Past Paper Questions: Geometry: 1
1 The scale of a map is 1 : 10 000 000.
On the map, the area of Slovakia is 4.9 cm2.
Calculate the actual area of Slovakia.
Give your answer in square kilometres.
................................................... km2 [3]
[Total: 3]
A, B and C are points on the circle, centre O.
Find the obtuse angle AOC.
Angle AOC = ................................................... [2]
[Total: 2]
2
The diagram shows a pyramid with a square base.
The triangular faces are congruent isosceles triangles.
(a) Write down the number of planes of symmetry of this pyramid.
................................................... [1]
(b) Using a ruler and compasses only, construct an accurate drawing of one of the triangular faces of the
pyramid.
[2]
[Total: 3]
3
The diagram shows two regular pentagons.
Pentagon FGHJK is an enlargement of pentagon ABCDE, centre O.
The area of pentagon FGHJK is 73.5 cm2.
The area of pentagon ABCDE is 6 cm2.
Find the ratio perimeter of pentagon FGHJK : perimeter of pentagon ABCDE in its simplest form.
.............................. : .............................. [2]
[Total: 2]
4
5 A model of a car has a scale 1 : 20.
The volume of the actual car is 12 m3.
Find the volume of the model.
Give your answer in cubic centimetres.
................................................... cm3 [3]
[Total: 3]
5
J, K, L and M are points on the circumference of a circle with diameter JL.
JL and KM intersect at N.
Angle JNK = 104° and angle MLJ = 22°.
Work out the value of d.
d = ................................................... [4]
[Total: 4]
6
ABC is an isosceles triangle.
BCD is a straight line.
Find the value of a.
a = ................................................... [2]
[Total: 2]
The points E, F and G lie on the circumference of a circle, centre O.
JGH is a tangent to the circle.
Find the value of x and the value of y.
x = ...................................................
y = ................................................... [2]
[Total: 2]
7
9 The scale drawing shows town A, town B and town C on a map.
There is a straight road between town A and town B.
The scale of the map is 1 centimetre represents 8 kilometres.
(a) Measure the bearing of town A from town B.
................................................... [1]
(b) Write the scale of the map in the form 1 : n.
1 : ................................................... [1]
(c) A straight road from town C is on a bearing of 246°.
It meets the road from town A to town B at point X.
On the map, draw the road from town C to point X.
Label the position of X.
[1]
8
(d) Josie is at point X at 10 50.
She arrives at town B 37 minutes later.
Work out the time that she arrives at town B.
................................................... [1]
[Total: 4]
10 Show that each interior angle of a regular pentagon is 108°.
[2]
[Total: 2]
11
The diagram shows a circle with diameter PQ.
SPT is a tangent to the circle at P.
Find the value of y.
y = ................................................... [5]
9
[Total: 5]
12
AC is parallel to FBD, ABC is an isosceles triangle and CBE is a straight line.
Find the value of x.
x = ................................................... [3]
[Total: 3]
13
The diagram shows a company logo made from a rectangle and a major sector of a circle.
10
The circle has centre O and radius OA.
OA = OD = 0.5 cm and AB = 1.5 cm.
E is a point on OC such that OE = 0.25 cm and angle OED = 90°.
(a) Calculate the perimeter of the logo.
................................................... cm [5]
(b) Calculate the area of the logo.
................................................... cm2 [3]
(c) A mathematically similar logo is drawn.
The area of this logo is 77.44 cm2.
(i) Calculate the radius of the major sector in this logo.
................................................... cm [3]
11
(ii) A gold model is made.
This model is a prism with a cross-section of area 77.44 cm2.
This gold model is 15 mm thick.
One cubic centimetre of gold has a mass of 19 grams.
Calculate the mass of the gold model in kilograms.
................................................... kg [3]
[Total: 14]
14
The diagram shows a circle, centre O.
AB and DE are chords of the circle.
M is the mid-point of AB and N is the mid-point of DE.
AB = DE = 9 cm and OM = 5 cm.
Find ON.
ON = ................................................... [1]
[Total: 1]
12
15
P, Q, R, S and T lie on the circle, centre O.
Angle PST = 75° and angle QTS = 85°.
Find the values of v, w, x and y.
v = ...................................................
w = ...................................................
x = ...................................................
y = ................................................... [6]
[Total: 6]
13
16 Two containers are mathematically similar.
The surface area of the larger container is 226 cm2 and the surface area of the smaller container is 94 cm2.
The volume of the larger container is 680 cm3.
Find the volume of the smaller container.
................................................... cm3 [3]
[Total: 3]
