Download algebra review - Durrington High School

Algebra Review.
So far this year we have covered many different aspects of algebra. Please complete as much as you can
and take a note of the questions that you are struggling with.
1.
Choose the correct word from the list to describe the following.
Equation
(a)
Formula
Identity
Expression
Inequality
2x + 6
(1)
(b)
2y + 7 = 18
(1)
(c)
A = πr2
(1)
(Total 3 marks)
2.
Solve these equations.
(a)
x = 12
2
(1)
(b)
3y – 11 = 4
(c)
4z + 8 = 3 – z
(2)
(3)
(d)
2t  5  7
3
(3)
3.
(a)
Find the value of
(b)
Find the value of
when p = 7 and q = –4
3p + 2q
(2)
x2 + y2
when x = –5 and y = 3
(2)
(c)
Use the formula
R = 5e – 3f
to find the value of e when R = 6 and f = 4
(3)
(Total 7 marks)
4.
Solve the equation
5x – 1 = 3(x + 2)
(Total 3 marks)
5.
Solve the equations.
(a)
4z – 5 = 11
(b)
7t – 3 = 6 + t
(2)
(3)
(c)
5x – 1 = 3(x + 2)
(3)
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6.
(a)
Solve the inequality 3x + 5 ≤ 16
HINT: Treat exactly the same as you would as equation.
(2)
7.
(a)
Factorise 10p – 4 HINT: Factorise means put into brackets.
(1)
(b)
2
Factorise q + 3q
(1)
(c)
Factorise r2 – r
(1)
(d)
Simplify t2 × t3
(1)
8.
Solve 5x – 4 = 3x + 2
(Total 3 marks)
9.
(a)
3d – 5e + 4d + e
Simplify
(2)
(b)
Multiply out
(c)
Solve
4(3x + 7)
(1)
4(3x + 7) = 28
(2)
10.
(a)
Simplify
10d + 3e – 2d – 7e
(2)
Expand and simplify (2x  3)(3x + 5)
(b)
(3)
(c)
Simplify
(i)
y4  y-3
(1)
(ii)
y4  y5
(1)
11.
(a)
Expand and simplify 4(m + 3) + 3(2m – 5)
(2)
(b)
Solve the simultaneous equations:
2x + 3y = 9
3x + 2y = 1
HINT: Multiply both the equations by different numbers so that there are an equal number of x’s in
both equations. Then multiply 1 equation from the other to find the value of y. Next substitute this
value into 1 of the equations to find x
(4)
(c)
(i)
Factorise x2 + 6x – 16 HINT: This means put into 2 brackets
(2)
(ii)
Hence solve the equation x2 + 6x – 16 = 0 HINT: use previous answer.
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12.
(a)
(i)
Factorise completely 2a2 – a
(2)
(ii)
Find the value of 2a2 – a when a = – 4.5
(2)
(b)
Expand and simplify (4x – 3) (x + 5)
(3)
(c)
Simplify
(i)
x5 × x–2
(1)
(ii)
y5 ÷ y–2
(1)
13.
Make x the subject of the formula HINT: This means rearrange the formula to get x on its own, do the
Same as you would with an equation.
w = x2 + y
(Total 2 marks)
14.
(a)
(i)
Factorise x2 – 7x – 8
(2)
(ii)
Hence solve the equation x2 – 7x – 8 = 0
(1)
(b)
Solve the simultaneous equations
5x + 3y = 13
3x + 5y = 3
(4)
15.
(a)
The nth term of a sequence is 4n + 1 HINT: To produce a sequence replace n with the number 1 for
the 1st number in the sequence, replace n with 2 for the 2nd number etc.
(i)
Write down the first three terms of the sequence.
(2)
(ii)
Is 122 a term in this sequence?
Explain your answer.
(1)
(b)
Tom builds fencing from pieces of wood as shown below.
Diagram 1
4 pieces of wood
Diagram 2
7 pieces of wood
Diagram 3
10 pieces of wood
How many of pieces of wood will be in Diagram n?
(2)
(Total 5 marks)
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16.
A pattern using pentagons is made of sticks.
(a)
Diagram 1
Diagram 2
Diagram 3
5 sticks
9 sticks
13 sticks
How many sticks are needed for Diagram 5?
(2)
(b)
Write down an expression for the number of sticks in Diagram n.
(2)
(c)
Which Diagram uses 201 sticks?
(3)
(Total 7 marks)
17.
On the grid draw the graph of y = 2x + 1 for values of x from 0 to 5.
y
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
x
(Total 3 marks)
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