Year : 
2020
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

1 - 10 of 40 Questions

# Question Ans
1.

Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)

A. (313)\(_3\)

B. (1000)\(_3\)

C. (1020)\(_3\)

D. (1222)\(_3\)

Detailed Solution

Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
(212)\(_3\) + (222)\(_3\) = 1211\(_3\)
→ 1211\(_3\) - 121\(_3\)
= 1020\(_3\)

There is an explanation video available below.
2.

Factorise (4a + 3) \(^2\) - (3a - 2)\(^2\)

A. (a + 1)(a + 5)

B. (a - 5)(7a - 1)

C. (a + 5)(7a + 1)

D. a(7a + 1)

Detailed Solution

[(4a + 3) \(^2\) - (3a - 2)\(^2\) = a\(^2\) - b\(^2\) = (a + b) (a - b)
= [(4a + 3) + (3a - 2)] [(4a + 3) - (3a - 2)]
= [4a + 3 + 3a - 2] [4a + 3 - 3a + 2]
= (7a + 1)(a + 5)
(a + 5) (7a + 1)
There is an explanation video available below.
3.

Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

A. 131

B. 125

C. 123

D. 120

Detailed Solution

Arrange in ascending order
89, 100, 108, 119, 120,130, 131, 131, 141, 161
Median = \(\frac{120 + 130}{2}\) = 125
There is an explanation video available below.
4.

Find all real number x which satisfy the inequality \(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4)

A. x < 11

B. x < -1

C. x > 6

D. x > 11

Detailed Solution

\(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4) = \(\frac{x + 1}{3} - 1\) > \(\frac{x + 4}{5}\)
\(\frac{x + 1}{3} - \frac{x + 4}{5} -1\) > 0
= \(\frac{5x + 5 - 3x - 12}{15}\)
2x - 7 > 15
2x > 22 = x > 11
There is an explanation video available below.
5.

Reach each number to two significant figures and then evaluate \(\frac{0.02174 \times 1.2047}{0.023789}\)

A. 0

B. 0.9

C. 1.1

D. 1.2

Detailed Solution

\(\frac{0.021741 \times 1.2047}{0.023789}\) = \(\frac{0.0255 \times 1.2}{0.024}\) (to 216)
= \(\frac{0.0264}{0.024}\) = 1.1
There is an explanation video available below.
6.

Four boys and ten girls can cut a field first in 5 hours. If the boys work at \(\frac{5}{4}\) the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?

A. 180

B. 60

C. 25

D. 20

Detailed Solution

Let x rep. numbers of boys that can work at \(\frac{5}{4}\) the rate at
which the 10 girls work
For 1 hrs, x boys will work for \(\frac{\frac{1}{5} \times 10}{4}\)
x = \(\frac{5}{4}\) x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
\(\frac{12 \times 5}{3}\) boys will be needed = 20 boys.
There is an explanation video available below.
7.

What is the circumference of latitude 0\(^o\)S if R is the radius of the earth?

A. cos \(\theta\)

B. 2\(\pi\)R cos \(\theta\)

C. R sin \(\theta\)

D. 2 \(\pi\) r sin \(\theta\)

Detailed Solution

Circumstances of latitude 0\(^o\)s where R is the radius of the earth 2\(\pi\)r cos \(\theta\)

There is an explanation video available below.
8.

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

A. \(\frac{15}{17}\)

B. \(\frac{8}{17}\)

C. \(\frac{8}{15}\)

D. \(\frac{12}{17}\)

Detailed Solution

ABCD is the floor. By pathagoras
AC\(^2\) = 144 + 81 = \(\sqrt{225}\)
AC = 15cm
Height of room 8m, diagonal of floor is 15m
Therefore, the cosine of the angle which a diagonal of the room makes with the floor is
EC\(^2\) = 15\(^2\) + 8\(^2\) cosine
\(\frac{adj}{Hyp} = \frac{15}{17}\)
EC\(^2\) = \(\sqrt{225 + 64}\)
EC = \(\sqrt{289}\)
= 17
There is an explanation video available below.
9.

Table:
The goals scored by 40 football teams from three league divisions are recorded belowWhat is the total number of goals scored by all the teams?

A. 21

B. 40

C. 91

D. 96

Detailed Solution

Let x represent number of goals \(\begin{array}{c|c|} x & F & Frequency(fx)\\\hline 0 & 4 & 0 \\\hline 1 & 3 & 3\\\hline 2 & 15 & 30 \\\hline 3 & 16 & 48\\ \hline 4 & 1 & 4 \\\hline 5 & 0 & 0 \\\hline 6 & 1 & 6 \\\hline & \sum Fx = 91& \end{array}\)
\(\sum fx\) = 91

There is an explanation video available below.
10.

In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12\(^o\). How many students are offering physics?

A. 18

B. 15

C. 10

D. 5

Detailed Solution

No of students offering physics are
\(\frac{12}{360}\) x 150 = 5
There is an explanation video available below.
1.

Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)

A. (313)\(_3\)

B. (1000)\(_3\)

C. (1020)\(_3\)

D. (1222)\(_3\)

Detailed Solution

Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
(212)\(_3\) + (222)\(_3\) = 1211\(_3\)
→ 1211\(_3\) - 121\(_3\)
= 1020\(_3\)

There is an explanation video available below.
2.

Factorise (4a + 3) \(^2\) - (3a - 2)\(^2\)

A. (a + 1)(a + 5)

B. (a - 5)(7a - 1)

C. (a + 5)(7a + 1)

D. a(7a + 1)

Detailed Solution

[(4a + 3) \(^2\) - (3a - 2)\(^2\) = a\(^2\) - b\(^2\) = (a + b) (a - b)
= [(4a + 3) + (3a - 2)] [(4a + 3) - (3a - 2)]
= [4a + 3 + 3a - 2] [4a + 3 - 3a + 2]
= (7a + 1)(a + 5)
(a + 5) (7a + 1)
There is an explanation video available below.
3.

Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

A. 131

B. 125

C. 123

D. 120

Detailed Solution

Arrange in ascending order
89, 100, 108, 119, 120,130, 131, 131, 141, 161
Median = \(\frac{120 + 130}{2}\) = 125
There is an explanation video available below.
4.

Find all real number x which satisfy the inequality \(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4)

A. x < 11

B. x < -1

C. x > 6

D. x > 11

Detailed Solution

\(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4) = \(\frac{x + 1}{3} - 1\) > \(\frac{x + 4}{5}\)
\(\frac{x + 1}{3} - \frac{x + 4}{5} -1\) > 0
= \(\frac{5x + 5 - 3x - 12}{15}\)
2x - 7 > 15
2x > 22 = x > 11
There is an explanation video available below.
5.

Reach each number to two significant figures and then evaluate \(\frac{0.02174 \times 1.2047}{0.023789}\)

A. 0

B. 0.9

C. 1.1

D. 1.2

Detailed Solution

\(\frac{0.021741 \times 1.2047}{0.023789}\) = \(\frac{0.0255 \times 1.2}{0.024}\) (to 216)
= \(\frac{0.0264}{0.024}\) = 1.1
There is an explanation video available below.
6.

Four boys and ten girls can cut a field first in 5 hours. If the boys work at \(\frac{5}{4}\) the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?

A. 180

B. 60

C. 25

D. 20

Detailed Solution

Let x rep. numbers of boys that can work at \(\frac{5}{4}\) the rate at
which the 10 girls work
For 1 hrs, x boys will work for \(\frac{\frac{1}{5} \times 10}{4}\)
x = \(\frac{5}{4}\) x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
\(\frac{12 \times 5}{3}\) boys will be needed = 20 boys.
There is an explanation video available below.
7.

What is the circumference of latitude 0\(^o\)S if R is the radius of the earth?

A. cos \(\theta\)

B. 2\(\pi\)R cos \(\theta\)

C. R sin \(\theta\)

D. 2 \(\pi\) r sin \(\theta\)

Detailed Solution

Circumstances of latitude 0\(^o\)s where R is the radius of the earth 2\(\pi\)r cos \(\theta\)

There is an explanation video available below.
8.

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

A. \(\frac{15}{17}\)

B. \(\frac{8}{17}\)

C. \(\frac{8}{15}\)

D. \(\frac{12}{17}\)

Detailed Solution

ABCD is the floor. By pathagoras
AC\(^2\) = 144 + 81 = \(\sqrt{225}\)
AC = 15cm
Height of room 8m, diagonal of floor is 15m
Therefore, the cosine of the angle which a diagonal of the room makes with the floor is
EC\(^2\) = 15\(^2\) + 8\(^2\) cosine
\(\frac{adj}{Hyp} = \frac{15}{17}\)
EC\(^2\) = \(\sqrt{225 + 64}\)
EC = \(\sqrt{289}\)
= 17
There is an explanation video available below.
9.

Table:
The goals scored by 40 football teams from three league divisions are recorded belowWhat is the total number of goals scored by all the teams?

A. 21

B. 40

C. 91

D. 96

Detailed Solution

Let x represent number of goals \(\begin{array}{c|c|} x & F & Frequency(fx)\\\hline 0 & 4 & 0 \\\hline 1 & 3 & 3\\\hline 2 & 15 & 30 \\\hline 3 & 16 & 48\\ \hline 4 & 1 & 4 \\\hline 5 & 0 & 0 \\\hline 6 & 1 & 6 \\\hline & \sum Fx = 91& \end{array}\)
\(\sum fx\) = 91

There is an explanation video available below.
10.

In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12\(^o\). How many students are offering physics?

A. 18

B. 15

C. 10

D. 5

Detailed Solution

No of students offering physics are
\(\frac{12}{360}\) x 150 = 5
There is an explanation video available below.