The year 5 entrance test is based on IGCSE paper type questions, a selection of which can be found below. Answer ALL TWENTY TWO questions.

Transcription

1 The year 5 entrance test is based on IGCSE paper type questions, a selection of which can be found below. Answer ALL TWENTY TWO questions. All formulas will be provided. A calculator is required. The entrance exam is normally 90 minutes. Write your answers in the spaces provided. You must write down all the stages in your working. 1 1 euro = 120 yen 1 = 1.2 euros Change 50 to yen. yen (Total for Question 1 is 2 marks) 2 (a) Work out the value of (b) Work out the value of (Total for Question 2 is 4 marks) Do NOT write in this space. *P44613A0324* 3

2 3 (a) Factorise 14x 35 (1) (b) Expand and simplify 3(2c 5) 2(c 4) (c) Simplify (4e 3 ) 2 (d) Expand and simplify (a + 5)(2a 1)... (Total for Question 3 is 7 marks) Do NOT write in this space. 4 *P44613A0424*

3 4 The diagram shows a shape with one line of symmetry. 10 cm Diagram NOT accurately drawn 12 cm 4 cm 15 cm Work out the area of the shape. cm 2 (Total for Question 4 is 4 marks) *P44613A0524* 5

4 5 A jar contains coloured beads. Ajit takes at random a bead from the jar. The probability that the bead is yellow is 0.08 The probability that the bead is pink is 0.1 The probability that the bead is blue is 0.25 (a) (i) Find the probability that the bead is yellow or blue. (ii) Find the probability that the bead is neither yellow nor pink. (4) Ajit replaces the first bead in the jar. He then takes at random a second bead from the jar. (b) Find the probability that the first bead is yellow and the second bead is blue. 6 *P44613A0624*

5 A second jar contains 100 coloured beads. 20 of these beads are brown. Ajit takes at random a bead from the jar. He records the colour of the bead and then returns the bead to the jar. He does this 60 times. (c) Work out an estimate for the number of times Ajit records a brown bead. (Total for Question 5 is 8 marks) 6 Solve 4(5y 1) = 3(6y + 7) Show clear algebraic working. y = (Total for Question 6 is 3 marks) *P44613A0724* 7

6 7 Eloy s height was 125 cm when his age was 7 years. His height was 153 cm when his age was 12 years. (a) Work out the percentage increase in Eloy s height between the ages of 7 and 12 years. Eloy s height at the age of 12 years was 85% of his height at the age of 20 years. (b) Work out Eloy s height when his age was 20 years. % (3) cm (3) (Total for Question 7 is 6 marks) Do NOT write in this space. 8 *P44613A0824*

7 8 B Diagram NOT accurately drawn 15 cm 10 cm A D 12.5 cm C ABC is a triangle. The point D lies on AC. Angle BDC = 90 BD = 10 cm, AB = 15 cm and DC = 12.5 cm. (a) Calculate the length of AD. Give your answer correct to 3 significant figures. cm (3) (b) Calculate the size of angle BCD. Give your answer correct to 1 decimal place. (3) (Total for Question 8 is 6 marks) *P44613A0924* 9

8 10 (a) Find the gradient of the line with equation 3y 2x = 6 (b) Find an equation of the line with gradient 3 that passes through the point (2, 5). (Total for Question 10 is 4 marks) *P44613A01124* 11

9 12 Solve the simultaneous equations 5y 4x = 8 y + x = 7 Show clear algebraic working. x = y = (Total for Question 12 is 3 marks) *P44613A01324* 13

10 19 E A B The Venn diagram shows all of the elements in sets A, B and E. (a) Write down the elements in A (1) (b) Find n(a B) (1) (c) Find the elements in (A B) (A B) (1) A C = Ø B C = {5, 6, 7, 8, 9} n(c) = 3 (d) Write down the elements in C. (1) (Total for Question 19 is 4 marks) Do NOT write in this space. 20 *P44613A02024*

11 2x 20 f:x 2x g:x where x 1 x 1 (a) Express the composite function gf in the form gf:x... Give your answer as simply as possible. gf:x (b) Express the inverse function g 1 in the form g 1 :x... g 1 :x (3) (Total for Question 20 is 5 marks) *P44613A02124* 21

12 21 Diagram NOT accurately drawn 15 cm A solid cone has a height of 15 cm. The volume of the cone is 320 cm 3 Work out the curved surface area of the cone. Give your answer correct to 3 significant figures. cm 2 (Total for Question 21 is 5 marks) 22 *P44613A02224*

13 Answer ALL TWENTY FOUR questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Becky counted the number of matches in each of 50 boxes. The table shows information about her results. Number of matches Work out the mean number of matches. Frequency (Total for Question 1 is 3 marks) Do NOT write in this space. *P44614A0320* 3

14 2 Diagram NOT accurately drawn 8 cm 17 cm 32 cm The diagram shows a circle inside a rectangle. Work out the area of the shaded region. Give your answer correct to 3 significant figures....cm 2 (Total for Question 2 is 3 marks) 3 A bag contains only red counters, blue counters and yellow counters. The number of red counters in the bag is the same as the number of blue counters. Mikhail takes at random a counter from the bag. The probability that the counter is yellow is 0.3 Work out the probability that the counter Mikhail takes is red.... (Total for Question 3 is 3 marks) 4 *P44614A0420*

15 4 On the grid, draw the graph of y = 3x 4 for values of x from 2 to 3 y O x (Total for Question 4 is 4 marks) *P44614A0520* 5

16 8 The diagram shows a triangle. Diagram NOT accurately drawn (3x 3x cm (4x + 2) cm The lengths of the sides of the triangle are 3x cm, (3x 5) cm and (4x + 2) cm. The perimeter of the triangle is 62 cm. Work out the value of x. Show clear algebraic working. (Total for Question 8 is 4 marks) x =... 8 *P44614A0820*

17 12 (a) Factorise c 2 5c... (b) Simplify d 5 d 7... (1) (c) Factorise x 2 + x (d) Make b the subject of P = 1 2 ab 2 2x + 1 x 5 (e) Solve + = Show clear algebraic working. b =... (Total for Question 12 is 11 marks) x =... (4) *P44614A01120* 11

18 13 (a) Write in standard form.... (1) The area covered by the Pacific Ocean is km 2 The area covered by the Arctic Ocean is km 2 (b) Write as an ordinary number. The area covered by the Pacific Ocean is k times the area covered by the Arctic Ocean. (c) Find, correct to the nearest integer, the value of k.... (1) k=... (Total for Question 13 is 4 marks) 14 Kwo invests HK$ for 3 years at 2.5% per year compound interest. Work out the value of the investment at the end of 3 years. HK$... (Total for Question 14 is 3 marks) 12 *P44614A01220*

19 17 x cm Diagram NOT accurately drawn 2x cm (x + 7) cm The diagram shows a trapezium. The trapezium has an area of 17 cm 2 (a) Show that 2x 2 + 7x 17 = 0 (3) (b) Work out the value of x. Give your answer correct to 3 significant figures. Show your working clearly. (Total for Question 17 is 6 marks) x =... (3) *P44614A01520* 15

20 21 The diagram shows a cylinder and a sphere. r cm Diagram NOT accurately drawn h cm 2r cm The cylinder has radius r cm and height h cm. The sphere has radius 2r cm. The volume of the cylinder is equal to the volume of the sphere. Find an expression for h in terms of r. Give your answer in its simplest form.... (Total for Question 21 is 3 marks) 18 *P44614A01820*

21 24 The diagram shows a sector OAPB of a circle, centre O. A P B Diagram NOT accurately drawn 6 cm 6 cm O AB is a chord of the circle. OA = OB = 6 cm. The area of sector OAPB 2 Calculate the perimeter of the shaded segment. Give your answer correct to 3 significant figures....cm (Total for Question 24 is 6 marks) TOTAL FOR PAPER IS 100 MARKS 20 *P44614A02020*