CONTENTS
ABOUT THIS BOOK .....................................................................2
THE NON-CALCULATOR PAPER ...............................................3
ALGEBRA ....................................................................................4
Number Systems ....................................................................... 4
Accuracy and Standard Form .................................................... 5
Sequences and Series ............................................................... 6
Sequences and Series – Applications ........................................ 8
Exponents.................................................................................. 8
Logarithms ............................................................................... 11
The Binomial Expansion .......................................................... 13
FUNCTIONS AND EQUATIONS ................................................. 15
Basics of Functions.................................................................. 15
Functions and Graphs with a GDC .......................................... 17
Graphs of Functions ................................................................ 19
Linear Functions ...................................................................... 21
Reciprocal Functions ............................................................... 22
Quadratic Functions................................................................. 24
Solving Quadratic Equations .................................................... 25
Exponential and Logarithmic Functions ................................... 27
CIRCULAR FUNCTIONS AND TRIGONOMETRY ..................... 28
Definitions and Formulae ......................................................... 28
Harder Trigonometric Equations .............................................. 31
Solution of Triangles ................................................................ 33
VECTORS ................................................................................... 36
Basics of Vectors ..................................................................... 36
Scalar Product ......................................................................... 38
Vector Equations of Lines ........................................................ 39
Lines in 3 Dimensions .............................................................. 41
STATISTICS AND PROBABILITY .............................................. 43
Basics of Statistics ................................................................... 43
Cumulative Frequency ............................................................. 46
Correlation ............................................................................... 49
Probability Notation and Formulae ........................................... 51
Lists and Tables of Outcomes.................................................. 52
Venn Diagrams ........................................................................ 53
Tree Diagrams ......................................................................... 54
Discrete Probability Distributions ............................................. 55
The Binomial Distribution ......................................................... 57
The Normal Distribution ........................................................... 60
CALCULUS ................................................................................ 64
Differentiation – The Basics ..................................................... 64
Differentiation from First Principles .......................................... 65
The Chain Rule ........................................................................ 66
Product and Quotient Rules ..................................................... 67
Second Derivative.................................................................... 68
Applications of Differentiation .................................................. 69
Indefinite Integration ................................................................ 72
Definite Integration................................................................... 74
Volumes of Revolution ............................................................. 75
Calculus – Using the Calculator ............................................... 76
Calculus – Non-Calculator Work .............................................. 77
MAXIMISING YOUR MARKS ..................................................... 79
ASSESSMENT DETAILS ........................................................... 80
PRACTICE QUESTIONS ............................................................ 81
IBDP Mathematics SL
Page 1
THE NON-CALCULATOR PAPER
The format of the two exam papers is the same – a section A
consisting of short answer questions, and a section B involving
extended response questions. However, calculators are only
allowed to be used in the Paper 2.
It is not intended that Paper 1 will test your ability to perform
complicated calculations with the potential for careless errors. It is
more to see if you can analyse problems and provide reasoned
solutions without using your calculator as a prop. However, this
doesn’t mean that there are no arithmetic calculations. You should,
for example, be able to:
Add and subtract using decimals and fractions:
Examples:
18.43  12.87, 2 21  3 52
Multiply using decimals and fractions (brush up your
multiplication tables):
Examples:
432  14, 12.6  5, 21  52  32  41 , (2  106 )  (5.1 104 )
Carry out simple divisions using decimals and fractions
Examples:
14  0.02, 1 21  53 , find x as a fraction is simplest form if 999x = 324
And don’t forget that divisions can be written as fractions, eg:
9  15  159  53  0.6
Fraction simplification can help with more complex calculations:
Convert 81km/h to m/s
81 1000 81 10 9  10 9  5 45




 22.5m/s
3600
36
4
2
2
Percentage calculations:
Examples:
15% of 600kg, Increase 2500 by 12%, what is 150 as a percentage
of 500.
Quadratic equations
You will be called on to solve quadratic equations many times
in the papers. Solving by factorisation is easier than using the
formula when you are not using a calculator.
Examples:
2
2
Solve x + 7x – 60 = 0; 3x – 19x + 20 = 0
NOTE: The Revision Guide contains many boxed questions which
are either worked examples or practice questions. Any which would
be hard to solve without a calculator will be shown with a double line
(as in this box). For the remaining questions, calculator use is either
irrelevant (for example, differentiating a function), or the question
could be answered both with and without a calculator. In the latter
case, it would be sensible for you to answer the question without a
calculator, and then check your answer with a calculator.
IBDP Mathematics SL
Page 3
ALGEBRA
Number Systems
Different situations require different types of number. For example,
populations of countries will always be given as positive whole
numbers, whereas the division of a reward will require the use of
fractions. These are known as number systems, and the ones you
need to know are:
 Natural numbers – positive whole numbers.
 Integers – whole numbers including negatives and zero.
 Rationals – numbers which can be written as fractions.
 Irrationals – numbers which can’t be written as fractions.
 Reals – the rationals and the irrationals put together. The
reals will include every possible number you could meet in
the course.
Symbols:
Naturals

Integers

Rationals

Irrationals

Reals

The diagram below shows how the sets are related to each other.
For example, every integer can be written as a rational ( 4  41 ) so
the integers are a subset of the rationals.
Reals
Rationals
Irrationals
Integers
Naturals
Decimals do not seem to feature in the list above – are they
rational or irrational?
 Recurring decimals can always be written as fractions so
they are rational numbers.
 Terminating decimals can also be written as fractions, so
they are rational numbers too.
 Non-recurring, non-terminating decimals (ie they carry on
for ever and never repeat) can never be written as an
exact fraction, so they are irrational numbers.
To be strictly accurate, x = 10
5
b
a
4
9
Page 4
Exact values: 4 = 2 since 4 is a square number. However, 10
cannot be written exactly, like the majority of square roots. It is
3.16228… (the dots indicate that the decimal places will continue
for ever without recurring). To 4 significant figures, 10 is 3.162,
but what do you do if the question asks for an exact value? The
answer is to use the square root notation:
x2 = 10  x = 10
and this is the only exact way to write down the solution. And,
especially if this is an intermediate answer to a question, it is often
better for calculation purposes.
eg: Find the lengths a and b.
a2 = 92 + 42 = 97  a = 97
b2 = a2 – 52 = 97 – 25 = 72
So b = 72. The calculation would have been longer (and possibly
less accurate) if we had worked out 97 as a decimal and used
that.
IBDP Mathematics SL