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Mathematical Studies Standard Level for the IB Diploma
Copyright Cambridge University Press 2014. All rights reserved. Page 1 of 15
Revision Topic 1: Number and algebra
Different types of numbers
You need to know that there are different types of numbers and recognise which group a particular number belongs to:
Type of number
Symbol
Contains
Explanation
Natural numbers
N
0, 1, 2, 3,
…
Zero followed by the counting numbers. Integers
Z
…,
−4,
−3,
−2,
−1,
0, 1, 2, 3,
…
The whole numbers with direction; consist of all natural numbers with a positive or negative sign. Rational numbers Q All fractions which are ratios of integers Includes all integers as they can be written as fractions too. Irrational numbers Numbers that cannot be expressed as ratios of integers, including special numbers like
or e and square roots of prime numbers If a number
can’t
be written as a fraction using integers, it is irrational. Real numbers R All the rational and irrational numbers together Rational and irrational numbers split the real numbers into two groups.
Approximation and estimation
Only round an answer at the end of a calculation, unless you are estimating.
Unless specified otherwise, round to 3 significant figures if your answer
isn’t
exact.
Estimate the answer by rounding numbers to make an easy calculation, and use this estimate to check that your answer makes sense. In summary, to round to a given number of decimal places or significant figures: Decimal places
–
count the number of places to the right starting from the decimal point. Significant figures
–
count the number of figures starting with the leftmost non-zero figure.
Chapter 1: Number
Mathematical Studies Standard Level for the IB Diploma
Copyright Cambridge University Press 2014. All rights reserved. Page 2 of 15
In both cases:
Count the number of places/figures.
Then look at the next digit to the right.
If this digit is 5 or above, add 1 to the previous digit; otherwise, leave the previous digit.
Leave off the rest of the digits.
Percentage errors
From your formula booklet, the percentage error
is given by , where is the exact value and is the approximate value of
v
. So, to calculate the percentage error, work out the difference between the exact value and your estimated value, then divide this difference by the exact value and multiply by 100.
Expressing very large and very small numbers in standard form
On your GDC, numbers are given in standard form (also called scientific notation) if they are too long to fit on the screen. You need to rewrite the calculator notation in the form
a
× 10
k
, where 1
≤
a
< 10 and
k
is an integer. You should use your GDC for all questions involving numbers expressed in standard form. The following table shows how numbers in standard form are displayed on your calculator and how you should interpret them.
Texas TI-84
Write this down on paper as
Casio
fx-9750GII
(don’t
forget to round to 3 s.f.) To input numbers written in standard form, use the following key presses:
Mathematical Studies Standard Level for the IB Diploma
Copyright Cambridge University Press 2014. All rights reserved. Page 3 of 15
Texas TI-84
How it will look written on paper
Casio
fx-9750GII
Mathematical Studies Standard Level for the IB Diploma
Copyright Cambridge University Press 2014. All rights reserved. Page 4 of 15
SI units
The following are the SI
‘base’
units that you should be familiar with:
Measuring Called
You write
Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Intensity of light candela cd You need to be able to convert between different units, and to give your answer in SI units. Other units are derived from these base units, such as m
2
for area or m
3
for volume; you might also use metres per second, , for speed.

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