2015 - JAMB Mathematics Past Questions and Answers - page 1
1
If y = \((x^2 + 3x − 1) ÷ (3x + 4).\) Find dy/dx
A
\( (3x^2 + 8x + 7) ÷ (3x + 4)^2 \)
B
\( x^2 + 2x + (1 ÷ (x + 1)^2) \)
C
\( 2x^2 + 4x + (1 ÷ (2x + 4)^2) \)
D
\( x^2 + 3x + (2 ÷ (x + 3)^2) \)
correct option: a
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
= \( 6x^2 + 3x + 1 \)
Users' Answers & Comments= \( 12x^2 + 6x + 2 \)
⇒ \( 12x^2 + 6 + 2 \)
Divide both sides by 2
\( \frac{12x^2}{2} − \frac{6x}2 − \frac{2}{2} \)
= \( 6x^2 + 3x + 1 \)
dy/dx
= \( 6x^2 + 3x + 1 \)
2
Integral ∫\( (5x^3 + 7x^2 − 2x + 5)\)dx
A
\( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)
B
\( \frac{5x}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)
C
\( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)
D
\( \frac{2x^2}{3} + \frac{x}{5} - C \)
correct option: b
\(∫ [(x^2 + 4x^2 + 1 ) ÷ x^2]dx = ∫ (x^3/x^2)dx + ∫(1/x^2)dx \)
⇒\( ∫ xdx + ∫ 4^{−1} or + ∫ (1/x^2)dx\)
= \( x^2/2 − 4x − 1/x^2 + C \)
Users' Answers & Comments⇒\( ∫ xdx + ∫ 4^{−1} or + ∫ (1/x^2)dx\)
= \( x^2/2 − 4x − 1/x^2 + C \)
3
Find the area of the curved surface of a cone whose base radius is 3cm and whose height is 4cm (π = 3.14)
A
17.1cm2
B
27.2cm2
C
47.1cm2
D
37.3cm2
correct option: 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
Users' Answers & Comments\( l^2 = h^2 + r^2(h = 4cm,r = 3cm)\)
\( l^2 = 4^2 + 3^2 = 16 + 9 = 25 \)
\( l^2 = √ 25 \)
Squaring both sides
l = 5cm
The area of curved surface (s) =π(3)(5)
15π = 15 × 3.14
= 47.1cm2
4
Simplify \( \frac{1}{(x + 1)} + \frac{1}{(x − 1)} \)
A
2x/(x + 1)(x−3)
B
2/(x + 1)(x−1)
C
2x/(x + 1)2
D
2x(x+1)2
correct option: b
[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)
Users' Answers & Comments= ((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)
5
The area of a circle of radius 4cm is equal to (Take π = 3.142 )
A
10.3cm2
B
15.7cm2
C
50.3cm2
D
17.4cm2
correct option: c
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)
Users' Answers & CommentsRadius = 4cm
π = 3.142
A = 3.142 × (4)2
= 3.142 × 16
= 50.272
A = 50.3cm2 (1dp)
6
The area of an ellipse is 132cm2.The length of its major axis is 14cm.Find the length of it minor axis
A
10.5cm
B
5cm
C
10cm
D
12cm
correct option: d
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
Users' Answers & CommentsLet 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
7
The volume of a cone (s) of height 6cm and base radius 5cm is
A
157cm3
B
155cm3
C
175cm3
D
145cm3
correct option: a
V = ⅓ πr2 h
Volume of a cone (Vc) = ⅓ × 3.14 × (5)2 × 6
= 156.93
157cm3
Users' Answers & CommentsVolume of a cone (Vc) = ⅓ × 3.14 × (5)2 × 6
= 156.93
157cm3
8
The probability of an outcome A is 1/6 . The probability of the B outcome is 1/4 . If the probability of A or B or both is 1/12 . What is the probability of both outcomes A and B?
A
1/2
B
1/3
C
2/5
D
3/4
correct option: b
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
Users' Answers & CommentsP(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
9
Given that Z = {1,2,4,5} what is the power of set Z?
A
16
B
8
C
10
D
12
correct option: a
Z has 4 elements, power = number of subset = 2p
Z = 2n = 24
= 16
Users' Answers & CommentsZ = 2n = 24
= 16
10
Calculate the value of x and y if (27x ÷ 81x+2y = 9 ,x + 4y = 0
A
x = 1, y = 1/2
B
x = 2, y = – 1/2
C
x − 0, y = 1
D
x = 2, y = –1
correct option: b
\(27^x ÷ 81^{(x + 2y)} = 9 \\
(27)x = 9 × 81^{(x+2y)} \\
(3^3 )^x =32 \times 3^{4(x + 2y)} \\
=3^{(2 + 4x + 8y)}\\
3^{3x} = 3^{ (2 + 4x + 8y)}\\
3x = 2 + 4x + 8y\\
3x − 4x − 8y = 2 … … … (1)\\
x + 4y = 0 … … … (2)\\
− 4y = 2\\
y = (− 2) ÷ 4 = − ½\\
y = − ½\ \)
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
Users' Answers & Comments(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