High Storrs School Mathematics Department
A-Level Bridging Unit – Assessment Task
Name: _________________________________________________
This task has been designed to be used to assess what you can remember from GCSE. This is so that we can
make the appropriate provisions for you, when you start in September. You must complete this assignment
and submit it to your Mathematics Teacher at the start of your first lesson.
If you are struggling with some of these questions the “Bridging Unit Support Pack” is designed to help you
with each one of these topics.
1 – Simplifying Like Terms
Mark:
Simplify the following like terms
a) 6y + 2x + 3y – x
b) 3x + 2x 2 + 7x + 9x 2 – x
(1)
(1)
d) 5y  3y
c) 2ac + 3ac + 4ac
2
2
4
6
(1)
e) 2x y  6x y
3 5
(1)
f)
3 4
12x
6
 4x
(2)
g) 20x y  5x y
7 4
3
(1)
h) (2a)
4 3
3
(2)
i)
____ /13
(1)
j)
2 3
(3x )
(1)
 4x 3 


 3 
2
(2)
2 – Expanding Brackets
Mark:
Simplify the following by removing the single brackets
a) 4(x + 6)
____ /14
b) x(x + 1)
(1)
c) 5(x – 2) – 3(x + 6)
(1)
d) 2x(x – 3) + 7x + 5x
2
(2)
Expand and simplify the following quadratics fully
e) (x – 2)(x – 4)
(2)
f)
3(x + 4)(x – 2)
(2)
g) (x + 4)
(2)
h) (x – 3) – 2x(x + 4)
2
2
(2)
(2)
3 – Factorising an Expression
Mark:
____ /6
Factorise the following expressions fully
a) 4x – 8
b) 14x – 4x 2
(1)
c) 16x + 24xy
2
(1)
d) 14x y – 7xy + 28xy
3
3 2
(2)
3
5
(2)
4 – Factorising a Quadratic
Mark:
Factorise the following quadratic equations
a) x 2 + 10x + 24
b) x 2 – 49
(1)
c) 4x – 9y
2
____ /7
(1)
d) 4x + 12x + 9
2
2
(2)
(1)
e) 3x – 10x – 8
2
(2)
5 – Laws of Indices for Rational Exponents
Mark:
____ /13
Evaluate the following, leaving your answers as fractions not decimals. Ensure that you show your working:
(you need to demonstrate that you can complete this exercise without a calculator)
a) 4 – 2
b) 3 – 4
(1)
c)
3
42
(1)
d)
2
643
(1)
3
e) 32−5
(1)
f)
1
164
(2)
g)
1
(1)
h)
643
2
83
(1)
i)
 36 


 49 
–
3
2
(1)
j)
Simplify:
(2)
 a3 
 2 
y 
–3
(2)
6 – Manipulating Surds
Mark:
____ /11
Simplify the following surds, leaving your answers in the form 𝑎√𝑏 where 𝑎 and 𝑏 are integers.
Do not calculate the exact answer.
a) 48
b) 75
(1)
c) 2 12
(1)
d) 4 24
(1)
e)
(1)
f)
5+3 5+6 5
50 – 72 + 18 – 32
(1)
g) 5 24
(2)
h) 27√96
3√3
2 50
(2)
(2)
7 – Solving Quadratics by Factorising
Mark:
____ /11
Solve the following quadratic equations (factorise where necessary)
a)
b) (x – 5)(x – 6) = 0
(x + 2)(x + 4) = 0
(1)
c)
(1)
d)
2
x – 7x + 12 = 0
(2)
2
x + 5x – 6 = 0
(2)
e).
f)
2
4x – 29x + 7 = 0
2
2x – 3 = x
(2)
(3)
8 – Solving Quadratics by Completing the Square
Mark:
____ /4
Solve the following quadratic equations by completing the square. Leave your answers in surd form.
a)
2
b)
x + 4x – 7 = 0
2
x + 12x + 9 = 0
(2)
(2)
9 – Solving Quadratics by Using the Formula
Mark:
____ /4
Solve the following quadratic equations by using the quadratic formula.
Give your answers to 3 significant figures.
a)
x2 – 5x – 13 = 0
b)
(2)
2x2 + 8x – 5 = 0
(2)
10 – Solving More Difficult Equations
Mark:
____ /13
Solve the following equations, some are linear and some are quadratic. They involve algebraic fractions so
you should find these a little tougher…
a)
b)
(2)
c)
(3)
d)
(3)
e)
(3)
(3)
11 – Applied Questions
Mark:
____ /11
These questions involve applying the skills from the exercises above to solve problems. They often give the
best indication of how prepared you are for A-Level questions.
a)
The diagram shows a solid triangular prism.
All the measurements are in centimetres.
The volume of the prism is V cm3.
Find a formula for V in terms of x.
Give your answer in simplified form.
(3)
b)
The diagram shows a pentagon.
All measurements are in centimetres.
Show that the area of this pentagon can be written
as 5x2 + x – 6
(4)
c)
Triangles ABC and DEF are mathematically similar.
The base, AB, of triangle ABC has length 2(x – 1) cm
The base, DE, of triangle DEF has length (x2 – 1) cm
The area of triangle ABC is 4 cm2
The area of triangle DEF is T cm2
Prove that
T = x2 + 2x + 1
(4)
High Storrs School Mathematics Department
A-Level Bridging Unit – Assessment
For internal marking use:
Score:
/107
Percentage:
%
Top 3 topics you need to study further are:
☺
☺
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Student Evaluation of Assignment:
Section
1
2
3
4
5
6
7
8
9
10
11
Simplifying Like Terms
Expanding Brackets
Factorising an Expression
Factorising a Quadratic
Laws of Indices for Rational Exponents
Manipulating Surds
Solving Quadratics by Factorisation
Solving Quadratics by Completing the Square
Solving Quadratics by Using the Formula
Solving More Difficult Equations
Applied Questions
  
Marks