2015 - JAMB Mathematics Past Questions and Answers - page 3
21
Given that tan x = \(\frac{2}{3}\), where 0o d" x d" 90o, Find the value of 2sinx.
A
\(\frac{2\sqrt{13}}{13}\)
B
\(\frac{3\sqrt{13}}{13}\)
C
\(\frac{4\sqrt{13}}{13}\)
D
\(\frac{6\sqrt{13}}{13}\)
correct option: c
tan x = \(\frac{2}{3}\)(given), is illustrated in a right-angled \(\Delta\)
thus m2 = 22 + 32
= 4 + 9 = 13
m = \(\sqrt{13}\)
Hence, 2sin x = 2 x \(\frac{2}{m}\)
2 x\(\frac{2}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)
= \(\frac{4\sqrt{13}}{13}\)
Users' Answers & Commentsthus m2 = 22 + 32
= 4 + 9 = 13
m = \(\sqrt{13}\)
Hence, 2sin x = 2 x \(\frac{2}{m}\)
2 x\(\frac{2}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)
= \(\frac{4\sqrt{13}}{13}\)
22
In a town of 6250 inhabitants, there were 62 births during 1984. Find the percentage birth rate
A
3%
B
1.0%
C
2.5%
D
5.40%
23
Simplify 1¼ ÷ (2 ÷ ¼ of 28)
A
1 \( \frac{3}{8}\)
B
2 \( \frac{3}{4}\)
C
4 \( \frac{3}{8}\)
D
3 \( \frac{1}{5}\)
correct option: c
1¼ ÷ [ 2 ÷ ¼] of 28
Apply BODMAS rules
\( \frac{5}{4}\) ÷ [ 2 ÷ ¼ × 28 ]
\( \frac{5}{4} ÷ \frac{2}{7} \)
\( \frac{5}{4} × \frac{7}{2} \)
\( \frac{35}{8}\)
= \(4 \frac{3}{8}\)
Users' Answers & CommentsApply BODMAS rules
\( \frac{5}{4}\) ÷ [ 2 ÷ ¼ × 28 ]
\( \frac{5}{4} ÷ \frac{2}{7} \)
\( \frac{5}{4} × \frac{7}{2} \)
\( \frac{35}{8}\)
= \(4 \frac{3}{8}\)
24
Factorize x2 + 9x + 20
A
(x − 5) 2
B
(x + 5)(x + 4)
C
(x – 5)(x + 3)
D
(x + 3) 2
correct option: b
\( x^2 + 9x + 20 \)
Find the two numbers whose product is 20 and its sum is 9}
\( 5x \times 4x = 20x^2\)
\(5x + 4x = 9x\)
\((x^2 + 5x) + (4x + 20)\)
\(
x(x + 5)+ 4(x + 5)
= (x + 5)(x + 4)\)
Users' Answers & CommentsFind the two numbers whose product is 20 and its sum is 9}
\( 5x \times 4x = 20x^2\)
\(5x + 4x = 9x\)
\((x^2 + 5x) + (4x + 20)\)
\(
x(x + 5)+ 4(x + 5)
= (x + 5)(x + 4)\)
25
If three staff of ASono Limited agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is N120,000.00K, How much does the second staff received
A
N36,000
B
N44,000
C
N40,000
D
N15,000
correct option: c
Users' Answers & Comments26
X and Y are two sets such that nX = 15, nY = 12 and n{∩ Y} = 7. Find ∩{X ∪ Y}
A
21
B
225
C
15
D
20
correct option: d
n(X ∩ Y) = nx + ny − n(xX ∩ Y)
= 15 + 12 − 7
∴ n(X ∩ Y) = 20
Users' Answers & Comments= 15 + 12 − 7
∴ n(X ∩ Y) = 20
27
Find the x and y intercepts of the graph of 3x - z \(\leq\) 9
A
(3, -9)
B
(-3, 9)
C
(-3, -9)
D
(-3, 0)
correct option: a
Starting from 3x − z \(\leq\) 9
x = 0, substitute the value of x (i.e. x = 0) into the equation 3x − z \(\leq\) 9
3(0) − z \(\leq\) − 9
z \(\leq\) − 9
If z = 0
Then, 3x − 0 \(\leq\) 9
3x \(\leq\) 9
x \(\leq\) 3
Intercept of x and z i.e (x,z)
= (3, -9)
Users' Answers & Commentsx = 0, substitute the value of x (i.e. x = 0) into the equation 3x − z \(\leq\) 9
3(0) − z \(\leq\) − 9
z \(\leq\) − 9
If z = 0
Then, 3x − 0 \(\leq\) 9
3x \(\leq\) 9
x \(\leq\) 3
Intercept of x and z i.e (x,z)
= (3, -9)
28
Simplify log101.5 + 3 log102 − log100.3
A
log104
B
log1040
C
log10-40
D
log104-
correct option: b
log101.5 + 3 log102 − log100.3
log101.5 + log1023 − log100.3
[log10(1.5 × 23) ÷ log100.3]
[log10(15/10 × 8 ) ÷ log10( 3/10)]
log10(15/10 × 8 × 10/3 )
log1040
Users' Answers & Commentslog101.5 + log1023 − log100.3
[log10(1.5 × 23) ÷ log100.3]
[log10(15/10 × 8 ) ÷ log10( 3/10)]
log10(15/10 × 8 × 10/3 )
log1040
29
Find the total surface area of a cylinder of base radius 5cm and length 7cm ( π = 3.14)
A
17.8cm2
B
15.8cm2
C
75.4cm2
D
54.7cm2
correct option: c
The total surface area of a cylinder = 2πrl + 2πr2
= 2πr(l + r)
= 2 × 3.14(7+%=5)
2 × 3.14 × 12
= 75.4cm (1DP)
Users' Answers & Comments= 2πr(l + r)
= 2 × 3.14(7+%=5)
2 × 3.14 × 12
= 75.4cm (1DP)
30
If x + y = 90 simplify (sinx + siny)2−2sinxsiny
A
1
B
\( 0 \)
C
2
D
-1
correct option: a
Users' Answers & Comments