11+ MATHEMATICS EXAMPLE ENTRANCE EXAMINATION PAPER

Transcription

1 11+ MATHEMATICS EXAMPLE ENTRANCE EXAMINATION PAPER NAME Entrance Number Time allowed: 60 minutes Answer as many questions as you can. You are not expected to answer every question. Do not spend too long on one question. If you cannot do a question, miss it out. Show the stages of your working clearly. You are not allowed to use a calculator. The total mark for this paper is 100.

2 Q1. Work out = =... Q2. (a) Write the answers. (4 + 2) 3 = (2 3) = = (b) Put brackets in the calculation to make the answer (c) Now put brackets in the calculation to make the answer /29 Total for the page

3 Q3. Work out the missing numbers. In each part, you can use the first line to help you. (a) = = 480 (b) = =... (c) = = 50 3/29 Total for the page

4 Q4. Add three to the number on each number line. The first one is done for you. 4/29 Total for the page

5 Q5. (a) The number chain below is part of a doubling number chain. Fill in the two missing numbers. (b) Find two different prime numbers so that when added together the answer is 32 and when multiplied the answer is 247. (c) How many mm are there in 2.01 m? (d) Write down two prime numbers smaller than 100, but bigger than 90. (e) Write down all factors of 30. (f) Now write down all the prime factors of 30 5/29 Total for the page

6 Q6. The diagram shows some shapes on a 10 by 6 square grid. (a) Which two shapes have the same area as shape A?... (b) Which two shapes have the same perimeter as shape A?... (c) How many of shape C would you need to cover a 10 by 6 square grid?... 6/29 Total for the page

7 Q7. 1 cm 1 cm (a) (i) Find the area of the shaded shape.... cm 2 (ii) Find the perimeter of the shaded shape.... cm 7/29 Total for the page

8 Q8. Here is a solid prism made from centimeter cubes. 1 cm 3 Find the volume of the solid prism.... cm 3 8/29 Total for the page

9 Q9. Diagrams NOT accurately drawn 200 cm 100 cm 50 cm 100 cm 20 cm 20 cm A carton measures 200 cm by 100 cm by 100 cm. The carton is to be completely filled with boxes. Each box measures 50 cm by 20cm by 20 cm. Work out the number of boxes which can completely fill the carton marks 9/29 Total for the page

10 Q10.. This diagram shows the floor plan of a room. Work out the area of the floor. Give the units with your answer /29 Total for the page

11 Q11. Write down the special mathematical name of each of these two 3-D shapes. (i) (ii) (i) (ii) 11/29 Total for the page

12 Q12. a) Write down the fraction of this shape that is shaded. (b) 3 Add enough shading so that 4 of the shapeis shaded altogether. (c) Write down the percentage of the shape that is now unshaded.... (d) Shade 10% of this grid. 12/29 Total for the page

13 Q13. (a) one. Which of these fractions is smaller than 2 1? Circle the correct ,,, (b) List five consecutive whole numbers which add up to 100. Q14. A meal in a restaurant costs the same for each person. For 11 people the total cost is 253 What is the total cost for 12 people? 13/29 Total for the page

14 Q15. (a) 9 28 (b) What is 27 28? You can use part (a) to help you.... Q16. Give the answer to each of the following as a fraction in its simplest form: + = = 14/29 Total for the page

15 Q17. (a) Write the missing numbers. 50% of 80 =... 5% of 80 =... 1% of 80 =... 3 marks (b) Work out 56% of 80 You can use part (a) to help you.... (c) Write down 5 4 as a percentage. s Q18. Simplify this expression. 5k k =... 15/29 Total for the page

16 Q19. (a) When x = 5, work out the values of the expressions below. 2x + 13 =... 5x 5 =... (b) When 2y + 11 = 17, work out the value of y Show your working. y =... 16/29 Total for the page

17 Q20. (a) Write each expression in its simplest form. b b (3d + 5) + (d 2)... 3m ( m)... (b) I think of a number. When multiplied by 4, then 8 is subtracted from the answer and then divided by 5 the answer is 4. What number did I think of? 17/29 Total for the page

18 Q21. (a) Here are two equations. k = a + b a + b + k = 30 What is the value of k? k =... (b) Look at this information. 10 = c + d c is one more than d What is the value of c? c =... 18/29 Total for the page

19 Q22. Kim is thinking of a number. Q23. The price of a coat is 6 In a sale the price is reduced by 15% What is the sale price of the coat? 19/29 Total for the page

20 Q24. The diagram shows triangle PQR. - Work out the sizes of angles a, b and c a = b =.. c =. 3 marks - 20/29 Total for the page

21 Q25. 2 tins balance 1 bottle. 1 tin and 1 bottle balance 1 box. (a) How many bottles do 6 tins balance?... (b) How many boxes do 6 tins balance?... 21/29 Total for the page

22 Q26. A shop sells school uniform. Two shirts and one jumper cost 29 One shirt and one jumper cost 21 How much does one jumper cost? Q27. (a) Look at these three numbers. Find the mean of the three numbers. Find the median of the three numbers. - 22/29 Total for the page

23 Q28. Write the missing numbers in these fraction sums. Q29. (a) Put these values in order of size with the smallest first smallest largest (b) Write down the next three terms in each of the following sequences: i) 10, 7, 4, 1, ii) 2, 3, 5, 7, 11, 13, 17, 19, 23/29 Total for the page

24 Q30. (a) A teacher asked her pupils if they recycled newspapers and glass. The pie chart shows the results pupils answered Neither. How many pupils answered Newspapers only? Show your working.. pupils 24/29 Total for the page

25 (b) The teacher asked a different class if they recycled newspapers and glass. There were 20 pupils in the class. 9 pupils answered Newspapers only. On a pie chart, what would the angle be for the sector Newspapers only? Do not draw the Pi chart. Show your working /29 Total for the page

26 Q31. Solve this equation k = 8k + 1 k =... Q32. Find the values of t. 2 t 3 6 t =... 26/29 Total for the page

27 Q33. A rectangular field has a length which is three times as long as the width. If the perimeter is 32 m, what is its area in m 2? Area =.... m 2 27/29 Total for the page

28 Q34. I have two bags of cubes. Each bag contains more than 20 but fewer than 30 cubes. (a) I can share the cubes in bag A equally between 9 people. How many cubes are in bag A?... (b) I can share the cubes in bag B equally between 4 people. How many cubes could be in bag B? There are two answers. Write them both.... or... 28/29 Total for the page

29 Q35. a) If 4(5x -7) = 2, calculate the value of 15-10x. b) Given that x y = 2x + y And 2m m n = n Work out the answer to: [(4 8) 3] 7 = 29/29 Total for the page