St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 1
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
©Julie Rocks 2003
1
3
3 1
4
5
St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 2
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
for 0 ≤ x ≤ 360.
4.
Sketch the graph of
y = cos2xº
5.
Solve algebraically the equation
6.
Solve the equation
7.
a) Factorise
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.
x2 – 6x = 0.
7cosxº - 2 = 0,
2x2 – 5x – 3
b) Hence, simplify
Q
24 cm
64º
R
68º
P
©Julie Rocks 2003
for 0 ≤ x ≤ 360.
2 x 2  5x  3
x2  9
3x + 5y = 11
2x + 4y = 9
St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 3
5(2x + 3)2
1.
Expand -
2.
Write down the exact value of tan45º.
a)
4 p2q
8 pq 2 r
3.
Simplify -
b)
4.
Solve, algebraically, the equation -
5.
Find the perimeter of this shape.
(Give your answer to 3 significant figures).
x 2  2x
2x  4
3t2 – 5t – 2 = 0
110º
8∙2 m
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
5sinxº - 2 = 0 ,
for 0 ≤ x < 360.
6.
 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.
©Julie Rocks 2003
St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 4
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
1
1
 ,x  0
3x 5x
10.
Solve, algebraically, the equation -
11.
Work out -
©Julie Rocks 2003
2
1
1
1
4
2
x2 = 10  3x
St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 5
y
1.
0∙5
0
x
360
-0∙5
The diagram shows the graph of y = acosbxº, 0 ≤ x < 360.
Find the values of a and b.
4x2  9 = 0
2.
Solve, algebraically, the equation -
3.
Express
4.
Construct a dot plot to represent the following information about shoe sizes of the pupils in a first year
class.
Shoe size
Number
33x  2
9x 2  4
3
2
in its simplest form.
3½
0
4
6
4½
8
5
9
5½
7
Describe the distribution of the dot plot.
5.
Work out the equation of the line which passes through the points -
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).
©Julie Rocks 2003
(2, 1) and (0, 2).
for 4 ≤ x ≤ 6.
Change the subject of this formula to t.
c 2c 2

a
a3
for 0 ≤ x ≤ 180.
6
5
St Andrew’s High School
Maths Department
S4 National 5 Mixed Home Exercise 6
No calculator for Q1-7
1.
Evaluate –
8·13 – 6
a)
1 83  14
b)
2.
Solve the inequality 8 – 4x > 3(x + 2)
3.
Given that
4.
a) Factorise
5.
M  32  p  q  Change the subject of the formula to p.
6.
Two functions are given below.
f(x) = x2 + 5x – 7
g(x) = –2x + 1
Find the values of x for which f(x) = g(x).
7.
Simplify -
8.
An ant weighs approximately 1  28  10 6 kilograms.
A sparrow is 26 times heavier.
Calculate the weight of the sparrow, give your answer in scientific notation.
9.
A laptop is sold for £850. This price includes VAT at 17·5%.
Calculate the price of the laptop without VAT.
10.
Solve the equation
f(x) = 3x 2 - 2x, evaluate f(-2)
4x 2  y 2
a)
b)
45  2 5
b)
2 x2  4 x  3  0
4 x2  y 2
6x  3 y
Hence simplify
a 7   a 3 
4
Give your answers correct to 1 decimal place.
y
11.
0·6 A
The diagram shows part of the graph of y = sinx°.
B
The line y = 0·6 is drawn and cuts the graph of
y = sinx° at A and B.
x
0
Find the x co-ordinates of A and B.
y = sinx°
12.
A table of pairs of values of x and y is shown below.
x 1·5 2
2·5
y 6
4·5 3·6
a)
b)
Explain why y varies inversely as x.
Write down the formula connecting x and y.
©Julie Rocks 2003