Mathematics
Department
Clyde Valley High School
1.
Solve the equation 5x(x+3) = (5x+2)(x+1)
2.
If f(x) = 5 – 3x – x2 , find f(-3).
3.
Find the equation of the straight line shown.
y
(0,3)
0
4.
(6,0)
x
Find x correct to 1 decimal place.
74°
5
x
5.
Expand the brackets (2x-3)(x2 – x – 3)
6.
The perimeter of the rectangle shown
95cm. Make an equation and find x.
x+4
3x+2
is
Mathematics
Department
Clyde Valley High School
7.
If M = 3.8(L+5), change the subject of the formula to L
and hence find L when M = 43.
8.
V = 108
V
7cm
12cm
The two shapes shown are similar.
Calculate the volume of the larger shape.
9.
29
x
21
13.3
37
Use similar triangles to find x.
10. Factorize fully a) 1 – x2
b) 2x2 – 11x + 12
c) 8x3 – 16x2
11. Solve the equations
5x – 2y = 6
2x + 3y = 10
Mathematics
Department
Clyde Valley High School
12. On square paper and on the same diagram draw the lines
y = 2x – 5 and y = 4 – x.
Determine the point where these lines meet.
13. After receiving a 5% pay rise a fireman now
receives £26000 per annum.
How much did he earn before the pay rise?
14. Find the gradient of the line joining the
points (-1,7) and (1,-10).
15.
y
y= 0.5x+3
A
0
x=5
x
Find the coordinates of point A in the diagram above.
16. The diagram shows a triangle inside a semi
circle. Find the sizes of all the sides and
angles of the large triangle.
7
6
Mathematics
Department
Clyde Valley High School
17. Solve the equation (x+3)2 = (x-1)2
18.
O
5
2.8
A
B
A circle centre O has a radius 5 cm. A chord AB is 2.8 cm from the
centre of the circle.
Find
a) The length of chord AB.
b) The size of angle AOB.
c) The length of the minor arc AB.
d) The area of sector AOB.
e) The area of triangle OAB.
d = 10cm
19.
13cm
9cm
50cm
The diagram shows four cylinders cut from a cuboid.
Calculate the volume of the shape.
Mathematics
Department
Clyde Valley High School
20. If f(x) = 2x3, find the values of f(4) and f(10).
If f(t) = 500, find the value of t.
21. A ship leaves a port and sails 80 km north. It then turns and sails 80
km west.
a) How far is the ship from the port?
b) What is the 3 figure bearing of the ship from the port?
c) What is the 3 figure bearing of the port from the ship?
22.
40m
23m
cows
goats
56m
sheep
pigs
84m
The diagram shows an arena at an agricultural show. The main arena
is rectangular in shape and this is split into areas for each of the
different animals. The goats region is an isosceles triangle.
a) Find the total length of fencing needed to make this arena.
b) What area in square metres is used for the sheep?