Mathematics
Department
Clyde Valley High School
1.
Calculate the volume of
the triangular prism shown in
the diagram.
Triangular
prism
11cm
12cm
10cm
2.
Simplify the expression (2x-3)(3x-2) – 6(x+1)2.
3.
Find the values of x which satisfy 3x + 1 ≥ x – 3 , where x is
a whole number.
4.
Find the equation of the straight
line shown in the diagram.
y
(0,2)
0
(4,0)
1
2
1
2
−1
2
5.
Remove the brackets and simplify 2x ( x − x ) .
6.
A function f(x) = 2x2 – 5. Find the values of
a) f(10)
b) f(-2)
If f(t) = 25, find the value of t.
x
Mathematics
Department
Clyde Valley High School
7.
V=340cm3
V
5cm
19cm
The two bevel shapes shown are similar.
Calculate the volume of the smaller shape.
8.
Solve the equation 5sinx + 4 = 0 , 0 ≤ x ≤ 360°.
9.
Solve the equation (x+3)(x+4) = x2 - 31
10. Write as a single fraction
2x + 1 x − 1
−
3
4
11. Solve the system of equations
xy = -2
x+y=1
12. The tables show the marks for pupils who sat a class test in
mathematics.
Calculate
a) The mean and standard deviation.
b) Work out the quartiles and draw a boxplot to represent
the data.
15 20 9 12 8
10 5 17 13 10
Mathematics
Department
Clyde Valley High School
13. For the seating arrangement shown below, copy and
complete the table.
Tables
People
1 table
1
2
3
4
5
2 tables
a) If there are n tables, how many people can be seated ?
b) How many people can be seated at 16 tables ?
c) If 232 people are seated, how many tables are used ?
14.
9cm
A
136cm2
15cm
The shapes shown are similar. Find area A.
15. The rectangle shown has an area of 73cm2. Make an equation
and solve it to find x. Hence state the length and the breadth
of the rectangle.
x
x+ 9
Mathematics
Department
Clyde Valley High School
16. The total number of visitors to an exhibition was 3.6 × 105.
The exhibition was open each day from 4th July to 5th
September inclusive. Calculate the average number of
visitors per day to the exhibition.
17. The diagram shows an arc AB
of a circle of radius 5.8cm.
The angle subtended at the
centre of the circle by
the arc is 74°.
Find
a) The length of arc AB.
b) The area of the sector.
A
74°
B
5.8cm
18. Express the algebraic fraction
x2 − 9
3x 2 − 7 x − 6
in its simplest form.
19. Simplify the expressions a) (3√2 – 5)(2√2 + 5) b) (5√2)3
20. Find the area of the shape shown
17cm
82°
11cm
13cm
72°
21cm