Transition Workbook
GCSE to A-Level
sparxmaths.com
© Sparx limited
,In this booklet, there are a range of questions from key topics that you will have seen in
GCSE and will be helpful for AS Level and A-Level.
Each topic has three sections:
• Introduce questions allow you to practise the key concepts.
• Strengthen questions build on your knowledge of the key concepts.
• Deepen questions will challenge your understanding.
Unless otherwise indicated, you may use a calculator.
Use the grid below to keep track of your progress in each topic. Tick the sections you
have attempted. If you use Sparx Maths you can find even more questions by searching
for the Sparx topic codes in Independent Learning.
I S D Sparx topic codes Teacher comment
Surds U499 U707 U281
Expanding brackets U768 U606
Factorising
U178 U858
quadratics
Simplifying
U662 U437
expressions
Operations with
U685 U457 U824
algebraic fractions
Solving quadratic U228 U960 U665
equations U150
Quadratic graphs U589 U769 U601
Linear simultaneous
U760 U757
equations
U315 U477 U848
Straight-line graphs
U669 U377 U898
Right-angled
trigonometry U283 U545 U170
Further trigonometry U952 U591
Page 2 © Sparx limited
,Key facts and formulae:
The Quadratic formula:
The solution of ax 2 + bx + c = 0
where a ≠ 0
-b ± b2 - 4ac
x=
2a
Trigonometry:
In any right-angled triangle ABC where a, b
and c are the length of the sides and c is the
hypotenuse:
a b a
sinA = cosA = tanA =
c c b
In any triangle ABC where a, b and c are the
length of the sides:
sine rule:
a =
b =
c
sinA sinB sinC
cosine rule: a2 = b2 + c2 - 2bc cosA
© Sparx limited Page 3
, Surds - Non Calculator Introduce
Q1 Expand and fully simplify 5 ( 5 + 7 )
Answer:
2 5
Q2 Rationalise the denominator of
6
Give your answer in its simplest form.
Answer:
Q3 Expand and fully simplify (6 + 5 )(1 + 5 )
Answer:
Page 4 © Sparx limited
GCSE to A-Level
sparxmaths.com
© Sparx limited
,In this booklet, there are a range of questions from key topics that you will have seen in
GCSE and will be helpful for AS Level and A-Level.
Each topic has three sections:
• Introduce questions allow you to practise the key concepts.
• Strengthen questions build on your knowledge of the key concepts.
• Deepen questions will challenge your understanding.
Unless otherwise indicated, you may use a calculator.
Use the grid below to keep track of your progress in each topic. Tick the sections you
have attempted. If you use Sparx Maths you can find even more questions by searching
for the Sparx topic codes in Independent Learning.
I S D Sparx topic codes Teacher comment
Surds U499 U707 U281
Expanding brackets U768 U606
Factorising
U178 U858
quadratics
Simplifying
U662 U437
expressions
Operations with
U685 U457 U824
algebraic fractions
Solving quadratic U228 U960 U665
equations U150
Quadratic graphs U589 U769 U601
Linear simultaneous
U760 U757
equations
U315 U477 U848
Straight-line graphs
U669 U377 U898
Right-angled
trigonometry U283 U545 U170
Further trigonometry U952 U591
Page 2 © Sparx limited
,Key facts and formulae:
The Quadratic formula:
The solution of ax 2 + bx + c = 0
where a ≠ 0
-b ± b2 - 4ac
x=
2a
Trigonometry:
In any right-angled triangle ABC where a, b
and c are the length of the sides and c is the
hypotenuse:
a b a
sinA = cosA = tanA =
c c b
In any triangle ABC where a, b and c are the
length of the sides:
sine rule:
a =
b =
c
sinA sinB sinC
cosine rule: a2 = b2 + c2 - 2bc cosA
© Sparx limited Page 3
, Surds - Non Calculator Introduce
Q1 Expand and fully simplify 5 ( 5 + 7 )
Answer:
2 5
Q2 Rationalise the denominator of
6
Give your answer in its simplest form.
Answer:
Q3 Expand and fully simplify (6 + 5 )(1 + 5 )
Answer:
Page 4 © Sparx limited
