Sec 2 G2 Maths Ratio and proportion worksheet with answers

A free Sec 2 G2 Maths worksheet on ratio and proportion: 5 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 G2 Maths worksheet: Ratio and 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

$x$	$2$	$p$
$y$	$3$	$12$

y

is inversely proportional to the square of

x

. The table shows two pairs of values of

x

and

y

. Find the positive value of

p

Answer[3]

(a)

y

is inversely proportional to

x

. When

x = 4

y = 10

. Find the value of

y

when

x = 10

Answer (a)[3]

(b)

y

is inversely proportional to

x

. When

x = 2

y = 6

. Find the value of

x

when

y = 1

Answer (b)[3]

Section B

(a)A map is drawn to a scale of

1 : 40\,000

. Two towns are

4.2

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answer (a)km[2]

(b)

y

is directly proportional to

x

. When

x = 24

y = 32

. Find the value of

y

when

x = 6

Answer (b)[3]

(a)The plan of a house is drawn to a scale of

1 : 200

. A room is

1.6

cm long on the plan. Find the actual length, in metres, of the room.

Answer (a)m[2]

$x$	$4$	$6$	$8$	$10$
$y$	$6$	$9$	$13$	$15$

(b)The table shows some values of

x

and

y

. State whether

y

is directly proportional to

x

Answer (b)[3]

(c)

y

is directly proportional to the square root of

x

. Given that

y = 20

when

x = 100

, find the value of

x

when

y = 12

Answer (c)[3]

(a)A car travels 48 km on 3 litres of petrol. Find the distance it travels on 23 litres of petrol.

Answer (a)km[2]

(b)

y

is inversely proportional to

x

. When

x = 8

y = 3

. Find the value of

y

when

x = 24

Answer (b)[3]

(c)

y

is directly proportional to the cube of

x

. Given that

y = 1080

when

x = 6

, express

y

in terms of

x

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: So

p = 1

.[3]

y = \dfrac{k}{x^2}

3 = \dfrac{k}{(2)^2}

3 = \dfrac{k}{4}

k = 3 \times 4

= 12

y = \dfrac{12}{x^2}

12 = \dfrac{12}{x^2}

x^2 = \dfrac{12}{12}

= 1

x = \sqrt{1}

= 1

p = 1

Question 2

(a)Answer:

= 4

[3]

y = \dfrac{k}{x}

10 = \dfrac{k}{4}

k = 10 \times 4

= 40

y = \dfrac{40}{x}

y = \dfrac{40}{10}

= 4

(b)Answer:

= 12

[3]

y = \dfrac{k}{x}

6 = \dfrac{k}{2}

k = 6 \times 2

= 12

y = \dfrac{12}{x}

1 = \dfrac{12}{x}

x = \dfrac{12}{1}

= 12

Question 3

(a)Answer:

4.2\text{ cm} : 1.68\text{ km}

[2]

\mathstrut 1 : 40\,000

\mathstrut 1\text{ cm} : 40\,000\text{ cm}

1\text{ cm} : 0.4\text{ km}

\mathstrut 4.2\text{ cm} : 4.2 \times 0.4\text{ km}

4.2\text{ cm} : 1.68\text{ km}

(b)Answer:

= 8

[3]

y = kx

32 = k(24)

k = \dfrac{32}{24}

= \dfrac{4}{3}

y = \dfrac{4}{3}x

y = \dfrac{4}{3}(6)

= 8

Question 4

(a)Answer:

1.6\text{ cm} : 3.2\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 1.6\text{ cm} : 1.6 \times 2\text{ m}

1.6\text{ cm} : 3.2\text{ m}

(b)Answer: NO[3]

In direct proportion,

\dfrac{y}{x}

is the same for every pair.

\dfrac{6}{4} = 1.5

\dfrac{9}{6} = 1.5

\dfrac{13}{8} = 1.625

\dfrac{15}{10} = 1.5

\dfrac{y}{x}

is not the same for every pair, so

y

is not directly proportional to

x

(c)Answer:

= 36

[3]

y = k\sqrt{x}

20 = k\sqrt{100}

20 = 10k

k = \dfrac{20}{10}

= 2

y = 2\sqrt{x}

12 = 2\sqrt{x}

\sqrt{x} = \dfrac{12}{2}

= 6

x = 6^2

= 36

Question 5

(a)Answer: The distance is

368

km.[2]

\text{Distance for 1 litre} = \dfrac{48}{3}

= 16

\text{Distance for 23 litres} = 16 \times 23

= 368

The distance is

368

km.

(b)Answer:

= 1

[3]

y = \dfrac{k}{x}

3 = \dfrac{k}{8}

k = 3 \times 8

= 24

y = \dfrac{24}{x}

y = \dfrac{24}{24}

= 1

(c)Answer:

y = 5x^3

[3]

y = kx^3

1080 = k(6)^3

1080 = 216k

k = \dfrac{1080}{216}

= 5

y = 5x^3

Sec 2 G2 Maths Ratio and 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

p

y

3

12

Section B

(a)A map is drawn to a scale of

1 : 40\,000

. Two towns are

4.2

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answer (a)km[2]

(b)

y

is directly proportional to

x

. When

x = 24

y = 32

. Find the value of

y

when

x = 6

Answer (b)[3]

x

4

6

8

10

y

6

9

13

15

Answers and worked solutions

Question 1

Answer: So

p = 1

.[3]

y = \dfrac{k}{x^2}

3 = \dfrac{k}{(2)^2}

3 = \dfrac{k}{4}

k = 3 \times 4

= 12

y = \dfrac{12}{x^2}

12 = \dfrac{12}{x^2}

x^2 = \dfrac{12}{12}

= 1

x = \sqrt{1}

= 1

p = 1

Question 2

(a)Answer:

= 4

[3]

y = \dfrac{k}{x}

10 = \dfrac{k}{4}

k = 10 \times 4

= 40

y = \dfrac{40}{x}

y = \dfrac{40}{10}

= 4

(b)Answer:

= 12

[3]

y = \dfrac{k}{x}

6 = \dfrac{k}{2}

k = 6 \times 2

= 12

y = \dfrac{12}{x}

1 = \dfrac{12}{x}

x = \dfrac{12}{1}

= 12

Question 3

(a)Answer:

4.2\text{ cm} : 1.68\text{ km}

[2]

\mathstrut 1 : 40\,000

\mathstrut 1\text{ cm} : 40\,000\text{ cm}

1\text{ cm} : 0.4\text{ km}

\mathstrut 4.2\text{ cm} : 4.2 \times 0.4\text{ km}

4.2\text{ cm} : 1.68\text{ km}

(b)Answer:

= 8

[3]

y = kx

32 = k(24)

k = \dfrac{32}{24}

= \dfrac{4}{3}

y = \dfrac{4}{3}x

y = \dfrac{4}{3}(6)

= 8

Question 4

(a)Answer:

1.6\text{ cm} : 3.2\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 1.6\text{ cm} : 1.6 \times 2\text{ m}

1.6\text{ cm} : 3.2\text{ m}

(b)Answer: NO[3]

In direct proportion,

\dfrac{y}{x}

is the same for every pair.

\dfrac{6}{4} = 1.5

\dfrac{9}{6} = 1.5

\dfrac{13}{8} = 1.625

\dfrac{15}{10} = 1.5

\dfrac{y}{x}

is not the same for every pair, so

y

is not directly proportional to

x

(c)Answer:

= 36

[3]

y = k\sqrt{x}

20 = k\sqrt{100}

20 = 10k

k = \dfrac{20}{10}

= 2

y = 2\sqrt{x}

12 = 2\sqrt{x}

\sqrt{x} = \dfrac{12}{2}

= 6

x = 6^2

= 36

Question 5

(a)Answer: The distance is

368

km.[2]

\text{Distance for 1 litre} = \dfrac{48}{3}

= 16

\text{Distance for 23 litres} = 16 \times 23

= 368

The distance is

368

km.

(b)Answer:

= 1

[3]

y = \dfrac{k}{x}

3 = \dfrac{k}{8}

k = 3 \times 8

= 24

y = \dfrac{24}{x}

y = \dfrac{24}{24}

= 1

(c)Answer:

y = 5x^3

[3]

y = kx^3

1080 = k(6)^3

1080 = 216k

k = \dfrac{1080}{216}

= 5

y = 5x^3