GCSE Mathematics a or Better Revison Sheets

GCSE Mathematics A or Better Revision (Edexcel)Name……………………………………………………………

GCSE Mathematics – Aiming for an A or Better

Grade Criteria and exemplar examination questions to get a Grade A or A* in the following topics:

1. Surds 2. Recurring Decimals 3. Limits of Accuracy 4. Indices 5. Proportionality 6. Rearranging Formulae 7. Algebraic Fractions 8. Using Graphs 9. Quadratic Equations 10. Simultaneous Equations 11. Algebraic Proofs 12. Circle Theorems 13. Trigonometry – for triangles which are not right-angled 14. Vectors 15. Similar Triangles 16. Congruent Triangles 17. Scale Factors – for volumes & surface areas of similar shapes (2D

or 3D)18. Stratified Samples 19. Histograms 20. Tree Diagrams 21. Mixed Questions

NC = non-calculator question

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GCSE Mathematics: Surds

Grade Criteria Can DoTo get a grade B you must be able to:

Work out the square roots of some decimal numbersTo get a grade A you must be able to:

Simplify surds by rewriting with the smallest integer inside the rootTo get a grade A* you must be able to:

Simplify surds by rationalising denominators Manipulate & simplify expressions involving surds

Question 1[i]

[ii]

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GCSE Mathematics: Recurring Decimals

Grade Criteria Can doTo get a grade A you must be able to:

Convert recurring decimals to fractions

Question 2

[ii]Convert the recurring decimal to a fraction.

………………………………(2)

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GCSE Mathematics: Limits of Accuracy


Find limits of accuracy for numbers given to whole number accuracy

To get a grade A you must be able to: Find limits of accuracy for numbers given to d.p. or s.f. accuracy

To get a grade A* you must be able to: Find limits of accuracy for compound measures (speed, gradient,

etc)

Question 3(i)

(ii)

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GCSE Mathematics: Indices

Grade Criteria Can DoTo get a grade C you must be able to:

Multiply and divide numbers in index formTo get a grade A you must be able to:

Know how to use indices rules for negative & fractional powers

Question 4

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GCSE Mathematics: Proportionality

Grade Criteria Can DoTo get a grade A you must be able to:

Find formulae that describe direct & inverse proportionality (or variation) and use them to solve problems

To get a grade A* you must be able to: Solve variation problems involving 3 variables

Question 5[i]

[ii]

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GCSE Mathematics: Rearranging Formulae


Rearrange more complicated formulaeTo get a grade A you must be able to:

Rearrange formulae where the subject appears twiceTo get a grade A* you must be able to:

Rearrange formulae where the subject appears with a power

Question 6

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GCSE Mathematics: Algebraic Fractions


Solve linear equations involving algebraic fractions where the subject (x) is part of the numerator

To get a grade A you must be able to: Combine algebraic fractions using all 4 operations

To get a grade A* you must be able to: Simplify algebraic fractions by factorising & cancelling Solve equations containing fractions with algebraic denominators

Question 7(i)

(ii)

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GCSE Mathematics: Using Graphs


Work out the coordinates in a table of values and plot graphs of the form y = ax2 + bx + c (quadratic), y = ax3 (cubic), y = a/x (reciprocal)

To get a grade A you must be able to: Give the equation of a line parallel or perpendicular to given lines &

passing through a given point Interpret more complex real-life graphs

To get a grade A* you must be able to: Transform graphs of a given function with the equation either

written in f(x) form or fully specified Identify a function’s equation from its graph which has been

transformed from a known function Solve equations using the intersection of two graphs

Question 8

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GCSE Mathematics: Quadratic Equations


Factorise a quadratic expression of the form x2 + bx + c Solve a quadratic equation of the form x2 + bx + c = 0

To get a grade A you must be able to: Solve a quadratic equation of the form ax2 + bx + c = 0 by

factorising or by using the formulaTo get a grade A* you must be able to:

Solve quadratic equations by completing the square Solve real problems requiring constructing & solving quadratic

equations

Question 9(i)

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(ii)

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GCSE Mathematics: Simultaneous Equations


Solve 2 linear simultaneous equationsTo get a grade A you must be able to:

Set up & solve 2 linear simultaneous equations from practical problems

To get a grade A* you must be able to: Solve 1 linear & 1 non-linear (probably quadratic, typically the

equation of a circle) simultaneous equations

Question 10(i)

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GCSE Mathematics: Algebraic Proof s


Verify results by substituting numbers into them Understand the proofs of simple theorems (an exterior angle of a

triangle is the sum of the two opposite interior angles, etc)To get a grade A you must be able to:

Show an algebraic statement is true by using both sides to justify your answer

To get a grade A* you must be able to: Prove algebraic results using rigorous & logical mathematical

arguments

Question 11[i]

[ii]

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[iii](a)Write down an expression, in terms of n, for the nth multiple of 5.

.............................(1)

(b)Hence or otherwise

(i) prove that the sum of two consecutive multiples of 5 is always an odd number,

(ii) prove that the product of two consecutive multiples of 5 is always an even number.

(5)(Total 6 marks)

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GCSE Mathematics: Circle Theorems


Find missing angles in circlesTo get a grade A you must be able to:

Use the alternate segment theorem to find missing angles in circlesTo get a grade A* you must be able to:

Use circle theorems to prove geometrical results

Question 12[i]

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GCSE Mathematics: Trigonometry


Use trigonometry to find the length of any side in right-angled triangles

Use trigonometry to solve problems involving right-angled trianglesTo get a grade A* you must be able to:

Use the sine rule & cosine rule to find missing lengths or angles Find the area of triangles using Area = ½ab sin C Solve 3D problems using SOH CAH TOA trigonometry Solve simple equations involving sin, cos or tan, using the shape of

the basic graphs or knowledge of CAST diagrams to find all possible solutions

Question 13 [i]

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[iii]

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GCSE Mathematics: Vectors


Solve problems involving addition & subtraction of vectorsTo get a grade A* you must be able to:

Solve more complex geometrical problems using vectors

Question 14[i]

[ii]

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GCSE Mathematics: Similar Triangles


Set up equations to find missing sides in similar trianglesTo get a grade A* you must be able to:

Solve practical problems involving similar triangles

Question 15

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GCSE Mathematics: Congruent Triangles


Know the conditions to show that two triangles are congruentTo get a grade A you must be able to:

Prove that two triangles are congruent

Question 16

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GCSE Mathematics: Scale Factors


Solve problems using area or volume scale factors for similar shapes

To get a grade A* you must be able to: Solve related problems e.g. involving mass or capacity

Question 17

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GCSE Mathematics: Stratified Samples


Calculate the numbers required for a stratified sample

Question 18[i]

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GCSE Mathematics: Histograms


Draw histograms given data in a frequency table Complete a frequency table given a histogram

Question 19[i]

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GCSE Mathematics: Tree Diagrams


Draw & use a tree diagram to work out the probability of combined events

To get a grade A you must be able to: Use “and” / “or” knowledge to find probabilities of specific

combinationsTo get a grade A* you must be able to:

Draw & use a tree diagram to work out dependent probabilities

Question 20[i]

Joan has two boxes of chocolates.The boxes are labelled A and B.

Box A contains 15 chocolates. There are 6 plain, 4 milk and 5 white chocolates.Box B contains 12 chocolates. There are 4 plain, 3 milk and 5 white chocolates.

Joan takes one chocolate at random from each box.Work out the probability that the two chocolates Joan takes are not of the same type.

………………………………(4)

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GCSE Mathematics: Mixed Questions

Question 21

The depth, D metres, of the water at the end of a jetty in the afternoon can be modelled by this formula

D = 5.5 + A sin 30(t – k)

where

t hours is the number of hours after midday,A and k are constants.

Yesterday the low tide was at 3 p.m.The depth of water at low tide was 3.5 m.

Find the value of A and k.

A = ………………………

k = ………………………(4)

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(a) On the grid above, draw the graphs of x2 + y2 = 100

and 2y = 3x – 4 (3)

(b) Use the graphs to estimate the solutions of the simultaneous equations x2 + y2 = 100

and 2y = 3x – 4

............................. . ............................ (2)

For all the values of x, x2 + 6x = (x + 3)2 – q

(c) Find the value of q.

q = .............................(2)

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y

x

8

4

–4

–12 –8 –4 126

4

12

O

–8

–12


One pair of integer values which satisfy the equation x2 + y2 = 100 is x = 6 and y = 8

(d) Find one pair of integer values which satisfy x2 + 6x + y2 – 4y – 87 = 0

x = .............., y = ...............(3)

(Total 10 marks)

(2)

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The graphs of y against x represent four different types of proportionality.

Write down the letter of the graph which represents the type of proportionality.

Type of proportionality Graph letter

y is directly proportional to x .........................

y is inversely proportional to x .........................

y is proportional to the square of x .........................

y is inversely proportional to the square of x .........................

(Total 2 marks)

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y

x

Graph A

y

x

Graph B

y

x

Graph C

y

x

Graph D

GCSE Mathematics a or Better Revison Sheets

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