GCSE Reivsion - Algebra - (Excluding Geometric problems and proofs)
[Nov 2013] 16(b)
Solve
h  7 2h  1 5


3
2
6
..............................................
(4)
(Total for Question 16 is 7 marks)
[Nov 2013] 11.
(a) Simplify
x7 × x3
..........................................
(1)
(b) Simplify
(m4)3
..........................................
(1)
36af 8
12a5 f 2
(c) Simplify
..........................................
(2)
(Total for Question 11 is 4 marks)
[Nov 2013] 20.
(a)
Solve
4(8 x  2)
 10
3x
..............................................
(3)
(b) Write as a single fraction in its simplest form
2
1

y3 y6
...........................................................................
(3)
1
[Nov 2013] 15.
Solve the simultaneous equations
3x + 4y = 5
2x – 3y = 9
x = ..........................................
y = ..........................................
(Total for Question 15 is 4 marks)
[March 2013] 14. A = 4bc
A = 100
b=2
(a) Work out the value of c.
..........................................
(2)
m
k 1
4
(b) Make k the subject of the formula.
..........................................
(3)
[March 2013] 17.
4x  1 x  4
Solve
+
=3
5
2
(Total for Question 14 is 5 marks)
x = ....................................
(Total for Question 17 is 3 marks)
[March 2013] 9.
(a)
Simplify
a4 × a5
..............................
(1)
2
45e 6 f 8
(b) Simplify
5ef 2
.........................................
(2)
1
(c) Write down the value of 9 2
.........................................
(1)
(Total for Question 9 is 4 marks)
[June 2013] 25.
Solve the simultaneous equations x2 + y2 = 9
x+y=2
Give your answers correct to 2 decimal places.
x = ............................ y = ............................
or x = ............................ y = ............................
(Total for Question 25 is 6 marks)
[June 2013] 18.
Make p the subject of the formula
y = 3p2 – 4.
..............................................
(Total for Question 18 is 3 marks)
___________________________________________________________________________
[June 2013] 19.
(a) Factorise
6 + 9x
..............................................
(1)
(b) Factorise
y2 – 16
..............................................
(1)
(c) Factorise
2p2 – p – 10
..............................................
(2)
3
[June 2013 Calc] 12(b)
Solve
2 y
=1
5
y = ..............................................
(2)
(Total for Question 12 is 5 marks)
[June 2013] 25.
values of x.
The expression x2 – 8x + 21 can be written in the form (x – a)2 + b for all
(a) Find the value of a and the value of b.
a = ..........................................
b = ..........................................
(3)
The equation of a curve is y = f(x) where f(x) = x2 – 8x + 21
The diagram shows part of a sketch of the graph of y = f(x).
The minimum point of the curve is M.
(b) Write down the coordinates of M.
(...................., ....................)
(1)
(Total for Question 25 is 4 marks)
4
[June 2013 NonCalc] 23. Simplify
4( x  5)
x  2 x  15
2
..............................................
(Total for Question 23 is 2 marks)
[June 2013 NonCalc] 18. Solve the simultaneous equations
4x + 7y = 1
3x + 10y = 15
x = ..........................................
y = ..........................................
(Total for Question 18 is 4 marks)
[Nov 2012 Calc] 22. (a)
Solve 2x2 + 9x – 7 = 0
Give your solutions correct to 3 significant figures.
......................................................................................................
(3)
(b) Solve
2
9
+
–7=0
2
y
y
Give your solutions correct to 3 significant figures.
......................................................................................................
(2)
(Total for Question 22 is 5 marks)
[Nov 2012 Calc] 20. Simplify
x 1 x  3
+
2
3
..............................................
(Total for Question 20 is 3 marks)
5
[Nov 2012 Calc] 14*(c)
(i)
Factorise
2t2 + 5t + 2
...............................................................................
(ii) t is a positive whole number.
The expression
2t2 + 5t + 2
can never have a value that is a prime number.
Explain why.
............................................................................................................................................
(3)
[Nov 2012 NonCalc] 24.
Make t the subject of the formula
p=
3  2t
4t
..............................................................................................
(Total for Question 24 is 4 marks)
[March 2012 Calc] 24.
Solve
5(2 x  1) 2
= 5x – 1
4x  5
..................................
(Total 5 marks)
[March 2012 Calc] 18.
Solve the equations
3x + 5y = 19
4x – 2y = –18
x = ............................
y = ............................
(Total 4 marks)
6
[March 2012 Calc] 19.
Solve the equation
5x2 + 8x – 6 = 0
Give each solution correct to 2 decimal places.
........................................................
(Total 3 marks)
[March 2012 Calc] 11.
(a)
On the number line below, show the inequality
–2 < y < 3
(1)
(b) Here is an inequality, in x, shown on a number line.
Write down the inequality.
.........................................................
(2)
(c) Solve the inequality
4t – 5 > 9
.....................................(2)
[March 2012 NonCalc] 15. (a)
Factorise fully
2x2 − 4xy
.....................................(2)
(b) Factorise
p2 – 6p + 8
.....................................(2)
(c) Simplify
( x  2) 2
x2
.....................................(1)
(d) Simplify
2a2b × 3a3b
.....................................(2)
7
[June 2012 Calc] 22.
Solve 3x2 – 4x – 2 = 0
Give your solutions correct to 3 significant figures.
.................................................................................
(Total for Question 22 is 3 marks)
[June 2012 Calc] 20.
Make t the subject of the formula
2(d – t) = 4t + 7
t = ..............................................
(Total for Question 20 is 3 marks)
[June 2012 NonCalc] 23.
(a)
Simplify fully
x 2  3x  4
2 x 2  5x  3
..............................................
(3)
(b) Write
4
3
+
as a single fraction in its simplest form.
x2
x2
..........................................................................
(3)
(Total for Question 23 is 6 marks)
[Nov 2011 Calc] 23. (a)
Factorise
x2 + px + qx + pq
.....................................
(2)
(b) Factorise
m2 – 4
.....................................
(1)
(c) Write as a single fraction in its simplest form
2
1
–
x4 x3
.....................................(3)
8
[Nov 2011 Calc] 19. Find the exact solutions of x +
3
=7
x
.....................................
(Total 3 marks)
[Nov 2011 Calc] 12. –2  n < 5
n is an integer.
(a) Write down all the possible values of n.
..........................................................................
(2)
(b) Solve the inequality
4x + 1 > 11
..........................................................................
(2)
(Total 4 marks)
[Nov 2011 Calc] 11(c)
Simplify
(2n3)4
.....................................
(2)
[Nov 2011 NonCalc] 20.
(a)
Factorise
2x2 – 9x + 4
.....................................
(2)
Hence, or otherwise,
(b) solve
2x2 – 9x + 4 = (2x – 1)2
.....................................
(4)
[Nov 2011 NonCalc] 17.
p = –10
q=3
y = p – 2qx2
x = –5
(a) Work out the value of y.
.....................................(2)
9
(b) Rearrange y = p – 2qx2
to make x the subject of the formula.
.....................................
(3)
(Total 5 marks)
[Nov 2011 NonCalc] 14.
The diagram shows the graph of y = x2 – 5x – 3
(a) Use the graph to find estimates for the solutions of
(i) x2 – 5x – 3 = 0
........................................................
(ii) x2 – 5x – 3 = 6
........................................................
(3)
(b) Use the graph to find estimates for the solutions of the simultaneous equations
y = x2 – 5x – 3
y=x–4
.....................................................................
(3)
10
[June 2011] 14.
The table shows six expressions.
n is a positive integer.
2n − 3
3n − 2
3(n + 4)
4n + 1
4(3n + 1)
2n + 1
(a) From the table, write the expression whose value is
(i) always even
...........................................
(ii) always a multiple of 3
...........................................
(2)
(b) From the table, write the expression which is a factor of 4n2 − 1
...........................................
(1)
(Total 4 marks)
[June 2011 NonCalc] 27. Solve the equation
x
2

 1.
2 x 1
(Total 4 marks)
[June 2011 NonCalc] 23. Make k the subject of the formula t =
k
.
k 2
.....................................
(Total 4 marks)
[June 2011 NonCalc] 12(b) Simplify completely
12 xy 3
.
3x 2 y 3
.....................................
(2)
11
[Nov 2010 Calc] 25. (a)
Expand and simplify (2x + 4y)(4x – 5y)
............................................................
(2)
(b) Simplify fully
( x  10) 5
( x  10) 4
.....................................
(1)
(c) Simplify fully
x 2  25
x 2  7 x  10
.....................................
(3)
For all values of x,
x2 + 6x – 2 = (x + p)2 + q
(d) Find the value of p and the value of q.
p = .............. q = ..............
(2)
[Nov 2010 NonCalc] 13.
Make v the subject of the formula t =
v
+2
5
v = ................................
(Total 2 marks)
12