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Question (1)

QN0029373

Which of the following is equal to (98 + 2)(98 − 2)?

(A) 9600
(B) 9604
(C) 9996
(D) 10000

Correct Answer: B

Explanation:

Use the identity (a + b)(a − b) = a² − b². Thus, (100² − 2²) = 10000 − 4 = 9604.

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Question (2)

QN0029374

A number is increased by 4 and another number is decreased by 3. If the original numbers are a and b, then the new product is

(A) ab + 4a − 3b − 12
(B) ab + 4b − 3a − 12
(C) ab + 4b + 3a + 12
(D) ab − 4b + 3a − 12

Correct Answer: B

Explanation:

Expand (a + 4)(b − 3) = ab − 3a + 4b − 12 = ab + 4b − 3a − 12.

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Question (3)

QN0029375

The simplified form of (2x + 5)² is

(A) 4x² + 25
(B) 4x² + 20x + 25
(C) 2x² + 10x + 25
(D) 4x² + 10x + 25

Correct Answer: B

Explanation:

Apply (a + b)² = a² + 2ab + b². Hence, (2x + 5)² = 4x² + 20x + 25.

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Question (4)

QN0029376

The expression (3y − 4)² is equal to

(A) 9y² − 24y + 16
(B) 9y² + 24y + 16
(C) 9y² − 16
(D) 9y² − 12y + 16

Correct Answer: A

Explanation:

Use (a − b)² = a² − 2ab + b². Therefore, (3y − 4)² = 9y² − 24y + 16.

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Question (5)

QN0029377

Which expression is equivalent to 51 × 49?

(A) 50² + 1
(B) 50² − 1
(C) 49² + 2
(D) 51² − 2

Correct Answer: B

Explanation:

Since 51 = 50 + 1 and 49 = 50 − 1, use (a + b)(a − b) = a² − b². Result = 50² − 1 = 2499.

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Question (6)

QN0029378

The simplified form of (x + 2)(x + 7) is

(A) x² + 9x + 14
(B) x² + 14x
(C) x² + 5x + 14
(D) x² + 9x + 9

Correct Answer: A

Explanation:

Expand using distributive property: x² + 7x + 2x + 14 = x² + 9x + 14.

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Question (7)

QN0029379

A student claims that (a − b)² = a² − b². The correct statement is

(A) The claim is always true.
(B) The claim is true only when a > b.
(C) The correct identity is a² − 2ab + b².
(D) The correct identity is a² + 2ab + b².

Correct Answer: C

Explanation:

The correct identity is (a − b)² = a² − 2ab + b². The middle term cannot be omitted.

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Question (8)

QN0029380

Using identities, the value of 203 × 197 is

(A) 39991
(B) 40000
(C) 39909
(D) 39891

Correct Answer: A

Explanation:

Write as (200 + 3)(200 − 3) = 200² − 3² = 40000 − 9 = 39991.

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Question (9)

QN0029381

If three consecutive integers are (n − 1), n and (n + 1), then the value of n² − (n − 1)(n + 1) is always

(A) 0
(B) 1
(C) 2
(D) Depends on n

Correct Answer: B

Explanation:

(n − 1)(n + 1) = n² − 1. Hence, n² − (n² − 1) = 1.

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Question (10)

QN0029382

A rectangular park has length (x + 5) m and breadth (x − 3) m. Its area is

(A) x² + 2x − 15
(B) x² + 8x − 15
(C) x² − 2x − 15
(D) x² − 8x − 15

Correct Answer: A

Explanation:

Area = (x + 5)(x − 3) = x² − 3x + 5x − 15 = x² + 2x − 15.

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Question (1)

Which of the following is equal to (98 + 2)(98 − 2)?

Explanation:

Link:

Question (2)

A number is increased by 4 and another number is decreased by 3. If the original numbers are a and b, then the new product is

Explanation:

Link:

Question (3)

The simplified form of (2x + 5)² is

Explanation:

Link:

Question (4)

The expression (3y − 4)² is equal to

Explanation:

Link:

Question (5)

Which expression is equivalent to 51 × 49?

Explanation:

Link:

Question (6)

The simplified form of (x + 2)(x + 7) is

Explanation:

Link:

Question (7)

A student claims that (a − b)² = a² − b². The correct statement is

Explanation:

Link:

Question (8)

Using identities, the value of 203 × 197 is

Explanation:

Link:

Question (9)

If three consecutive integers are (n − 1), n and (n + 1), then the value of n² − (n − 1)(n + 1) is always

Explanation:

Link:

Question (10)

A rectangular park has length (x + 5) m and breadth (x − 3) m. Its area is

Explanation:

Link:

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