Amelia has 3,425 ml of paint. She pours 275 ml into one pot and 450 ml into another. She then uses the rest to fill small bottles of 125 ml each. How many full small bottles can she fill? Show your working.
(3)
2
A school orders 48 boxes of pencils. Each box holds 24 pencils. The pencils are packed into pencil cases that hold 12 pencils each. How many pencil cases are needed to hold all the pencils?
(2)
3
Callum buys 3 games that cost 7.95, 12.50 and 4.60 pounds. He pays with a 50 pound note. How much change does he get? Show working in pounds and pence.
(3)
4
A baker makes 72 cupcakes. She packs them into boxes with 6 cupcakes in each box. After packing, she sells 7 boxes. How many cupcakes are left unpacked or unsold?
(3)
5
Priya has eight 250 g bars of chocolate and three 120 g bars. She melts all the chocolate and pours it into 100 g moulds. How many full moulds can she fill?
(2)
6
Explain your answer. Yusuf says that doubling 3.75 gives 7.5 and then adding 1.25 gives 8.75. He uses this to find 3.75 x 2.5. Is Yusuf correct? Explain your answer.
(3)
7
A museum sells tickets at 6.80 pounds for children and 9.50 pounds for adults. On one day they sell 42 child tickets and some adult tickets. The total takings are 618.10 pounds. How many adult tickets were sold?
(3)
8
A recipe needs 2 3/4 cups of flour to make 12 scones. How much flour is needed to make 20 scones? Give your answer as a mixed number in cups.
(2)
9
Order these numbers from smallest to largest: 0.208, 208/1000, 0.28
(2)
10
A garden centre sells bags of soil in 25 kg sacks. A landscaper needs 7.5 tonnes of soil. How many full 25 kg sacks should they buy? Show full working.
(3)
11
A bus journey takes 2 hours 45 minutes. If a driver completes 5 such journeys in a week, how many minutes does the driver spend driving on those journeys?
(2)
12
Sofia reads 64 pages in 80 minutes. At that rate, how many pages will she read in 3 hours 20 minutes? Show working.
(2)
13
A shop reduces the price of a jacket by 15%. The original price is 84 pounds. What is the sale price? Show your working.
(3)
14
Complete the function machine. Input 24 gives output 6. Input 40 gives output 10. What is the rule of the function? Show the operation.
(2)
15
A charity collected 1,275 stamps. They pack them into envelopes with 15 stamps in each. They want to share the envelopes equally between 7 schools. How many envelopes will each school get and how many stamps are left over (not in envelopes)?
(2)
16
Multiply 3,206 by 4. Then subtract 1,078. Show your working and give the answer.
(2)
17
A cyclist travels 18.4 km in 55 minutes. What is the average speed in km per hour, to one decimal place? Show your working.
(2)
18
Explain your answer. Two different methods are given to calculate 7/10 of 350. Method A: 350 ÷ 10 = 35, then 35 x 7 = 245. Method B: 350 x 0.7 = 245. Are both methods correct and why? Give a clear explanation.
(3)
19
There are 4 shelves. Each shelf holds 18 boxes. Each box contains 9 tins. How many tins are there in total? Then find the total if one shelf is removed and replaced with two extra shelves of the same size (so number of shelves changes by +1).
(2)
20
Oliwia buys 3 packs of notebooks. Each pack has 14 notebooks. She wants to share them equally between 5 friends. How many notebooks does each friend get and how many are left over?
(2)
Mark scheme · KS2.M-Y5R1 Reasoning: Number and Calculation
Question 1
M1 Correct subtraction to find remaining paint: 3,425 - 275 - 450 = 2,700 ml
B2 Division of remainder by 125 gives 21 full bottles (21 cao)
M1 Find flour per scone: 2 3/4 = 11/4 cups; 11/4 ÷ 12 = 11/48 cups per scone
B1 Multiply by 20: 11/48 x 20 = 220/48 = 55/12 = 4 7/12 cups cao
Answer: 4 7/12
Question 9
M1 Convert or compare decimals/fractions correctly, noting 208/1000 = 0.208
B1 States that 0.208 and 208/1000 are equal, with 0.28 the largest cao
Answer: 0.208 = 208/1000 (equal, smallest), then 0.28 (largest)
Question 10
M1 Convert tonnes to kg: 7.5 t = 7,500 kg
B2 Sacks needed 7,500 / 25 = 300 cao
Answer: 300 sacks
Question 11
M1 Convert 2 hours 45 minutes to minutes: 2 x 60 + 45 = 165 minutes
B1 Total for 5 journeys 165 x 5 = 825 minutes cao
Answer: 825 minutes
Question 12
M1 Find pages per minute: 64/80 = 0.8 pages per minute or 4/5
B1 Convert 3 h 20 min to 200 minutes and multiply: 0.8 x 200 = 160 pages cao
Answer: 160 pages
Question 13
M1 Correct calculation of 15% of 84 = 0.15 x 84 = 12.6 or 12.60
B2 Sale price 84 - 12.60 = 71.40 cao
Answer: 71.40
Question 14
M1 Recognises operation needed: dividing both inputs by 4 gives outputs
B1 Rule is divide by 4 or 'divide by 4' cao
Answer: Divide by 4
Question 15
M1 Envelopes made: 1,275 / 15 = 85 envelopes
B1 Each school gets 85 / 7 = 12 envelopes each with 1 envelope left over; stamps left not in envelopes = 0 because all stamps put in envelopes, so answer: 12 each, 0 stamps left cao
Answer: 12 envelopes each, 0 stamps left
Question 16
M1 Correct multiplication 3,206 x 4 = 12,824
B1 Correct subtraction 12,824 - 1,078 = 11,746 cao
Answer: 11,746
Question 17
M1 Convert 55 minutes to hours: 55/60 = 11/12 hours and set up speed = 18.4 / (11/12)
B1 Correct speed = 18.4 x 12/11 = 20.0727... so 20.1 km/h to one decimal place cao
Answer: 20.1 km/h
Question 18
M1 Recognises both methods find same value and are equivalent
B2 Clear explanation linking fraction and decimal: 7/10 = 0.7 so both give 245, with correct reasoning cao
Answer: Both are correct. 7/10 = 0.7 so 350 x 7/10 = 350 x 0.7 = 245
Question 19
M1 Total initially 4 x 18 x 9 = 648 tins
B1 After change shelves = 4 - 1 + 2 = 5 so 5 x 18 x 9 = 810 tins cao
Answer: Initially 648, then 810
Question 20
M1 Total notebooks 3 x 14 = 42
B1 Each friend gets 42 ÷ 5 = 8 with 2 left over (8 and 2 cao)