Er
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Contents
Section 1
Number 1
Section 2
Number 2
Section 3
Algebra 1
Section 4
Algebra 2
Section 5
shape 1
Section 1 Number 1
1. Evaluate:
a) 3
-2
b) 2
-3
c) 2
0
d) b
0
y 3 × y -2
e)
y4
(10)
2. A shop has a sale of 20% off everything. A shirt costs £32 in the sale. What
was the original price of the shirt?
(4)
1
5
4
7
(ℎ) − − =
3
(𝑖)1 ÷ 2 =
7
(𝑗)
3 1
×
4 5
1 4
×
5 3
=
(20)
5. Express the following as decimals:
i)
5
8
ii)
5
9
(4)
3. Expand and simplify the following:
i) 4 ( 2 + 3 )
ii)
2 ( 2 + 8)
iii)
3 ( 2 + 12 )
iv) (4  3 )(4 - 3 )
v) (2  5 )(4  3 )
vi) (3  6 )(2 - 3 )
(12)
4. Rationalise the denominator and simplify where possible:
1
i)
3
ii)
3
5
iii)
2
6
(6)
3. Solve the following equations:
𝑎) 3𝑡 − 7 = 20
(2)
𝑏) 5(2𝑥 + 8) = 45
(2)
𝑐) − (3𝑦 + 7) = 26
(2)
3
2
𝑑) (𝑥 − 12) =
9
2
(2)
d)
4 2p
2
6
(2)
e)
2y
+6=2
3
(2)
4. Solve the following pairs of simultaneous equations:
b) 3x – 3y = 24
x – 2y = 9
a) 3x + y = 26
x + y = 10
x = …………….
x =…………….
y = ……………
y =…………….
(3)
(3)
5. The graph of y=5x - 4 is shown below:
a) On the same axes, draw the graph of x + y = 5
(2)
b) Using the graphs, find the solution of the simultaneous equations:
y = 5x – 4
x+y=5
6.
(2)
A
B
C
D
y = 2x + 6
3y + 6x= 9
2y = 4x + 6
y = 3 + 4x
Using the equations of the graphs in the four boxes given above:
a) Write down two graphs that are parallel to each other
b) Write down two graphs that cross the y-axis at the same point.
c) Write down any graphs that go through the point (2,10)
d) Write down any graphs that cross the x-axis at x = -3.
(6)
7. Find the length between the points A = (-1,4) and B=(3,-2). Express your answer in
the form √k where k is an integer.
(4)
8. Find the equation of the line parallel to the line y = 4 + 3x and passing through the
point (-4,-1)
(4)
9. Find the equation of the line that passes through the points (1,-1) and (3,3).
(4)
10. Match the equations with the correct graph using the list below
Note: You will have to find a missing equation and complete the blank graph.
3
x
y  x2 - 3
y  x3 - 3
x  y -3
y
Equation:
Equation:
Equation:
5
4
3
2
1
0
1
2
3
4
5
4. i) Simplify
4
6
+
x x+2
(4)
ii) Hence, or otherwise, solve
4
6
+
=2
x x+2
(4)
5. Solve the following, giving your answers to 1 decimal place.
i)
x² + 5x + 1 = 0
ii)
2x² +13x – 5 = 2
CALCULATORS
ARE NOW
ALLOWED
(5)