Mathematics (Core), 2018, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2018

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

51 - 60 of 62 Questions

#	Question	Ans
51.	Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A. 210 B. 1050 C. 21400 D. 25200 Show Content Detailed Solution To form words having 3 consonants and 2 vowels out of 7 consonants and 4 vowels, the number of such words is 7/3C x 4/2C = 35 x 6 = 210 There is an explanation video available below.	A
52.	From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P and R. A. 5km B. 12km C. 13km D. 17km Show Content Detailed Solution Using Pythagoras theorem PR\(^2\) = 5\(^2\) + 12\(^2\) 25 + 144 = 169 PR = √(169)= 13km There is an explanation video available below.	C
53.	If y = 23\(_{five}\) + 101\(_{three}\) find y leaving your answer in base two A. 1110 B. 10111 C. 11101 D. 111100 Show Content Detailed Solution First we convert the numbers to base ten 23\(_{five}\)= 2 x 51 + 3 x 50 = 10 + 3 = 13 101\(_{five}\) = (1 x 32) + (0 x 31) + (1 x 30) = 9 + 0 + 1 = 10 So, y = 13 + 10 = 23 To convert 23 to base 2 (as in the diagram above) Y = 23 = 10111\(_{five}\) Answer is B There is an explanation video available below.	B
54.	A box contains two red balls and four blue balls. A ball is drawn at random from the box and then replaced before a second ball is drawn. Find the probability of drawing two red balls. A. \(\frac{2}{3}\) B. \(\frac{1}{3}\) C. \(\frac{1}{4}\) D. \(\frac{1}{9}\) Show Content Detailed Solution Total number of balls = 2 + 4 = 6 P(of picking a red ball) = \(\frac{2}{6}\) = \(\frac{1}{3}\) P(of picking a blue ball) = \(\frac{4}{6}\) = \(\frac{2}{3}\) With replacement, P( picking two red balls) = \(\frac{1}{3}\) × \(\frac{1}{3}\) = \(\frac{1}{9}\) There is an explanation video available below.	D
55.	Which one of the following gives the members of the set A1 n B n C? A. Φ B. {s} C. {t, u} D. {y, z} Show Content Detailed Solution A1 = Elements in the universal set but not in A = {s, w, x, y, z} B = {r, s. t, u} C = {t, u, v, w, x} A1 n B n C = elements common to the three sets = none = empty set = Φ There is an explanation video available below.	A
56.	Calculate the area of an equilateral triangle of side 8cm A. 8√3 B. 16 C. 4√3 D. 16√3 Show Content Detailed Solution An equilateral triangle has all sides equal and all angles equal as 600 Area = \(\frac{1}{2}\) absinθ Area = \(\frac{1}{2}\) x 8 x 8 x sin60 = \(\frac{1}{2}\) x 64 x \(\sqrt{\frac{3}{2}}\) = 16√3 cm\(^2\) There is an explanation video available below.	D
57.	Approximate 0.9875 to 1 decimal place. A. 1.1 B. 1.0 C. 0.9 D. 0.10 Show Content Detailed Solution 9 is on one decimal place, the next number to it is 8 which will be rounded up to 1 because it is greater than 5 and then added to 9 to give 10, 10 cannot be written, it will then be rounded up to 1 and added to 0. So the answer is 1.0 There is an explanation video available below.	B
58.	Simplify 25\(\frac{1}{2}\) × 8\(\frac{-2}{3}\) A. 1\(\frac{1}{4}\) B. 2\(\frac{1}{4}\) C. 6 D. 10 Show Content Detailed Solution Using law of indices 25\(\frac{1}{2}\) × 8\(\frac{-2}{3}\) = √25 x (\(\sqrt[3]{8}\)) -2 = 5 x 2-2 = 5 x \(\frac{1}{2^2}\) = \(\frac{5}{4}\) = \(\frac{11}{4}\) Answer is A There is an explanation video available below.	A
59.	From a point R, 300m north of P, a man walks eastwards to a place; Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree A. 026\(^o\) B. 045\(^o\) C. 210\(^o\) D. 240\(^o\) Show Content Detailed Solution Cos θ = \(\frac{adj}{hyp}\) = \(\frac{300}{600}\) = 0.5 θ = Cos - 10.5 = 60 ∠ RPQ = ∠ PQs So the bearing of P from Q is 180 + 60 = 240\(^o\) Answer is D There is an explanation video available below.	D
60.	Add 54 \(_{eight}\) and 67\(_{eight}\) giving your answers in base eight A. 111 B. 121 C. 123 D. 143 Show Content Detailed Solution 54 \(_{eight}\) and 67\(_{eight}\) = 1438 Starting with normal addition, 4 + 7 gives 11 (it is more than the base, 8) 8 goes in 11 just 1 time, remaining 3, the remainder will be written, and the 1 will be added to the sum of 5 and 6 which gives 12 altogether, 8 goes in 12 one time remaining 4, the remainder 4 was written and then the 1 that was the quotient was then written since nothing to add the 1 to. So answer is 143 in base eight There is an explanation video available below.	D

51.	Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A. 210 B. 1050 C. 21400 D. 25200 Show Content Detailed Solution To form words having 3 consonants and 2 vowels out of 7 consonants and 4 vowels, the number of such words is 7/3C x 4/2C = 35 x 6 = 210 There is an explanation video available below.	A
52.	From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P and R. A. 5km B. 12km C. 13km D. 17km Show Content Detailed Solution Using Pythagoras theorem PR\(^2\) = 5\(^2\) + 12\(^2\) 25 + 144 = 169 PR = √(169)= 13km There is an explanation video available below.	C
53.	If y = 23\(_{five}\) + 101\(_{three}\) find y leaving your answer in base two A. 1110 B. 10111 C. 11101 D. 111100 Show Content Detailed Solution First we convert the numbers to base ten 23\(_{five}\)= 2 x 51 + 3 x 50 = 10 + 3 = 13 101\(_{five}\) = (1 x 32) + (0 x 31) + (1 x 30) = 9 + 0 + 1 = 10 So, y = 13 + 10 = 23 To convert 23 to base 2 (as in the diagram above) Y = 23 = 10111\(_{five}\) Answer is B There is an explanation video available below.	B
54.	A box contains two red balls and four blue balls. A ball is drawn at random from the box and then replaced before a second ball is drawn. Find the probability of drawing two red balls. A. \(\frac{2}{3}\) B. \(\frac{1}{3}\) C. \(\frac{1}{4}\) D. \(\frac{1}{9}\) Show Content Detailed Solution Total number of balls = 2 + 4 = 6 P(of picking a red ball) = \(\frac{2}{6}\) = \(\frac{1}{3}\) P(of picking a blue ball) = \(\frac{4}{6}\) = \(\frac{2}{3}\) With replacement, P( picking two red balls) = \(\frac{1}{3}\) × \(\frac{1}{3}\) = \(\frac{1}{9}\) There is an explanation video available below.	D
55.	Which one of the following gives the members of the set A1 n B n C? A. Φ B. {s} C. {t, u} D. {y, z} Show Content Detailed Solution A1 = Elements in the universal set but not in A = {s, w, x, y, z} B = {r, s. t, u} C = {t, u, v, w, x} A1 n B n C = elements common to the three sets = none = empty set = Φ There is an explanation video available below.	A

56.	Calculate the area of an equilateral triangle of side 8cm A. 8√3 B. 16 C. 4√3 D. 16√3 Show Content Detailed Solution An equilateral triangle has all sides equal and all angles equal as 600 Area = \(\frac{1}{2}\) absinθ Area = \(\frac{1}{2}\) x 8 x 8 x sin60 = \(\frac{1}{2}\) x 64 x \(\sqrt{\frac{3}{2}}\) = 16√3 cm\(^2\) There is an explanation video available below.	D
57.	Approximate 0.9875 to 1 decimal place. A. 1.1 B. 1.0 C. 0.9 D. 0.10 Show Content Detailed Solution 9 is on one decimal place, the next number to it is 8 which will be rounded up to 1 because it is greater than 5 and then added to 9 to give 10, 10 cannot be written, it will then be rounded up to 1 and added to 0. So the answer is 1.0 There is an explanation video available below.	B
58.	Simplify 25\(\frac{1}{2}\) × 8\(\frac{-2}{3}\) A. 1\(\frac{1}{4}\) B. 2\(\frac{1}{4}\) C. 6 D. 10 Show Content Detailed Solution Using law of indices 25\(\frac{1}{2}\) × 8\(\frac{-2}{3}\) = √25 x (\(\sqrt[3]{8}\)) -2 = 5 x 2-2 = 5 x \(\frac{1}{2^2}\) = \(\frac{5}{4}\) = \(\frac{11}{4}\) Answer is A There is an explanation video available below.	A
59.	From a point R, 300m north of P, a man walks eastwards to a place; Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree A. 026\(^o\) B. 045\(^o\) C. 210\(^o\) D. 240\(^o\) Show Content Detailed Solution Cos θ = \(\frac{adj}{hyp}\) = \(\frac{300}{600}\) = 0.5 θ = Cos - 10.5 = 60 ∠ RPQ = ∠ PQs So the bearing of P from Q is 180 + 60 = 240\(^o\) Answer is D There is an explanation video available below.	D
60.	Add 54 \(_{eight}\) and 67\(_{eight}\) giving your answers in base eight A. 111 B. 121 C. 123 D. 143 Show Content Detailed Solution 54 \(_{eight}\) and 67\(_{eight}\) = 1438 Starting with normal addition, 4 + 7 gives 11 (it is more than the base, 8) 8 goes in 11 just 1 time, remaining 3, the remainder will be written, and the 1 will be added to the sum of 5 and 6 which gives 12 altogether, 8 goes in 12 one time remaining 4, the remainder 4 was written and then the 1 that was the quotient was then written since nothing to add the 1 to. So answer is 143 in base eight There is an explanation video available below.	D

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