2015 - JAMB Mathematics Past Questions and Answers - page 2

√30 × √40

√(30 × 40)

√(3 × 10 × 4 × 10)

√(400 × 3)

√400 × √3

20 × √3

20√3

√(2x + 2 ) − √x = 1

√(2x + 2) = 1 + √x

Square both sides

√(2x + 2)² = (1 + √x)²

((2x + 2)²)^½ = 1 + √x + √x+ x

2x + 2 = 1 + 2√x +x

Collect the like term together

2x − x + 2 − 1 = 2 √x
x + 1 = 2√x

Square both sides

(x + 1)² = (2√x)²

x² + 2x + 1 = 4x

x² + 2x − 4x + 1 = 0

(x²− x)(x + 1)= 0

x(x − 1) −1(x − 1)

(x − 1)(x −1)

Either (x − 1) = 0 or (x − 1) = 0

x = 1 or 1

x = 1 twice

Let x represent the first number;

Then, the other is (5 − x) , since their sum is 5 and their product is 14

x(5 − x) = 14

5x − x² = 14

x² − 5x − 14 = 0

(x² − 7x) + (2x − 14) = 0

x(x − 7) + 2(x − 7) = 0

(x − 7)(x + 2) = 0

Either (x − 7) = 0 or (x + 2) = 0

x = 7 or x = − 2

The two numbers are 7 and − 2

\( 5^{(x − 2)} = (125^{−1} )^{(x + 3)}\\
5^{(x − 2)} = (5− 3)^{x + 3}\\
5^{(x − 2)} = 5^{− 3x − 9}\\
x + 3x = − 9 + 2\\
4x = − 7\\
x = \frac{−7}{4} \)

Each exterior angle = 180 − 120=60

Exterior angle =360/n

60 = 360/n

n =360/6

= 6

25% of N80 = 25/100 × 80

= N20.00

2.04 x 3.7
=
204
x 37
-----
7548 = 7.548

= 7.55(2dp)

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

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)

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