Download LC HL scheme

St Vincent’s Secondary School Glasnevin
Maths Department
Scheme of work (full Project maths)
Leaving Certificate , Higher level
66 weeks (396 classes max; 264 hours)
YEAR 1
Date
Sept.
Topic
Time
Frame
Polynomial Expressions: Students will 1 Week
be able to add and subtract polynomial
expressions.
Multiply
polynomial
expressions. They will learn about
perfect squares, division of algebraic
expressions,
Polynomial Functions: Students will
meet problems like area of a rectangle
with sides represented by expressions
in 𝑥. They will learn the expression
𝐴(𝑥) for this
Factorising algebraic expressions:
Students will learn to find the highest
common factor by inspection, they will
group terms, they will factorise by
finding the difference of 2 squares,
factorise quadratic expressions, they
will meet expressions of the form 𝑥 3 ±
𝑦 3 and factorise these.
Algebraic fractions and identities:
students will learn to perform addition,
subtraction, multiplication and division
on algebraic fractions. They will work
with algebraic identities in particular
algebraic identities with factors
0.5
weeks
2 weeks
1 week
Assessment
Unless stated
otherwise assessment
will be graded
exercises from the
book for homework as
per the school’s
homework policy
Manipulating Formulae: Students will
learn to re-arrange and manipulate
formulae to put and equation in terms
of another variable.
Solving equations: Students will learn
to solve linear equations and
simultaneous linear equations.
REVISION
TEST
0.5
weeks
0.5
weeks
0.5
Weeks
1 class
Quadratic formula: Students will learn 0.5
to solve quadratic equations using the weeks
−𝑏±√𝑏2 −4𝑎𝑐
quadratic formula 𝑥 =
and
2𝑎
also using graphs
Nature of quadratic roots: Students
will learn about the nature of quadratic
roots be they real, imaginary, equal,
rational
Solving
quadratic
and
linear
equations: Student will be able to solve
the points of intersection of a linear
and quadratic graph and will be able to
form quadratic equations from their
roots as well as finding the max and
min of a quadratic graph
Surds: Students will learn to reduce
surds to their lowest form, simplify
surd quotients, add and subtract surds,
multiply and divide surds.
Surds and the factor theorem:
Students will be able to use surds to
solve algebraic equations and will learn
the factor theorem to factorise cubic
equations.
Cubic polynomials: Students will learn
to plot the graphs of cubic polynomials
REVISION
0.5
weeks
1.5
weeks
0.5
weeks
1 week
0.5
weeks
0.5 week
Chapter test after 6
weeks, results to be
added to ePortal
TEST
1 class
After these five weeks
there will be a
chapter test, results
to be added to
ePortal
Co-ordinate Geometry
MidNov.
Revision of formulae: Students will 1 week
revise the formulae from junior cert coordinate geometry. Area of a triangle:
Students will also learn to find the area
of a triangle using formula
1
𝐴 = |𝑥1 𝑦2 − 𝑥2 𝑦1 |
2
Dividing a line in a given ratio:
Students will learn the formulae for
division of a line internally and
externally in given ratios. They will
apply these formulae to problems
Concurrencies in triangle: Students will
learn the circumcentre, orthocentre
and centroid of triangles
Perpendicular distance from a point to
a line: students will solve real life
problems such as the distance from a
plane to a tower and so on using this
formula.
The angle between two lines: Students
will derive the formula for the angle
between two lines and solve related
problems.
REVISION
TEST
0.5
weeks
0.5
weeks
0.5
weeks
0.5
weeks
0.5
weeks
1 Class
A test on coordinate
geometry of the line
after
3.5
weeks.
Results to be added
to ePortal. (may be
put off due to the inhouse
Christmas
exams)
Trigonometry
Start
Jan.
Radian measure: Students will learn to
measure angles with radians as
opposed to degrees. They will also be
introduced to length of a sector and
area of a sector
Trigonometric ratios: Students will use
trig ratios sin, cos and tan and will
learn the special angles
Trigonometric functions and the Unit
circle: Using the unit circle students
will learn to find the size of an angle
greater than 90˚.
The sine and cosine rules: Students will
learn to use these rules with
confidence. They will be able to use
them to solve problems.
3-D problems: This topic is generally a
difficult one for some students as they
find it hard to visualise the 3-D shapes.
Extra time should be given here.
Graphs of trig functions: Students will
learn to plot the graphs of sin, cos and
tan functions
Trig identities:
Compound angles: Students will learn
to use already established rules like the
cosine rule to solve compound angles
such as sin(a-b)
Double angle and half angle: using
knowledge from compound angles we
will discuss double angles and half
angles.
Sum difference and product rules:
Students will use these rules to solve
problems
Inverse trig functions: Using inverse
trig functions we will be able to discuss
0.5
weeks
0.5
weeks
0.5
weeks.
1.5
weeks
1 week
0.5
weeks
0.5
weeks
1.5/2
weeks
0.5
weeks
differences between angles and ratios
REVISION
TEST
0.5
weeks
1 Class
(also to coincide roughly with midterm)
Complex numbers
Late
Feb.
Irrational numbers and constructing
lines of length √𝟐 and √𝟑 and so on:
Students will use their knowledge of
number systems to classify numbers as
rational or irrational. They will use
compass sets to draw lines of different
lengths
Complex numbers: Students will learn
about complex numbers as roots of
negative terms and will learn the rules
of addition, multiplication and division
Equality of complex numbers: here
we will discuss equating real parts with
real and imaginary with imaginary
Argand diagrams: Students will learn
to plot complex numbers on an Argand
diagram and find the modulus. They
will then translate and transform these
numbers.
Conjugate roots: Using this theorem
students will be able to solve
quadratics in the form of complex
numbers.
Polar form: Students will learn to put
complex numbers in polar form from
rectangular and then do this in radians.
De Moivres theorem: Using this
theorem students will solve problems
in complex numbers.
REVISION
0.5
weeks
1 week
0.5
weeks
1 week
0.5
weeks
0.5
weeks
1 week
0.5
weeks
After 7.5 weeks of
trigonometry we will
have a class test,
results
will
be
entered on ePortal.
TEST
1 Class
There will be a class
test after five weeks.
Area and volume
Start
April
Revision of formulae and trapeziums:
Students will revise JC formulae and
will be introduced to trapeziums
Sectors of circles: Most of this
information will be remembered from
trigonometry. Students will use their
knowledge to solve problems
3-D objects: Students will tackle 3
dimensional problems here.
Trapezoidal rule: Consolidating all their
knowledge from area and volume
students will use the trapezoidal rule.
Nets of shapes: Students will learn to
visualise shapes as nets
REVISION
TEST
0.5
weeks
0.5
weeks
0.5
weeks
0.5
weeks
2 classes
0.5
weeks
1 Class
Sequences and Series
Early
May
Sequences: Students will look at
patterns in a sequence of numbers and
will learn to come up with a formula to
represent the nth term,
Arithmetic sequences: Students will
learn that a sequence which is
increasing by a constant is call
arithmetic and will learn to find the nth
term of these.
Arithmetic series: Students will learn
to find an expression for the sum of a
sequence of numbers.
Geometric sequences: Students will
see that these increase by a given
ration and will have a formula to solve
them
Geometric series/ exponential
functions and sum to infinity: Students
2 classes
0.5
weeks
0.5
weeks
0.5
weeks
1 week
There will be a class
test after four weeks.
will also learn to put recurring decimals
in the form of a series.
REVISION
0.5
weeks
TEST
1 Class
END
YR 1
There will be a class
test after 3 weeks.
(May be cancelled
due to proximity of
summer exams)
End of year 1. Revision until summer exams
YEAR 2
Geometry Theorems and Constructions
Keywords: Students will become
familiar with new keywords for this
section including Axiom, converse,
theorem, corollary, if and only if,
implies, congruent, proof
Theorems: students will learn all
theorems up to theorem 21 but and
how to apply these, they will learn the
proofs of theorems 11,12,13
Corollaries: Students will learn the
relevant corollaries and axioms and
also the converse of theorems where
relevant
Problems: Student will spend some
classes working on problems related to
the theorems and corollaries.
Enlargements: Students will discuss the
scale factor and its relationship to area
and volume; they will learn how to
draw and enlargement through a given
centre or to find the centre of
enlargement.
Constructions: Student will recap their
junior cert constructions (2 classes
max) and will then learn the required
constructions for leaving cert. (16-22)
1 class
1 week
1 week
2 classes
0.5
weeks
0.5
weeks
REVISION
0.5
Weeks
1 class
TEST
Statistics
Late
Sept.
Keywords: Students will learn new
keywords and terms of which there are
many in this section.
Surveys: Students will learn how to
design suitable surveys and the
different sampling methods available
to them.
Averages: Students will learn the
different types of average mean
median and mode as well as when its
best to use either one. The will be reintroduced to frequency tables and
how to find their mean.
Variability of data: Students will learn
how data varies be it range,
interquartile range or standard
deviation.
Standard Deviation: Students will find
the standard deviation of a sample of
data and will learn to draw histograms
of the available data.
Percentiles/ stemplots: Students will
learn to find a percentile score and
construct stem and leaf plots. They will
find the range, median, upper quartile,
lower quartile and interquartile range
of these stemplots
Histograms and curves: Using
histogram drawn students will learn to
see a pattern in the shapes and
discover normal distributions and
skewed distributions.
2 classes
1 week
//
1 week
0.5
weeks
1 week
1 week
1 week
There will be a
chapter test at this
stage after 4.5 weeks.
Results will be added
to ePortal
REVISION
TEST
0.5
weeks
1 Class
There will be a class
test after 8 weeks.
Results
will
be
entered onto ePortal
Probability
Late
Nov.
Start
Jan.
The fundamental principle of
1 week
counting: Student will learn to find the
number of different ways of choosing
things froma list. They will discuss the
differences between combinations and
premutations. The will recap
elementary probability
Sample spaces and experimental
0.5
probability: Students will draw sample weeks
spaces and discuss probability based
on results of previous trials.
CHRISTMAS EXAMS
Mutually exclusive events,
1.5
multiplication rule and conditional
weeks
probability:
Tree Diagrams: Students will draw tree 1 week
diagrams and discuss expected
probability to decide for example
whether fairground competitions are
biased or fair.
Binomial distribution/ Bernoulli trials: 0.5
Students will learn when to use
weeks
bernoulii trials once they satisfy the
conditions such as n number of trials
success or failure etc.
To show events are independent:
0.5
weeks
The normal distribution: using the
1 week
normal distribution to solve probability
problems
REVISION
0.5
weeks
TEST
1 Class
There will be a class
test on all of the
probability.
Statistics 2
Late
Feb.
Scatter diagrams, correlation and
causality.
The normal distribution: following on
from work on the normal distribution
in probability we will look at the
statistics behind it.
Margin of error and hypothesis testing
REVISION
TEST
1 week
1 week
1 week
0.5
weeks
1 Class
There will be a class
test on these three
weeks of statistics.
NOTE: Statistics and probability are major parts of the new project maths course
and take up a considerable amount of time. It is foreseen that the time allocated
above may not be adequate and therefore not set in stone.
Financial maths
Late
March
Compound interest and depreciation: 1 week
Students will learn where the formula
for compound interest comes from and
will use it to calculate compound
interest. They will also look at
depreciation of for example cars.
Savings instalments (annuities)/loans 1 week
and mortgages
Pensions
0.5
weeks
REVISION
0.5
weeks
TEST
1 Class
There will be a class
test after 3 weeks.
Functions (including Differential calculus/Integral calculus)
Logs
Indices
Inequlities
The circle (co-ord geometry)
Methods of proof
Induction
Exam paper revision
Start
May
See note below
Extra
classes
necessary
NOTE: At this stage is will not be practical to
include time frames. From the course this year it
has been evident that the new Leaving Cert
higher level course is too large and there is not
adequate time to fully prepare students for what
they are required to learn. Extra classes had to
be given this year in the mornings at 8am for
months to be at the stage we are now. THE
COURSE IS TOO PACKED AND IS IMPOSSIBLE TO
TEACH IN THE ALLOTTED TIME.