ENTRANCE EXAMINATIONS Time allowed: 1 hour and 15 minutes
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1 ENTRANCE EXAMINATIONS 2018 MATHEMATICS FIRST FORM Time allowed: 1 hour and 15 minutes Answer ALL questions. Show all necessary working on the question paper in the spaces provided and write your answers in the appropriate places. The marks for each question are given at the end of the question. There are 30 questions in this paper. The total number of marks is 100. If you cannot do a question, move to the next one so you do not lose time. CALCULATORS ARE NOT ALLOWED. DO NOT WRITE IN THE RIGHT-HAND MARGIN.
2 1. Evaluate the following: (a) Answer:. (2) Answer:. (1) (c) Answer:. (3) (d) Answer:. (3) Q1 ( Total 9 marks ) 2
3 2. What fraction of the shape below is shaded? Answer:. (2) Q2 ( Total 2 marks ) 3. A bottle of medicine holds a quarter of a litre of medicine when full. (a) Write this quantity in millilitres. Alex must take 5 ml of medicine three times a day for nine days. Answer: ml (1) When Alex has finished taking the medicine, how many millilitres are left in the bottle? Answer: ml (3) Q3 ( Total 4 marks ) 3
4 4. Kate has 63 sweets. She keeps for herself and shares the rest equally between her two friends Mary and Lucy. Lucy then gives of her sweets to Jill How many sweets does Lucy keep? Answer:. (3) Q4 5. In the diagram below, the area of the parallelogram is 2800 mm 2. (The diagram is not accurately drawn) (a) Find the length h. The area of the triangle is 600 mm 2. Answer: h = mm (2) What is the length x of the base of the triangle? Answer: x = mm (2) Q5 ( Total 4 marks ) 4
5 6. You are given the following nine number cards: Using these number cards fill in the following table. Each card must be used only once. (3) Q6 7. N 24 is a fraction where N is a whole number. How many possible values are there for N if N 24 is more than 1 6 but less than 3 8? Answer:. (2) Q7 ( Total 2 marks ) 5
6 8. The diagram shows three identical shapes A, B and C. (The diagram is not accurately drawn) Four fifths of shape A is shaded. Three quarters of shape B is shaded. What fraction of shape C is shaded? Answer:. (3) Q8 9. (a) If the three-digit number 6M8 is divisible by 9, find M. If the four-digit number 37N5 is divisible by 35, find N. Answer: M =. (2) Answer: N =. (2) Q9 ( Total 4 marks ) 6
7 10. (a) In the sequence below, the term to term difference is always the same. 6, b, c, d, 18, Find the value of d. Answer: d =. (2) Find the sum of the terms in the 11 th pair of brackets. 1, 3, 5, 7, 9, 11, 13, 15,... Answer:. (2) Q10 ( Total 4 marks ) 11. Find: (a) 15% of of 288 Answer:. (2) Answer:. (2) Q11 ( Total 4 marks ) 7
8 12. In the puzzle below, the numbers 2 to 10 inclusive are placed in the circles so that the sum of the numbers in each shaded triangle is 18. Complete the puzzle. (3) Q Mark was in a car race that lasted 2 hours and 31 minutes. The race started at 14:45 At what time did the race finish? Answer:. (2) Q Nina buys 4 bottles of water for a camping trip. She drinks 1 5 of one bottle. What percentage of her water supply has she drunk? ( Total 2 marks ) Answer:. (2) Q14 ( Total 2 marks ) 8
9 15. Here are parts of two different number lines. Write in each box the number indicated by the arrow. (a) (1) Q15 (2) 16. Sarah bought 10 exercise books and 4 pencils. Rebecca bought 4 exercise books and 10 pencils. Sarah paid 1.20 more than Rebecca. Pencils cost 40 cents each. How much does an exercise book cost? Answer: cents (3) Q16 9
10 17. The ages of ten children are 2, 3, 5, 6, 6, 7, 7, 7, 8 and 9 years. (a) Find their mean age? Answer:. (3) In four year s time, what will their mean age be? Answer:. (1) Q17 ( Total 4 marks ) 18. Work out the perimeter and area of this shape. (The diagram is not accurately drawn) Answer: cm cm 2 (5) Q18 ( Total 5 marks ) 10
11 19. Points A, B and D have been plotted on the centimetre square co-ordinate grid below. Point A has coordinates (1, 6), B (4, 2) and D (5, 9). ABCD is a square. (a) On the grid above, plot and label point C. The area of the square ABCD is 25 cm 2. (1) Calculate the perimeter of the square. Answer: cm (2) Q19 11
12 20. Use the fact that = 5.98, to work out: (a) Answer:. (1) Answer:. (1) Q20 ( Total 2 marks ) 21. Ed is chasing Bruno. They are both running on the same straight track. Ed is running at a speed of 7.5 metres per second. Bruno is 60 metres ahead of Ed and running at a speed of 4.5 metres per second. How many seconds does it take Ed to catch up with Bruno? Answer:. (3) Q21 12
13 22. Paul does the following calculation on his calculator He gets the following digits in the display without the decimal point Give the answer with the decimal point in the correct place. Answer:. (1) Q22 ( Total 1 mark ) 23. In the diagram below, AB = AC and BCD is a straight line Calculate the value of angle x. (The diagram is not accurately drawn) x = (3) Q23 13
14 24. George has the two-stage number machine shown below. (a) Work out the output when the input is 14 Answer:. (1) Work out the input when the output is 3 Answer:. (2) When George puts a number in the machine, the same number comes out. (c) What number did George put in? Answer:. (1) Q24 ( Total 4 marks ) 25. This shape has a perimeter of 80 cm. It is made from square tiles. (The diagram is not accurately drawn) Find the area of the shape. Answer: cm 2 (4) Q25 ( Total 4 marks ) 14
15 26. Pizza Palace prices are shown in the table below: Pizza size Small (S) Medium (M) Large (L) Extra toppings Peppers Olives Feta Halloumi Tuna Shrimp Mia orders a pizza. She asks for a medium pizza with four toppings: peppers, olives, feta and tuna. (a) How much does she have to pay? Claudia orders a small pizza with three different toppings. The cost of Claudia s pizza is 6.20 Answer:. (3) What three toppings did Claudia order? Answer:... (2) Q26 ( Total 5 marks ) 15
16 27. The following question is on pattern blocks. Answer:. (3) Q Calculate the value of angle x. (The diagram is not accurately drawn) x = (3) Q28 16
17 29. In a restaurant, a service charge of 10% is added to the cost of a meal. A family meal costs (a) What service charge will be added to the bill for this meal? A family gets a final bill (including the service tax) for Answer:. (1) What was the cost of the meal? Answer:. (2) Q Erin only has 8 cent and 12 cent stamps. She can make a total of 92 cents by using ten 8 cent stamps and one 12 cent stamp. Find two more ways in which she can make a total of 92 cents. Write your answer like the example in the table below. 1 st way: 2 nd way: = 92 cents (2) Q30 ( Total 2 marks ) END TOTAL : 100 MARKS 17
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