National 5
N5 Expressions and
Formulae Unit Test
Preparation Booklet 1
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Exercise 1
Simplify, giving your answer in surd form:
(a)
(b)
(c)
(d)
(e)
(f)
Exercise 2
1. Simplify:
(a)
(b)
(c)
2. (a) There are 3.1 x
(d)
(e)
seconds in a solar year.
How many seconds are there in 5 solar years? Give your answer in scientific notation.
(b) The lotto jackpot of £8.4 x
was shared equally among 3 winners.
How much did each winner receive? Give your answer in standard form.
Exercise 3
1. Expand and simplify where appropriate:
(a)
(b)
(c)
(d)
(e)
Exercise 4
1. Factorise:
(a)
(b)
(c)
(f)
Exercise 5
1.
Express:
(a)
in the form
(b)
in the form
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–
(d)
(e)
Exercise 6
1. Write:
(a)
in its simplest form.
(b)
in its simplest form.
Exercise 7
1. Write each of the following as a single fraction:
(a)
(b)
(c)
(f)
(g)
(h)
(d)
(e)
Exercise 8
1. Each set of points represents a straight line.
Calculate the gradient of the lines joining AB and PQ:
(a) A(-2, 1) and B (1, 4)
(b) P (-4, 2) and Q (6, 4)
Exercise 9
1. Calculate the volume of a sphere with radius 14 cm, giving your answer correct to two
significant figures.
14cm
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Exercise 10
1. Calculate the length of the minor arc in the following diagrams:
(a)
(b)
110°
87°
20m
115cm
2. AB is a minor arc of the circle with centre O. The radius OB is 8cm. Angle AOB is
(a) Calculate the length of the minor arc AB in the following diagram:
O
135°
A
8cm
B
(b) The diagram above represents the base of a party hat.
A shop wants to decorate the base with a ribbon. They have 125 metres of ribbon in
stock. What is the maximum number of hats they can decorate from the 125 metres?
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Exercise 11
1. Calculate the volume of the cylinder:
5cm
9cm
2. Calculate the volume of the cone:
11cm
22cm
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3. On 12 July 1912, the battle of Largs was commemorated with the unveiling of a
newly built stone tower popularly known as "The Pencil". The Pencil is made up of a
cylindrical base with a conical roof.
The dimensions of the base and the roof are shown below:-
19m
2m
2.5m
2.5m
2m
2m
Calculate the total volume of the Pencil giving your answer to 3 significant figures.
(End of Question Paper)
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Answers
Exercise 1
(a)
(b)
(c)
(d)
(e)
(f)
Exercise 2
1.
(a)
(b)
2. (a) 1.55 x
(c)
(d)
(e)
(b) 2.8 x
Exercise 3
1. (a) 5
(b)
(c)
(d)
(e)
Exercise 4
1. (a)
(b)
(c)
(d)
(f)
Exercise 5
1. (a)
(b)
Exercise 6
1. (a)
(b)
Exercise 7
1. (a)
(b)
(c)
(d)
(e)
(f) 2 (g)
Exercise 8
1. (a) Mab = 1 (b) Mpq =
Exercise 9
1.
Exercise 10
1. (a) 174.6cm (b) 12.222...m
2. (a) 18.85cm (b) 663 hats
Exercise 11
1. 706.86
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2. 2787.63
3. 96.5
(h)
(e)