Name: ___________________________

GCSE (1 – 9)

Pythagoras

Instructions

• Use black ink or ball-point pen.

• Answer all Questions.
• Answer the Questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.

Information

• The marks for each Question are shown in brackets

– use this as a guide as to how much time to spend on each Question.

Advice

• Read each Question carefully before you start to answer it.

• Keep an eye on the time.
• Try to answer every Question.
• Check your answers if you have time at the end

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1
A 4.8 cm B

3.6 cm

C
Calculate the length of AC.

…......................................cm
(Total for question 1 is 3 marks)

2
A B

6.75 cm 17.55 cm

C
Calculate the length of AB.

…......................................cm
(Total for question 2 is 3 marks)
3 A

14 cm
6 cm

B C

Calculate the length of BC.

Give your answer to 1 decimal place.

…......................................cm
(Total for question 3 is 3 marks)

4 A

4.2 cm

B C
5.6 cm

Calculate the length of AC.

…......................................cm
(Total for question 4 is 3 marks)
 C 10 m
5 Calculate the length of the AD. B D
Give your answer to 3 significant figures.
19 m

B 14 m A

…......................................m
(Total for question 5 is 4 marks)

B
6 Calculate the length of the AB.
Give your answer to 3 significant figures.

9.5 cm

A C

4 cm
7 cm

…......................................cm
(Total for question 5 is 4 marks)
7 A 17 cm B

8 cm

D C

ABCD is a rectangle .
Calculate the length of the diagonal AC.

Give your answer correct to 1 decimal place.

…......................................cm
(Total for question 7 is 3 marks)

8 ABCD is a trapezium. A 15 cm B
Calculate the length of BC.

12 cm
C

17 cm

…......................................cm
(Total for question 8 is 3 marks)
 A
9 ABC is an isosceles triangle.

Calculate the perpendicular height of ABC.

Give your answer correct to 3 significant figures..
10 cm

C B
8 cm

…......................................cm
(Total for question 9 is 3 marks)

C
10 ABCD is a trapezium.
13 cm
Calculate the length of AC.
Give your answer correct to 3 significant figures..
B 8 cm

3 cm

A D

…......................................cm
(Total for question 10 is 4 marks)
11 A ship leaves point A and sails for 3.7 km due North.
The ship then sails for 2.4 km due East to reach point B.

Calculate the the shortest distance between point A and point B.

Give your answer correct to 1 decimal place.

.................................................km
(Total for question 11 is 3 marks)

12 A ladder reaches 2.5 m up a vertical wall.

The base of the ladder is 70 cm from the base of the wall on a horizontal ground.

Find the length of the ladder.

.................................................
(Total for question 12 is 4 marks)
 A B
13 ABCD is a square.
The diagonal of the square is 8 m.

Calculate the perimeter of the square.

Give your answer correct to one decimal place.
8m

D C

…......................................m
(Total for question 13 is 3 marks)

14 A television has a diagonal length of 50 inches.

The ratio of the length of the television to the width of the television is 4:3

Calculate the length and the width of the television.

Give your answers correct to 1 decimal place.

Length …...................................… inches

Width …...................................... inches

(Total for question 14 is 3 marks)