INTEGERS
whole numbers (both positive and negative, including zero).
…-3, -2, -1, 0, 1, 2, 3…
NATURAL NUMBERS
positive integers.
1, 2, 3…
RATIONAL NUMBERS
can be written as a fraction where numerator and denominator
are integers.
1/2, 4, 1.75 (=7/4).
IRRATIONAL NUMBERS
which cannot be written as fractions where numerator and
denominator are integers.
SQUARE NUMBERS
can be obtained by multiplying an integer by itself
36 is a square number because it is 6 x 6.
PRIME NUMBERS
numbers which has ONLY two divisors, 1 and itself
2, 3, 5, 7, 11……..
REAL NUMBERS
All rational and irrational numbers.
-3, 3.25, 1.7897
HIGHEST COMMON FACTOR
The highest common factor (HCF) of two or more numbers is
the largest number which can divide all of them.
LOWEST COMMON MULTIPLE
The lowest common multiple (LCM) of two or more numbers is
the smallest number that all of them can divide.
STANDARD FORM
Standard form helps you to write very large or very small
numbers in an easily readable manner.
The standard form is of the format A x 10^n,
A is a decimal between 1 and 10.
n is an integer.
40000 = 4 x 10000 = 4
x 10^4
42300 = 4.23 x 10000
= 4.23 x 10^4
0.0423 = 4.23/100 =
4.23 x 10^-2
0.0000423 =
4.23/100000 = 4.23 x 10^-5
RATIOS
Ratios are equivalent to fractions.
Ahmed has $30 and Jane has $60.
The ratio of Ahmed’s money to Jane's money is 30 : 60 = 1 :
2 in simplified form.
The ratio of Ahmed’s money to total sum is 30 : 90 = 1: 3 in
simplified form.
The ratio of Jane's money to total sum is 60 : 90 = 2 : 3 in
simplified form.
DIRECT PROPORTION
a is proportional to b.
If a increases, b will increase.
If a decreases, b will decrease.
INVERSE PROPORTION
a inversely proportional to b.
If a increases, b will decrease.
If a decreases, b will increase.
INEQUALITY
To solve an inequality, you may
- Add a number to both sides.
- Subtract a number from both sides.
- Multiply both sides by a number.
- Divide both sides by a number.
Note that if you multiply/divide an inequality by a negative
number, the inequality sign will reverse.
SETS
Set is a collection of objects (elements).
A = { 1, 2, 3, 4, 5}. This set has 5 elements.
EQUAL SETS & NULL SET
Two sets are said to be equal if they have same elements.
A = { 1,2,3,4,5} B =
{ 1,5,3,4,2} C = { 1,3,5,7,9}
A and B are equal sets, A = B.
A and C are not equal sets, A ≠ C.
Null set has no elements. It is denoted by { }.
UNION OF TWO SETS
Set of all elements that appear in either set.
A = { 1, 2, 3, 4, 5 }
B = { 2, 4, 5, 7, 8 }
A U B = { 1, 2, 3, 4, 5, 7, 8 }
If an element appears in both sets, write it only once.
INTERSECTION OF TWO SETS
Set of all elements that appear in both sets.
A ={ 1, 2, 3, 4, 5 }
B = { 2, 4, 5, 7, 8 }
A intersection B = { 2, 4, 5 }
SUBSET
Set A is a subset of B, if all elements of A are in B.
A = { 2, 4, 5 }
B = { 2, 4, 5, 7, 8 }
MATRICES
Matrix is an arrangement of elements in rows and columns
enclosed in brackets.
If a matrix has only one row, it is called ROW MATRIX.
If a matrix has only one column, it is called COLUMN MATRIX.
If a matrix has equal number of rows and columns, it is
called SQUARE MATRIX.
ORDER OF A MATRIX is Number of rows x Number of columns.
Two matrices can be added or subtracted if they are of the
same order.
Add or subtract corresponding elements.
Scalar multiplication is the operation of multiplying a
matrix by a scalar(number).
Multiply all elements in the matrix by the scalar.
LINE OF SYMMETRY
If a shape has a line of symmetry, the line of symmetry will
divide the shape into two equal parts.
One half of the shape can be folded along the line of
symmetry to fit exactly onto the other half.
ROTATIONAL SYMMETRY
If rotating a shape through an angle (< 360 degrees) produces an
identical shape, it has rotational symmetry.
When rotating through 360 degrees, an equilateral triangle matches
its own outline 3 times. So it has rotational symmetry of order 3.
