2015 - JAMB Mathematics Past Questions and Answers - page 1

dy/dx \( (4x^3 + 3x^2 + 2x + 1) \)

= \( 12x^2 + 6x + 2 \)

⇒ \( 12x^2 + 6 + 2 \)

Divide both sides by 2

\( \frac{12x^2}{2} − \frac{6x}2 − \frac{2}{2} \)

= \( 6x^2 + 3x + 1 \)

dy/dx

= \( 6x^2 + 3x + 1 \)

\(∫ [(x^2 + 4x^2 + 1 ) ÷ x^2]dx = ∫ (x^3/x^2)dx + ∫(1/x^2)dx \)

⇒\( ∫ xdx + ∫ 4^{−1} or + ∫ (1/x^2)dx\)

= \( x^2/2 − 4x − 1/x^2 + C \)

Find the slant height

\( l^2 = h^2 + r^2(h = 4cm,r = 3cm)\)

\( l^2 = 4^2 + 3^2 = 16 + 9 = 25 \)

\( l^2 = √ 25 \)

Squaring both sides

l = 5cm

The area of curved surface (s) =π(3)(5)

15π = 15 × 3.14

= 47.1cm²

[1 ÷ (x+1)] + [1 ÷ (x − 1)]

= ((x − 1) + [(x + 1)) ÷ (x+1)(x − 1)]

Using the L.C.M.

= (x − 1 + x + 1) ÷ (x + 1)(x − 1)

= (x + 2 − 1 + 1) ÷ (x + 1)(x − 1)

= 2x ÷ (x + 1)(x − 1) =2x ÷ (x + 1)(x − 1)

Area of a circle (A) = πr²

Radius = 4cm

π = 3.142

A = 3.142 × (4)²

= 3.142 × 16

= 50.272

A = 50.3cm² (1dp)

The area of an ellipse (e) =πab/4

Let a rep. the length of its major axis = 14cm

Let b rep. the length of its minor axis = ?

π = 3.142

Area of an ellipse = 132cm²

132 = (π14 × b) ÷ 4

132 = (3.142 × 14b) ÷ 4

3.142 × 14b =132 × 4

b = (1324 × 4) ÷ (3.142 × 14)
= 528/43.988

= 12cm

The length of its minor axis (b) = 12cm

V = ⅓ πr² h

Volume of a cone (Vc) = ⅓ × 3.14 × (5)² × 6

= 156.9³

157cm3

Prob.(A outcome) = \(\frac{1}{6}\), Prob.(B outcome) = ¼

P(A ∪ B) = 1/12, Prob.(A ∩ B)

Prob.(A ∩ B) = Prob.(A) + Prob.(B) − Prob.(A ∪ B)

1/6 + 1/4 − 1/12

= (2 + 3 − 1) ÷ 12

= 4/12

= 1/3

Prob.(A ∩ B) = 1/3

Z has 4 elements, power = number of subset = 2p

Z = 2_n = 2₄

= 16

\(27^x ÷ 81^{(x + 2y)} = 9 \\
(27)x = 9 × 81^{(x+2y)} \\
(3^3 )^x =32 \times 3^{4(x + 2y)} \\
=3^{(2 + 4x + 8y)}\\
3^{3x} = 3^{ (2 + 4x + 8y)}\\
3x = 2 + 4x + 8y\\
3x − 4x − 8y = 2 … … … (1)\\
x + 4y = 0 … … … (2)\\
− 4y = 2\\
y = (− 2) ÷ 4 = − ½\\
y = − ½\ \)

Substitute the value of y into equation (2)

i.e x + 4y = 0

x + 4( − 1/2) = 0

x − 2 = 0

x = 2

∴ x = 2,y = − ½)

Method II

\( 27^x ÷ 31^{(x + 2y) }= 9\\
3^{3x} × 3^{( − 4x − 8y)} = 32\\
3^{(3x − 8y)} = 32\\
− x − 8y=2 ……… (1)\\
x + 4y = 0 ……… (2)\\
− 4 = 2\\
y= 2/4 = ½\\
y = ½ \)

Substitute the value of y into equation 2

x + 4y=0

x + 4 (− 1) ÷ 2) = 0

x − 2 = 0

x = 2

x = 2, y = ½