
Chapter 1  Rational numbers
 Standard form of Rational Number
 Equivalent Rational Numbers
 Equivalent Rational Number with given Numerator
 Equivalent Rational Number with given Denominator
 Comparison of Rational numbers
 Sum of Rational Numbers whose Denominators are equal
 Sum of Rational Number with unequal Denominators
 Additive Inverse
 Subtraction of Rational Number When Denominators are Equal
 Subtraction of Rational Number with Different Denominators
 Finding number that should be added or subtracted
 Finding Rational Number, when its sum & other number given
 Finding Rational Number whose product & other number given
 Multiplication of Rational Numbers
 Reciprocal or Multiplicative Inverse of Rational Number
 Division of Rational Numbers
 Problem based on Division of Rational Numbers

Chapter 2  Playing with numbers
 Finding two Digit number when sum of its digit is given
 Finding two digit number when digits are interchanged
 Finding three digit number
 Test of Divisibility by 2
 Test of Divisibility by 3
 Test of Divisibility by 5
 Test of Divisibility by 9
 Finding missing digit so that number is divisible by 2
 Finding missing digit so that number is divisible by 3
 Finding missing digit so that number is divisible by 5
 Finding missing digit so that number is divisible by 9

Chapter 3  Percentage
 Convert a Percentage into a Fraction
 Convert Percentage into decimal
 Convert a given ratio into Percentage
 Converting a Fraction into Percentage
 Expressing a given Percentage as a Ratio
 Finding a number, whose percentage value is given
 Find what percentage of a given term is another term (litre)
 Find what percentage of a given term is another term (m)
 Find what percentage of a given term is another term (kg)
 Net Increase or Decrease Percentage in a Number
 Finding a number when its decreased percentage is given
 Finding a number when its increased percentage is given
 Salary saved

Chapter 4  Quadrilaterals

Chapter 5  Parallelograms

Chapter 6  Time and Work
 Finding time taken by one person to finish a piece of work
 Three person – Time taken by third to finish work
 Time taken by 3 person to finish work
 Time taken by two taps to fill a cistern together
 Time to finish work by 2 person when individual time given
 Time to finish work by more efficient person
 Two taps – One filling and one emptying the cistern

Chapter 7  Compound interest
 Maturity Amount – Compounded Annually
 Calculating Amount If rates are different for different year
 Computation of Compound Interest (with time 2 years)
 Computation of C.I Compounded Half Yearly (time 2 years)
 Computation of Compound Interest (with time 3 years)
 Computation of difference between C.I and S.I (Quarterly)
 Computation of difference between C.I and S.I (Half yearly)
 Computation of difference between C.I and S.I (for 1 year)
 Computation of Maturity Amount (with time 2 years)
 Computation of Principal
 Finding TIME when Principal, Amount and ROI are given
 Population at a Future date
 Population at an Earlier Date
 Maturity Amount – Compounded half yearly (with time 2 years)
 Computation of RATE (for 2 years)

Chapter 8  Exponents
 Addition of more than two exponential term
 Calculate the value of ‘n’
 Division of exponents using exponential identities
 Evaluating the value of exponent with whole number base
 Evaluating the value of exponents with fractional base
 Evaluating the value of more than two exponential term
 Evaluating the value of terms given in Square root
 Evaluating the value using identity
 Expressing as an Exponential form
 Expressing variable and constant term in exponential form
 Expressing variable term in exponential form
 Finding the Reciprocal of exponential term
 Finding the value of x using exponential identities
 Finding the value of given equation
 Finding the value of unknown index ‘y’
 Finding the value of unknown term
 Simplifying exponents with power rule
 Simplifying using power rule of exponent
 Simplifying variable exponents

Chapter 9  Polygons
 Find exterior angle of polygon if number of sides are given
 Find interior angle of polygon if number of sides are given
 Find number of sides of polygon if its exterior angle given
 Find number of sides of polygon if number of Diagonal given
 Finding if a Polygon with a given exterior angle exists
 Finding number of sides of polygon its interior angle given
 Finding number of sides of polygon its interior angle given
 Number of Diagonals in a Polygon
 Sum of interior angle when number of sides are given

Chapter 10  Profit and Loss
 Finding gain or loss percent
 Finding Gain% when C.P and S.P are given
 Finding Gain% when C.P and S.P are given
 Finding Gain% if C.P,S.P & Transportation charges are given
 Finding Loss% when C.P and S.P are given
 Finding Loss% when C.P and S.P are given
 Finding Loss% if C.P,S.P & Transportation charges are given
 Finding M.P when C.P and Discount% are given
 Finding Original price of an item if VAT is included
 Finding Price if Sales Tax is charged
 Finding S.P or C.P when Gain% is given
 Finding S.P or C.P when Loss% is given
 Finding S.P when M.P and Discount are given
 Word problems on finding S.P

Chapter 11  Square and square roots
 Finding the number to be multiplied to make perfect square
 Finding the perfect square
 Finding the square of two digit & three digit number
 Finding the value of expression using identity
 finding the value of square root term
 Finding the value of unknown term ‘x’
 Finding the value of unknown term using identity
 Finding value of given expression using identity
 Finding values using identity
 Word problems on Square root
 Word problems on finding number of members in the group

Chapter 12  Cube and cube roots
 Cube of a Decimal Number
 Cube of a Number
 Cube of Even Number
 Cube of Odd number
 Cube Root of a Negative Number
 Cube root of product of integers
 Cube Roots of a Positive Number
 Cube Roots of a Rational Number
 Finding smallest number to be divided to make perfect cube
 Make a number a Perfect Cube
 Whether a Number forms a Perfect Cube

Chapter 13  Factorization

Chapter 14  Linear equation
 Computing income earned when tax on income is given
 Dividing a number into two parts
 Find 4 consecutive Positive Integers, if difference is given
 Finding the Value of Variable
 Finding variable when subtracted from a number
 Finding 3 consecutive numbers if their sum is given
 Finding angles of a Triangle
 Finding the value of variable if certain number is subtract
 Finding the value of three consecutive odd natural number
 Finding the value of Variable if sum is given
 Finding the value of variable if the difference is given
 Finding the value of variable when increased by a number
 Finding two consecutive even numbers if their sum is given
 Finding two consecutive odd numbers if their sum is given
 Finding two numbers whose difference and ratios are given
 Finding two numbers whose sum and ratios are given
 Finding value of Variable in the given equation
 Finding value of Unknown term
 Linear Equation In one variable
 Linear Equation Problems on ages
 Number lying between two numbers

Chapter 15  Direct and inverse proportion

Chapter 16  ThreeDimensional figures

Chapter 17  Area of trapezium and a polygon
 Area of a Triangle when its base and height are given
 Area of Trapezium
 Find Parallel sides of Trapezium when their difference given
 Finding Base of a Triangle whose Height and area is given
 Finding height of a Triangle whose base and area is given
 Finding Length of one of Parallel sides of Trapezium
 Finding parallel sides of Trapezium
 Finding the Area of Irregular Polygons

Chapter 18  Probability

Chapter 19  Graph

Chapter 20  Pie charts

Chapter 21  Volume and surface area of solids
 Finding the Capacity of water tank
 Finding the cost of graveling
 Finding the length of pole
 Finding the number of bricks to make a Wall
 Finding the number of person can be accommodate in a hall
 Finding the rise in level of earth
 Finding the surface area and Total surface area of cuboid
 Finding the volume of reservoir
 Finding the volume of solid
 Finding the volume of Wooden Box
 Height of Water level in the Pool
 Weight of iron
Reciprocal or Multiplicative Inverse of Rational Number
Rational numbers – Reciprocal or Multiplicative Inverse of Rational Number
Question : –
Find the reciprocal of ?
Explanation : –
In order to find Reciprocal or Multiplicative Inverse of any Rational Number, we simply reverse the Fraction i.e, the Numerator becomes Denominator , andthe Denominator becomes Numerator.
In , 11 is the Numerator and 7 is the Denominator
Hence, the Reciprocal of is
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