ZNOTES.ORG
UPDATED TO 2022 SYLLABUS
CAIE CHECKPOINT
MATHEMATICS
SUMMARIZED NOTES ON THE PROBLEM SOLVING SYLLABUS
CAIE CHECKPOINT MATHEMATICS
1. Using understanding and
Strategies in solving
problems
1.1. Stage 7
Strategic thinking allows us to carefully solve any
problem.
Data presented in the form of graphs must be carefully
analysed (frequency, mode, median etc).
Mathematical symbols (+, -, /, x) are used as operations in
problems.
In more advanced mathematics, symbols such as pi are
used.
Mathematical patterns must be identified by proper
analysis.
E.g. 1, 1, 2, 3, 5, 8…(the pattern is to add the previous two
numbers together to get the next number)
Working logically will require the use of applying past
learned concepts to a given problem (e.g. proportion,
graphs, area, algebra etc)
We must always check what the question is asking us to
find.
Explaining results must include the calculations we did,
what methods we use, our findings as well as the unit (if
applicable).
1.2. Stage 8
Mathematical symbols can be identified with the proper
understanding of the question.
E.g. “AND” => To add, “OR” => To make multiple cases.
Exceptional/counter examples are the method of finding
what is NOT asked, and this is commonly used in
probability questions.
The truth of a statement can only be proved when the
findings (answers) are substituted into the question.
The solutions and answers must be accurate in terms of
significant figures (5 or more for working, 3 or more for
answers).
To reason out solutions, make sure to include evidence
from the question about specific details.
Comparing solutions can be done by presenting it in
different ways (e.g. pie charts, bar graphs, providing
detailed solutions for reasoning etc).
Refining approaches while discussing with others can
help us double-check our methods and see if there is any
simpler or more logical way of solving a question.
WWW.ZNOTES.ORG
E.g. Finding out the official provided solution, asking the
teacher for simplified working, etc.
1.3. Stage 9
Multiple data can be stored in the form of statistical
diagrams (table, stem-and-leaf, histogram, bar chart, pie
chart etc).
While creating a diagram, keep in mind the titles for the
data of each set.
Irrelevant facts must not be paid attention to.
Counter-examples can be used to prove a statement not
true.
E.g. For every integer n, prove that n^3 is positive.
Solution:
If n is positive, then n^3 is positive (3^3 = 27).
If n is negative, then n^3 is negative ([-3]^3 = -27)
Thus proved false.
Reasoned solutions must include given facts from the
question as evidence.
Assumptions (unless stated in the question), have the
ability to prove a statement for more general questions,
but they can lead to wrong answers for more specific
questions.
Recognising connections and similarities between subparts of questions will allow us to become more efficient
in solving questions.
It is important to read through the entire question at
least once without solving.
Alternative strategies often help building a stronger
foundation, allowing us to be able to answer more
general questions on the same topic.
2. Using Techniques and
Skills in Solving Mathematical
Problems
2.1. STAGE 7
The laws of arithmetic (PEMDAS) will be used while
calculating complex mathematical equations.
PEMDAS ==> Parentheses, exponent, multiplication, division,
addition, subtraction
Multiplication and division can be done on which
operation comes first. The same goes for addition and
subtraction.
Other operations such as modulus, absolute value, floor
and ceiling functions, will help us with calculations in
higher mathematics.
Units of measurement, such as meters, kilograms, and
litres, are used in our daily lives while performing
CAIE CHECKPOINT MATHEMATICS
activities (e.g. weight, driving, gasoline etc)
Two-dimensional shapes have length and width (breadth),
while 3D figures also have depth as a dimension.
To draw accurate mathematical diagrams and graphs,
create a frequency table to simplify raw data.
To check whether the answer is true, check the answer of
the inverse and then subtract it from 1 in probability
questions.
In questions requiring us to approximate, we must round
off the values and then calculate.
Working must always be double-checked in order not to
miss anything out.
The usual number of significant figures is 3. More than 3
figures are also accepted.
During intermediate working, we have to round off nonterminating decimals to 5 significant figures or more.
2.2. STAGE 8
To simplify algebraic expressions, we can either factorise
or move all terms to one side.
Estimation of measurements of units can be done by
using the ratios.
Solving quadratic equations can be done by using the
quadratic formula.
2.3. STAGE 9
Significant figures are numbers or digits required in
mathematics in order to give a proper quantity.
WWW.ZNOTES.ORG
Double-checking the answer will help us to realize
whether we made a mistake or not.
E.g. If we get an answer as -4:30 p.m., we can immediately
interpret that our answer is wrong since time cannot be
negative.
It is important to pay attention to the UNITS.
CAIE CHECKPOINT
Mathematics
Copyright 2022 by ZNotes
These notes have been created by Kartik for the 2022 syllabus
This website and its content is copyright of ZNotes Foundation - © ZNotes Foundation 2022. All rights reserved.
The document contains images and excerpts of text from educational resources available on the internet and
printed books. If you are the owner of such media, test or visual, utilized in this document and do not accept its
usage then we urge you to contact us and we would immediately replace said media.
No part of this document may be copied or re-uploaded to another website without the express, written
permission of the copyright owner. Under no conditions may this document be distributed under the name of
false author(s) or sold for financial gain; the document is solely meant for educational purposes and it is to remain
a property available to all at no cost. It is current freely available from the website www.znotes.org
This work is licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International License.