Mathematics and/or Further Mathematics
The Summer Bridging Work MUST be handed into the Sixth Form on Friday 9 September
2016.
Your work will be assessed in September by your class teachers.
Anyone not completing the work or producing work of poor quality will be re-interviewed
regarding their place on the course and in the Sixth Form.
The aims are for you to understand if you like the course and for you to be ready to start
learning at post-16 level.
All work is due in on Friday 9 September 2016.
Things you will need to succeed every day in the Sixth Form:
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Pens
Highlighters
A pencil case
Your own lined paper
A single-hole punch (available from the school shop for £1)
A pair of scissors
Glue
Things you will need for this course:
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A lever-arch folder for storing work at home
A ring-binder for work for the current unit
A pack of at least 20 file dividers
A scientific calculator
Your Summer Bridging Work Project:
Much of the first module that you will study revises and extends work you have done at GCSE on
algebra and trigonometry. A reasonable level of fluency at core algebraic skills is essential if you are to
get through the first half term successfully, and will help you throughout the course.
The purpose of this Starter Pack is to ensure that you have this fluency. The pack consists of some
questions to enable to you check your understanding and practise the techniques, and references to
MyMaths for help if you need it.
For each section, look at the questions first. If you are unsure what to do, work through the MyMaths
references before trying the questions.
The work should be completed on A4 file paper.
Contents
1.
Algebraic simplification
Mathematics and/or Further Mathematics
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Expanding brackets
Factorising
Indices
Surds
Solving linear equations
Solving quadratic equations
Simultaneous equations
Finding the gradient of a line
Pythagoras Theorem
Trigonometry
MyMaths school login: cheney
password: factor
MyMaths personal username:
password:
Section 1
Algebraic simplification
MyMaths:
Algebra/ Algebraic manipulation/Simplifying 1
Algebra/ Algebraic manipulation /Simplifying 2
Questions:
1.
Multiply these terms.
(a)
2.
mn × mn
(b)
pq × 4p
(c)
9b × 2a2
(d)
a3 × g3
Simplify these.
(a)
(d)
12a2 – a + 9a2
(b)
8p2 + 3pq + 5q2 – pq (e)
b3 + 2b – b3
(c)
4m2 + mn – 6n + nm (f)
8x – 4xy – 2y + 6xy
x + 2xy + x – 4xy
Section 2
Expanding brackets
MyMaths:
Algebra/ Algebraic manipulation /Single Brackets and Brackets
Questions:
1.
Multiply out these brackets
(a)
2.
3.
6(4a – 3b)
(b)
p(n – p)
(c)
6m(n – m)
(d)
3n(4m + 7n)
Multiply out these brackets and simplify
(a)
x(6x – 2) + 2x(5x + 3)
(b)
8x(2y + 3x) + x(6x – 3y)
(c)
4(3a + b) – (3a – 2b)
(d)
p(5p – 4) – 2(2p2 – 3)
Multiply out these brackets and simplify
(a)
(w + 2)(w + 6)
(b)
(y + 9)(y + 5)
(c)
(x – 3)2
(d)
(v – 2)(v – 3)
(e)
(b – 3)(b + 5)
(f)
(b – 3)(b – 5)
Mathematics and/or Further Mathematics
(g)
(h + 5)(h – 5)
(h)
(t – 3)(t + 3)
(j)
(2p + 1)2
(k)
(5x + 6)(3x – 2)
(i)
(2w – 3)(2w + 3)
(l)
Section 3
Factorising
MyMaths:
Algebra/ Algebraic manipulation / Factorising Linear
Algebra/ Algebraic manipulation / Factorising Quadratics 1
(3g – 7)(4g – 5)
Questions:
1.
2.
Factorise these fully
(a)
m + 3mn
(b)
8pq + 4q
(c)
3y – 12xy
(d)
2b2 + 10b
(e)
18ab + 24bc (f)
x2y – 2xy
(g)
9a2b + 6ab2
(h)
12m2n -9mn
Factorise the following expressions
(a)
x2 + 4x + 4
(b)
x2 + 9x + 20
(c)
x2 + 3x – 4
(d)
x2 + 2x – 15
(e)
x2 – x – 6
(f)
x2 – 11x + 10
(g)
x2 – 2x – 8
(h)
x2 – 3x + 2
(i)
x2 – 4x + 4
(j)
x2 – 9
(k)
x2 – 64
(l)
4x2 – 49
(e)
(j)
(p)
640
4-2
82/3
(k)
(q)
(d)
(h)
(l)
53 × 5
(5-2)3
(71/2)-1/2
Section 4
Indices
MyMaths:
Number/ Powers and Roots/Indices1, 2 and 3
Questions:
1.
Write down the exact answers to the following questions
(a)
(f)
(l)
(r)
2.
34
811/2
81/3
25-3/2
(b)
(g)
(m)
25
(c)
161/2 (h)
1251/3 (n)
13
6-1
49-1/2
(d)
(i)
(o)
Write these expressions in their simplest form
(a)
(e)
(i)
(m)
(p)
25 × 23
53 × 5-1
(4-2)-3
31/2 × 31/2
10-1/3 × 10-5/3
(b)
(f)
(j)
(n)
(102)3
6-2 × 6-3
(81/2)6
5-2/3 ÷ 5-1/3
(c)
(g)
(k)
(o)
Section 5
Surds
MyMaths:
Number / Powers and Roots /Surds 1
Number / Powers and Roots /Surds 2
Questions
1.
1000
18-1
64-1/3
Simplify
810 ÷ 84
3-2 ÷ 33
(6-2/3)3
21/4 ÷ 2-5/4
2-4
163/2
Mathematics and/or Further Mathematics
(a)
(f)
2.
√18
(c)
√75
(b)
√12 + √75
(d)
√44
(c)
√500 + √5
(e)
√128
√18 + √32
(d)
√20 + √45
Expand these brackets and simplify
(a)
4.
(b)
Simplify
(a)
3.
√32
√80
(√2 + 1)(√2 – 1)
(√3 + 1)(√3 – 2)
(b)
(c)
(√3 + 6)(4 - √3)
Simplify each of these
(a)
6 12
2 3
(b)
3 15
(c)
3
28
7
Section 6
Solving linear equations
MyMaths:
Algebra/ Equations-Linear/Equations1, 2, 3 and 4
Algebra/ Equations-Linear/Equations 5-fractions
(d)
750
10
Questions
1.
Solve these equations
(a)
(c)
3(2x – 5) = 12
5(6x + 9) = 12x
(b)
4(5x + 1) = 3(4x + 12)
(d)
(f)
3(x + 1) = 9(5x – 9)
4
/5(2x + 3) = 14
(e)
2
(g)
3
/4(2x – 4) = 2(x + 5) (h)
2
(i)
(k)
5
(j)
 10
2x  1
3(2 x  1) 2(6 x  3)

4
5
/3(x – 1) = 8
/3(x – 1) = 3/5(x + 4)
3
5

x  1 2x  3
Section 7
Solving quadratic equations
MyMaths:
Algebra/ Equations-Quadratic/Quadratic equations 1
Algebra/ Equations-Quadratic/Quadratic formula
Questions
1.
Solve these quadratic equations by factorising
(a)
x2 + 5x – 84 = 0
(b)
x2 – 8x + 7 = 0
(c)
x2 + 3x – 54 = 0
(d)
x2 – 15x + 36 = 0
(e)
x2 + 8x + 12 = 0
(f)
x2 – 4x – 320 = 0
(g)
(i)
x2 – 11x – 60 = 0
x2 + 6x = 135
(h)
x2 – 14x + 48 = 0
Mathematics and/or Further Mathematics
2.
(j)
(l)
x2 – 8x = 65
x2 + 28 = 16x
(k)
x2 + 20 = 9x
(m)
x2 = 3x
(n)
x2 – 64 = 0
(o)
x2 – 196 = 0
Solve these quadratic equations to 2 dp
(a)
(c)
x2 – 5x + 3 = 0
x2 + 8x + 1 = 0
(b)
x2 + 6x – 2 = 0
(d)
x2 – 3x – 1 = 0
(e)
2x2 + 3x – 6 = 0
(f)
3x2 + x – 3 = 0
(g)
4x2 + x – 1 = 0
(h)
x2 – x = 3
(i)
7x2 + 3x = 5
Section 8
Simultaneous equations
MyMaths:
Algebra/ Equations-Simultaneous /Simultaneous equations 1, 2 and 3
Algebra/ Equations-Simultaneous /Simultaneous Negatives
Questions
1.
Solve these pairs of simultaneous equations
(a)
4x + y = 14
x + 5y = 13
(b)
3x – 5y = 7
4x + 5y = -14
(c)
7x + 3y = 13
5x + y = 7
(d)
4x – 3y = 1
x - 2y = 4
(e)
5x + y = 7
2x + 3y = -5
(f)
3x – 2y = 4
2x + 3y = -6
Section 9
Finding the gradient of a line
MyMaths:
A level/Core 1/Coordinate Geometry/Gradients/pages 1-5
Questions
1.
Find the gradients of the lines joining these points
(a)
(3, 5) and (5, 9)
(b)
(3, 1) and (4, 8)
(c)
(d)
(-2, -2) and (0, 2)
(e)
(5, -1) and (8, 4)
(f) (9, -3) and (-5, -1)
Section 10
Pythagoras Theorem
MyMaths:
Shape/ Pythagoras /Pythagoras Theorem
Questions
1.
Find the missing lengths in each of these triangles
4m
(a)
xm
(b)
6m
2.4 m
ym
3.7 m
(2, 8) and (3, 4)
Mathematics and/or Further Mathematics
Section 11
Trigonometry
MyMaths:
Shape/ Trigonometry/Trig missing angles
Shape/Trigonometry/Trig missing sides
Questions
1.
Find the missing sides in these triangles. Give your answers to 3 significant figures.
(a)
(b)
(c)
3m
xm
35°
18°
xm
7m
xm
100 m
40°
(d)
(e)
(f)
xm
6m
50°
8m
xm
47°
35°
xm
2.
Find the marked angles in these triangles. Give your answers to 3 significant figures.
(a)
(b)
(c)
7.3 50°
m
θ°
6.8 m
3.8 m
7.2 m
16.3 m
8.4m
Staff contact: [email protected]
Exam board: OCR
Specification: www.ocr.org.uk/Images/67746-specification.pdf
Wider Reading and Discovery List:
Books
 See the Cambridge University Reading List:
http://www.maths.cam.ac.uk/undergrad/admissions/readinglist.pdf
Websites
 www.mymaths.co.uk
12 m
Mathematics and/or Further Mathematics
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www.ocr.org.uk
www.cut-the-knot.org
www.maa.org/pubs/books/mtm.html
www.stepmathematics.org.uk
Things to do
 Science Museum – Mathematics Gallery
 British Museum – Maths Challenge
 V&A Museum – Maths and Islamic Art & Design
 St Paul’s Cathedral – ‘Let’s Build a Cathedral’ Workshop
 Bank of England Museum
 London Metal Exchange
 Wembley Stadium
Things to watch
 www.ted.com Talks
 https://www.youtube.com/watch?v=qEdUZg13Jlg&list=PLZt9bXMy6CcBIHHbdcwvuJmh9sFzLB97
Things to listen to
 Radio 4 Maths Collection: http://www.bbc.co.uk/radio4/features/collections/mathematics/
 Radio 4 Maths and Magic: http://www.bbc.co.uk/programmes/b03ls7y2
 Radio 4 A Brief History of Maths: http://www.bbc.co.uk/programmes/b00srz5b
Moocs
Cracking Mechanics: Further Maths for Engineers: https://www.futurelearn.com/courses/crackingmechanics
Examiners Report
www.ocr.org.uk
Subject Ambassador 1
Rebecca Hann
Has studied AS Mathematics and is starting
A2 Mathematics.
“Maths is, although a challenge, really
interesting as everything starts to fit
together”
Subject Ambassador 2
Eleanor Krige
Has studied A2 Mathematics and is starting
A2 Further Mathematics.
“Though lots of hard work, this course can
be really enjoyable and rewarding”.