Chapter 1: Numbers and Language
Natural numbers
A set of whole numbers from 0 to +∞.
N= {0,1,2, 3,…}.
Integers
Set of whole numbers from - to +0.
Z= {…, -3,-2,-1,0,1,2,3,…).
Rational numbers
All numbers that can be written as a fraction, whose denominator is not zero, or terminating and recurring decimals, as they can be written as a fraction.
Q={…,0. 2,…,2/9…,7,…}.
Chapter 2: Accuracy
Approximation
They can be rounding, decimal places or significant figures.
Rounding
A number can be reported to various levels of accuracy, i.e., the nearest 1,000 of 28,617 would be rounded up to 29,000; the nearest 10 of 8847 would be rounded up to 8850.
Decimal place (d.p.)
When a number has decimals, it can be approximated to a decimal point, given a decimal place (d.p.), e.g.: 7.864 to 1 d.p. is 7.9.
Significant figures (s.f.)
The number of digits in a value, which contribute to the degree of accuracy of the value. E.g.: 43.25 to 3 s.f. is 43.3.
Estimate
Done by rounding numbers in a way that the calculations become straightforward.
Chapter 3: Calculations and other
Ordering
The mathematics symbols have a specific meaning:
= is equal to
is greater than
is greater than or equal to
< is less than
< is less than or equal to.
The order of operations
By following the BIDMAS rule:
- Brackets {[0]}
- Indices √(x) xn
- Division +
- Multiplication x
- Addition +
- Subtraction -
Chapter 4: Integers, fractions, decimals, and percentages
Chapter 5: Further percentages
Chapter 6: Ratio and proportion
Direct proportion
Ratio method
x:y=z: w
Unitary method
Value of one unit = Total value / No. of units
Chapter 7: Indices and standard form
Index
It's the power to which a number is raised.
Standard form
Aka scientific notation, it involves the writing of numbers in term of powers of 10.
Chapter 8: Money and finance
Interest
SI (simple interest) = P (principal, amount borrowed) x t (time in years) x r% (interest rate)
I (compound interest) = P (principal, amount borrowed) x [ 1 +r% (interest rate)] (time in years) - P
Chapter 9: Time
1 year= 365 days; 1 day= 12 hours; 1 hour= 60 minutes; 1 minute= 60 seconds.
Chapter 10: Set notation and Venn diagrams.
Set
A set is a defined group of elements. An element is an object or a symbol. I.e., if e belongs to a set S: e E S, if e does not belong to a set S: e # S.
Subset
If all elements of a set X are also elements of another set Y, then X is the subset of Y i.e., XY. A set is subset of all sets if it is empty, there are not any elements, it is called an empty set. To find the number of subsets: 2n
Universal set
It is a set which has all the possible elements of a problem. It is written as:
Complement
The complement of a set A is the sets of all elements that are in and not in A.
Venn diagrams
It is the principal way of showing sets of diagrams. The intersection of sets is represented by n. The union of sets is represented by U.
