MATH101 Comprehensive Maths Concepts:
Numbers, Algebra, Ratios, Proportions, Geometry,
Trigonometry, Probability, Statistics, Matrices
Prime factorisation - Writing a number as a product of its prime factors (use a factor tree,
until all bottom numbers are prime)
Natural numbers - Whole, positive
Integers - Whole, positive, negative
Real numbers - Integers including decimals - two subsets
Real numbers - rational - Integers or fractions
Real numbers - irrational - Decimals or numbers that cannot be written as a fraction
Percentage change - change/original x 100
Compound interest - amount x 1. percentage to number of years
Order of operations - BEDMAS
Dividing fraction - first term x reciprocal of second term
-3²=-9 - (-3)²=9
Exponential growth - Use same formula as compound interest
∅ - The empty set (proper subset)
,ℰ - Universal set
∈ - is an element of {set}
∉ - is not an element of {set}
A ⊂ B - A is a proper subset of B
A ⊆ B - A is a subset of B
Proper subset - All subsets except the original set (P)
Venn diagrams - A' - Complement of A (all items not in A)
A ∩ B - Intersection of A and B (items in both)
A ∪ B - Union of A and B (items in A or B or both)
2-² - 1/4 (The reciprocal of the number without the negative)
Vulgar fraction - A fraction represented by a numerator and denominator and not by
decimals.
Multiplying with indices - Add indices, numbers stay
Dividing with indices - Subtract indices, numbers stay
Adding and subtracting indices - Powers and variables must be the same
n(A) - Number of elements in set A
Vulgar fractions - All fractions excluding mixed fractions
0.7 recurring as a fraction - 10f = 7.777..., 10f-f=7, 9f=7, f=7/9
, 0.3181818 recurring as a fraction - 100f =31.818181..., 100f-f=31.5, 99f=31.5,
f=315/990=7/22
Upper and lower bounds - Minimum and maximum any rounded number could possibly
be
x to the power of ½ - the square root of x
x to the power of ¾ - (the fourth root of x)cubed x to the power of -¼ - 1/the fourth
root of x
x to the power of -¾ - 1/(the fourth root of x)cubed
x to the power of -5 - The reciprocal of x to the power of 5 (1/x to the 5)
ax to the power of -5 - a/x to the power of 5
Solve Inverse proportion (a ∝ the reciprocal of b) - Find total by multiplying values (a=k/b,
k=constant)
Solve Direct proportion (a ∝ b) - Divide to find the constant of proportionality (a=kb,
k=constant)
Average speed - Distance/time
Increase or decrease by a percentage - Find the multiplier (24%=0.24)
Currency conversions - Use value that is not one for both exchanges (either times by for
currency represented by 1 or divide by for currency represented by point
something)
Numbers, Algebra, Ratios, Proportions, Geometry,
Trigonometry, Probability, Statistics, Matrices
Prime factorisation - Writing a number as a product of its prime factors (use a factor tree,
until all bottom numbers are prime)
Natural numbers - Whole, positive
Integers - Whole, positive, negative
Real numbers - Integers including decimals - two subsets
Real numbers - rational - Integers or fractions
Real numbers - irrational - Decimals or numbers that cannot be written as a fraction
Percentage change - change/original x 100
Compound interest - amount x 1. percentage to number of years
Order of operations - BEDMAS
Dividing fraction - first term x reciprocal of second term
-3²=-9 - (-3)²=9
Exponential growth - Use same formula as compound interest
∅ - The empty set (proper subset)
,ℰ - Universal set
∈ - is an element of {set}
∉ - is not an element of {set}
A ⊂ B - A is a proper subset of B
A ⊆ B - A is a subset of B
Proper subset - All subsets except the original set (P)
Venn diagrams - A' - Complement of A (all items not in A)
A ∩ B - Intersection of A and B (items in both)
A ∪ B - Union of A and B (items in A or B or both)
2-² - 1/4 (The reciprocal of the number without the negative)
Vulgar fraction - A fraction represented by a numerator and denominator and not by
decimals.
Multiplying with indices - Add indices, numbers stay
Dividing with indices - Subtract indices, numbers stay
Adding and subtracting indices - Powers and variables must be the same
n(A) - Number of elements in set A
Vulgar fractions - All fractions excluding mixed fractions
0.7 recurring as a fraction - 10f = 7.777..., 10f-f=7, 9f=7, f=7/9
, 0.3181818 recurring as a fraction - 100f =31.818181..., 100f-f=31.5, 99f=31.5,
f=315/990=7/22
Upper and lower bounds - Minimum and maximum any rounded number could possibly
be
x to the power of ½ - the square root of x
x to the power of ¾ - (the fourth root of x)cubed x to the power of -¼ - 1/the fourth
root of x
x to the power of -¾ - 1/(the fourth root of x)cubed
x to the power of -5 - The reciprocal of x to the power of 5 (1/x to the 5)
ax to the power of -5 - a/x to the power of 5
Solve Inverse proportion (a ∝ the reciprocal of b) - Find total by multiplying values (a=k/b,
k=constant)
Solve Direct proportion (a ∝ b) - Divide to find the constant of proportionality (a=kb,
k=constant)
Average speed - Distance/time
Increase or decrease by a percentage - Find the multiplier (24%=0.24)
Currency conversions - Use value that is not one for both exchanges (either times by for
currency represented by 1 or divide by for currency represented by point
something)
