Write the ratio 3:5 as a fraction in its simplest form.
(Total for Question 1 is 1 mark)
2
Convert the ratio 2:7 into a fraction.
(Total for Question 2 is 1 mark)
3
A recipe uses ingredients in the ratio 4:1 (flour : sugar). What fraction of the mixture is sugar?
(Total for Question 3 is 1 mark)
4
Write the ratio 6:9 as a fraction in simplest form.
(Total for Question 4 is 2 marks)
5
The ratio of boys to girls in a class is 5:8. What fraction of the class are girls?
(Total for Question 5 is 2 marks)
6
A paint mix uses red : white in the ratio 7:3. Work out the fraction of the mix that is red and give the answer as a percentage.
(Total for Question 6 is 3 marks)
7
Write the relationship between x and y as a linear function y = kx when y is directly proportional to x with ratio 4:1 (y:x = 4:1). State the value of k.
(Total for Question 7 is 3 marks)
8
Priya mixes squash and water in the ratio 1:6 (squash : water). Let s be the amount of squash in litres and w the amount of water. Write w as a linear function of s in the form w = ks and give k.
(Total for Question 8 is 4 marks)
9
Sam and Erin split money in the ratio 3:2. If Sam receives x pounds, write an expression for the total amount of money T in pounds in terms of x.
(Total for Question 9 is 4 marks)
10
A map scale shows that 1 cm represents 3 km. Express the distance d in kilometres as a linear function of the map length m in centimetres in the form d = km. Give k.
(Total for Question 10 is 5 marks)
11
A gardener uses compost and soil in the ratio 2:5. If the gardener uses x kg of compost, show that the total mixture M in kg can be written as M = 7/2 x, then simplify this expression to a single decimal.
(Total for Question 11 is 6 marks)
12
Oliwia buys pens and pencils in the ratio 4:3. She spends 21 pounds in total. How much does one part represent, and how much did she spend on pens? Write your answer as a fraction of the total spent and as a decimal for the amount on pens.
(Total for Question 12 is 4 marks)
Mark scheme · 5.1F Writing a Ratio as a Fraction or Linear Function: Foundation Tier Practice
Question 1
B1 3/5 cao
Answer: 3/5
Question 2
B1 2/7 cao
Answer: 2/7
Question 3
B1 1/5 cao
Answer: 1/5
Question 4
M1 shows dividing both terms by common factor 3 or equivalent method
A1 2/3 cao
Answer: 2/3
Question 5
M1 writes fraction as 8/(5+8) or equivalent
A1 8/13 cao
Answer: 8/13
Question 6
M1 writes fraction 7/(7+3) or 7/10
A1 7/10 cao
A1 70% cao
Answer: 7/10 and 70%
Question 7
M1 recognises y/x = 4/1 so k = 4 or writes y = 4x
A1 y = 4x cao
B1 k = 4 stated explicitly
Answer: y = 4x, k = 4
Question 8
M1 uses ratio w/s = 6/1 or writes w = 6s
A1 w = 6s cao
B1 states k = 6
B1 units or variable consistent (litres) or equivalent statement
Answer: w = 6s, k = 6
Question 9
M1 recognises Sam's share is 3 parts so one part = x/3 or writes Erin = (2/3)x
M1 adds shares to form total T = x + (2/3)x or equivalent
A1 T = (5/3)x cao
B1 alternatively T = 5 * (x/3) and equivalent simplified form stated
Answer: T = (5/3)x
Question 10
M1 identifies ratio d:m = 3:1 or d = 3 m
M1 writes d = 3m with units
A1 d = 3m cao
B1 states k = 3
B1 units consistent: d in km when m in cm or equivalent
Answer: d = 3m, k = 3
Question 11
M1 uses ratio compost:soil = 2:5 so total parts = 7 and one part = x/2 (since compost is 2 parts = x)
M1 writes total mixture as M = 7 * (x/2) or equivalent
A1 shows M = 7/2 x cao
B1 correct explanation that total parts = 7 so total = 7 times one part, and one part = x/2, so M = 7 * x/2 oe
M1 converts 7/2 to a decimal: 7/2 = 3.5
A1 simplifies to M = 3.5x cao
Answer: M = 7/2 x = 3.5x
Question 12
M1 uses total parts 4 + 3 = 7 and finds one part = 21/7 = 3
A1 one part = 3 pounds cao
M1 calculates pens cost = 4 parts = 4 * 3 = 12
A1 pens cost 12 pounds and fraction 12/21 = 4/7 cao, decimal 12.00 or 12.0
Answer: One part = 3 pounds; spent on pens = 12 pounds, which is 12/21 = 4/7 of the total, amount 12.0 pounds