Edexcel C1

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Personalised Revision Tool for

Edexcel C1

Aims

This Revision Tool aims to make your revision smarter and more effective. It aims to:-

Identify gaps in your understanding and knowledge.

Give a short summary & example for each sub-topic.

Provide hyperlinks to MyMaths lessons for most sub-topics.

Using the short tests

There are 2 mini-assessments for each sub-topic.

Use the first test to identify which topics you need to work on. If you get a good

mark you will not need to use the second test on this topic.

Use the second test to measure the level of improvement after remedial work has

been undertaken.

This PRT is not a substitute for, or an alternate to, doing past papers.

A programme of completing whole past papers is essential for success.

Edexcel C1

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Topic Sub-topic with link to examples MyMaths T1 A1 T2 A2

1 Algebra

1.1 Basic Simplifying algebraic expressions

Linear Equations

Changing the subject of a formula

1.2 Quadratic Functions Factorisation

Solving quadratic equations

Completing the Square

1.3 Simultaneous Equations Linear simultaneous equations

Linear & Non-linear simultaneous equations

1.4 Inequalities Solving Inequalities

Quadratic Inequalities

1.5 Indices Laws of Indices

Surds

Rationalising the denominator

1.6 Curve Sketching Plotting and Sketching curves

The minimum value of a quadratic

Using transformations to sketch the curves

of functions

2 Coordinate Geometry

2

Properties of Lines

Gradient of a line between two points

Equations of lines

Intersection of lines

3 Sequences and Series

3.1 Series Be familiar with and use Σ notation

3.2 Arithmetic Sequences Can use standard formulae associated with arithmetic

sequences & series

4 Differentiation

4.1 Basics Be able to differentiate y = axn

4.2 Tangent/Normal Be able to find the equation of a tangent and normal at

any point on the curve

4.3 Increasing/Decreasing Be able to classify functions as increasing or decreasing

4.4 Turning Points Use differentiation to find turning points on a curve

5 Integration

5.1 Inverse of Be able to integrate kxn as an indefinite integral & find

the constant of integration given relevant information

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Differentiation Be able to evaluate definite integrals

5.2 Area under a curve Be able to find the area between a curve and the x-axis

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Back to Contents Page

1.1 Algebra - Basics

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Back to Contents Page

1.2 Algebra – Quadratic Functions

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Back to Contents Page

1.3 Algebra – Simultaneous Equations

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Back to Contents Page

1.4 Algebra – Inequalities

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Back to Contents Page

1.5 Algebra – Indices

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Back to Contents Page

1.6 Curve Sketching

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Back to Contents Page

2 Coordinate Geometry – Properties of Lines

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3.1 Sequences and Series – Summing Series

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3.2 Sequences and Series – Arithmetic Series

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Back to Contents Page

4.1 Differentiation – Basics

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4.2 Differentiation – Tangent/Normal

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4.3 Differentiation – Increasing/Decreasing Functions

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4.4 Differentiation – Turning Points

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5.1 Integration – Inverse of Differentiation

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Back to Contents Page

5.2 Integration – Area under a Curve

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1.1 Basic Algebra

Question 1

Simplify fully 2(3x + 4) – 3(4x – 5) (2)

Question 2

(2)

Question 3

(3)

Question 4

(3)

Total / 10

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1.2 Quadratic Functions

Question 1

Solve x2 + 6x + 8 = 0 (2)

Question 2

Solve the equation 2x2 – 35x + 98 = 0 (3)

Question 3

Solve x2

+ 6x = 4 (3)

Give your answers in the form p q, where p and q are integers.

Question 4

Show that x2 – 4x + 15 can be written as (x + p)

2 + q for all values of x.

State the values of p and q. (2)

Total / 10

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1.3 Simultaneous Equations

Question 1

(4)

Question 2

Solve the simultaneous equations

x2 + y2 = 25

y = x – 7

(6)

Total / 10

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1.4 Inequalities

Question 1

(3)

Question 2

(3)

Question 3

(4)

Total / 10

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1.5 Indices

Question 1

Question 2

Question 3

(3)

Total / 10

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1.6 Curve Sketching

Question 1

Question 2

(2)

(1)

Question 3

Total / 10

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2.1 Properties of Lines

Question 1

(3)

Question 2

Question 3

(3)

Total / 10

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3.1 Series

Question 1

Question 2

Question 3

Question 4

Total / 10

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3.2 Sequences and Series - Arithmetic Series

Question 1

(5)

Question 2

Total / 10

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4.1 Differentiation Basics

Question 1

Question 2

Question 3

Total / 10

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4.2 Differentiation - Tangent & Normal

Question 1

Question 2

Total / 10

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4.3 Differentiation - Increasing / Decreasing Functions

Question 1

The gradient of a curve is given by

Find the set of values of x for which y is an increasing function

(5)

Question 2

(5)

Total / 10

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4.4 Differentiation - Turning Points

Question 1

Question 2

Total / 10

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5.1 Integration Basics

Question 1

(3)

Question 2

(4)

Question 3

Total / 10

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5.2 Integration -Area under a curve

Question 1

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Question 2

Total / 10

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1.1 Basic Algebra

Question 1

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

Question 2

(2)

Question 3

Solve 3

–40 x = 4 + x

(3)

Question 4

Make m the subject of the formula 2(2p + m) = 3 – 5m (3)

Total / 10

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1.2 Quadratic Functions

Question 1

(3)

Question 2

(3)

Question 3

(4)

Total / 10

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1.3 Simultaneous Equations

Question 1

Solve the simultaneous equations

4x + 2y = 8

2x – 5y = 10

(3)

Question 2

Solve the simultaneous equations

x2 + y

2 = 29

y – x = 3

(7)

Total / 10

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1.4 Inequalities

Question 1

(3)

Question 2

(4)

Question 3

(3)

Total / 10

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1.5 Indices

Question 1

Question 2

Question 3

(3)

Total / 10

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1.6 Curve Sketching

Question 1

Question 2

(3)

(1)

(2)

(2)

Total / 10

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2 Properties of Lines

Question 1

(2)

Question 2

Question 3

Question 4

(2)

Total / 10

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3.1 Sequences and Series

Question 1

Question 2

Question 3

Total / 10

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3.2 Sequences and Series - Arithmetic Series

Question 1

Question 2

Total / 10

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4.1 Differentiation Basics

Question 1

Question 2

Question 3

(4)

Total / 10

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4.2 Differentiation - Tangent & Normal

Question 1

Question 2

(3)

Question 3

Total / 10

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4.3 Differentiation - Increasing / Decreasing Functions

Question 1

(5)

Question 2

Total / 10

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4.4 Differentiation - Turning Points

Question 1

Question 2

Total / 10

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5.1 Integration Basics

Question 1

(3)

Question 2

Question 3

(3)

Total / 10

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5.2 Integration - Area under a curve

Question 1

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Question 2

(4)

Total / 10

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1.1 Basic Algebra

Question 1

Simplify fully 2(3x + 4) – 3(4x – 5) (2)

Solution:

6x + 23

6x + 8 12x + 15

M1 for 3 of the 4 terms 6x, +8, 12x, + 15 correct

A1 cao

Question 2

(2)

Solution:

6xy(2x² - 3y) 1 mark per term

Question 3

(3)

Solution:

Question 4

(3)

Jan 2008 Q1

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Solution:

Total / 10

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1.2 Quadratic Functions

Question 1

Solve x2 + 6x + 8 = 0 (2)

Solution:

(x + 2)(x + 4) = 0

M1 (x ± 2)(x ± 4)

–2, –4 A1

Question 2

Solve the equation 2x2 – 35x + 98 = 0 (3)

Solution:

(2x – 7)(x – 14) = 0

M1 x2 term and constant term ( 98 obtained

or 2x(x – 14) – 7(x – 14) or x(2x – 7) – 14(2x – 7)

M1 for (2x – 7)(x – 14)

x = 2

7; x = 14 A1

Question 3

Solve x2

+ 6x = 4 (3)

Give your answers in the form p q, where p and q are integers.

Solution:

– 3 13 M1 for substitution into formula, condone incorrect signs

M1 for 2

526

A1 cao

Question 4

Show that x2 – 4x + 15 can be written as (x + p)

2 + q for all values of x.

State the values of p and q. (2)

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Solution:

x2 – 4x + 15

= (x – 2)2 – 4 + 15

(x – 2)2

+ 11

p = –2

q = 11

M1 for sight of (x – 2)2

A1 for p = –2 and q = 11

Total / 10

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1.3 Simultaneous Equations

Question 1

(4)

Solution:

Question 2

Solve the simultaneous equations

x2 + y2 = 25

y = x – 7

(6) Solution:

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Total / 10

1.4 Inequalities

Question 1

(3)

Solution:

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Question 2

(3)

Solution:

Question 3

(4) Solution:

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Total / 10

1.5 Indices

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Question 1

Solution:

Question 2

Solution:

Question 3

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(3)

Solution:

Total / 10

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1.6 Curve Sketching

Question 1

Solution:

Question 2

Solution:

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Question 3

Solution:

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Total / 10

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2 Properties of Lines

Question 1

(3)

Solution:

(2)

(1)

Question 2

Solution:

Question 3

(3)

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Solution:

Total / 10

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3.1 Series

Question 1

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Question 2

Question 3

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Question 4

Total / 10

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3.2 Sequences and Series - Arithmetic Sequences

Question 1

(5)

5 5

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Question 2

Total / 10

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4.1 Differentiation Basics

Question 1

Question 2

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Question 3

Total / 10

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4.2 Differentiation - Tangent & Normal

Question 1

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Question 2

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Total / 10

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4.3 Differentiation - Increasing / Decreasing Functions

Question 1

The gradient of a curve is given by

Find the set of values of x for which y is an increasing function

(5)

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Question 2

(5)

Total / 10

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4.4 Differentiation - Turning Points

Question 1

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Question 2

Total / 10

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5.1 Integration Basics

Question 1

(3)

B1 for each

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Question 2

(4)

max 4

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Question 3

Total / 10

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5.2 Integration - Area under a curve

Question 1

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Question 2

Total / 10

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1.1 Basic Algebra

Question 1

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

Solution:

2x + 3 2

6x – 3 – 4x +6 = 2x + 3

B1 for either 6x – 3 or – 4x +6

B1 cao

Question 2

(2)

Solution:

4wy(5w + 6y²) (1 mark per term)

Question 3

Solve 3

–40 x = 4 + x

(3) Solution:

7

40 – x = 3(4 + x)

40 – x = 12 + 3x

40 – 12 = x + 3x

4x = 28

M1 multiplying through by 3: 3 × 3

x–40 = 3 × 4 + 3 × x

A1 40 – 12= x + 3x

A1 cao

Question 4

Make m the subject of the formula 2(2p + m) = 3 – 5m (3)

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Solution:

m = 7

43 p 3

4p + 2m = 3 5m

2m + 5m = 3 4p

M1 for expanding or splitting into 4 correct terms

M1 (indep) rearranging 4 terms correctly to isolate m terms

(A1 for m = 7

4p3 oe fully simplified)

Total / 10

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1.2 Quadratic Functions

Question 1

(3) Solution:

Question 2

(3) Solution:

Question 3

(4) Solution:

Total / 10

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1.3 Simultaneous Equations

Question 1

Solve the simultaneous equations

4x + 2y = 8

2x – 5y = 10

(3) Solution :

4x + 2y = 8

4x – 10y = 20

12y = –12

y = –1

4x + 2(–1) = 8

x = 2.5

x = 2.5

y = –1

M1 for correct process to eliminate either x or y (condone one arithmetical

error)

M1 (dep) for substituting found value into either equation

A1 for x = 2.5, y = −1

[SC: B1 for x = 2.5 or y = −1 if M0]

Question 2

Solve the simultaneous equations

x2 + y

2 = 29

y – x = 3

(7)

Solution :

x2 + 6x + 9

x = 2 and y = 5

or

x = – 5 and y = – 2

(x + 3)2 + x

2 = 29

x2 + 6x + 9 + x

2 = 29

2x2 + 6x + 9 = 29

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2x2 + 6x – 20 = 0

2(x – 2)(x + 5) = 0

M1 for rearranging to y = x + 3

M1 for correct substitution for their y to give (ax + b)2

+ x2 = (29)

A1 ( ) for correct exp of (ax + b)2

seen

M1 for reduction to a 3 term quadratic = 0

M1 (dep on 3rd

M1) for correct factorisation ( ) or correct use of formula

( ) or completing the square ( )

A1 for at least 2 correct values of x or y

A1 cao, values must be paired

Total / 10

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1.4 Inequalities

Question 1

(3) Solution:

Question 2

(4) Solution:

Question 3

(3) Solution:

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Total / 10

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1.5 Indices

Question 1

Solution:

Question 2

(2) Solution:

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Question 3

(3) Solution:

Total / 10

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1.6 Curve Sketching

Question 1

Solution:

Question 2

(3)

(1)

(2)

(2)

Solution:

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Total / 10

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2 Properties of Lines

Question 1

(2)

Solution:

(1)

(1)

Question 2

Solution:

Question 3

Solution:

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Question 4

(2)

Solution:

Only award 1 M mark

Total / 10

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3.1 Series

Question 1

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Question 2

Question 3

Total / 10

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3.2 Sequences and Series - Arithmetic Series

Question 1

Question 2

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Total / 10

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4.1 Differentiation Basics

Question 1

Question 2

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Question 3

(4)

1

4

Total / 10

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4.2 Differentiation - Tangent & Normal

Question 1

Question 2

(3)

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Question 3

Total / 10

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4.3 Differentiation - Increasing / Decreasing Functions

Question 1

(5)

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Question 2

Total / 10

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4.4 Differentiation - Turning Points

Question 1

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Question 2

Total / 10

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5.1 Integration Basics

Question 1

(3)

3 total

Question 2

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Question 3

(3)

3 marks

Total / 10

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5.2 Integration - Area under a curve

Question 1

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Question 2

(4)

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A1

Total / 10