##### Mathematics Paper 3: reasoning (May 2017) – with hints

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# Mathematics

## Paper 3 (May 2017): reasoning, with hints

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completed this test on Wednesday, 26-Jun-19 06:31:16 UTC

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- Question 1 of 25
##### 1. Question

1Write the missing number to make this**division**correct.- 75 ÷ (10) = 7.5

1 mark(s)CorrectIncorrect##### Hint

75 is bigger than 7.5 – how many times bigger?

- Question 2 of 25
##### 2. Question

2A group of friends earns £80 by washing cars.

They share the money

**equally**.They get £16 each.

How many friends are in the group?- (5)

1 mark(s)CorrectIncorrect##### Hint

Could you work out the answer if they got £8 each? It would be 80 divided by 8. Ok then. £16 is twice £8, so the group must be half that size, for them to get twice as much money.

- Question 3 of 25
##### 3. Question

3Chen uses these digit cards.She makes a 2-digit number and a 1-digit number.She multiplies them together.Her answer is a**multiple of 10**What could Chen’s multiplication be?- (9) (5, 6)
**x**(6, 5)

1 mark(s)CorrectIncorrect##### Hint

When you multiply two numbers, you can work out last digit of the answer by multiplying just the last digits of the two numbers and looking at the last digit of that. Example: 325 x 3 ends in a five because 5 x 3 = 15.

Chen has made a 2-digit number and a single-digit number to multiply, and her answer ends in a zero. We know that, because every number which is a multiple of ten ends in a zero. Examples: 10, 50, 120.So concentrate on finding the last digits. The digits to choose from are 5, 6 and 9. Which ones, multiplied together, give an answer that ends in a zero?

- Question 4 of 25
##### 4. Question

4This graph shows the temperature in °C from 2 am to 3 pm on a cold day.How many degrees**warmer**was it at 3 pm than at 3 am?- (7)
**°C**

1 mark(s)CorrectIncorrect##### Hint

You can do this in two ways. Either:

1) On a sheet of paper, write down the temperature at 3am. Then write down the temperature at 3pm. Subtract the lower temperature from the higher, to find the difference. Be careful, subtracting a negative number is like adding a positive number. Or;2) Find the two temperatures on the graph and carefully count the number of squares between them on the temperature axis.

- Question 5 of 25
##### 5. Question

At 6 pm the temperature was 4 degrees lower than at 3 pm.What was the temperature at 6 pm?- (-2)
**°C**

1 mark(s)CorrectIncorrect##### Hint

Find the temperature at 3pm and subtract 4 degrees.

- Question 6 of 25
##### 6. Question

5The children at Farmfield School are collecting money for charity.Their target is to collect £360

So far they have collected £57.73

How much**more**money do they need to reach their target?**£**(302.27)

1 mark(s)CorrectIncorrect##### Hint

The amount they still need to collect is the difference between their target and the amount they have already. To find the difference between two numbers, subtract the smaller number from the larger number.

- Question 7 of 25
##### 7. Question

6William wants to travel to Paris by train.

He needs to arrive in Paris by

**5:30 pm**.What is the**latest time**that William can leave London?- (14:01, 2.01pm)

1 mark(s)CorrectIncorrect##### Hint

The timetable uses the 24-hour clock but you are given William’s arrival latest time as 5:30pm. First, you’ll need to convert this time into 24-hour format. Then look at the timetable to see where that time fits in with trains arriving in Paris.

- Question 8 of 25
##### 8. Question

7Here are some triangles labelled A, B, C and D, drawn on a coordinate grid.Triangle A is translated**7 right**and**5 up**.Which triangle matches triangle A in its new position?Tick**one**.1 mark(s)CorrectIncorrect##### Hint

Translation by itself does not cause rotation too.

- Question 9 of 25
##### 9. Question

8Write three factors of 30 that are**not**factors of 15Write your answer in the boxes, in order of size starting with the smallest.- (2, 6) (6, 10) (10, 30)

2 mark(s)CorrectIncorrect##### Hint

A number bigger than another cannot be a factor of it. So 30 cannot be a factor of 15.

Also, any number is also a factor of itself. So 15 is a factor of 15.

Also, 2 is a factor of every even number (except zero) but 2 is not a factor of any odd number. - Question 10 of 25
##### 10. Question

9Here is the morning timetable for Chen’s class this week.What is the total number of hours for**English**on this timetable?- (5)
**hours**

1 mark(s)CorrectIncorrect##### Hint

How long is every section before break? How long is every section after break?

- Question 11 of 25
##### 11. Question

10A bottle contains 568 millilitres of milk.Jack pours out**half a litre**.How much milk is left?- (68, 68ml, 68 ml, 0.068l, 0.068 l, 68 millilitres, 0.068 litres)

1 mark(s)CorrectIncorrect##### Hint

Remember to include the units in your answer; either

**ml**(for millilitres) or**l**(for litres). - Question 12 of 25
##### 12. Question

11A bicycle wheel has a diameter of 64 cm.What is the**radius**of the bicycle wheel?- (32)
**cm**

1 mark(s)CorrectIncorrect##### Hint

The diameter of a circle is twice the radius, because the diameter is measured across the widest part and the radius is just between the centre and the edge, which is halfway across.

Your answer should be in centimetres. - Question 13 of 25
##### 13. Question

12Adam buys 6 bags of white balloons.

Chen buys 3 bags of red balloons.

Adam says,**‘I have four times as many balloons as Chen.’**Tick the answer that best explains why Adam is correct.Tick**one**.1 mark(s)CorrectIncorrect##### Hint

Look for an answer that is complete, and is not vague. It must also be accurate and you must know it is completely true.

- Question 14 of 25
##### 14. Question

13Find the**pentagon**with exactly**four acute angles**.Tick

**one**.1 mark(s)CorrectIncorrect##### Hint

Not every shape here is a pentagon.

- Question 15 of 25
##### 15. Question

143 pineapples cost the same as 2 mangoes.

One mango costs £1.35

How much does**one**pineapple cost?Show

your

method- £ (0.90)

2 mark(s)CorrectIncorrect##### Hint

Start by working out how much 2 mangoes would cost.

- Question 16 of 25
##### 16. Question

15Look at the letters below.Find the letter below that has both parallel**and**perpendicular lines.1 mark(s)CorrectIncorrect##### Hint

Lines that meet at 90 degrees are perpendicular. Lines that would never meet, however long you extended them, are parallel.

- Question 17 of 25
##### 17. Question

16There are 2,400 leaflets in a box.

William and Ally take 450 leaflets each.

Adam and Chen share the rest of the leaflets equally.

How many leaflets does Adam get?Show

your

method- (750)

2 mark(s)CorrectIncorrect##### Hint

How many are left in the box after William and Ally have taken their share? This is the amount you then have to divide between Adam and Chen.

- Question 18 of 25
##### 18. Question

17Tick every statement which is correct.2 mark(s)CorrectIncorrect##### Hint

What is a half as a decimal fraction? What is a quarter as a decimal fraction? What is three-fifths as a decimal fraction? Hint: three-fifths is the same as six-tenths. Hint: Which is bigger? Five-hundredths or forty-hundredths?

- Question 19 of 25
##### 19. Question

18A**square**number and a**prime**number have a total of 22What are the two numbers?- square number (9)
**+**prime number (13) = 22

1 mark(s)CorrectIncorrect##### Hint

Write down a few prime numbers and a few squares and see if you can find a pair that add up to 22.

Example: Primes 2, 3, 5… Squares 1, 4, 9, 25…

- Question 20 of 25
##### 20. Question

19Dev thinks of a whole number. He multiplies it by 4

He rounds his answer to the nearest 10

The result is 50

Write all the possible numbers that Dev could have started with.

- (12 13, 12,13, 12, 13, 13 12, 13,12, 13, 12)

2 mark(s)CorrectIncorrect##### Hint

Work backwards by reversing the steps that Dev took. So you’ll start by making a list of all the numbers for which 50 is the nearest 10. Most of these numbers can’t be divided by 4 and give a whole number. Those that can are your answer.

- Question 21 of 25
##### 21. Question

20A square tile measures 20 cm by 20 cm.

A rectangular tile is 3 cm

**longer**and 2 cm**narrower**than the square tile.What is the**difference in area**between the two tiles?Show

your

method- (14)
**cm**^{2}

3 mark(s)CorrectIncorrect##### Hint

The area is found by multiplying the width by the height.

Either: Work out the width and height of the rectangular tile. Then compare it with the area of the square tile, for which the width and height are the same – 20cm each.

Or: Compared to the square tile, the rectangular tile is longer in one direction and narrower in the other. Work out the area of the longer bit: 3 x (20 – 2) cm. Take away the area of the narrower bit: 2 x 20 cm. You’re left with the difference in area between the two tiles.

- Question 22 of 25
##### 22. Question

21The numbers in this sequence increase by the same amount each time.What are the values of A and B?Tick

**one**.2 mark(s)CorrectIncorrect##### Hint

You might find it easier to convert from quarters to eighths.

- Question 23 of 25
##### 23. Question

22In this diagram, the shaded rectangles are all of equal width ().**w**Calculate the width () of one shaded rectangle.**w**Show

your

method- (7)
**cm**

2 mark(s)CorrectIncorrect##### Hint

Imagine you can slide the top shaded rectangle all the way over to the right, so it lines up above a similar one. This might help you to see that 34cm is equal to 18cm + w + 9cm

So w = 34 – 18 – 9 cm. - Question 24 of 25
##### 24. Question

23Here is a pattern of number pairs.Complete the**rule**for the number pattern.*b*= (10) ×*a*– (1)

1 mark(s)CorrectIncorrect##### Hint

From one row to the next, how much does

go up each time? This goes in the first box.*b*Then, looking at the formula, what do you need to subtract to get the right value for

? This goes in the second box.*b* - Question 25 of 25
##### 25. Question

24Cube A and cuboid B have the same volume.Calculate the missing length on cuboid B.Show

your

method- (9)
**cm**

2 mark(s)CorrectIncorrect##### Hint

The volume of the cube = 6 x 6 x 6 cubic cm.

The volume in cubic cm of the cuboid is 6 x 4 x the missing length. These two volumes are the same, so it’s OK to put them in an equation.

6 x 6 x 6 = 6 x 4 x the missing length