Last Minute Review:(check list)
Quantitative section
 Basic mathematic rules and Arithmetic questions:
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Type of numbers:
Natural Numbers
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
Integers
Integers consist of positive natural numbers, their negatives and the number zero. Fraction or decimal values
are not considered as integer numbers (…. -3, -2, -1, 0, 1, 2, 3 ....)
Rational Numbers
A rational number is a number which can be expressed as a ratio of two integers. Non-integer rational numbers
(commonly called fractions) are usually written as a/b, where b is not zero.
Irrational Numbers
An irrational number is any real number that is not a rational number. We cannot express irrational number as
fraction a/b, where a and b non-zero. An example of an irrational number is π ≈ 3.141592653589793...
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Mathematical operations:
(+, −, ×, ÷) are the arithmetic operations
Besides these operations we have parentheses(brackets). Exponents and Radicals (roots) as well
Order of operations:
1.
2.
3.
4.
Parentheses (brackets)
Exponents or radicals (roots)
Division / Multiplication
Addition / Subtraction
For 3. and 4. we follow the order from left to right
Example:
Compute 4 − 8 x (3 + 2) + 42
Step 1: first solve parentheses
(3+2) = 5
So, 4 – 8 x (3+2) + 42 = 4 – 8 x 5 + 42
Step 2: solve exponent (power)
4 – 8 x 5 + 42 = 4 – 8 x 5 + 16
Step 3: solve multiplication/division
4 – 8 x 5 + 16 = 4 – 40 + 16
Step 4: solve addition and subtraction (from left to right)
4 – 40 + 16 = - 36 + 16
= - 20 ans
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Composite and Prime number:
A composite number is a number with more than 2 factors while a prime number is a number with 2 factors
only: 1 and the number itself.
A) 2, 3, 5, 7, 11, 13 …. are prime numbers since they are only divisible by themselves
B) 4, 6, 8, 9, 10, 12 …. are composite numbers since all of them have multiple factors
Example:
1) 121 – 121 is a product of 11 x 11. Since, 121 is divisible by other number besides itself it is not
considered as a prime number. It is a composite number
2) 123 – this on the other hand is only divisible by itself so this is a prime number
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Divisibility:
A divisibility test is a rule for determining whether one whole number is divisible by another. It is a quick
way to find factors of large numbers.
2
3
The sum of all digits of the given
number must be divisible by 3
4
if last two digits of any number are
divisible by 4, whole number is
divisible by 4
5
Any number that ends with ‘0’ or
‘5’ is divisible by 5
For a number is to be divisible by
6 it must be divisible by both 2
and 3
6
2
Divisibility test
The number must be even
Example
161 – it is an odd number so it is
not divisible by 2.
322 – it is an even number so it is
divisible by 2.
134 – 1+3+4=8, since 8 is not
divisible by 3,134 isn’t divisible by
3 as well.
882 – 8+8+2=18, as 18 is divisible
by 3, 882 is divisible by 3
234 – 34 is not divisible by 4 so
234 isn’t divisible by 4
284 – 84 are divisible by 4 so 284
as whole is divisible by 4 as well
505 – as this number ends with
digit 5 it is divisible by 5
162 – it is an even number so it is
divisible by 2.
1+6+2 = 9, as 9 is divisible by 3,
162 as whole is divisible by 3 as
well.
Since, 162 is divisible by both 2
and 3 so, it is divisible by 6 as
well.
7
Take the last digit of the number,
double it Then subtract the result
from the rest of the number If the
resulting number is evenly
divisible by 7, so is the original
number.
It is similar to the divisibility test
for 4. For a number to be divisible
by 8, its last three digits must be
divisible by 8
8
9
Its divisibility test is similar to that
of 3.
The sum of all digits of a number
must be divisible by 9.
10
Numbers that end with 0 are
divisible by 10
11
Take the alternating sum of the
digits in the number, read from left
to right. If that is divisible by 11,
so is the original number.
Rest of the numbers
Divisibility tests for numbers after
11 are similar to the rule used to
check divisibility of 6
184 – it is an even number so it is
divisible by 2, but since 1+8+4 =
13, and 13 is not divisible by 3,
184 is not a multiple of 3
As 184 is divisible by 2 but, not
divisible by 3, we cannot divide
184 by 6.
651 –
Double of last digit --> 1x2 = 2
65 - (1x2) = 63, as 63 is
divisible by 7, 651 as whole is
also divisible by 7.
1168 – 16 as well as 8 is divisible
by 8 so, 1168 as whole is also
divisible by 8.
1227 – this is not divisible by 8 as
227 is not divisible by 8.
189 – 1+8+9=18. Since, 18 is
divisible by 9 so 189 is divisible by
9.
277 – 2+7+7 =16. as 16 is not
divisible by 9, 277 is not a multiple
of 9.
10, 20, 30, 100, 200, 350, 1010 all
these are examples of numbers
divisible by 10 since, their last
digits are 0.
396 –
3 - 9 + 6 = 0, hence 396 is
divisible by 11.
3729 –
3 - 7 + 2 – 9 = -11, as –11 is
divisible by 11, 3729 is divisible by
11.
For example, if we want to check
whether a number is divisible by
12 or not. The number must be
divisible by 3 and 4
e.g. 264 is divisible by 3 as well
as 4 so it is divisible by 12.
For example, if we want to check
whether a number is divisible by
15 or not. We will have to check
the number for its divisibility by 3
and 5
e.g. 255 is divisible by both 3 and
5 so, it is divisible by 15 as well.
Using divisibility tests makes it easier to identify factors of any number. This also help us to check whether
a number is divisible by other numbers or not. Hence, we can identify prime numbers easily as well.
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3
HCF and LCM:
HCF: Highest Common Factor - Highest Common Factor (HCF) of two non-zero integers are the largest
positive integer that divides both numbers without remainder.
LCM: Least Common Multiple - The Least Common Multiple (LCM) of two integers is the smallest
positive integer that is a multiple of both numbers. Since it is a multiple, each integer divides it without
remainder. If there is no such positive integer, then LCM between the two integers is defined as zero.
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Fractions:
Addition / subtraction of fractions:
Steps:
1.
2.
3.
4.
5.
The denominators of fractions must be same before we add two or more fractions
We take LCM of all denominators
We multiply a constant factor with numerator and denominator of each fraction (to obtain equivalent
fractions)
Now that all fractions have same denominator, the denominator is taken common for all fractions and
numerators are added/subtracted
Lastly, we can simplify the final fraction by cancellation if possible.
Multiplication / Division of fractions:
Multiplying fractions:
1.
2.
3.
Multiply all numerators together to get numerator of answer
Multiply all denominators together to get denominators of answers
Simplify the fraction obtained
Dividing fractions:
1.
2.
3.
4
Change the division sign to multiplication
Take reciprocal of fraction on the right side of division sign
Follow same steps as used for multiplication of fractions
To simplify calculations while multiplication of fractions we can perform cancellation before multiplying the
values of numerators or denominators. Cancellation is only possible between a numerator of denominator
(not necessarily of same fraction)
Types of fractions:
Proper fraction
A fraction where numerator is
smaller than denominator is
known as proper fraction.
Proper fraction is always
smaller than 1.
Improper fraction
A fraction where numerator is
greater than denominator is
known as improper fraction.
Improper fraction is always
greater than 1.
Converting improper fraction to mixed fraction:
5
Mixed fraction
Improper fractions can be
converted to mixed fractions
and vice versa.
Converting mixed fraction to improper fraction:
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 Rules to solve:
a. Exponents
b. Square root
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Geometry questions:
Angles:
TYPES OF ANGLES
Complementary
angle
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DESCRIPTION
Sum of angles = 90
DIAGRAM
Supplementary angle
Sum of angles = 180
Corresponding angle
Angles with same
relative positions are
equal
Alternate angles
Vertical angles
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If two line intersect
opposite angles are
equal
Properties of shapes:
Properties of triangles
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Area of a triangle:
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Pythagoras Theorem (used for right angle triangles only)
Hypotenuses2 = Base2 + Perpendicular2
h2 = b2 + p2

Special triangles:
Type
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Diagram
30-60-90 degree triangle
45-45-90 degree triangle
3-4-5 triangle
5-12-13 triangle
–
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Angle properties of circle:
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Perimeter, Area, surface area and volume of 2D and 3D shapes respectively
Perimeter: sum of boundaries of any shape
Perimeter of circle is known as circumference of the circle. The formula for circumference is 2 pi r
Area: space occupied by any 2D shape
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Surface area and volume of 3D shapes
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14
Algebra questions:
Algebraic identities (important)
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Age related
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Distance speed time relation
Definition:
Speed is rate of change of distance.
This definition gives us the formula of speed -->
Basic formula:
Speed=distance/time
Now if we rearrange this formula, we get
Distance = speed x time
And
time=distance/speed
Make sure to keep these formulae in mind
Next, we should know proportionality rules:

If we say quantity A is directly proportional to quantity B
It means A=KB where K is the constant of proportionality

if we say quantity A is inversely proportional to quantity B it means
A=K(1/B), where k is constant of proportionality
For example:
If distance is constant.
Then using the formula speed=distance/time, we know that constant distance serves for the value of K
the proportionality constant
So, if distance is constant
speed= distance(1/time)
15
this looks like inverse relationship
we say speed is inversely proportional to time in this case
Which means if car has more speed it takes less time to convert certain distance, whereas for same
distance less speed of car will need more time
Similarly, if we say time is constant
For example, 2 cars, car A and B cover different distances at different speeds but they take same amount
of time to reach the destination we will say that time is constant
In this case
speed= distance(1/time)
1/time acts as constant
So, distance and speed are said to be directly proportional
This is an important concept as it is used in many questions even beside speed distance time problems
Another important concept related to this section is relative speed:

If two objects are travelling in opposite directions their
relative speed = sum of speeds of both objects

And if they travel in same direction
relative speed = difference of both speeds
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Word problems
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Statistical and analytical questions:
Pie chart
graphs
Percentage
Data interpretation
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Comparison questions:
Includes question from all of the above sections