CBSE Class 8 Maths Complete Study Checklist | Ganita Prakash NCERT (Part 1 & 2)

  

CBSE Class 8 Mathematics (Ganita Prakash)

Chapter-wise Checklist with Topics, Key Points & Questions (Based on New NCERT)

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Part-1

CHAPTER 1: A SQUARE AND A CUBE

Topic	Important Formulas / Key Points
1.1 Introduction	Square Number (Varga): A number obtained by multiplying an integer by itself (e.g., $n\times n=n^2$). Represents the area of a square.
1.2 Properties of Square Numbers	• A perfect square never ends in 2, 3, 7, or 8. • A perfect square ending in zeros must have an even number of zeros. • Squares of even numbers are even; squares of odd numbers are odd. • Pattern: $1^2=1$; $2^2=4$; $3^2=9$.
1.3 Patterns in Squares	Sum of Odd Numbers: The sum of the first $n$ odd natural numbers is $n^2$. Example: $1+3+5+7=16=4^2$.
1.4 Finding the Square of a Number	• Column method • Diagonal method • Using the identity $(a+b{)}^2=a^2+2ab+b^2$.
1.5 Square Roots	Square Root (Varga-mula): The inverse operation of squaring. If $a^2=b$, then $a$ is the square root of $b$ ($a=\sqrt{b}$).
1.6 Finding Square Roots	Prime Factorization Method: Express the number as a product of primes and group them into pairs of equal factors. Take one factor from each pair and multiply. Example: $\sqrt{1764}=\sqrt{2^2\times 3^2\times 7^2}=2\times 3\times 7=42$.
1.7 Cube Numbers	Cube Number (Ghana): A number obtained by multiplying an integer by itself twice (e.g., $n\times n\times n=n^3$). Represents the volume of a cube.
1.8 Properties of Cube Numbers	• Cubes of even numbers are even. • Cubes of odd numbers are odd. • If a number has a digit 'k' in its units place, its cube ends in a specific digit (e.g., if units digit is 1, cube ends in 1; if 2, cube ends in 8; etc.).
1.9 Cube Roots	Cube Root (Ghana-mula): The inverse operation of cubing. If $a^3=b$, then $a$ is the cube root of $b$ ($a=\sqrt[3]{b}$).
1.10 Finding Cube Roots	Prime Factorization Method: Express the number as a product of primes and group them into triplets of equal factors. Take one factor from each triplet and multiply. Example: $\sqrt[3]{1728}=\sqrt[3]{2^3\times 3^3}=2\times 3=6$. Hardy-Ramanujan Number (1729): The smallest number that can be expressed as a sum of two cubes in two different ways: $1729={12}^3+1^3={10}^3+9^3$.

✓	Question / Concept	Page	Type
☐	The locker puzzle: Which lockers remain open and why? (Based on factors)	1-3	In-text
☐	Find the smallest number by which 176 must be multiplied to get a perfect square.	10	Figure it Out
☐	Is 9720 a perfect cube? If not, find the smallest number to divide it by to get a perfect cube.	11	Figure it Out
☐	What will be the number of unit squares on each side of a square graph paper if the total unit squares are 256?	10	Figure it Out
☐	Find the square root of 196 by the method of repeated subtraction (subtracting successive odd numbers).	10	Figure it Out
☐	A hall has a capacity of 2704 seats. If rows = seats per row, find seats per row.	11	Figure it Out
☐	Find the cube root of 13824 by prime factorization.	16-17	Figure it Out
☐	The difference of two perfect cubes is 189. If the cube root of the smaller is 3, find the cube root of the larger.	17	Figure it Out

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CHAPTER 2: POWER PLAY

Topic	Important Formulas / Key Points
2.1 Introduction	Exponential Notation: A way to represent repeated multiplication of the same factor. $a^n$, where '$a$' is the base and '$n$' is the exponent or power.
2.2 Laws of Exponents	For any non-zero integers $a,b$ and integers $m,n$: • Product: $a^m\times a^n=a^{m+n}$ • Quotient: $a^m÷a^n=a^{m-n}$ • Power of a Power: $(a^m{)}^n=a^{m\times n}$ • Power of a Product: $(a\times b{)}^n=a^n\times b^n$ • Power of a Quotient: $(\frac{a}{b}{)}^n=\frac{a^n}{b^n}$
2.3 Zero and Negative Exponents	• Zero Exponent: $a^0=1$ (where $a\mathrm{\ne }0$) • Negative Exponent: $a^{-n}=\frac{1}{a^n}$
2.4 Scientific Notation	Expressing very large or very small numbers as a product of a number between 1 and 10 and a power of 10. Example: Earth's mass = $5.976\times {10}^{24}$ kg.

✓	Question / Concept	Page	Type
☐	The paper folding puzzle: If you fold a paper 46 times, its thickness reaches the moon. Why?	20-21	In-text
☐	Simplify and express in exponential form: (a) $2^3\times 2^5$ (b) $p^7÷p^4$	22	Figure it Out
☐	Evaluate: (a) $(-4{)}^3$ (b) $(\frac{2}{3}{)}^4$	22	Figure it Out
☐	Simplify: $(2^3\times 2^2{)}^2$	23	Figure it Out
☐	Express the following in exponential form: (a) $5\times 5\times 7\times 7\times 7$ (b) $a\times a\times a\times b\times b$	23	Figure it Out
☐	Find the value of $x$ if $2^{x-1}=16$.	44	Figure it Out
☐	Express 0.0000457 in scientific notation.	45	Figure it Out
☐	Write 3.2 × 10⁵ in usual form.	45	Figure it Out

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CHAPTER 3: A STORY OF NUMBERS

Topic	Important Formulas / Key Points
3.1 Introduction	History and evolution of number systems: from natural numbers to integers, and then to rational numbers.
3.2 Integers	Integers (Z): ... -3, -2, -1, 0, 1, 2, 3, ...
3.3 Rational Numbers	Rational Numbers (Q): Numbers that can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\mathrm{\ne }0$.
3.4 Properties of Rational Numbers	Rational numbers follow the commutative, associative, and distributive laws for addition and multiplication. • They have an additive identity (0) and additive inverse (-a). • They have a multiplicative identity (1) and multiplicative inverse (reciprocal, $1\mathrm{/}a$) for non-zero numbers.

✓	Question / Concept	Page	Type
☐	Find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.	(Refer Book)	Figure it Out
☐	Verify the commutative property of addition for $\frac{-3}{4}$ and $\frac{2}{5}$.	(Refer Book)	In-text
☐	Find the multiplicative inverse of: (a) -13 (b) $\frac{-5}{8}$ (c) $\frac{7}{11}$	(Refer Book)	In-text
☐	Simplify using distributive property: $\frac{3}{5}\times \frac{7}{8}+\frac{3}{5}\times \frac{1}{8}$	(Refer Book)	In-text
☐	Is 0.3 a rational number? If yes, write it in $\frac{p}{q}$ form.	(Refer Book)	In-text

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CHAPTER 4: QUADRILATERALS

Topic	Important Formulas / Key Points
4.1 Introduction	A quadrilateral is a four-sided polygon. Sum of its interior angles = ${360}^{\circ }$.
4.2 Types of Quadrilaterals	• Parallelogram: Opposite sides parallel and equal, opposite angles equal, diagonals bisect each other. • Rectangle: Parallelogram with all angles ${90}^{\circ }$. Diagonals are equal. • Rhombus: Parallelogram with all sides equal. Diagonals are perpendicular bisectors of each other. • Square: Rectangle with all sides equal (or rhombus with all angles ${90}^{\circ }$). Diagonals are equal and perpendicular bisectors. • Trapezium (or Trapezoid): One pair of opposite sides parallel. • Kite: Two pairs of adjacent sides equal.
4.3 Key Theorems	• Mid-point Theorem: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it. [citation:10?]

✓	Question / Concept	Page	Type
☐	In a parallelogram ABCD, if ∠A = 110°, find the measures of ∠B, ∠C, and ∠D.	(Refer Book)	In-text
☐	Prove that the diagonals of a rectangle are equal.	(Refer Book)	In-text
☐	Show that the diagonals of a rhombus are perpendicular bisectors of each other.	(Refer Book)	In-text
☐	Prove the Mid-point Theorem.	(Refer Book)	Figure it Out
☐	In triangle ABC, D and E are mid-points of AB and AC. If DE = 4 cm, find the length of BC.	(Refer Book)	In-text

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CHAPTER 5: NUMBER PLAY

Topic	Important Formulas / Key Points
5.1 Introduction	Exploring fun and interesting patterns with numbers, including divisibility rules, puzzles, and palindromes.
5.2 Divisibility Rules	Rules for checking divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
5.3 Number Puzzles	Solving cryptarithms and letter puzzles where letters stand for digits. (e.g., AB + BA = 99).
5.4 Palindromic Numbers	Numbers that read the same forwards and backwards (e.g., 121, 3443).

✓	Question / Concept	Page	Type
☐	If a number 123456789A is divisible by 9, find the value of A.	(Refer Book)	Figure it Out
☐	Check the divisibility of 2146587 by 3 and 11.	(Refer Book)	In-text
☐	Solve the cryptarithm: AB × 3 = CAB (where A, B, C are digits).	(Refer Book)	Figure it Out
☐	Find the next two palindromic numbers after 1331.	(Refer Book)	In-text

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CHAPTER 6: WE DISTRIBUTE, YET THINGS MULTIPLY

Topic	Important Formulas / Key Points
6.1 Introduction	Introduction to algebraic expressions, terms, factors, and coefficients.
6.2 Types of Polynomials	• Monomial: Expression with one term (e.g., $3x,4xy$). • Binomial: Expression with two terms (e.g., $a+b,2x-3y$). • Trinomial: Expression with three terms (e.g., $x^2+2x+1$).
6.3 Operations on Algebraic Expressions	• Addition and Subtraction: Combine like terms. • Multiplication: Multiply coefficients and add exponents of like variables.
6.4 Algebraic Identities	• $(x+a)(x+b)=x^2+(a+b)x+ab$ • $(a+b{)}^2=a^2+2ab+b^2$ • $(a-b{)}^2=a^2-2ab+b^2$ • $a^2-b^2=(a+b)(a-b)$

✓	Question / Concept	Page	Type
☐	Classify into monomials, binomials, and trinomials: $x+y,1000,7+y+5x,pqr,ab+bc+cd+da$.	(Refer Book)	Important Q
☐	Subtract $4a-7ab+3b+12$ from $12a-9ab+5b-3$.	(Refer Book)	Important Q
☐	Find the product using a suitable identity: (a) ${102}^2$ (b) ${998}^2$ (c) $297\times 303$	(Refer Book)	Important Q
☐	The length of a rectangle is $(x+9y)$ and its area is $x^2+12xy+27y^2$. Find its breadth.	(Refer Book)	Important Q
☐	Fill in the blanks: (a) $(a-b{)}^2+\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}=a^2-b^2$ (b) $a^2-b^2=(a+b)\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$	(Refer Book)	Important Q

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CHAPTER 7: PROPORTIONAL REASONING - 1

Topic	Important Formulas / Key Points
7.1 Introduction	Understanding relationships between two quantities.
7.2 Direct Proportion	Two quantities $x$ and $y$ are in direct proportion if they increase or decrease together such that their ratio remains constant. $\frac{x}{y}=k$ (constant).
7.3 Inverse Proportion	Two quantities $x$ and $y$ are in inverse proportion if an increase in one causes a decrease in the other, and vice versa, such that their product remains constant. $x\times y=k$ (constant).

✓	Question / Concept	Page	Type
☐	If 15 eggs cost ₹120, what is the cost of 25 eggs?	(Refer Book)	Figure it Out
☐	A car travels 120 km in 2 hours. How long will it take to travel 300 km at the same speed?	(Refer Book)	In-text
☐	If 6 workers can build a wall in 15 days, how many days will 9 workers take to build the same wall?	(Refer Book)	Figure it Out
☐	Check whether the following are in direct or inverse proportion: (a) Speed of a car and time taken to cover a fixed distance. (b) Number of books and their total weight (if each book weighs the same).	(Refer Book)	In-text

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Part-2

CHAPTER 1: FRACTIONS IN DISGUISE

Topic	Important Formulas / Key Points
1.1 Introduction	Understanding fractions and their various representations.
1.2 Equivalent Fractions	Fractions that represent the same value. Obtained by multiplying or dividing the numerator and denominator by the same non-zero number.
1.3 Comparison of Fractions	To compare fractions, convert them into equivalent fractions with a common denominator.

✓	Question / Concept	Page	Type
☐	Find three equivalent fractions for $\frac{3}{5}$.	(Refer Book)	In-text
☐	Arrange the following in ascending order: $\frac{2}{3},\frac{5}{6},\frac{3}{4}$.	(Refer Book)	Figure it Out
☐	Ravi ate $\frac{1}{4}$ of a pizza and his sister ate $\frac{2}{8}$. Did they eat the same amount? Explain.	(Refer Book)	In-text

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CHAPTER 2: BAUDHYANA'S THEOREM

Topic	Important Formulas / Key Points
2.1 Introduction	The ancient Indian origin of the theorem now known as the Pythagoras Theorem.
2.2 Baudhyana's Theorem (Pythagoras Theorem)	In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. ${\text{(Hypotenuse)}}^2={\text{(Base)}}^2+{\text{(Perpendicular)}}^2$
2.3 Converse of Pythagoras Theorem	If in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

✓	Question / Concept	Page	Type
☐	Find the length of the hypotenuse of a right triangle with legs 3 cm and 4 cm.	(Refer Book)	Figure it Out
☐	A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.	(Refer Book)	In-text
☐	Check whether a triangle with sides 5 cm, 12 cm, and 13 cm is a right-angled triangle.	(Refer Book)	Figure it Out

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CHAPTER 3: PROPORTIONAL REASONING - 2

Topic	Important Formulas / Key Points
3.1 Introduction	Advanced applications of direct and inverse proportions.
3.2 Percentage as a Proportion	A percentage is a fraction with denominator 100.
3.3 Unitary Method	Finding the value of one unit first, then the value of the required number of units.

✓	Question / Concept	Page	Type
☐	If 20% of a number is 50, find the number.	(Refer Book)	Figure it Out
☐	45 men can complete a work in 16 days. How many men are needed to complete the same work in 30 days?	(Refer Book)	In-text
☐	A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (a) the length of the shadow cast by another pole 10 m 50 cm high. (b) the height of a pole which casts a shadow 5 m long.	(Refer Book)	Figure it Out

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CHAPTER 4: EXPLORING SOME GEOMETRIC THEMES

Topic	Important Formulas / Key Points
4.1 Introduction	Exploring geometric properties of different shapes.
4.2 Congruence of Plane Figures	Two figures are congruent if they have the same shape and size.
4.3 Congruence of Triangles	CPCT: Corresponding Parts of Congruent Triangles are equal. • SSS Congruence: Three sides equal. • SAS Congruence: Two sides and the included angle equal. • ASA Congruence: Two angles and the included side equal. • RHS Congruence: Right angle, Hypotenuse, and a side.

✓	Question / Concept	Page	Type
☐	In the figure, AB = AC and AD is the bisector of ∠BAC. Prove that ∆ABD ≅ ∆ACD.	(Refer Book)	In-text
☐	Which congruence criterion do you use to prove ∆XYZ ≅ ∆MON, if XY = MO, YZ = ON and XZ = MN?	(Refer Book)	Figure it Out
☐	In a kite, if one diagonal is the perpendicular bisector of the other, prove that the kite has two pairs of equal adjacent sides.	(Refer Book)	In-text

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CHAPTER 5: TALES BY DOTS AND LINES

Topic	Important Formulas / Key Points
5.1 Introduction	Introduction to graphs as a way to represent data visually.
5.2 A Line Graph	A graph that uses points connected by straight lines to show how a quantity changes over time.
5.3 Linear Graphs	A graph that is a straight line.
5.4 Coordinates	An ordered pair $(x,y)$ that locates a point on a plane. • x-coordinate (Abscissa): Horizontal distance from the y-axis. • y-coordinate (Ordinate): Vertical distance from the x-axis.

✓	Question / Concept	Page	Type
☐	Plot the points (2, 3), (-1, 2), and (0, -2) on a graph sheet.	(Refer Book)	Figure it Out
☐	In which quadrant or on which axis do the points (3, -4), (-5, 0), and (-2, -3) lie?	(Refer Book)	In-text
☐	Draw a line graph for the temperature recorded at different times of a day.	(Refer Book)	Figure it Out

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CHAPTER 6: ALGEBRA PLAY

Topic	Important Formulas / Key Points
6.1 Introduction	Revisiting algebraic expressions and equations.
6.2 Solving Linear Equations	An equation where the variable's highest power is 1. To solve, perform the same operation on both sides to isolate the variable.
6.3 Equations Reducible to Linear Form	Equations that can be simplified to the form $ax+b=0$.

✓	Question / Concept	Page	Type
☐	Solve: (a) $2x+5=9$ (b) $\frac{3y}{2}=15$ (c) $\frac{2x}{3}+1=\frac{7x}{15}+3$	(Refer Book)	Figure it Out
☐	The sum of three consecutive multiples of 11 is 363. Find these multiples.	(Refer Book)	In-text
☐	The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?	(Refer Book)	Figure it Out

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CHAPTER 7: AREA

Topic	Important Formulas / Key Points
7.1 Introduction	Finding the area of plane figures.
7.2 Area of a Trapezium	Area of a Trapezium: $\frac{1}{2}\times (\text{sum of parallel sides})\times \text{height}$
7.3 Area of a Quadrilateral	Area of a general Quadrilateral: $\frac{1}{2}\times \text{diagonal}\times (\text{sum of offsets})$
7.4 Area of a Polygon	Area of polygons can be found by splitting them into known shapes like triangles, rectangles, and trapeziums.

✓	Question / Concept	Page	Type
☐	Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm.	(Refer Book)	Figure it Out
☐	The area of a trapezium is 450 cm² and the lengths of the parallel sides are 37 cm and 23 cm. Find the distance between them.	(Refer Book)	In-text
☐	Find the area of the given polygon (a figure with multiple sides will be provided in the book).	(Refer Book)	Figure it Out

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How to Use This Checklist:

1. Print or save this checklist.

2. Tick the box $(\mathrm{✓})$ when you have understood a topic and completed the associated questions.

3. Refer to your NCERT Ganita Prakash textbook for the exact "Figure it Out" and in-text questions mentioned above.

4. Revise the ticked topics and questions regularly before exams.

5. Practice unticked questions until you master them.

All the best for your CBSE Class 8 Mathematics Exam!