the range. range = 34 – 13 = 21 Each student then revised for a week. After the week, they sat a similar assessment. This time • the mean mark was 31 • the range was 14 (c) Write two comments comparing the results before revision with the results after revision. Higher mean → Class have improved overall Lower Range → The results are closer together. 3 Explain Threshold 1 out of 3 explain

  13. 14 Sixty pupils were asked where they lived. The table below shows the results. To help you complete the pie chart, fill in the blanks in the table. Total = 60 So 60 pupils → 3600 1 pupil → 360 ÷ 60 = 60 Village: 18 pupils → 18 X 6 = 1080 Town: 30pupils → 30 X 6 = 1800 City: 12 pupils → 12 X 6 = 720 Pie Chart: Angles Correct Sectors labelled 3

  14. 15 A spinner has 5 edges as shown in the diagram. When it is spun it comes to rest on one edge. What is the probability that it comes to rest on a number greater than 2? p(more than 2) = 3/5 1 Outcome 3 Threshold 5 out 9

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