Mathematics (Core), 2020, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

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) $_{3}$ Show Content 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.	C
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) Show Content 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.	C
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 Show Content 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.	B
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 Show Content 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 = $\frac{5 x + 5 - 3 x - 12}{15}$ 2x - 7 > 15 2x > 22 = x > 11 There is an explanation video available below.	D
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 Show Content 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.	C
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 Show Content 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.	D
7.	What is the circumference of latitude 0 $^{o}$ S if R is the radius of the earth? A. cos $θ$ B. 2 $π$ R cos $θ$ C. R sin $θ$ D. 2 $π$ r sin $θ$ Show Content Detailed Solution Circumstances of latitude 0 $^{o}$ s where R is the radius of the earth 2 $π$ r cos $θ$ There is an explanation video available below.	B
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. $\frac{12}{17}$ Show Content 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 $\frac{a d j}{H y p} = \frac{15}{17}$ EC $^{2}$ = $\sqrt{225 + 64}$ EC = $\sqrt{289}$ = 17 There is an explanation video available below.	A
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 Show Content Detailed Solution Let x represent number of goals $\begin{array}{cc} x & F & F r e q u e n c y (f x) \\ 0 & 4 & 0 \\ 1 & 3 & 3 \\ 2 & 15 & 30 \\ 3 & 16 & 48 \\ 4 & 1 & 4 \\ 5 & 0 & 0 \\ 6 & 1 & 6 \\ \sum F x = 91 \end{array}$ $\sum f x$ = 91 There is an explanation video available below.	C
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 Show Content Detailed Solution No of students offering physics are $\frac{12}{360}$ x 150 = 5 There is an explanation video available below.	D

1.	Evaluate (212) $_{3}$ - (121) $_{3}$ + (222) $_{3}$ A. (313) $_{3}$ B. (1000) $_{3}$ C. (1020) $_{3}$ D. (1222) $_{3}$ Show Content 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.	C
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) Show Content 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.	C
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 Show Content 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.	B
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 Show Content 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 = $\frac{5 x + 5 - 3 x - 12}{15}$ 2x - 7 > 15 2x > 22 = x > 11 There is an explanation video available below.	D
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 Show Content 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.	C

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 Show Content 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.	D
7.	What is the circumference of latitude 0 $^{o}$ S if R is the radius of the earth? A. cos $θ$ B. 2 $π$ R cos $θ$ C. R sin $θ$ D. 2 $π$ r sin $θ$ Show Content Detailed Solution Circumstances of latitude 0 $^{o}$ s where R is the radius of the earth 2 $π$ r cos $θ$ There is an explanation video available below.	B
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. $\frac{12}{17}$ Show Content 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 $\frac{a d j}{H y p} = \frac{15}{17}$ EC $^{2}$ = $\sqrt{225 + 64}$ EC = $\sqrt{289}$ = 17 There is an explanation video available below.	A
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 Show Content Detailed Solution Let x represent number of goals $\begin{array}{cc} x & F & F r e q u e n c y (f x) \\ 0 & 4 & 0 \\ 1 & 3 & 3 \\ 2 & 15 & 30 \\ 3 & 16 & 48 \\ 4 & 1 & 4 \\ 5 & 0 & 0 \\ 6 & 1 & 6 \\ \sum F x = 91 \end{array}$ $\sum f x$ = 91 There is an explanation video available below.	C
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 Show Content Detailed Solution No of students offering physics are $\frac{12}{360}$ x 150 = 5 There is an explanation video available below.	D