Year : 
2019
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

51 - 60 of 80 Questions

# Question Ans
51.

A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?

A. N20,000

B. N28,000

C. N31,200

D. N41,000

Detailed Solution

Let the number of days worked by the assistant = t
\(\therefore\) The bricklayer worked (t + 10) days.
1500(t + 10) + 500(t) = N 95,000
1500t + 15,000 + 500t = N 95,000
2000t = N 95,000 - N 15,000
2000t = N 80,000
t = 40 days
\(\therefore\) The assistant worked for 40 days and received N (500 x 40)
= N 20,000
There is an explanation video available below.
52.

Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)

A. 4x + 2y = 3

B. 4x - 3y = 1

C. 4x - 2y = 1

D. 4x + 2y = -1

Detailed Solution

Since A(x, y) is the point of equidistance between B and C, then
AB = AC
(AB)\(^2\) = (AC)\(^2\)
Using the distance formula,
(x - 0)\(^2\) + (y - 2)\(^2\) = (x - 2)\(^2\) + (y - 1)\(^2\)
x\(^2\) + y\(^2\) - 4y + 4 = x\(^2\) - 4x + 4 + y\(^2\) - 2y + 1
x\(^2\) - x\(^2\) + y\(^2\) - y\(^2\) + 4x - 4y + 2y = 5 - 4
4x - 2y = 1
There is an explanation video available below.
53.

A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?

A. N21,850

B. N18,780

C. N27,400

D. N32,500

Detailed Solution

Education = \(\frac{15}{100} \times N 50,000\)
= N 7,500
Food = N 13,600
Electricity = \(\frac{3}{100} \times N 50,000\)
= N 1,500
Leftover : N (50,000 - (7,500 + 13,600 + 1,500))
= N 27,400
There is an explanation video available below.
54.

A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5

A. 35

B. 59

C. 28

D. 87

Detailed Solution

a Δ b = a + 3b + 2
(3 Δ 2) Δ 5 = (3 + 3(2) + 2) Δ 5
= 11 Δ 5
= 11 + 3(5) + 2
= 28
There is an explanation video available below.
55.

If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

A. 36

B. 63

C. 47

D. 81

Detailed Solution

\(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\).
\(\therefore M \propto \frac{N}{\sqrt{P}}\)
\(M = \frac{k N}{\sqrt{P}}\)
when M = 3, N = 5 and P = 25;
\(3 = \frac{5k}{\sqrt{25}}\)
\(k = 3\)
\(M = \frac{3N}{\sqrt{P}}\)
when M = 2 and N = 6,
\(2 = \frac{3(6)}{\sqrt{P}} \implies \sqrt{P} = \frac{18}{2}\)
\(\sqrt{P} = 9 \implies P = 9^2\)
P = 81
There is an explanation video available below.
56.

Table:
This table below gives the scores of a group of students in a Further Mathematics Test.Find the mode of the distribution.

A. 7

B. 10

C. 5

D. 4

Detailed Solution

Mode = Score with the highest frequency
= 5
There is an explanation video available below.
57.

Table:
This table below gives the scores of a group of students in a Further Mathematics Test.Calculate the mean deviation for the distribution

A. 4.32

B. 2.81

C. 1.51

D. 3.90

Detailed Solution

Mean = \(\frac{\sum fx}{\sum f}\)
= \(\frac{156}{40}\)
= 3.9
M.D = \(\frac{\sum f|x - \bar{x}|}{\sum f}\)
= \(\frac{60.4}{40}\)
= 1.51
There is an explanation video available below.
58.

Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\).

A. \(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)

B. \(2x^2 + \frac{7}{3} x^3 - 5x + 6\)

C. \(12x^2 + 14x - 5\)

D. \(-12x^{-4} - 14x + 5\)

Detailed Solution

\(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\)
= \(\frac{4x^{-3 + 1}}{-3 + 1} - \frac{7x^{2 + 1}}{2 + 1} + \frac{5x^{1 + 1}}{1 + 1} - 6x\)
= \(-2x^{-2} - \frac{7}{3} x^3 + \frac{5}{2} x^2 - 6x\)
There is an explanation video available below.
59.

Find the probability that a number selected at random from 21 to 34 is a multiple of 3

A. \(\frac{3}{11}\)

B. \(\frac{2}{9}\)

C. \(\frac{5}{14}\)

D. \(\frac{5}{13}\)

Detailed Solution

S = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34}
n(S) = 14
multiples of 3 = {21, 24, 27, 30, 33}
n(multiples of 3) = 5
Prob( picking a multiple of 3) = 5/14
There is an explanation video available below.
60.

If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

A. \(\frac{1}{3}\)

B. \(\frac{1}{9}\)

C. \(\frac{2}{3}\)

D. \(\frac{2}{9}\)

Detailed Solution

\(T_n = ar^{n - 1}\) (terms of a G.P)
\(T_3 = ar^2 = 9\) ... (i)
\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)
Divide (i) by (ii);
\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)
\(r^4 = \frac{1}{81}\)
\(r^4 = (\frac{1}{3})^4\)
\(r = \frac{1}{3}\)
There is an explanation video available below.
51.

A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?

A. N20,000

B. N28,000

C. N31,200

D. N41,000

Detailed Solution

Let the number of days worked by the assistant = t
\(\therefore\) The bricklayer worked (t + 10) days.
1500(t + 10) + 500(t) = N 95,000
1500t + 15,000 + 500t = N 95,000
2000t = N 95,000 - N 15,000
2000t = N 80,000
t = 40 days
\(\therefore\) The assistant worked for 40 days and received N (500 x 40)
= N 20,000
There is an explanation video available below.
52.

Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)

A. 4x + 2y = 3

B. 4x - 3y = 1

C. 4x - 2y = 1

D. 4x + 2y = -1

Detailed Solution

Since A(x, y) is the point of equidistance between B and C, then
AB = AC
(AB)\(^2\) = (AC)\(^2\)
Using the distance formula,
(x - 0)\(^2\) + (y - 2)\(^2\) = (x - 2)\(^2\) + (y - 1)\(^2\)
x\(^2\) + y\(^2\) - 4y + 4 = x\(^2\) - 4x + 4 + y\(^2\) - 2y + 1
x\(^2\) - x\(^2\) + y\(^2\) - y\(^2\) + 4x - 4y + 2y = 5 - 4
4x - 2y = 1
There is an explanation video available below.
53.

A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?

A. N21,850

B. N18,780

C. N27,400

D. N32,500

Detailed Solution

Education = \(\frac{15}{100} \times N 50,000\)
= N 7,500
Food = N 13,600
Electricity = \(\frac{3}{100} \times N 50,000\)
= N 1,500
Leftover : N (50,000 - (7,500 + 13,600 + 1,500))
= N 27,400
There is an explanation video available below.
54.

A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5

A. 35

B. 59

C. 28

D. 87

Detailed Solution

a Δ b = a + 3b + 2
(3 Δ 2) Δ 5 = (3 + 3(2) + 2) Δ 5
= 11 Δ 5
= 11 + 3(5) + 2
= 28
There is an explanation video available below.
55.

If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

A. 36

B. 63

C. 47

D. 81

Detailed Solution

\(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\).
\(\therefore M \propto \frac{N}{\sqrt{P}}\)
\(M = \frac{k N}{\sqrt{P}}\)
when M = 3, N = 5 and P = 25;
\(3 = \frac{5k}{\sqrt{25}}\)
\(k = 3\)
\(M = \frac{3N}{\sqrt{P}}\)
when M = 2 and N = 6,
\(2 = \frac{3(6)}{\sqrt{P}} \implies \sqrt{P} = \frac{18}{2}\)
\(\sqrt{P} = 9 \implies P = 9^2\)
P = 81
There is an explanation video available below.
56.

Table:
This table below gives the scores of a group of students in a Further Mathematics Test.Find the mode of the distribution.

A. 7

B. 10

C. 5

D. 4

Detailed Solution

Mode = Score with the highest frequency
= 5
There is an explanation video available below.
57.

Table:
This table below gives the scores of a group of students in a Further Mathematics Test.Calculate the mean deviation for the distribution

A. 4.32

B. 2.81

C. 1.51

D. 3.90

Detailed Solution

Mean = \(\frac{\sum fx}{\sum f}\)
= \(\frac{156}{40}\)
= 3.9
M.D = \(\frac{\sum f|x - \bar{x}|}{\sum f}\)
= \(\frac{60.4}{40}\)
= 1.51
There is an explanation video available below.
58.

Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\).

A. \(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)

B. \(2x^2 + \frac{7}{3} x^3 - 5x + 6\)

C. \(12x^2 + 14x - 5\)

D. \(-12x^{-4} - 14x + 5\)

Detailed Solution

\(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\)
= \(\frac{4x^{-3 + 1}}{-3 + 1} - \frac{7x^{2 + 1}}{2 + 1} + \frac{5x^{1 + 1}}{1 + 1} - 6x\)
= \(-2x^{-2} - \frac{7}{3} x^3 + \frac{5}{2} x^2 - 6x\)
There is an explanation video available below.
59.

Find the probability that a number selected at random from 21 to 34 is a multiple of 3

A. \(\frac{3}{11}\)

B. \(\frac{2}{9}\)

C. \(\frac{5}{14}\)

D. \(\frac{5}{13}\)

Detailed Solution

S = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34}
n(S) = 14
multiples of 3 = {21, 24, 27, 30, 33}
n(multiples of 3) = 5
Prob( picking a multiple of 3) = 5/14
There is an explanation video available below.
60.

If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

A. \(\frac{1}{3}\)

B. \(\frac{1}{9}\)

C. \(\frac{2}{3}\)

D. \(\frac{2}{9}\)

Detailed Solution

\(T_n = ar^{n - 1}\) (terms of a G.P)
\(T_3 = ar^2 = 9\) ... (i)
\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)
Divide (i) by (ii);
\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)
\(r^4 = \frac{1}{81}\)
\(r^4 = (\frac{1}{3})^4\)
\(r = \frac{1}{3}\)
There is an explanation video available below.