Mathematics
Department
Clyde Valley High School
1.
Solve the equation
2x − 3 x − 1 1
= , giving your answer
−
4
3
2
correct to 1 decimal place.
2.
4
5
If P = (T + 9) , change the subject of the formula to T.
Find T when P = 12.
3.
4.
Solve the trig. equation 3tanx-8 = 0 , 0 ≤ x ≤ 360°.
y
y=x2-5x
0
A
x
B
The diagram shows the graph of the quadratic y = x2 – 5x.
The graph has a minimum at point B and cuts the x axis at
point A. Determine the coordinates of points A and B.
5.
A function f is defined by f(x) = 2x3 – 5.
Determine the values of
a) f(-2)
b) f(10)
If f(t) = 34, find the value of t.
Mathematics
Department
Clyde Valley High School
6.
The diagram shows a regular hexagon
inside a circle of diameter 10cm.
Calculate
a) The area of the hexagon.
b) The area between the circle
and the hexagon.
7.
Solve the equation x(x-4) = 1, giving your answers correct
to 1 decimal place.
8.
AB is a diameter of a circle centre C.
D is a point on the circumference of
the circle. If BD=6cm and DC=5cm
calculate the values of
a) AD
Ah
b) angle DCB
c) Area of triangle DCB.
9.
D
h
5cm
6cm
h
C
hB
Simplify √80 - √45 + √20.
10. Simplify the expression
1
2
3
2
4 x × 3x
.
6 x −1
11. Calculate the shaded area A.
Hence or otherwise, find the volume
of the shape.
h
h h
h
h h
hh
28cm
h
h
hh
h h
h h
hh
9cm
A
22 cm
Mathematics
Department
Clyde Valley High School
12. The temperature of a liquid in °C is plotted against time t
(minutes).
a) Find an equation connecting T and t
b) Find T when t = 10.
c) How long does it take to reach a temperature of 96°C ?
T
18
(5, 30)
time t
13. Remove the brackets and simplify (2x+1)2(x-4).
14. An air company brings new aero planes into service. Each
new aero plane costs £1,345,000. An aero plane depreciates
by 24% each year. Find the value of a new aero plane in 3
years time.
15. The diagram shows a rhombus.
Calculate its area.
8cm
28°
8cm
Mathematics
Department
Clyde Valley High School
16. The tables show the marks for pupils who were taught
English and Mathematics. To compare the success rates in
teaching these two subjects the pupils sat a test in both. The
tests were marked out of 30. For each subject calculate
a) The mean and standard deviation.
b) Work out the quartiles and draw a boxplot to represent
each set of data.
English
17
25
23
12
23
15
18
19
15
Mathematics
26
23
5
17
28
8
19
12
14
Which subject do you think pupils did better in?
Sample Standard Deviation:
s=
∑ (x − x )2
n −1
where n is the sample size.
2
=
∑ x 2 − ( ∑ x)
n −1
/n
Mathematics
Department
Clyde Valley High School
17. A ladder 18m long rests over a wall 7m high.
The ladder makes an angle of 37° with the ground.
What length of the ladder hangs over the wall?
ladder
wall
ground
18. A motorist covers the first 50 miles of his journey at an
average speed of V mph and the next 70 miles at (V+10)
mph.
Show that the time taken for the whole journey is given by
T=
500 + 120V
V (V + 10)
Hence find an expression in terms of V for the average speed
over the whole journey.
19. We see that 4 × 6 = 24 and 8 × 10 = 80 .
Prove that the product of any two consecutive even numbers
is divisible by 8.
20. The volume of an ice cube is numerically equal to its total
surface area. What is the length of the side of the ice cube?