Year 10 Higher Easter 2017 Revision

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1 Year 10 Higher Easter 2017 Revision 1. A show is on Friday, Saturday and Sunday. 2 5 of the total tickets sold are for the Saturday show. 240 tickets are sold for the Saturday show. Three times as many tickets are sold for the Sunday show as for the Friday show. How many tickets are sold for the Sunday show? 2. Express as a fraction in its simplest form Work out 3 5 Give your answer in its simplest form. 4. Use approximations to estimate the value of You must show your working

2 5. Jake, Kim and Lee share some money in the ratio 1 : 3 : 6 Kim gets 9 more than Jake. How much does Lee get? 6. X divides the line PQ in the ratio 2 : 3 P is (2, 1) and Q is (12.5, 7.5) y Q Not drawn accurately X P O x Work out the coordinates of the point X. 7. Here are five numbers Work out the difference between the largest and smallest numbers. Give your answer in standard form.

3 8. Work out ( ) ( ) Give your answer in standard form to 2 significant figures. x 9. Solve = Give your answer in standard form. 10. Work out Solve the equation x 2 1 = Circle the value that is equivalent to Show that ( ) 2 can be written as a integer. 14. Rationalise the denominator and simply 24 6

4 15. All lengths are in centimetres. Work out the area of this rectangle. Give your answer in the form a + b 2, where a and b are integers. 16. Solve the simultaneous equations. 2x + y = 13 x + 2y = 17 Do not use trial and improvement.

5 17. A tea and a two buns costs 3.00 Two teas and three buns costs 5.10 Work out the cost of two teas and a bun. 18. The diagram shows a sector of a circle. 45 Not drawn accurately The arc length is 18 cm Work out the radius. 19. The diagram shows a sector of a circle of radius 5 cm Not drawn accurately 5 cm The area of the sector is 5 cm 2 Work out the arc length. Give your answer in terms of

6 20. The area of this triangle is 180 cm 2 Work out the length of the perimeter. You must show your working. Not drawn accurately 40 cm 21. ADC is a straight line. B y 19 cm C Not drawn accurately 10 cm 2x cm D x cm Work out angle y. A 35

7 22. Work out the area of this triangle. [4 marks] 17 cm 8 cm Not drawn accurately 23. Alex has an 80% chance of passing a test. Brad has a 60% chance of passing the test. Alex Brad pass pass fail pass fail Work out the probability that Alex and Brad both fail the test. fail

8 24. ξ = {230 students in a school} 147 students take French (F). 94 students take Spanish (S). 15 students do not take French or Spanish. (a) Complete the Venn diagram. [3 marks] ξ F S (b) A student is chosen at random. Work out the probability that the student takes Spanish but not French 25. A square has a side of 8 cm The area of the square increases by 50% Work out the percentage increase in the length of the side.

9 26. The table shows the mass of 50 gerbils. Mass, m (grams) Frequency 50 < m < m < m < m < m 75 8 (a) Work out an estimate of the mean mass of the gerbils. (b) What assumption have you made in calculating the mean mass?

10 27. Trevor stood by a turnstile at a football ground. He counted the number of males and females that passed through for 1 minute. The table shows the results. Male 148 Female 22 (a) In total people attended the match. Estimate the number of women that attended the match. (b) What assumption have you made in making your estimate? 28. The table shows information about the distances travelled to make 500 deliveries. Distance, d (miles) Frequency Cumulative frequency 0 < d < d < d < d < d

11 3 (a) Complete the cumulative frequency column. [1 mark] 3 (b) Show the information on a cumulative frequency graph. [3 marks] Cumulative frequency Distance, d (miles) 29.

12 30. The table and histogram give some information about the masses of 600 hamsters. Mass, m (g) Frequency 60 < m < m < m < m < m Total = 600 Frequency density Complete the table and the histogram. Mass m (g) 31. Solve 3w 5 = w The diagram shows two rectangles.

13 33. All dimensions are in cm x 1 Not drawn accurately 3 7 2x + 3 The shaded area is 84.5 cm 2 Work out the perimeter of the white rectangle. 34. The rectangle and the equilateral triangle have equal perimeters. Not drawn accurately 6(x 2) 3(4x + 2) Work out an expression, in terms of x, for the length of a side of the triangle. Give your answer in its simplest form.

14 35. AB = AC AB is parallel to CD. C 66 D Not drawn accurately A 48 B Prove that triangle BCD is isosceles. 36.

15 37. All angles are in degrees. C 40 Not drawn accurately x + 12 A 2x D x B Work out the size of angle CDB. 38. Solve 2x = 4( x 1)

16 39.

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