Mathematics Class VII

8 Topics | 2 Quizzes

Integers on number line

Additive Inverse of An Integer

Properties Of Addition And Subtraction Of Integers

Multiplication Of Integers

Properties Of Multiplication Of Integers

Division Of Integers

Properties Of Division Of Integers

Concept Checkers-Integers-Class VII

Olympiad Questions-Integers-Class VII

Fractions and Decimals

8 Topics | 3 Quizzes

Types Of Fractions

Converting an Improper Fraction into a Mixed Fraction

Multiplication Of Fractions

Division Of Fractions

Decimal Numbers

Multiplication Of Decimal Numbers

Division of Decimal Numbers

Concept Checkers – Fractions and Decimals – Class VII

Practice Questions – Fractions and Decimals – Class VII

Olympiad Questions – Fractions and Decimals – Class VII

Exponents and Powers

4 Topics | 3 Quizzes

The Expanded Form Of Natural Numbers

Laws Of Exponents

Miscellaneous Examples Using The Laws Of Exponents

Concept Checkers – Exponents and Powers – Class VII

Practice Questions – Exponents and Powers – Class VII

Olympiad Questions – Exponents and Powers – Class VII

Algebraic Equations

6 Topics | 3 Quizzes

Terms Of An Expression

Like And Unlike Terms

Monomials, Binomials, Trinomials And Polynomials

Addition And Subtraction Of Algebraic Expressions

Finding The Value Of An Expression

Concept Checkers – Algebraic Expressions – Class VII

Practice Questions – Algebraic Expressions – Class VII

Olympiad Questions – Algebraic Expressions – Class VII

Simple Linear Equations

6 Topics | 3 Quizzes

Algebraic Expressions

Important Points Related to the Equation

How to form equations using statements?

Balanced Equation

The Solution of an Equation

Applications Of Simple Equations To Practical Situations

Concept Checkers – Simple Linear Equations – Class VII

Practice Questions – Simple Linear Equations – Class VII

Olympiad Questions – Simple Linear Equations – Class VII

Lines and Angles

4 Topics | 3 Quizzes

Transversal of Parallel Lines

Concept Checkers – Lines and Angles – Class VII

Olympiad Questions – Lines and Angles – Class VII

Practice Questions – Lines and Angles – Class VII

Comparing Quantities

6 Topics | 3 Quizzes

Equivalent Ratios

Fun with estimation

Buying and Selling

Concept Checkers – Comparing Quantities – Class VII

Practice Questions – Comparing Quantities – Class VII

Olympiad Questions – Comparing Quantities – Class VII

The triangle and its properties

8 Topics | 3 Quizzes

Medians Of A Triangle

Altitudes Of A Triangle

Exterior Angle Of A Triangle And Its Property

Angle Sum Property Of A Triangle

Two Special Triangles: Equilateral And Isosceles

Sum Of The Lengths Of Two Sides Of A Triangle

Right-Angled Triangles And Pythagoras Property

Concept Checkers – Triangles – Class VII

Practice Questions – Triangles – Class VII

Olympiad Questions – Triangles – Class VII

Congruence of Triangles

7 Topics | 2 Quizzes

Congruence Of 2D Shapes

Congruence Among Line Segments

Congruence Of Angles

Congruence Of Triangles

Criteria For Congruence Of Triangles

Congruence Among Right-Angled Triangles

Concept Checkers – Congruence of Triangles – Class VII

Practice Questions – Congruence of Triangles – Class VII

Rational Numbers

5 Topics | 3 Quizzes

Positive And Negative Rational Numbers

Properties of Rational Numbers

Rational Numbers On A Number Line

Absolute value of a Rational Number

Concept Checkers – Rational Numbers – Class VII

Practice Questions – Rational Numbers – Class VII

Olympiad Questions – Rational Numbers – Class VII

Perimeter and Area

7 Topics | 3 Quizzes

Squares And Rectangles

Area Of A Parallelogram

Area Of A Triangle

Conversion Of Units

Concept Checkers – Perimeter and Area – Class VII

Practice Questions – Perimeter and Area – Class VII

Olympiad Questions – Perimeter and Area – Class VII

9 Topics | 2 Quizzes

Collecting Data

Organisation of Data

Representative Values

Arithmetic Mean

Use Of Bar Graphs With A Different Purpose

Chance And Probability

Concept Checkers – Data Handling – Class VII

Practice Questions – Data Handling – Class VII

Practical Geometry

7 Topics | 1 Quiz

Construction Of A Line Parallel To A Given Line, Through A Point Not On The Line

Construction Of Triangles

Constructing A Triangle When The Lengths Of Its Three Sides Are Known (SSS Criterion)

Constructing A Triangle When The Lengths Of Two Sides And The Measure Of The Angle Between Them Are Known. (SAS Criterion)

Constructing A Triangle When The Measures Of Two Of Its Angles And The Length Of The Side Included Between Them Is Given. (ASA Criterion)

Constructing A Right-Angled Triangle When The Length Of One Leg And Its Hypotenuse Are Given (RHS Criterion)

Concept Checkers – Practical Geometry – Class VII

4 Topics | 1 Quiz

Introduction: Symmetry

Lines Of Symmetry For Regular Polygons

Types of Symmetry

Line Symmetry And Rotational Symmetry

Concept Checkers – Symmetry – Class VII

Visualising Solid Shapes

4 Topics | 1 Quiz

Introduction: Plane Figures And Solid Shapes

Nets For Building 3-D Shapes

Drawing Solids On A Flat Surface

Viewing Different Sections Of A Solid

Concept Checkers – Visualizing Solid Shapes – Class VII

Mock Test 1 – Class VII

Mock Test 2 – Class VII

Mock Test 3 – Class VII

Olympiad Questions – Exponents and Powers – Class VII

Mathematics Class VII Exponents and Powers Olympiad Questions – Exponents and Powers – Class VII

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Question 1 of 20

1. Question
What is the value of \( \left(3^{0} – 4^{0}\right) \times 5^{2}\) ?
- 25
- 0
- -25
- 1
Correct

Incorrect

Hint

$\left(1 - 1\right) \times 5^{2} = 0 \times 25 = 0$
Question 2 of 20

2. Question
What is the value of \(\left(\dfrac{16}{81}\right)^{2}\) ?
- \(\dfrac{9}{2}\)
- \(\dfrac{2}{9}\)
- \(\left(\dfrac{2}{3}\right)^{8}\)
- \(\dfrac{27}{8}\)
Correct

Incorrect

Hint

$\left(\dfrac{16}{81}\right)^{2} = \left(\dfrac{4^{2}}{9^{2}}\right)^{2} = \left(\dfrac{4}{9}\right)^{4} = \left(\dfrac{2}{3}\right)^{8}$
Question 3 of 20

3. Question
Which is true ?
- \(10 \times 10^{11} = 100^{11}\)
- \(2^{3} \times 3^{2} = 6^{5}\)
- \(2^{3} > 3^{2} \)
- \(p^{0} = \left(1000\right)^{0}\)
Correct

Incorrect
Question 4 of 20

4. Question
What is the value of \( \left(12 \times 3^{0} – 8 \times 5^{0}\right)\) ?
- \(\dfrac{1}{2}\)
- \( 2 \)
- \( 4 \)
- \(\dfrac{1}{4}\)
Correct

Incorrect

Hint

$12 \times 1 - 8 \times = 12 - 8 = 4$
Question 5 of 20

5. Question
What is the value of \( 2^{7} \times 5{3}\) ?
- 7500
- 16000
- 11200
- 140000
Correct

Incorrect
Question 6 of 20

6. Question
Which is least ? \( (-1)^{3}, (-10)^{3}, (1)^{5}, (-1)^{4} \)
- \(1^{5}\)
- \(\left(-10\right)^{3}\)
- \(\left(-1\right)^{4}\)
- \(\left(-1\right)^{3}\)
Correct

Incorrect
Question 7 of 20

7. Question
\( (-11)^{2} \times (-11)^{4} = (-11)^{x} \). What is the value of x ?
- 2
- 4
- 6
- -2
Correct

Incorrect

Hint

$\left(-11\right)^{2 + 4} = \left(-11\right)^{x} \rightarrow x = 6$
Question 8 of 20

8. Question
Which is correct ?
- \(\left(2^{3}\right)^{2}\ and \ \left(3^{2}\right)^{4} \) are not the same
- \(\left(2^{3}\right)^{2}\ and \ \left(3^{2}\right)^{4} \) are the same
- \(\left(7^{50}\right)^{2} = \left(7^{50.2}\right) \)
- \(\left(5^{7}\right)^{3} = \left(5^{73}\right) \)
Correct

Incorrect
Question 9 of 20

9. Question
What is the sum of the powers of the prime factors in \( 108 \times 192 \) ?
- 5
- 7
- 8
- 12
Correct

Incorrect

Hint

$108 = 2^{3} \times 3^{3} , 192 = 2^{6} \times 3^{1}$
The sum $= 2 + 3+ 6+ 1 = 12$
Question 10 of 20

10. Question
Express \( (-2)^{3} \div (m)^{3} \) in the form of \(\left(\dfrac{a}{b}\right)^{m} \).
- \(\dfrac{-2^{3}}{m^{3}}\)
- \(\left(\dfrac{-2}{m}\right)^{3}\)
- \(\dfrac{\left(-2\right)^{3}}{m^{3}}\)
- \( – \left(\dfrac{2}{n}\right)\left(\dfrac{-2}{m}\right)\)
Correct

Incorrect
Question 11 of 20

11. Question
What is the value of \( \left[\left(\dfrac{1}{4}\right)^{2} – \left(\dfrac{1}{4}\right)^{3}\right] \times 2^{6} \) ?
- 1
- 2
- 3
- 4
Correct

Incorrect

Hint

$\left[\dfrac{1}{64} - \dfrac{1}{64}\right] \times 2^{6} = \dfrac{3}{64} \times 2^{6} = \dfrac{3}{2^{6}} \times 2^{6} = 3$
Question 12 of 20

12. Question
What is the result of \(\dfrac{2 \times 3^{4} \times 2^{5}}{9 \times 4^{2}} \) ?
- 36
- 42
- 46
- 48
Correct

Incorrect

Hint

$\dfrac{2 \times 3^{4} \times 2^{5}}{9 \times 4^{2}} = 2^{2} \times 3^{2} = 4 \times 9 = 36$
Question 13 of 20

13. Question
Express \(\dfrac{729 \times 64}{270} \) as a product of prime factors.
- \(2^{5} \times 3^{4} \)
- \(\dfrac{2^{5} \times 3^{3}}{5} \)
- \(\dfrac{2^{6} \times 3^{3}}{5^{3}} \)
- \(\dfrac{2^{6} \times 3^{3}}{5^{2}} \)
Correct

Incorrect

Hint

$\dfrac{3^{6} \times 2^{6}}{3^{3} \times 2 \times 5} = \dfrac{2^{5} \times 3^{3}}{5}$
Question 14 of 20

14. Question
How is 65950 expressed in standard form ?
- \(6.59 \times 10^{6} \)
- \(6.59 \times 10^{5}\)
- \(6.595 \times 10^{4}\)
- \(6.595 \times 10^{5}\)
Correct

Incorrect
Question 15 of 20

15. Question
Find the value of \(16^{\frac{3}{4}} \times 4^{\frac{-1}{2}} \).
- 8
- 1
- 4
- 0
Correct

Incorrect

Hint

$16^{\frac{3}{4}} \times 4^{\frac{-1}{2}} = 2^{3} \times 2^{-1} = 8 \times \dfrac{1}{2} = 4$
Question 16 of 20

16. Question
Find the numerical value of \(4096^{\frac{-3}{4}} \).
- \(1024\)
- \(512\)
- \(256\)
- \(\dfrac{1}{512} \)
Correct

Incorrect

Hint

$4096^{\dfrac{-3}{4}} = \left(2^{12}\right)^\frac{-3}{4} = 2^{-9} = \dfrac{1}{2^{9}} = \dfrac{1}{512}$
Question 17 of 20

17. Question
Simplify \( \dfrac{\left(9m^{2}\right)^{\frac{1}{3}}}{6^{4}} \times \dfrac{\left(4n^{2}\right)^{\frac{1}{3}}}{5m} \).
- \(\dfrac{1}{5}\left[\frac{n^{2}}{m6^{10}}\right]^\frac{1}{3} \)
- \(\dfrac{1}{n} \)
- \(\dfrac{1}{m} \)
- \(\dfrac{2}{n} \)
Correct

Incorrect

Hint

$\dfrac{6^{\frac{-10}{3}}m^{\frac{-1}{3}}n^{\frac{2}{3}}}{5} = \dfrac{1}{5}\left[\dfrac{n^{2}}{m6^{10}}\right]^\frac{1}{3}$
Question 18 of 20

18. Question
Solve \( 9^{4x} \div 3^{2x} = 2187 \).
- \(\dfrac{6}{7} \)
- \(\dfrac{-7}{6} \)
- \(\dfrac{7}{6} \)
- \(\dfrac{-6}{7} \)
Correct

Incorrect

Hint

$9^{4x} \div 3^{2x} = 2187 \\ \rightarrow \left(3^{2}\right)^{4x} \div 3^{2x} = 2187 \\ \rightarrow 3^{6x} = 3^{7} \rightarrow 6x = 7 \rightarrow x = \dfrac{7}{6}$
Question 19 of 20

19. Question
Simplify \(\dfrac{p^{4}q^{3} \times p^{2}r^{4} \times q^{-2}r^{3}}{p^{-3}q^{3}r^{3}} \).
- \(p^{3}q^{4}r^{7} \)
- \(p^{3}q^{4}r^{10} \)
- \(p^{-9}q^{2}r^{-4} \)
- \(p^{9}q^{-2}r^{4} \)
Correct

Incorrect

Hint

$\dfrac{p^{4}q^{3} \times p^{2}r^{4} \times q^{-2}r^{3}}{p^{-3}q^{3}r^{3}} = p^{9}q^{-2}r^{4}$
Question 20 of 20

20. Question
Find the numerical value of \(256^{0.75} \).
- \(64\)
- \(256\)
- \(1\)
- \(4^{-3}\)
Correct

Incorrect

Hint

$256^{\dfrac{3}{4}} = \left(4^{4}\right)^{\dfrac{3}{4}} = 4^{3} = 64$

Olympiad Questions - Exponents and Powers - Class VII

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