MCQ

algebraic-expressions-and-identities-l2 MCQ - Practice Questions with Answers

Solve 30 algebraic-expressions-and-identities-l2 questions for RAS/RPSC preparation.

Practice questions

Q1A pattern has 4, 8, 12, 16 dots at positions 1, 2, 3, 4 respectively. If n represents the position number, which expression gives the number of dots?

A n + 4

B 4 + n

C n - 4

D 4n

Explanation

The dots increase as four times the position number: position 1 gives 4, position 2 gives 8, and so on. Adding or subtracting 4 treats the pattern as a simple shift, not as repeated multiplication.

Q2Which statement best describes an identity in algebra?

A An equality that is true for all permitted values of its variables

B An equality that becomes true only after solving for one value

C Any expression that contains two unlike terms

D A product written after taking out a common factor

Explanation

An identity is true for every permitted value of the variables, such as a square identity after expansion. An equation is usually true only for selected values, while unlike terms and common factors describe other ideas.

Q3Which identity explains (m + 3)^2?

A a2 - b2 = (a + b)(a - b)

B (a - b)^2 = a2 - 2ab + b2

C (a + b)^2 = a2 + 2ab + b2

D a(b + c) = ab + ac

Explanation

The square of a sum has two equal middle rectangles. Devika should write (m + 3)^2 as m2 + 2.m.3 + 9, which is m2 + 6m + 9.

Q4Match the instruction with the correct result for 6x + 9.

A Factorise -> 3(2x + 3)

B Expand -> 3(2x + 3)

C Evaluate -> 3(2x + 3)

D Collect like terms -> 15x

Explanation

Factorisation rewrites the whole expression as a product. Karan should notice that both 6x and 9 share factor 3, giving 3(2x + 3).

Q5Which pair of terms is like terms?

A 4xy and -9yx

B 7x and 7x2

C 3a and 3b

D 5 and 5m

Explanation

4xy and -9yx are like terms because xy and yx represent the same variable part. Asha should combine them by adding coefficients only, not by changing the literal factor.

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6Consider the statements about variables. Statement 1: In one expression or equation, the same variable symbol refers to the same value at that moment. Statement 2: Across a pattern or situation, a variable may take different permitted values. Which option is correct?

AOnly Statement 1 is correct

BOnly Statement 2 is correct

CBoth Statement 1 and Statement 2 are correct

DNeither Statement 1 nor Statement 2 is correct

7A learner writes (p + q)^2 = p2 + q2. Which feedback is best?

AAccept it because both p and q have been squared.

BAsk the learner to draw the square of side p + q and locate two pq parts.

CTell the learner to memorise the formula without discussion.

DChange the topic to equations because identities are too advanced.

8A learner writes (m - 7)^2 = m^2 - 49. Which correction targets the exact error?

ATell the learner to combine only like terms.

BReplace the square identity with the distributive law only.

CAsk the learner to cancel m from both sides.

DShow that the middle term -14m is missing.

9A student says that 7p + 3q = 10pq. Which teacher response best names and fixes the misconception?

AAdd 7 and 3, then write both variables together because both terms have letters.

BIt is wrong because every expression with two variables must first be factorised.

CTreat p and q as the same variable for quick simplification in objective tests.

DThese are unlike terms; only terms with the same variable part and powers can be combined.

10A learner expands 4(a - 2). Which option shows the common missed-distribution MCQ trap?

A4a - 2

B4a - 8

C4a + 8

Da - 8

11In a distributive station, learners use an area model for 4(a + 2). Which teacher prompt is most mathematically useful?

AWhy is the outside 4 multiplied with both a and 2?

BCan we add a and 2 first to get 6?

CCan we cancel 4 with the bracket?

DShould the answer be 4a + 2 because 4 already touched the bracket?

12Which statement best describes a variable in algebraic expressions?

AA number that is fixed in every situation

BA symbol that can stand for a changing number in a pattern, expression, formula, or equation

CA sign that always connects two equal expressions

DThe numerical multiplier written with a variable

13Simplify: 3x + 5y + 2x.

A10xy

B5x + 5y

C3x + 7y

D5x + y

14Which statement about expressions, equations and identities is correct?

AAn expression must always contain an equality sign.

BAn equation is true for all values of variables by definition.

CAn identity is an equality true for all permitted variable values.

DFactorisation means replacing variables with numbers.

15For the equation 3x + 5 = 20, what is the value of x?

D15

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