Download 1: Linear Equations:

GCSE to A-Level Core Maths Transition Material
1) Linear Equations:
Solve the following equations
a)
5x + 10 = 60
b)
7 = 7 + 7x
c)
7 – 3x = 5 – 2x
d)
x + 10 = 20
100
e)
-3 + x =-1 – x
5
10
5
5
f)
2(3x – 1) = 3(x – 1)
g)
7(2x – 4) + 3(5 – 3x) = 2
h)
7x – (2 – x) = 0
i)
3(x – 3) – 7(2x – 8) – (x – 1) = 0
j)
(x + 3)(x – 1) = x2 + 5
k)
(2x + 1)2 – 4(x – 3)2 = 5x + 10
l)
Hint: Use Pythagoras’ Theorem.
m)
The area of the square is half the area of the rectangle. Find x.
n)
5 =3
x
p)
x+3 = x–4
2
5
o)
9 = 5
.
x
x–3
Solve the following problems by first forming an equation.
q)
The sum of four consecutive numbers is 90. Find the numbers.
r)
The three angles in a triangle are in the ratio 1:3:5. Find them.
s)
A man buys x cans of cola at 30p and (x + 4) cans of lemonade at 35p each.
The total cost was £3.35. Find x
t)
A man is 32 years older than his son. Ten years ago he was three times as old
as his son was then. Find the present age of each.
u)
A man runs to a telephone and back in 15 minutes. His speed on the way to
the telephone is 5m/s and his speed on the way back is 4m/s. Find the distance
to the telephone. Hint: units must be the same.
2) Simultaneous Equations:
Solve the following pairs of simultaneous equations.
a)
3x + y = 10
x–y=2
b)
x + 2y = 1
2x + 3y = 4
Solve each of the following problems by first forming a pair of simultaneous
equations.
c)
Find two numbers with a sum of 15 and a difference of 4.
d)
A fishing enthusiast buys fifty maggots and twenty worms for £1.10 and her
mother buys thirty maggots and forty worms for £1.50. Find the cost of one
maggot and one worm
e)
Half the difference between two numbers is 2. The sum of the greater number
and twice the smaller number is 13. Find the numbers.
f)
A wallet containing £40 has three times as many £1 coins as £5 notes. Find
the number of each kind.
3) Quadratic Equations:
Factorise the following expressions
a)
x2 + 7x + 10
b)
x2 – 8x + 16
c)
x2 – 5x – 24
d)
x2 – 49
e)
6x2 – 27x + 30
f)
8x2 – 10x – 3
g)
9x2 – 1
Solve the following equations
h)
x2 + 7x + 12 = 0
i)
x2 + 5x – 14 = 0
j)
4x2 – 29x + 7 = 0
k)
6x2 + 17x – 3 = 0
l)
2 – 5
= 0
x
2x – 1
m)
x–3= x+2.
x–2
n)
1 + x + 1 = 13
x
3