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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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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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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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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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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!