Mathematics
Department
Clyde Valley High School
1.
Solve the quadratic equation 2x2 – 6x + 1 = 0, giving your
answers correct to 2 decimal places.
2.
y
0
A
D
B
x
C
The diagram shows the graph of the quadratic y = x2 – 6x – 7.
The graph cuts the x axis at points A and B and the y axis at
point D. The quadratic has a minimum turning point at C.
Determine the coordinates of points A, B, C and D.
3.
Simplify the following
2 4
a) (3x )
3
b) 5x × 8x
4
12 y 7
c)
5y4
d) ( x 3 y 2 ) 5
4.
Solve the equation 8cosx – 7 = 0, 0 ≤ x ≤ 360°.
5.
y varies directly as the cube of x. If x is doubled, find the
effect on y.
6.
Factorize and solve
a) 3x2 + 7x = 0
b) 3x2 – 4x + 1 = 0
Mathematics
Department
Clyde Valley High School
7.
y varies inversely as the square of x.
Copy and complete the table.
x 3 3.5 4 4.5
y 4
8.
Show that there is a root of the equation y = 12 + x – x3
between x = 2 and x = 3. Find this root correct to 1 decimal
place.
9.
If f(x) = 8x evaluate
a) f(0)
2
3
b) f( )
c) f(-2)
10. The diagram shows a right angled
triangle with sides x, x+5 and x+7.
Make an equation and solve it to
find x correct to 1 decimal place.
x+7
x
x+5
11.
Cereal
A manufacturer claims that its breakfast cereal contains at
least 22% fruit. A 750 gm packet of the cereal was checked
and found to contain 172 gm of fruit.
What actual percentage of the cereal is fruit?
Mathematics
Department
Clyde Valley High School
12. Find the largest angle in the
triangle shown.
Hence find the area of the triangle.
5.8cm
4.6cm
5.2cm
13.
d = 8cm
9cm
13cm
28cm
The diagram shows three cylinders each of diameter 8cm and
height 9 cm, cut out of a cuboid. Calculate the volume of the
shape which remains.
Mathematics
Department
Clyde Valley High School
D
14.
4cm
A
3cm
C
B
The diagram shows a circle centre C and radius 3cm.
AD is a chord in the circle 4cm long.
a) Find the sizes of all the sides and angles of triangle ABD.
b) Calculate the area of triangle ADB.
15. The braking force F kilonewtons , required to stop a train
varies directly as the square of the speed, V km/hr and
inversely as its stopping distance S kilometers.
a) A train travelling at 160km/hr has a braking force of 140
kilonewtons applied to it. If it takes 1.2km to stop, find a
formula for F in terms of V and S.
b) Further down the track, the train driver sees a cow grazing
on the track. The cow is 0.6km away from the train when
the train is travelling at a speed of 100km/hr. If the driver
applies the brakes with a force of 210 kilonewtons will the
train stop before reaching the cow?
Mathematics
Department
Clyde Valley High School
16. The bearings and distances of two ships A and B from
Dundee are given by A[035°,98km] and B[162°, 78km].
Make a diagram and show clearly the positions of the two
ships. Calculate the distance between the ships. ( do not use a
scale drawing ).
17.
A
h
ground
The diagram shows 3 identical circles of radius 5cm.
Calculate the height of point A above the ground.