Write the number four hundred and seven thousand, two hundred and sixteen in figures.
(1)
2
Find the missing number: 8 x [ ] = 96
(1)
3
A minibus can carry 9 passengers. 124 pupils from a primary school are going on a trip and every pupil needs a seat. Work out the smallest number of minibuses needed.
(2)
4
A quadrilateral has two pairs of parallel sides, all four sides the same length, and no right angles. Write down the mathematical name of this shape.
(1)
5
Aaliyah has £84 in her savings account. She spends 3/7 of it on a new bicycle helmet and cycling gloves. Work out how much money she has left.
(2)
6
Tom buys a sandwich for £2.65 and a carton of juice for £1.35. He pays with a £5 note. Work out how much change he gets.
(2)
7
A train leaves Leeds station at 09:47 and arrives in York at 10:15. Work out how many minutes the journey takes.
(2)
8
A rectangular vegetable patch is 3.5m long and 2m wide. Priti wants to put edging all the way around the perimeter of the patch. Edging costs £1.20 per metre. Work out the total cost of the edging.
(2)
9
Four friends' times for a 100m race were: Ben 14.6 seconds, Chloe 14.58 seconds, Deepak 14.65 seconds, Priya 14.09 seconds. Write the four times in order, starting with the fastest.
(2)
10
A bookshop reduces the price of a £24 boxed set of books by 25% in a sale. Priya has £20 to spend. Explain, showing your working, whether she has enough money to buy the boxed set.
(3)
11
The bar chart shows the number of books read by four children in June.
(a)Work out how many more books Zara read than Kwame.(1)
(b)Work out the total number of books read by all four children.(1)
12
In a school choir, the ratio of girls to boys is 5:3. There are 40 children in the choir altogether. Work out how many more girls than boys there are.
(3)
13
A cinema sells tickets for £6.50 for adults and £4.25 for children. A family of 2 adults and 3 children buys tickets, and also spends £9.90 on popcorn and drinks. Work out the total amount the family spends.
(3)
14
Three angles meet at a point on a straight line. Two of the angles are 65 degrees and 48 degrees. Work out the size of the third angle.
(2)
15
Point A is at (2, 5) on a coordinate grid.
(a)Point A is translated 4 units right and 3 units down to point B. Write down the coordinates of point B.(1)
(b)Point B is then reflected in the x-axis to point C. Write down the coordinates of point C.(2)
16
The first four terms of a sequence are 4, 9, 14, 19.
(a)State the term-to-term rule for this sequence.(1)
(b)Work out the 10th term of the sequence.(2)
17
Work out 2 3/4 + 1 5/6. Give your answer as a mixed number in its simplest form.
(3)
18
Sam earns £45 doing weekend jobs. He saves 2/5 of it and spends the rest equally between a book and a film ticket. Work out how much Sam spends on the film ticket.
(3)
19
Rosie thinks of a number. She multiplies it by 4, subtracts 9, then divides the result by 3. Her final answer is 13. Work out the number Rosie started with.
(3)
20
A water tank holds 18 litres when full. Water leaks out of a crack at a constant rate of 150ml per hour.
(a)Work out how many hours it will take for the tank to leak completely empty, starting from full.(2)
(b)The tank started leaking at 22:00 on 21/07/2026. Work out the date and time when the tank will be completely empty.(2)
Mark scheme · KS2.M-R8 Reasoning Practice Paper 8
Question 1
B1 407216 cao
Answer: 407216
Question 2
B1 12 cao
Answer: 12
Question 3
M1 124 / 9 = 13 remainder 7 (or 13.7... seen) oe
A1 14 (minibuses) cao, with recognition that 13 minibuses would leave 7 pupils without a seat
Answer: 14 minibuses
Question 4
B1 rhombus cao
Answer: Rhombus
Question 5
M1 84 / 7 = 12, then 12 x 3 = 36 (method to find 3/7 of 84) oe
A1 £48 cao
Answer: £48
Question 6
M1 2.65 + 1.35 = 4.00 oe
A1 £1.00 cao
Answer: £1.00
Question 7
M1 splits the time into 09:47 to 10:00 (13 minutes) and 10:00 to 10:15 (15 minutes) oe
A1 28 minutes cao
Answer: 28 minutes
Question 8
M1 perimeter = 2 x (3.5 + 2) = 11 (m) oe
A1 ft 11 x 1.20 = £13.20, ft their perimeter
Answer: £13.20
Question 9
B1 Priya identified as fastest and Deepak identified as slowest
B1 Priya (14.09), Chloe (14.58), Ben (14.6), Deepak (14.65) cao (all four in correct order)
Answer: Priya (14.09s), Chloe (14.58s), Ben (14.6s), Deepak (14.65s)
Question 10
M1 10% of 24 = 2.40, so 25% = 2.40 x 2.5 = 6 (or equivalent method) oe
dM1 sale price = 24 - 6 = 18, dependent on correct 25% found
A1 cso; correct conclusion that she has enough money, since 18 is less than 20 (with £2 left over)
Answer: Yes, the boxed set costs £18 in the sale, which is less than her £20, so she has enough money (with £2 left over)
Question 11
(a) B1 5 cao
(a) Answer: 5 books
(b) B1 33 cao
(b) Answer: 33 books
Question 12
M1 5 + 3 = 8 (total parts), 40 / 8 = 5 (value of one part) oe
dM1 girls = 5 x 5 = 25, boys = 3 x 5 = 15, dependent on correct value of one part
A1 10 cao
Answer: 10 more girls than boys
Question 13
M1 2 x 6.50 = 13.00 oe
M1 3 x 4.25 = 12.75 oe
A1 13.00 + 12.75 + 9.90 = £35.65 cao
Answer: £35.65
Question 14
M1 180 - 65 - 48 oe
A1 67 degrees cao
Answer: 67 degrees
Question 15
(a) B1 (6, 2) cao
(a) Answer: (6, 2)
(b) M1 shows understanding that reflecting in the x-axis keeps the x-coordinate and reverses the sign of the y-coordinate oe
(b) A1 ft (6, -2), ft their point B
(b) Answer: (6, -2)
Question 16
(a) B1 add 5 (each time) oe
(a) Answer: Add 5 to the previous term
(b) M1 nth term = 5n - 1, or repeated addition of 5 from the 4th term, oe
(b) A1 49 cao
(b) Answer: 49
Question 17
M1 converts both fractions to a common denominator of 12: 2 9/12 + 1 10/12 oe
M1 adds to give 3 19/12, dependent on correct common denominator