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JAMB Mathematics Past Questions & Answers - Page 93

461.

Factorize $a^2 − b^2 − 4a + 4$

(a + b)(a − b)

(a − 2 + b)(a - 2- b)

(a + 1)(a − 2 + b)

(a + b) 2

View answer & explanation

Correct answer is B

The trinomial = $a^2 − 4a + 4 \\ a^2 − b^2− 4a + 4 = (a^2 − 4a + 4) − b^2 \\ (a^2 − 2a − 2a + 4) − b^2 \\ a(a − 2)− 2(a − 2)] − b^2 \\ (a − 2)2 − b^2 \\ (a − 2 + b)(a − 2 − b )$

462.

Rationalize 5 ÷ (2 − √3)

3(2 + √5)

2(3 + √5)

5(2 + √3)

3 √2 + 1

View answer & explanation

Correct answer is C

5÷ (2 − √3)

Using conjugate surds

[5 ÷ (2 − √3)]×(2 + √3) ÷ (2 + √3)]

[5(2+√3)÷((2− √3))2]

[5(2 +√3) ÷ (2)2− (√3)2]

[5(2 +√3) ÷(4− 3)]

= 5(2 + √3)

463.

A public car dealer marked up the cost of a car at 30% in an attempt to make 20% gross profit. Due to the value of dollar, he now placed 20% discount on the car. What profit or loss will he make?

View answer & explanation

Correct answer is C

Let assume the cost price is 100%

Marked up price + cost price = 20 + 100 = 120%

Discount at 20% = 20/100 × 120 % of cost price

Selling price = cost price − gain

= (120 − 24)% of cost price

= 96% of cost price

Loss = (100− 96)% of cost price

= 4% of cost price

∴ He will wake 4% loss