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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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2 Properties of Lines
Question 1
(2)
Question 2
Question 3
Question 4
(2)
Total / 10
Edexcel C1
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4.2 Differentiation - Tangent & Normal
Question 1
Question 2
(3)
Question 3
Total / 10
Edexcel C1
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4.3 Differentiation - Increasing / Decreasing Functions
Question 1
(5)
Question 2
Total / 10
Edexcel C1
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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
Edexcel C1
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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)
Edexcel C1
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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
Edexcel C1
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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:
Edexcel C1
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2 Properties of Lines
Question 1
(3)
Solution:
(2)
(1)
Question 2
Solution:
Question 3
(3)
Edexcel C1
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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)
Edexcel C1
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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)
Edexcel C1
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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
Edexcel C1
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1.2 Quadratic Functions
Question 1
(3) Solution:
Question 2
(3) Solution:
Question 3
(4) Solution:
Total / 10
Edexcel C1
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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
Edexcel C1
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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
Edexcel C1
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1.4 Inequalities
Question 1
(3) Solution:
Question 2
(4) Solution:
Question 3
(3) Solution:
Edexcel C1
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2 Properties of Lines
Question 1
(2)
Solution:
(1)
(1)
Question 2
Solution:
Question 3
Solution: