Sec 2 G1 Maths Direct and inverse proportion worksheet with answers

A free Sec 2 G1 Maths worksheet on direct and inverse proportion: 6 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 2 G1 Maths worksheet: Direct and inverse proportion

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

y

is directly proportional to

x

. When

x = 3

y = 6

. Find the value of

y

when

x = 6

Answer[3]

(a)To bake 5 cakes, a baker needs 300 g of sugar. Find the mass of sugar needed to bake 9 cakes.

Answer (a)g[2]

(b)

y

is directly proportional to

x

. When

x = 15

y = 20

. Find the value of

y

when

x = 33

Answer (b)[3]

(a)A cyclist travelling at an average speed of 16 km/h takes 2 hours for a journey. Find the average speed needed to make the same journey in 4 hours.

Answer (a)km/h[2]

(b)

y

is inversely proportional to

x

. When

x = 4

y = 4

. Find the value of

y

when

x = 2

Answer (b)[3]

(a)7 identical taps fill a tank in 10 minutes. Find the time, in minutes, that 14 of these taps would take to fill the tank.

Answer (a)minutes[2]

(b)

y

is inversely proportional to

x

. When

x = 7

y = 11

. Find the value of

y

when

x = 11

Answer (b)[3]

Section B

(a)2 pumps can empty a swimming pool in 18 hours. Find the number of pumps needed to empty the pool in 6 hours.

Answer (a)pumps[2]

$x$	$2$	$5$	$8$	$11$
$y$	$24$	$60$	$96$	$132$

(b)The table shows some values of

x

and

y

. State whether

y

is directly proportional to

x

Answer (b)[3]

(a)A cyclist travelling at an average speed of 20 km/h takes 48 minutes for a journey. Find the time, in minutes, that the same journey would take at an average speed of 15 km/h.

Answer (a)minutes[2]

(b)(i)A car travels 75 km on 5 litres of petrol. Find the distance it travels on 22 litres of petrol.

Answer (b)(i)km[2]

(b)(ii)

y

is directly proportional to

x

. When

x = 2

y = 12

. Find the value of

y

when

x = 8

Answer (b)(ii)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 12

[3]

y = kx

6 = k(3)

k = \dfrac{6}{3}

= 2

y = 2x

y = 2(6)

= 12

Question 2

(a)Answer: The mass of sugar is

540

g.[2]

\text{Mass of sugar for 1 cake} = \dfrac{300}{5}

= 60

\text{Mass of sugar for 9 cakes} = 60 \times 9

= 540

The mass of sugar is

540

(b)Answer:

= 44

[3]

y = kx

20 = k(15)

k = \dfrac{20}{15}

= \dfrac{4}{3}

y = \dfrac{4}{3}x

y = \dfrac{4}{3}(33)

= 44

Question 3

(a)Answer:

= 8

km/h[2]

\text{Distance} = 16 \times 2

= 32

\text{Speed} = 32 \div 4

= 8

km/h

(b)Answer:

= 8

[3]

y = \dfrac{k}{x}

4 = \dfrac{k}{4}

k = 4 \times 4

= 16

y = \dfrac{16}{x}

y = \dfrac{16}{2}

= 8

Question 4

(a)Answer:

= 5

minutes[2]

\text{1 tap} \to 7 \times 10

= 70

minutes

\text{Number of minutes} = \dfrac{70}{14}

= 5

minutes

(b)Answer:

= 7

[3]

y = \dfrac{k}{x}

11 = \dfrac{k}{7}

k = 11 \times 7

= 77

y = \dfrac{77}{x}

y = \dfrac{77}{11}

= 7

Question 5

(a)Answer:

= 6

pumps[2]

\text{1 pump} \to 2 \times 18

= 36

hours

\text{Number of pumps} = \dfrac{36}{6}

= 6

pumps

(b)Answer: YES[3]

In direct proportion,

\dfrac{y}{x}

is the same for every pair.

\dfrac{24}{2} = 12

\dfrac{60}{5} = 12

\dfrac{96}{8} = 12

\dfrac{132}{11} = 12

\dfrac{y}{x}

is the same for every pair, so

y

is directly proportional to

x

Question 6

(a)Answer:

= 64

minutes[2]

\text{Distance} = 20 \times \dfrac{48}{60}

= 16

\text{Time} = \dfrac{16}{15} \times 60

= 64

minutes

(b)(i)Answer: The distance is

330

km.[2]

\text{Distance for 1 litre} = \dfrac{75}{5}

= 15

\text{Distance for 22 litres} = 15 \times 22

= 330

The distance is

330

km.

(b)(ii)Answer:

= 48

[3]

y = kx

12 = k(2)

k = \dfrac{12}{2}

= 6

y = 6x

y = 6(8)

= 48

Sec 2 G1 Maths Direct and inverse proportion worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

x

2

5

8

11

y

24

60

96

132

Answers and worked solutions

Question 1

Answer:

= 12

[3]

y = kx

6 = k(3)

k = \dfrac{6}{3}

= 2

y = 2x

y = 2(6)

= 12

Question 2

(a)Answer: The mass of sugar is

540

g.[2]

\text{Mass of sugar for 1 cake} = \dfrac{300}{5}

= 60

\text{Mass of sugar for 9 cakes} = 60 \times 9

= 540

The mass of sugar is

540

(b)Answer:

= 44

[3]

y = kx

20 = k(15)

k = \dfrac{20}{15}

= \dfrac{4}{3}

y = \dfrac{4}{3}x

y = \dfrac{4}{3}(33)

= 44

Question 3

(a)Answer:

= 8

km/h[2]

\text{Distance} = 16 \times 2

= 32

\text{Speed} = 32 \div 4

= 8

km/h

(b)Answer:

= 8

[3]

y = \dfrac{k}{x}

4 = \dfrac{k}{4}

k = 4 \times 4

= 16

y = \dfrac{16}{x}

y = \dfrac{16}{2}

= 8

Question 4

(a)Answer:

= 5

minutes[2]

\text{1 tap} \to 7 \times 10

= 70

minutes

\text{Number of minutes} = \dfrac{70}{14}

= 5

minutes

(b)Answer:

= 7

[3]

y = \dfrac{k}{x}

11 = \dfrac{k}{7}

k = 11 \times 7

= 77

y = \dfrac{77}{x}

y = \dfrac{77}{11}

= 7

Question 5

(a)Answer:

= 6

pumps[2]

\text{1 pump} \to 2 \times 18

= 36

hours

\text{Number of pumps} = \dfrac{36}{6}

= 6

pumps

(b)Answer: YES[3]

In direct proportion,

\dfrac{y}{x}

is the same for every pair.

\dfrac{24}{2} = 12

\dfrac{60}{5} = 12

\dfrac{96}{8} = 12

\dfrac{132}{11} = 12

\dfrac{y}{x}

is the same for every pair, so

y

is directly proportional to

x

Question 6

(a)Answer:

= 64

minutes[2]

\text{Distance} = 20 \times \dfrac{48}{60}

= 16

\text{Time} = \dfrac{16}{15} \times 60

= 64

minutes

(b)(i)Answer: The distance is

330

km.[2]

\text{Distance for 1 litre} = \dfrac{75}{5}

= 15

\text{Distance for 22 litres} = 15 \times 22

= 330

The distance is

330

km.

(b)(ii)Answer:

= 48

[3]

y = kx

12 = k(2)

k = \dfrac{12}{2}

= 6

y = 6x

y = 6(8)

= 48