Test on Chapter 1 [57 marks]
1. [Maximum mark: 7]
A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35
cm and a height of 0.5 cm.
(a) Calculate the volume of this pan. [3]
A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a
sphere.
(b) Find the radius of the sphere in cm, correct to one decimal place. [4]
2. [Maximum mark: 2]
Two towns A and B are located close to each other as shown in the diagram.
Find the bearing of town B from town A.
3. [Maximum mark: 4]
Find the angle .
4. [Maximum mark: 2]
cos+sin
Let = √ 2 −
,
where = 36∘ , = 18∘ , = 9 and = 1.8.
Find and answer in the form × 10 , where 1 ≤ < 10, ∈ ℤ.
5. [Maximum mark: 5]
In triangle ABC, AB = 5, BC = 14 and AC = 11.
Find all the interior angles of the triangle. Give your answers in degrees to one decimal
place.
6. [Maximum mark: 1]
Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and
BP, are attached to the same point, P, on the base of a hot air balloon which is vertically
above the line AB. The length of BP is 30 m and angle BAP is 48°.
On the diagram, draw and label with an x the angle of depression of B from P.
7. [Maximum mark: 6]
The following diagram shows quadrilateral ABCD.
∧ ∧ ∧
AB = 11 cm, BC = 6 cm, BAD = 59∘ , BDA = 100∘ and CBD = 82∘
(a) Find DB. [3]
(b) Find DC. [3]
8. [Maximum mark: 16] (slightly different numbers compared to the question in the book)
The diagrams represent the pyramid of Cheops. You are given that the vertical height
VB=146.62312 meters and the side of the square base EF=230.32561 meters. M is the
midpoint of [EF].
(a) Find all the sides and angles of the ∆ VBM. [4]
(b) Find all the sides and angles of ∆ VBF. [3]
(c) Find all the sides and angles of ∆ VEF and its area. [6]
(d) The Ancient Greek historian Herodotus claimed that the Cheops pyramid was
designed so that the square of its height was equal to the area of each of its faces.
Find the percentage error in the claim of Herodotus. [3]
9. [Maximum mark: 14]
The Tower of Pisa is well known worldwide for how it leans.
Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a
diagram showing a non-right triangle, ABC.
On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is
60°. AX is the perpendicular height from A to BC.
(a.i) Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning
relative to the horizontal, is 85° to the nearest degree. [5]
(a.ii) Use Giovanni's diagram to calculate the length of AX. [2]
(a.iii) Use Giovanni's diagram to find the length of BX, the horizontal displacement of the
Tower. [2]
Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX,
is 3.9 metres.
(b) Find the percentage error on Giovanni’s diagram. [2]
(a) Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is
formed.
Find the angle of elevation of A from D. [3]
