Kilsyth Academy
National 5 Maths
Revision Exercises
Booklet Number
National 5 Maths Mixed Revision Exercises
Ex 1
No Calculator for Q1
1
Work out –
a)
18·74 + 0·37 – 6·8
b)
5·76 × 70
c)
0·296 ÷ 8
d)
3
of 632 g
4
e)
1
2
2 3
8
5
f)
5% of £74
25 – 3x2y
2.
Evaluate
3
Sketch the line with equation
4
Solve –
a)
5
y = 5x – 2
3(2x – 5) + 4 = 5x + 17
b)
¼x – 7 = 3x + 2
Factorise –
a)
6
when x = 4 and y = –2
3a + 12b
b)
18x2 – 50y2
x + 2y = –3
Solve the system of equations:
3x + y = 1
7
p  ab
Change the subject of the formula to b.
8
Expand -
3(2x – 5)2
9
Find the gradient of the line joining the points (4,–1) and (3, –5)
10
A hi-fi is sold for £150.
This price includes VAT at 17·5%.
Calculate the price of the hi-fi without VAT.
11
These shapes are similar.
Work out x.
3m
8m
x
18 m
c)
6x2 + 7x – 10
National 5 Maths Mixed Revision Exercises
Ex 2
No Calculator for Q1
1
Work out –
2
a)
6·3 + 1·8 × 5 – 4
b)
0·04 ÷ 20
c)
2
4
6 3
7
5
d)
1
5
1 2
3
8
e)
7½% of £3200
f)
1 5
of  
4 9
Expand –
a) 10 – 4(2h – 3)
3
b) (5p + 2q)(p – 3q)
c) (x + 1)3
Factorise –
a) 6x2 – 18x
4
1

7
b) 4a2 – 36b2
c) 10y2 + y – 2
y = –2x – 1
Solve, using a substitution method -
y = 3x + 14
5
2x + 3y = –2
Solve, simultaneously -
4x + y = 1
6
Sketch a graph of the line with equation y = 4sinx + 1 for 0º ≤ x ≤ 360º
7
Find the equation of the line which passes through the points (4 , -8) and (0 , 2).
8
Find the area of this isosceles triangle.
18 cm
18 cm
12 cm
9
P = 3x2 – t.
10
The sales of a new childrens book over a two week period are given below.
Change the subject to x.
48
37
58
30
47
49
51
56
a)
Work out the median.
b)
Work out the Quartiles, Q1 and Q3.
c)
Work out the interquartile range.
d)
Show the information in a boxplot.
53
48
46
52
47
46
National 5 Maths Mixed Revision Exercises
Ex 3
1.
Work out the standard deviation for these numbers 2
3
4
4
5
7
9
10
2.
Expand -
3(2x – 1)(x + 3)
3.
Factorise -
2x2 + 7x – 4
4.
Work out the gradient of the line joining the points A(-2, 4) and B(5, -1).
5.
Sketch the graph of y = 2sinx for 0º ≤ x ≤ 360º.
6.
Solve the equation
7.
Factorise 9a2 – 25
8.
M = R2 t – 7
Change the subject of the formula to R.
9.
Solve algebraically the inequality
10.
Solve algebraically the system of equations
11.
Work out the length of BC in the triangle below.
4sinx + 1 = 0 for 0 < x ≤ 360.
2 + 5y ≥ 8y – 16
2p + 4q = -7
3p – 5q = 17
C
420 m
B
50º
500 m
A
12.
Write down the exact value of sin30º.
13.
Work out
1
3
3 1
4
5
National 5 Maths Mixed Revision Exercises
Ex 4
1.
Work out the standard deviation for these numbers 13, 20, 16, 24, 19, 16
2.
Work out the equation of the line joining the points P(-1, -1) and (0 , 3)
3.
Change the subject of the formula to t
f 
t n
p
4.
Sketch the graph of
5.
Solve algebraically the equation
6.
Solve the equation
for 0 ≤ x ≤ 360.
y = cos2xº
x2 – 6x = 0.
7cosxº - 2 = 0,
2x – 5x – 3
2
for 0 ≤ x ≤ 360.
7.
a) Factorise
b) Hence, simplify
8.
Solve the equation - 5x2 – 13x – 6 = 0
9.
Solve, algebraically, the system of equations -
10.
Solve the equation - x2 + 2x – 6 = 0
Give your answers correct to 2 significant figures.
11.
In the triangle below, work out the length of PR.
Q
24 cm
64º
R
68º
P
2 x 2  5x  3
x2  9
3x + 5y = 11
2x + 4y = 9
National 5 Maths Mixed Revision Exercises
Ex 5
5(2x + 3)2
1.
Expand -
2.
Write down the exact value of tan45º.
3.
Simplify -
4.
Solve, algebraically, the equation -
5.
Find the perimeter of this shape.
(Give your answer to 3 significant figures).
a)
4 p2q
8 pq 2 r
b)
x 2  2x
2x  4
3t2 – 5t – 2 = 0
110º
8∙2 m
5sinxº - 2 = 0 ,
for 0 ≤ x < 360.
6.
Solve, algebraically, the equation -
7.
Find the gradient of the line passing through the points (5 , -2) and (-3 , -1)
8.
If
9.
The data below shows the number of letters in a sample of 40 words from the new
Henry Trotter book.
f x  
2
,
x2
find
 1
f .
 2
8 , 2 , 4 , 3 , 1 , 4 , 10 , 6 , 4 , 4 , 3 , 7 , 3 , 3 , 4 , 6 , 2 , 6 , 2 , 3
5 , 4 , 7 , 2 , 4 , 2 , 3 , 3 , 1 , 7 , 7 , 6 , 1 , 3 , 6 , 3 , 5 , 1 , 4 , 11
a) Work out the quartiles Q1, Q2, and Q3.
b) Show this information in a boxplot.
c) Work out the semi-interquartile range.
National 5 Maths Mixed Revision Exercises
Ex 6
1.
Work out the standard deviation for these numbers –
12
2.
13
14
14
15
17
19
20
x + 2y = 0∙6
4x + 3y = 1∙3
Solve, algebraically, the system of equations y
3.
3
0
360
x
-3
The diagram shows the graph of y = ksinaxº, 0 ≤ x < 360.
Find the values of a and k.
x2 = 9x .
4.
Solve, algebraically, the equation -
5.
g(t) = 5t – 4t2
Find g(-2).
6.
Solve -
7.
The data below shows the takings (in pounds) over a fortnight, for Sugar’s Sweet
Shop.
6sinx° + 2 = 0
for 0 ≤ x < 360.
546, 283, 420, 692, 189, 364, 475, 263, 349, 731, 684, 319, 482, 353
Show this information in an ordered stem-and-leaf diagram.
(Remember to include a key!)
8.
Draw a sketch of the line with equation y = 2x  3.
Your sketch must indicate clearly the coordinates of 2 points on the line.
9.
Express as a single fraction in its simplest form
10.
1
1
 ,x  0
3x 5x
Solve, algebraically, the equation -
x2 = 10  3x
National 5 Maths Mixed Revision Exercises
y
Ex 7
1.
0∙5
0
360
x
-0∙5
The diagram shows the graph of y = acosbxº, 0 ≤ x < 360.
Find the values of a and b.
2.
Solve, algebraically, the equation -
3.
Express
33x  2
9x2  4
4x2  9 = 0
in its simplest form.
4.
The cylinder shown has radius 2·5 metres, and it’s
curved surface area is 84·5 square metres.
height
What height will the cylinder be?
2·5 m
5.
Work out the equation of the line which passes through the points (2, 1) and (0, 2).
6.
Sketch the graph of the function y = x2  2x  8
What is the minimum value of this function?
7.
h = k + 5√t
8.
Simplify –
9.
Solve, algebraically, the equation - 5 tanxº + 5 = 0
10.
Solve the following equation x2  4x + 2 = 0
(Give your answer to 2 decimal places).
11.
Given that f(p) = p2  4p, evaluate f(3).
for 4 ≤ x ≤ 6.
Change the subject of this formula to t.
c 2c 2

a
a3
for 0 ≤ x ≤ 180.
National 5 Maths Mixed Revision Exercises
Ex 8
1.
8·13 – 6
a)
2.
3.
4.
5.
6.
84
1
3

1
Evaluate –
b)
Solve the inequality 8 – 4x > 3(x + 2)
f(x) = 3x - 2x, evaluate f(-2)
2
Given that
xy
4

22
a) Factorise
b)
32Mpq

63
4
22


xy
Hence simplify
Change the subject of the formula to p.
On a ferry crossing, 3 vans and 2 cars cost £205, and 2 vans and 3 cars cost £195.
Find the cost for a car and for a van.
473


aa

4525
7.
Simplify -
8.
12810
6

An ant weighs approximately
kilograms.
A sparrow is 26 times heavier.
Calculate the weight of the sparrow, give your answer in scientific notation.
9.
10.
a)
b)
A laptop is sold for £850. This price includes VAT at 17·5%.
Calculate the price of the laptop without VAT.
2430

xx
2
Solve the equation
Give your answers correct to 1 decimal
place.
y
11.
0·6
0
A
The diagram shows part of the graph of y
= sinx°.
The line y = 0·6 is drawn and cuts the
graph of y = sinx° at A and B.
B
x
Find the x co-ordinates of A and B.
y = sinx°