Topics
Rational Numbers
- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Concept of Reciprocals or Multiplicative Inverses
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
- Multiples and Common Multiples
Linear Equations in One Variable
- Constants and Variables in Mathematics
- Equation in Mathematics
- Expressions with Variables
- Word Problems on Linear Equations
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to Linear Equations
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Basic Concept of Polygons
- Classification of Polygons
- Properties of Quadrilateral
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Quadrilaterals
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
Data Handling
Practical Geometry
- Geometric Tool
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
- Ratio
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Calculation of Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Classification of Terms in Algebra
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Exponents and Powers
Visualizing Solid Shapes
Direct and Inverse Proportions
Factorization
- Factors and Common Factors
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
Playing with Numbers
Definition
- Cost Price (C.P.): The amount for which an article is bought is called its Cost Price (C.P.).
- Selling Price (S.P.): The price at which a product is sold is known as its selling price (S.P.).
- Profit or Gain: When the S.P. is more than the C.P., then there is a profit or gain.
- Loss: When the S.P. is less than the C.P., then there is a loss.
- Discount: A Discount is the reduction given on the marked price of an article by the seller, usually to attract customers.
- Marked Price (M.P.): Marked Price (also called Tag Price) is the price printed or written on an article by the shopkeeper, which is usually higher than the cost price
Formula
- Profit = Selling Price - Cost Price, which means CP < SP.
- Loss = Cost Price - Selling Price, which means CP > SP.
- Selling Price = Marked Price – Discount
- Discount% = `"Discount"/"Marked Price"` × 100%
Example
Hamidbhai bought bananas worth 2000 rupees and sold them all for 1890 rupees. Did he make a profit or a loss? How much was it?
He bought bananas for Rs. 2000.
Hence, Cost price = Rs. 2000
Selling price = Rs. 1890
Cost price is greater than selling price. Therefore, Hamidbhai suffered a loss.
Loss = Cost price - Selling price
= 2000 - 1890
= Rs. 110
∴ Hamidbhai suffered a loss of Rs. 110 in this transaction.
Example
Harbhajan Singh bought 500 kg of rice for 22000 rupees and sold it all at the rate of Rs. 48 per kg. How much profit did he make?
The cost price of 500 kg rice is Rs. 22000.
Selling price of 500 kg of rice is = 500 × 48 = Rs. 24000
Selling price is greater than cost price.
Therefore, there is a profit.
Profit = Selling price - Cost price
= 24000 - 22000
= Rs. 2000
∴ In this transaction, Harbhajan Singh made a profit of Rs. 2000.
Example
Javedbhai bought 35 electric mixers for Rs. 4300 each. To transport them to the shop, he spent Rs. 2100. If he expects to make a profit of Rs. 21000, at what price should he sell each mixer?
Cost price of one mixer Rs. 4300.
Hence cost price of 35 mixers = 4300 × 35 = Rs. 150500
Total cost price = cost of mixers + cost of transport
= 150500 + 2100
= Rs. 152600
Javedbhai wants a profit of 21000 rupees.
∴ Hence, amount expected on selling = 152600 + 21000 = Rs. 173600
Selling price of 35 mixers = Rs. 173600
∴ Selling price of one mixer = 173600 ÷ 35 = Rs. 4960
Javedbhai should sell every mixer for Rs. 4960.
Example
The cost of a flower vase is Rs. 120. If the shopkeeper sells it at a loss of 10%, find the price at which it is sold.
Given: CP = Rs. 120 and Loss percent = 10.
Loss of 10% means if CP is Rs. 100, Loss is Rs. 10
Therefore,
SP would be Rs.(100 - 10) = Rs. 90
When CP is Rs. 100, SP is Rs. 90.
Therefore, if CP were Rs. 120 then
SP = `90/100 xx 120` = Rs. 108.
Given: CP = Rs. 120 and Loss percent = 10.
Loss is 10% of the cost price
= 10% of Rs. 120
= `10/100 xx 120`
= Rs. 12
Therefore,
SP = CP - Loss = Rs. 120 - Rs. 12 = Rs. 108
Example
Selling price of a toy car is Rs. 540. If the profit made by the shopkeeper is 20%, what is the cost price of this toy?
Given: SP = Rs. 540 and the Profit = 20%.
20% profit will mean if CP is Rs. 100, profit is Rs. 20.
Therefore, SP = 100 + 20 = 120
Now, when SP is Rs. 120, then CP is Rs. 100.
Therefore, when SP is Rs. 540,
Then CP = `100/120 xx 540` = Rs. 450.
Given: SP = Rs. 540 and the Profit = 20%.
Profit = 20% of CP and SP = CP + Profit
So, 540 = CP + 20% of CP
= CP + `20/100 xx "CP" = [1 + 1/5]"CP"`
= `6/5 "CP"`.
Therefore, `540 xx 5/6` = CP or Rs. 450 = CP
Example
Meenu bought two fans for ₹ 1200 each. She sold one at a loss of 5% and the other at a profit of 10%. Find the selling price of each. Also, find out the total profit or loss.
