Dalkeith High School National 5 Maths Exam Paper Revision Booklet (Based on Credit Papers )

Transcription

1 Dalkeith High School National 5 Maths Exam Paper Revision Booklet (Based on Credit Papers 005-0)

2 NATIONAL 5 MATHS FORMULAE LIST The roots of are Sine Rule: Cosine Rule: or Area of a triangle: Volume of a sphere: Volume of a cone: Volume of a pyramid: Standard deviation: sample size., where n is the

3 Practice Paper (Based on 005).... Multiply out the brackets and collect like terms: 5. 6.

4 7. Change the subject of the formula to s: 8. The arch of a railway bridge is represented by a parabola. The equation of the parabola is a) State the coordinates of the maximum turning point of the parabola. b) State the equation of the axis of symmetry 9. a) Express in its simplest form. b) Express as a single fraction. x 0 and x -

5 [End of Paper ] 5

6 Practice Paper (Based on 005). The cost of hiring a car depends on the number of days the car is hired and the number of litres of petrol used. a) David hired a car for days and used 50 litres of petrol. The total cost was Let x pounds be the cost of hiring a car, and y pounds the cost per litre of petrol. Write an equation in x and y which satisfies the above condition. b) Anne hired the same model of car for days and used 60 litres of petrol. The total cost was.00 Write a second equation in x and y which satisfies the above condition c) Find the cost of hiring a car for 5 days and using 70 litres of petrol.... 6

7 5. Is the slab in the shape of a right angled triangle? Show your working. 6. 7

8 If u = and v = find 9. 8

9 0.. [End of Paper ] 9

10 Practice Paper (Based on 006)

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12 9.

13 0.. The vectors u and v are as stated below: Find the magnitude of giving your answer as a surd in its simplest form. [End of Paper ]

14 Practice Paper (Based on 006)...

15 . 5. 5

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17 8. 9. [End of Paper ] 7

18 Practice Paper (Based on 007)

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21 .. a) Write x 6x + 0 in the form (x + a) + b. b) State the equation for the line of symmetry. c) Find the coordinates of the y intercept. [End of Paper ]

22 Practice Paper (Based on 007)....

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24 Given a = and b = find: a) a - b b) Hence find

25 . 5

26 .. [End of Paper ] 6

27 Practice Paper (Based on 008)

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29 0. The diagram shows a regular hexagon PQRSTW. and represent vectors u and v respectively. What is in terms of u and v? [End of Paper ] 9

30 Practice Paper (Based on 008)... 0

31 . 5.

32 6. 7.

33 8. 9. a) Write in the form. b) State the values of p and q. 0. [End of Paper ]

34 Practice 5 Paper (Based on 009)....

35 In the diagram, OABCDE is a regular hexagon with centre M. Vectors a and b are represented by OA and respectively. (a) Express AB in terms of a and b. (b) Express in terms of a and b. 5

36

37 0.. [END OF PAPER ] 7

38 Practice 5 Paper (Based on 009)... 8

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40 7. 0

41 8. 9. [End of Paper ]

42 Solutions Practice Paper.88 7/ 7.50 x + x - 5 y = -x x = /5 7 S = q(r k) / t 8 a) (, 0) b) x = 9 a) a b) 6x + 6 / x(x + ) 0 6cm a) 5 b) t = ½ x = 7/ cm Practice Paper a) x + 50y = b) x + 60y =.00 c) 7.50 Mean = 79.5min S = 7.09 min 87.5cm² X =., -. 5 Not right angled 6 x = 8m 7 AB = 8. km x = x = 5.,.7 Practice Paper y = x a) (x + y)(x y) b) 6 x = ml 8 a) x + y = 0 b) 5x + y = 79 c) games 9 y = (x ) 0 a) 50m b) m c) 9 sessions Practice Paper 80. 9/0 m = (p + 8)/ x + x a a½ 6 f = /5d + 7 Yes, the length of board is 90cm and 90> a) x + y = 00 b) x + 6y = 80 c) 0 standard and 90 deluxe 0 b = and c = cm (x - ) + x = (0, 0) Practice Paper.6 x 0 8 km a) mean: 76.5 bpm SD: 6.7 b) The children, on average, have a higher pulse rate than the adults as the mean pulse rate is higher. There is a smaller spread in pulse rates for the children as the standard deviation is lower. 00 a) x + x b) m / + m 5/ c) 5. to d.p. 6 a) b) 05m 7 a) 50cm b) 7.cm (to d.p.) c) 09. seconds (to d.p.) 8 0.5g 9 a).87m (to d.p.) b) 50.6 seconds (to d.p.) Practice Paper and -.5 a) Mean = and SD = 7 b) On average, more birds visit Erin s table as 5 >. The number of birds visiting Erin s table is less consistent as 5 < 7. x < km cm 8 0cm 9.0 and a) b)8.5 units a) A = (0 x)(6 x) = x 6x + 60 b) cm a).cm b).78cm 9 600

43 Practice Paper 5.8 5(x+)(x-) H= y = -x a) (,0) & (8,0) b.5 units 7 8 AC = 9 a = 5, b = -7 0 v + u Practice Paper 5900 tonnes 56.5 Aaron has fifteen 50p coins 5 5.6m 6 a. 6.9m b. x = 90 7 a. 50 b. 5.8cm 8 a & 58.7 b a) b) p =, q = 5 0 a) 08 o b).68 cm Practice 5 Paper 7. a)9 b)±7 a) (x-y)(x+y) b) c) a) b-a b) (b-a) 8 a) 6x+y= b) 5x-y= c) x=, y=9 9 Practice 5 Paper.x0 8 -., 5..5cm 5 7, 7 6 No (5.%) 7 a) y=x+ b) 8 a) 0 o b) 55.6m c) o 9 a) 0cm b) 5.cm 0 a) seconds b) 98m 0.