Mathematics
Department
Clyde Valley High School
1. Solve the inequation 3(x-8) ≤ 5x - 9
2. Remove the brackets a) (2x+1)(x2 – 6x – 5)
b) (x+2)(x-1)(x-3)
3. If f(x) = 3x , find a) f(4) b) f(1.5)
4. Solve the equation
5x
7
=
x−2 2
4
5
5. If T = ( M + 8) , change the subject of the formula to M and
hence find M if T = 33.
6. Solve the equations y = 2x + 3
2x + 3y = 25
7. If f(x) = 3 – 5x find
a) f(-2) b) f(0.5) c) f(10) d) If f(t) = -27 , find the value of t.
8. If t =
1
1
, v = , find the value of t2 – v2 giving your answer as
2
4
a vulgar fraction in its simplest form.
9. The diagram shows
two similar shapes.
Find the area of the
larger shape.
40cm2
A
8cm
11cm
Mathematics
Department
Clyde Valley High School
10. On square paper draw the line with equation y = 4 – 2x.
On the same diagram draw the line x = 6. Where do the two lines
meet?
11.
9cm
The larger bottle contains 2
6cm
1
litres of wine. The bottles are similar
2
in shape. How much wine does the smaller bottle hold?
12. If V = πr 2 h , change the subject of the formula to r and hence
find r when V = 1000 cm3 and h = 12cm.
13. For each line state the gradient and the intercept.
a) y = 3x – 7 b) y = 4 – 2x c) y = 1 + 2x
d) 2y – 5x – 1 = 0 e) 4y – x = 0
14. Factorize fully
a) 2x2 – 9x + 9 b) 4x3 – x
c) 8x2 + 16x
Mathematics
Department
Clyde Valley High School
15. The hours of sunshine recorded in each of 10 consecutive days
is shown in the table.
a) Make up a stem and leaf diagram.
b) Calculate the mean and standard deviation.
c) Find the quartiles.
d) Draw a boxplot.
5.8 3.6 7.4 6.2 3.2
4.7 6.5 5.2 5.5 5.7
16. Find the gradient of the line joining the points (-6,-2)
and (4,3).
17.
Calculate the area of the kite shown
in the diagram.
19cm
9cm
18. Expand the brackets (2x-5)(2x+5)(x+1)
Mathematics
Department
Clyde Valley High School
19. If sinx =
5
, and x is an acute angle, find the exact
13
value of cosx.
20. The diagram shows a large cube of side x.
A small cube whose sides are half the
size of the sides of the large cube sits on the top.
Find an expression in its simplest form for the
volume of the shape.
21. Consider the sequence of numbers
15 , 21 , 27 , 33 , 39 , - , - , a) Find a formula for the nth term of the sequence.
b) Find the 43rd term.
c) Is 2146 a term of the sequence?
22.
4cm
6cm
11cm
Calculate the volume of the shape shown above.
x
Mathematics
Clyde Valley High School
Department