Woodhouse Maths Department GCSE to A-Level transition work for September 2020 Many students state that they find the transition from GCSE to A-Level maths to be a challenge. This summer work

will keep your brains ticking over and ensure that you are adequately prepared for that challenge. It covers some

of the key topics from GCSE which are essential foundations for A-Level mathematics, as well as providing some

opportunities for further investigation.

AMSP Transition Resources:

You should be working your way through the Advanced Mathematics Support Programme resources found here.

There are six sets of resources, each providing roughly 3 hours of work, consisting of skills checks, opportunities for

exploration and ideas for further investigation. Work completed from the AMSP website should be clearly

organised into a folder and brought to the first lesson. We recommend you aim to complete one ‘set’ of each of

every week.

GCSE questions to be completed: All students should complete the attached pack of GCSE questions and bring them to their first lesson. This will be

checked for full completion by your teacher in your first maths lesson. These questions have been selected as

they cover key topics from GCSE which are required for, or expanded upon in, A-Level mathematics.

Further Support If you need further practice on any of the topics present in the below questions, there is an Edexcel transition pack

available here. The questions below are referenced to this pack by topic. This is an extensive document with

examples and many questions - it is not expected that you complete this and bring it on the first day. It is advised

that you look at these questions and ensure you are familiar with all the content, however.

Further enrichment resources: At Woodhouse we love to explore beyond the curriculum. Here are some great resources if you just can’t get

enough maths over the summer!

• Alex Bellos’ Monday puzzle – a great puzzle blog released every two weeks.

• @robeastaway, @cshearer41, @edsouthall – twitter mathematicians often posting problems and puzzles.

• Chalkdust Magazine – a magazine for the mathematically curious.

• Numberphile, 3blue1brown – videos about numbers.

Woodhouse Maths Department GCSE to A-Level transition work for September 2020 This pack of GCSE questions should be completed and brought to your first

maths lesson in September to show to your teacher. You should complete all

the questions without looking at the mark scheme, then afterwards go through

and mark/correct your work. If you cannot do a question – don’t look straight at

the mark scheme! First, check the other resources provided and try and figure

out how to proceed yourself.

If you need further practice on any of the topics in this booklet please refer to

the Edexcel transition materials, where there are examples and more questions

for each topic.

Q1. – Expanding brackets and simplifying expressions, rules of indices

(a) Expand and simplify (x – 2)(2x + 3)(x + 1)

...........................................................

(3)

(b) Find the value of n.

...........................................................

(2)

(c) Solve 5x2 – 4x – 3 = 0

Give your solutions correct to 3 significant figures.

...........................................................

(3)

(Total for question = 8 marks)

Q2. – surds and rationalising the denominator

(a) Rationalise the denominator of

Give your answer in its simplest form.

...........................................................

(2)

(b) Show that can be written in the form where a and b are integers.

(3)

(Total for question = 5 marks)

Q3. – Completing the Square

(x − 8)(x + 4) = (x − a)2 + b for all values of x.

Find the value of a and the value of b.

a = ...........................................................

b = ...........................................................

(Total for question = 3 marks)

Q4. – Solving Quadratic Equations

The diagram shows a right-angled triangle.

All the measurements are in centimetres.

The area of the triangle is 27.5 cm2

Work out the length of the shortest side of the triangle. You must show all your working.

........................................................... cm

(Total for question = 4 marks)

Q5. – Sketching Quadratic Graphs

Sketch the graph of

y = 2x2 – 8x – 5

showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.

(Total for question = 5 marks)

Q6. – Solving Quadratic & Linear Simultaneous Equations

Solve algebraically the simultaneous equations

x2 + y2 = 25 y − 2x = 5

...........................................................

(Total for question = 5 marks)

Q7. – Solving Simultaneous Equations Graphically

(a) On the grid, draw the graph of x2 + y2 = 12.25

(2)

(b) Hence find estimates for the solutions of the simultaneous equations

x2 + y2 = 12.25 2x + y = 1

........................................................................................

(3)

(Total for question = 5 marks)

Q8. – Quadratic Inequalities

Here is a rectangle and a right-angled triangle.

All measurements are in centimetres. The area of the rectangle is greater than the area of the triangle.

Find the set of possible values of x.

...........................................................

(Total for question = 5 marks)

Q9. – Linear Inequalities

(a) Solve 14n > 11n + 6

...........................................................

(2)

(b) On the number line below, show the set of values of x for which –2 < x + 3 ≤ 4

(3)

(Total for question = 5 marks)

Q10. – Sketching Cubic & Reciprocal Graphs

Here are six graphs.

Write down the letter of the graph that could have the equation

(a) y = x3

...........................................................

(1)

(b)

...........................................................

(1)

(Total for question = 2 marks)

Q11. – Translating Graphs

The graph of y = f(x) is shown on the grid.

(a) On the grid, draw the graph with equation y = f(x + 1) – 3

(2)

Point A(–2, 1) lies on the graph of y = f(x).

When the graph of y = f(x) is transformed to the graph with equation y = f(–x), point A is mapped to point B.

(b) Write down the coordinates of point B.

( ................ , ................ )

(1)

(Total for question = 3 marks)

Q12. – Straight Line Graphs

The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2 passes through the origin and has gradient −3

The lines L1 and L2 intersect at point P.

Find the coordinates of P.

( ........................................ , ........................................ )

(Total for question = 4 marks)

Q13. – Parallel and Perpendicular Graphs

P has coordinates (–9, 7) Q has coordinates (11, 12)

M is the point on the line segment PQ such that PM : MQ = 2 : 3

Line L is perpendicular to the line segment PQ. L passes through M.

Find an equation of L.

...........................................................

(Total for question = 5 marks)

Q14. – Pythagroras’ Theorem

Here is a right-angled triangle.

All measurements are in centimetres. The area of the triangle is 2.5 cm2.

Find the perimeter of the triangle. Give your answer correct to 3 significant figures. You must show all of your working.

........................................................... cm

(Total for question is 6 marks)

Q15. - Proportion

y is inversely proportional to d2 When d = 10, y = 4

d is directly proportional to x2 When x = 2, d = 24

Find a formula for y in terms of x. Give your answer in its simplest form.

...........................................................

(Total for question = 5 marks)

Q16. – Circle Theorems

S and T are points on the circumference of a circle, centre O. PT is a tangent to the circle. SOP is a straight line. Angle OPT = 32°

Work out the size of the angle marked x. You must give a reason for each stage of your working.

(Total for question = 4 marks)

Q17. - Trigonometry

ABC and ADC are triangles.

The area of triangle ADC is 56 m2

Work out the length of AB. Give your answer correct to 1 decimal place.

........................................................... m

(Total for question = 5 marks)

Q18. Rearranging Formulae

Make m the subject of

...........................................................

(Total for question = 4 marks)

Q19. – Volume and Surface Area of 3D Shapes

The diagram shows a solid metal cylinder.

The cylinder has base radius 3x cm and height h cm.

The metal cylinder is melted. All the metal is then used to make 270 spheres.

Each sphere has a radius of x cm.

Find an expression, in its simplest form, for h in terms of x.

...........................................................

(Total for question = 3 marks)

Q20. – Area Under a Graph

Here is a speed-time graph for a train.

(a) Work out an estimate for the distance the train travelled in the first 20 seconds.

Use 4 strips of equal width.

........................................................... m

(3)

(b) Is your answer to (a) an underestimate or an overestimate of the actual distance the train travelled?

Give a reason for your answer.

.............................................................................................................................................

.............................................................................................................................................

(1)

(Total for question = 4 marks)

Mark Scheme Q1.

Q2.

Q3.

Q4.

Q5.

Q6.

Q7.

Q8.

Q9.

Q10.

Q11.

Q12.

Q13.

Q14.

Q15.

Q16.

Q17.

Q18.

Q19.

Q20.

Q21.