GCSE Revision
The following pages consist of a variety of different questions on different topics that we have studied this year.
I recommend you choose a few questions from each section to practice and revise.
Do not do all the questions, they will take up all of your free time.
The questions are provided so each of you can choose questions to suit your own needs.
Examples Problems
Mixed geometry questions
(angle facts, area of a triangle, Pythagoras’ theorem, trigonometry, sine rule and cosine rule, similarity)
1.
[pic]
XY = 3.2 cm.
XZ = 1.7 cm.
Calculate the length of YZ.
Give your answer correct to 3 significant figures.
…………………………. cm
(Total 3 marks)
2.
[pic]
AC = 12 cm.
Angle ABC = 90°.
Angle ACB = 32°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
................................. cm
(Total 3 marks)
3.
[pic][pic]
BEG and CFG are straight lines.
ABC is parallel to DEF.
Angle ABE = 48°.
Angle BCF = 30°.
(a) (i) Write down the size of the angle marked x.
x = ...................°
(ii) Give a reason for your answer.
...........................................................................................................................
(2)
(b) (i) Write down the size of the angle marked y.
y = ...................°
(ii) Give a reason for your answer.
...........................................................................................................................
(2)
(Total 4 marks)
4.
[pic]
BE is parallel to CD.
AB = 9 cm, BC = 3 cm, CD = 7 cm, AE = 6 cm.
(a) Calculate the length of BE.
………………… cm
(2)
(b) Calculate the length of DE.
………………… cm
(2)
(Total 4 marks)
5.
[pic]
BC = 8.5 cm.
Angle ABC = 90°.
Angle ACB = 38°.
Work out the length of AC.
Give your answer correct to 3 significant figures.
......................... cm
(Total 3 marks)
6.
[pic]
AC = 7 cm,
BC = 10 cm,
Angle ACB = 73°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
……………………. cm
(Total 3 marks)
7.
[pic]
AB = 2.3 cm.
BC = 5.4 cm.
Angle BAC = 90°.
Work out the size of angle ABC.
Give your answer correct to 3 significant figures.
.....................................°
(Total 3 marks)
8.
[pic]
AB = 12 m.
AC = 10 m.
BC = 15 m.
Calculate the size of angle BAC.
Give your answer correct to one decimal place.
................................°
(Total 3 marks)
9. The diagram represents a vertical flagpole, AB.
The flagpole is supported by two ropes, BC and BD, fixed to the horizontal ground at C and at D.
[pic]
AB = 12.8 m.
AC = 6.8 m.
Angle BDA = 42°.
(a) Calculate the length of rope BC.
Give your answer correct to 3 significant figures.
………………………… m
(3)
(b) Calculate the length of the rope BD.
Give your answer correct to 3 significant figures.
………………………… m
(3)
(c) Calculate the size of angle BCA.
Give your answer correct to 3 significant figures.
…………………………°
(3)
(Total 9 marks)
10.
[pic]
ABC is a straight line and BD = CD.
(a) Work out the size of angle x.
....................................º
(2)
(b) Work out the size of angle y.
....................................º
(3)
(Total 5 marks)
11.
[pic]
AB is parallel to XY.
The lines AY and BX intersect at P.
AB = 6 cm.
XP = 12.5 cm.
XY = 15 cm.
Work out the length of BP.
............................ cm
(Total 3 marks)
12.
[pic]
Work out the area of triangle ABC.
………………. cm2
(Total 2 marks)
13.
[pic]
AB = 8 cm, BC = 14 cm
Angle ABC = 106[pic]
Calculate the area of the triangle.
Give your answer correct to 3 significant figures.
………………..cm2
(Total 3 marks)
14.
[pic]
AB = 7 cm, BC = 8 cm.
Work out the area of the triangle.
............................ cm2
(Total 2 marks)
15.
[pic]
AC = 12.6 cm.
BC = 4.7 cm.
Angle ABC = 90°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
………………….. cm
(Total 3 marks)
16.
[pic]
AC = 8 cm,
BC =15 cm,
Angle ACB = 70°.
(a) Calculate the length of AB.
Give your answer correct to 3 significant figures.
................................ cm
(3)
(b) Calculate the size of angle BAC.
Give your answer correct to 1 decimal place.
...................................°
(2)
(Total 5 marks)
17.
[pic]
ABCD is a trapezium.
AD is parallel to BC.
Angle A = angle B = 90°.
AD = 2.1 m,
AB = 1.9 m,
CD = 3.2 m.
Work out the length of BC.
Give your answer correct to one decimal place.
………………………… m
(Total 4 marks)
18.
[pic]
ABCD is a trapezium.
AD is parallel to BC.
Angle C = angle D = 90°.
Angle B = 50°.
AD = 5.8 cm.
AB = 4.3 cm.
Calculate the length of BC.
Give your answer correct to one decimal place.
............................... cm
(Total 4 marks)
-----------------------
1. Find angle A.
[pic]
2. Find angle Z.
[pic]
3. Find angle C.
[pic]
1. Find angle C.
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AB is Opposite C. BC is Adjacent C.
Tan C = 8/11 C = Tan -1(8/11) = 36.0°
2. Find angle P.
[pic]
QR is Opposite P. PR is the Hypotenuse.
Sin P = 15/19 P = Sin -1(15/19) = 52.1°
3. Find angle R.
[pic]
QR is Adjacent R. PR is the Hypotenuse.
Cos R = 15/19 R = Cos -1(15/19) = 37.9°
1. B
A [pic]C
AB = 3m Angle ACB = 25°
Find AC.
2. B
A[pic]C
BC = 5.2 Angle ACB = 33°
Find AB.
3. . B
A[pic]C
BC = 5.8 Angle ABC = 73°
Find AB.
1. Find side AB.
[pic]
AB is the Adjacent. AC is the Hypotenuse.
AB = Cos 41 × 12.6 = 9.51m
2. A ladder makes an angle of 60° with the ground. The base of the ladder is 2.5 metres from the wall. How long is the ladder?
Length of ladder is Hypotenuse.
Base length is Adjacent.
Ladder = 2.5 ÷ cos 60 = 5 metres
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