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Algebra Play – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 13. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Algebra uses letters for unknown numbers. Forming and solving simple linear equations turns word puzzles into quick answers.

Expressions

Terms with the same variable and power are like terms (3x and −5x); only like terms can be added.
Substitute values to evaluate an expression: if x = 2, 3x + 4 = 10.

Linear equations

An equation has an equals sign; the solution makes both sides equal.
Solve by doing the same operation to both sides (transposing changes the sign).
Word problems: let the unknown be x, form the equation, solve, then check.

Key terms

Variable: a letter that stands for an unknown number
Like terms: terms with the same variables and powers
Linear equation: equation with the highest power of the variable 1

Formulas

ax + b = c ⇒ x = (c − b)/a

Important questions with answers

Simplify 3(2x − 1) − 2(x − 4).2 marks

6x − 3 − 2x + 8 = 4x + 5.

Solve (x − 3)/5 = (x + 1)/7.3 marks

7(x − 3) = 5(x + 1), 7x − 21 = 5x + 5, 2x = 26, x = 13.

The length of a rectangle is 4 m more than its breadth and its perimeter is 64 m. Form an equation, find the dimensions and the area, and verify.5 marks

Let breadth = x, length = x + 4. 2(x + x + 4) = 64 gives 4x + 8 = 64, x = 14. Breadth 14 m, length 18 m, area = 252 m². Check: 2(14 + 18) = 64 ✓.

Quick revision

Only like terms combine.
Transposing changes + to − and × to ÷.
Always verify the solution.

Exam tips

Check the answer by putting it back into the original equation.
Consecutive numbers: x, x + 1, x + 2; consecutive even/odd: x, x + 2, x + 4.

Practice MCQs

4x + 3x equals
1. x
2. 12x
3. 7x²
4. 7x
Show answer
Answer: (d) 7x. Like terms.
If x + 7 = 12, then x =
1. 19
2. 5
3. 7
4. −5
Show answer
Answer: (b) 5. 12 − 7.
Solve 3x − 5 = 16
1. 7
2. 11/3
3. 5
4. 21
Show answer
Answer: (a) 7. 3x = 21.
Value of 2a² − 3 when a = −2 is
1. −5
2. −11
3. 11
4. 5
Show answer
Answer: (d) 5. 2 × 4 − 3.
Solve 5x + 4 = 3x + 12
1. x = 2
2. x = 3
3. x = 8
4. x = 4
Show answer
Answer: (d) x = 4. 2x = 8.
The sum of three consecutive numbers is 72. The largest is
1. 23
2. 24
3. 25
4. 26
Show answer
Answer: (c) 25. x + x + 1 + x + 2 = 72 ⇒ x = 23.
A father is 3 times as old as his son. In 12 years he will be twice as old. The son's age now is
1. 10
2. 12
3. 14
4. 36
Show answer
Answer: (b) 12. 3x + 12 = 2(x + 12) ⇒ x = 12.
Think of a number, double it, add 10, halve it, subtract the number. The result is always
1. 0
2. 5
3. 10
4. the number
Show answer
Answer: (b) 5. (2n + 10)/2 − n = 5.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.