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Page 1: crashMATHS Schemes of Work · crashMATHS Schemes of Work New A Level Maths (2017) This scheme of work is for a class: ... and ‘sample’

CM © crashMATHS Limited

crashMATHS Schemes of Work

New A Level Maths (2017)

This scheme of work is for a class:

• with one teacher

• with 5 contact hours each week

• sitting the AS exams

Textbook references are for our Pure/Applied Textbook (Edexcel version). The scheme of work is applicable for all exam boards, but some

modification may be needed in places.

This is for the AS/Year 1 content only. It will be updated to include A2/Year 2 content for teaching post-exams after the publication of our A2

textbooks.

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CM © crashMATHS Limited

Week Topic(s) + Length of

time

Specification references Teaching suggestions CM Textbook

references

1 5 hours on: Proof • understand and use the structure of

mathematical proof, proceeding from given

assumptions through a series of logical

steps to a conclusion

• proof by deduction

• proof by exhaustion

• disproof by counter-example

Introduce the idea of

proof, including relevant

logic symbols, ⇒ , ⇐ ,

⇔ , ∴ and logic

connectives.

Introduce the three

methods of proof with

examples (either one-by-

one or simultaneously)

AS/Year 1 Pure

Textbook – Chapter

1, Sections 1.1-1.4

2

2 hours on: Proof

• understand and use the structure of

mathematical proof, proceeding from given

assumptions through a series of logical

steps to a conclusion

• proof by deduction

• proof by exhaustion

disproof by counter-example

More examples/recap.

Potential for use of CM

end of topic test (45

minutes)

AS/Year 1 Pure

Textbook – Chapter

1, Sections 1.1-1.4

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CM © crashMATHS Limited

Week 2

(cont.)

3 hours on: Algebra

• GCSE algebra (expanding/factorising)

• Solution of quadratic equations

Take some time to go

through the basics to

ensure students develop

fluency.

Use CM mid-topic test

AS/Year 1 Pure

Textbook – Chapter

2, Sections 2.1

Week 3

5 hours on: Algebra • Understand and use the laws of indices for

all rational exponents

• Use and manipulate surds including

rationalising the denominator

• Solving quadratics in a function of the

unknown (powers of x )

Plenty of examples are

important here to build

fluency.

Use CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

2, Sections 2.2-2.5

Week 4 5 hours on:

Equations and

Inequalities

• Solve simultaneous equations in two

variables by elimination and by substitution,

including one linear and one quadratic

equation

• Solve linear and quadratic inequalities in

single variable and interpret such

inequalities graphically

• Express solutions using set notation

Potential to link back to

algebra – can act as a

recap. Encourage Ss to

check answers by

substitution at the end

Brief/informal overview of

quadratic graphs is

advised.

AS/Year 1 Pure

Textbook – Chapter

3, Sections 3.1-3.5

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Week 5 2 hours: Equations

and inequalities

• Represent inequalities graphically CM End of Topic test AS/Year 1 Pure

Textbook – Chapter

3, Section 3.6

1 hour: Large Data

Set

• Introduce the large data set and the

variables involved Get students to use Excel

to look and familiarise

themselves with the

variables

AS/Year 1 Applied

Textbook – Chapter

1, Section 1.1

2 hours: Sampling • Understand and use the terms ‘population’

and ‘sample’

• Use samples to make informal inferences

about the population

• Understand and use sampling techniques,

including simple random sampling

Use a real sampling frame

of students in a class and

use simple random

sampling to select

students to answer recap

questions on prior topics

AS/Year 1 Applied

Textbook – Chapter

2, Sections 2.1-2.2

Week 6

2 hours: Sampling

• Understand and use opportunity sampling,

stratified sampling, systematic sampling and

quota sampling

• Select and critique sampling techniques in

the context of solving a statistical problem,

including understanding that different

samples can lead to different conclusions

Focus on the difference in

systematic and quota

sampling

CM end of topic test

AS/Year 1 Applied

Textbook – Chapter

2, Sections 2.3-2.5

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about the population

Week 7

5 hours: Functions

• Work with quadratic functions and their

graphs

• The discriminant of a quadratic function,

including the conditions for real and

repeated roots

• Understand and use graphs of functions;

sketch curves defined by simple equations,

including polynomials and reciprocal graphs

Ensure Ss understand

what the function notation

means

For any graph, to find x

intersections, set y=0; to

find y intersections, set x =

0.

Link quadratic graphs and

the discriminant

Similarity between

polynomial curves.

Distinction between a root

repeated 2n times and

(2n+1) times ( n∈! )

AS/Year 1 Pure

Textbook – Chapter

4, Sections 4.1-4.4

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Week 8

5 hours: Functions

• Interpret algebraic solution of equations

graphically; use intersection points of

graphs to solve equations

• Understand and use proportional

relationships and their graphs

• Understand the effect of simple

transformations, including

y = af x( ),y = f x( ) + ay = f ax( )y = f x + a( )

Stress the idea that,

simultaneous equations

tells us where two

equations have the same x

value and y value, i.e. the

same coordinates

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

4, Sections 4.5-4.8

Week 9

5 hours: The Factor

Theorem

• Simple algebraic long division

• Use of the factor theorem

Even though the remainder

theorem is off-spec, it is

good to teach it and then

teach the factor theorem

as a special case

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

5

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CM © crashMATHS Limited

Week 10&11

10 hours: Coordinate

geometry in the (x,y)

plane {6 hours on

straight lines, 4

hours on circles}

• Understand and use the equation of a

straight line

• Gradient conditions for two straight lines to

be perpendicular

• Be able to use straight lines to model in a

variety of contexts

• Understand and use the coordinate

geometry of a circle

• Completing the square to find centre and

radius

• Circle theorems to assist in geometry

problems

Teach y − y1 = m x − x1( )

as a special case of

y = mx + c , with

c = y1 −mx1 .

Encourage Ss to make use

of diagrams

CM end of topic test on

straight lines and circles

AS/Year 1 Pure

Textbook – Chapter

5

Week 12 3 hours: the binomial

expansion

• Understand and use the binomial expansion

of a + bx( )n for positive integers n; the

notations n! and nCr ; link to binomial

probabilities

In exams, Ss often make

sign errors/struggle to deal

with fractions and the

algebra. Use plenty of

examples of this type (can

be found in the book)

AS/Year 1 Pure

Textbook – Chapter

6

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Week 13 5 hours: measures of

central tendency

• Interpret measures of central tendency:

mean, median and mode

• Select suitable measures of central

tendency depending on context

Make students very clear

on the conventions for

grouped data (gaps/no

gaps) and that discrete

data is treated as cts

Excellent opportunity for

large data set exploration

CM topic test

AS/Year 1 Applied

Textbook – Chapter

3, Sections 3.1-3.5

Week 14 4 hours: measures of

dispersion

1 hour: measures of

central tendency and

dispersion + LDS*

• Measures of dispersion: variance, standard

deviation, range and interpercentile range

• Use coding

*See classroom activities

for lesson plan of this LDS

centred lesson

CM end of topic test

AS/Year 1 Applied

Textbook – Chapter

1/4, Sections 1.1,

4.1-4.3

Week 15

5 hours:

representation of

data

• Cumulative frequency diagrams, frequency

polygons and box plots (without outliers)

{1 hour}

• Histograms

• Outliers and data failure, including box plots

• Bivariate data

Recap on GCSE diagrams

(excl. histograms) in a

single lesson. Since Ss

should be familiar with

these already, this is a

good chance to explore the

AS/Year 1 Applied

Textbook – Chapter

5, Sections 5.1-5.5

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LDS again

CM end of topic test

Week 16&17

10 hours:

trigonometry

• Sine, cosine and tangent functions – unit

circle definitions, graphs and

transformations {1 lesson}

• The sine and cosine rule & ambiguous case

of the sine rule {2 lessons}

• Area of a triangle {1 lesson}

• Understand use trigonometric identities {2

lessons}

• Solving simple trigonometric equations in a

given interval, including quadratic types {3

lessons}

{1 lesson for recap}

½ ab for right-angled

triangles as a special case

of ½ ab sin C

Proof of trigonometric

identities for 0-90o

CM end of topic test

AS/Year 1 Pure

Textbook – Chapters

8&9, Sections 8.1-

8.6, 9.1-9.3

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Week 18 5 hours: exponentials

and logarithms

• Know and use the function ax and its graph,

where a is positive

• Know that the gradient of ekx is k ekx and

hence understand why the exponential

model is suitable in many applications

• Know and use the definition of the

logarithm

• Know and use the function lnx and its graph

• Understand and use the laws of logarithms

• Solve equations of the form ax = b

Difference between a <1

and a >1 (link to laws of

indices)

Link to logic connectives

with x = loga y⇔ y = ax

Proof of laws of logarithms

to improve understanding

AS/Year 1 Pure

Textbook – Chapter

10, Sections 10.1-

10.4

Week 19 5 hours: exponentials

and logarithms

• Understand and use the laws of logarithms

• Solve equations of the form ax = b

• Use logarithmic graphs to estimate

parameters of the form y = axn and

y = kbx

• Understand and use exponential growth and

decay

Ss to establish results

themselves to recap on

straight lines

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

10, Sections 10.4-

10.6

Week 20

5 hours: probability

• Understand and use mutually exclusive and

independent events when calculating

AS/Year 1 Applied

Textbook – Chapter

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probabilities

• Venn diagrams and tree diagrams

• Understand and use simple, discrete

probability distributions

• Link to continuous and discrete distributions

Probability mass/density

functions

CM end of topic test

6, Sections 6.1-6.4

Week 21

5 hours: probability

• The binomial distribution as a model;

calculate probabilities using the binomial

distribution

Link to binomial expansion.

Explain reasoning behind

the formula, including nCr

Use of calculator and

tables to find probabilities

CM end of topic test

AS/Year 1 Applied

Textbook – Chapter

6, Sections 6.5-6.8

Week 22 5 hours: hypothesis

testing

• Understand and apply the language of

statistical hypothesis testing

• Conduct a statistical hypothesis test

Distinction between one-

tailed and two-tailed tests

CM end of topic test

AS/Year 1 Applied

Textbook – Chapter

7, Sections 7.1-7.4

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Week 23&24:

10 hours:

differentiation

• Understand and use the derivative of f(x) as

the gradient of the tangent to the graph of y

= f(x) at the general point (x,y); the gradient

of the tangent as a limit; interpretation as a

rate of change

• Differentiation from first principles

• Turning & stationary points

• Sketching the gradient function for a given

curve

• Tangents and normal

• Identify where functions are increasing and

decreasing

• Maxima/minima problems

Make Ss calculate gradient

using tangent-method (so

they see why we need an

alternative).

Introduce (informally) what

a limit is and practice

calculating limits; in

particular, limits to 0

Link to straight lines and

inequalities

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

11, sections 11.1-

11.10

Week 25

5 hours: Integration

• Know and use the Fundamental Theorem of

Calculus

• Integrate xn

• Evaluate definite integrals

• Area under curves

Use integration as the

reverse process of

differentiation

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

12, sections 12.1-

12.6

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CM © crashMATHS Limited

Week 26 5 hours: vectors

• Use vectors in two dimensions

• Calculate the magnitude and direction of a

vector and convert between component

form and magnitude/direction form

• Vector manipulation and their geometric

interpretations

• Understand and use position vectors; use

vectors to calculate the distance between

two points

• Use vectors to solve problems

Make sure students know

the conventions for the

direction of a vector

Extension of the formula

for length of a line

segment

CM end of topic test

AS/Year 1 Pure

Textbook – Chapter

13, sections 13.1-

12.5

Week 27 5 hours: models in

mechanics and

kinematics

• Understand the modelling assumptions in

mechanics

• Understand and use the language of

kinematics: position; displacement; distance

travelled; velocity; speed; acceleration.

{1 lesson}

• Understand, use and interpret graphs in

kinematics {1 lesson}

• Solve problems involving constant and

variable acceleration {3 lessons}

Simple non-kinematic

cases of calculating area

under a graph, where the

region is a trapezium

Link to

differentiation/integration

CM end of topic test

AS/Year 1 Applied

Textbook – Chapters

8/9, sections 8.1,

9.1-9.4

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Week 28 5 hours: Newton’s

Laws

• Newton’s laws {1 lesson}

• Motion in 2D {1 lesson}

• Connected particles and pulleys {2 lessons}

• Recap lesson {1 lesson}

Link to vectors

CM end of topic test

AS/Year 1 Applied

Textbook – Chapter

10, sections 10.1-

10.4

Remaining time is revision time!