Mathematics (Core), 2015, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2015

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

1 - 10 of 62 Questions

#	Question	Ans
1.	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% Show Content Detailed Solution Percentage birthrate = \(\frac{62}{6250} \times 100%\) = \(\frac{6200}{6250}\) = 0.992% \(\approx\) 1.0%. There is an explanation video available below.	B
2.	Simplify 1¼ ÷ (2 ÷ ¼ of 28) A. 1 \( \frac{3}{8}\) B. 2 \( \frac{3}{4}\) C. 4 \( \frac{3}{8}\) D. 3 \( \frac{1}{5}\) Show Content Detailed Solution There is an explanation video available below.	C
3.	Factorize x² + 9x + 20 A. (x − 5) ² B. (x + 5)(x + 4) C. (x – 5)(x + 3) D. (x + 3) ² Show Content Detailed Solution There is an explanation video available below.	B
4.	If three staff of Myschool 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 Show Content Detailed Solution Total of their ages: 18 + 20 + 22 = 60 The second staff will get \(\frac{20}{60} \times 120,000\) = N40,000.00K There is an explanation video available below.	C
5.	X and Y are two sets such that n(X) = 15, n(Y) = 12 and n{X ∩ Y} = 7. Find ∩{X ∪ Y} A. 21 B. 225 C. 15 D. 20 Show Content Detailed Solution n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y) = 15 + 12 − 7 ∴ n(X ∪ Y) = 20 There is an explanation video available below.	D
6.	Find the x and z intercepts of the graph of 3x - z \(\leq\) 9 A. (3, -9) B. (-3, 9) C. (-3, -9) D. (-3, 0) Show Content Detailed Solution 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) There is an explanation video available below.	A
7.	Simplify log₁₀1.5 + 3 log₁₀2 − log₁₀0.3 A. log₁₀4 B. log₁₀40 C. log₁₀-40 D. log₁₀4^- Show Content Detailed Solution There is an explanation video available below.	B
8.	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 E. \(377.0cm^{2}\) Show Content Detailed Solution The total surface area of a cylinder = 2πrl + 2πr2 = 2πr(l + r) = 2 × 3.14 x 5(7+5) 2 × 3.14 × 12 x 5 = 377.1cm (1DP) There is an explanation video available below.	E
9.	If x + y = 90 simplify (sinx + siny)2−2sinxsiny A. 1 B. 0 C. 2 D. -1 Show Content Detailed Solution Given: \(x + y = 90° ... (1)\) \((\sin x + \sin y)^{2} - 2\sin x \sin y = \sin^{2} x + \sin^{2} y + 2\sin x \sin y - 2\sin x \sin y\) = \(\sin^{2} x + \sin^{2} y ... (2)\) Recall: \(\sin x = \cos (90 - x) ... (a)\) From (1), \(y = 90 - x ... (b)\) Putting (a) and (b) in (2), we have \(\sin^{2} x + \sin^{2} y \equiv \cos^{2} (90 - x) + \sin^{2} (90 - x)\) = 1 There is an explanation video available below.	A
10.	A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much income tax expenses does he pay each year? A. 15 B. 50 C. 70 D. 25 Show Content Detailed Solution His annual salary = N2000 His allowances = N600 So his taxable income = Annual salary − allowance = N2000 − N600 = N1400 He pay at 5% Then, his allowance income tax 5/100 × 1400 = N70 There is an explanation video available below.	C

1.	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% Show Content Detailed Solution Percentage birthrate = \(\frac{62}{6250} \times 100%\) = \(\frac{6200}{6250}\) = 0.992% \(\approx\) 1.0%. There is an explanation video available below.	B
2.	Simplify 1¼ ÷ (2 ÷ ¼ of 28) A. 1 \( \frac{3}{8}\) B. 2 \( \frac{3}{4}\) C. 4 \( \frac{3}{8}\) D. 3 \( \frac{1}{5}\) Show Content Detailed Solution There is an explanation video available below.	C
3.	Factorize x² + 9x + 20 A. (x − 5) ² B. (x + 5)(x + 4) C. (x – 5)(x + 3) D. (x + 3) ² Show Content Detailed Solution There is an explanation video available below.	B
4.	If three staff of Myschool 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 Show Content Detailed Solution Total of their ages: 18 + 20 + 22 = 60 The second staff will get \(\frac{20}{60} \times 120,000\) = N40,000.00K There is an explanation video available below.	C
5.	X and Y are two sets such that n(X) = 15, n(Y) = 12 and n{X ∩ Y} = 7. Find ∩{X ∪ Y} A. 21 B. 225 C. 15 D. 20 Show Content Detailed Solution n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y) = 15 + 12 − 7 ∴ n(X ∪ Y) = 20 There is an explanation video available below.	D

6.	Find the x and z intercepts of the graph of 3x - z \(\leq\) 9 A. (3, -9) B. (-3, 9) C. (-3, -9) D. (-3, 0) Show Content Detailed Solution 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) There is an explanation video available below.	A
7.	Simplify log₁₀1.5 + 3 log₁₀2 − log₁₀0.3 A. log₁₀4 B. log₁₀40 C. log₁₀-40 D. log₁₀4^- Show Content Detailed Solution There is an explanation video available below.	B
8.	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 E. \(377.0cm^{2}\) Show Content Detailed Solution The total surface area of a cylinder = 2πrl + 2πr2 = 2πr(l + r) = 2 × 3.14 x 5(7+5) 2 × 3.14 × 12 x 5 = 377.1cm (1DP) There is an explanation video available below.	E
9.	If x + y = 90 simplify (sinx + siny)2−2sinxsiny A. 1 B. 0 C. 2 D. -1 Show Content Detailed Solution Given: \(x + y = 90° ... (1)\) \((\sin x + \sin y)^{2} - 2\sin x \sin y = \sin^{2} x + \sin^{2} y + 2\sin x \sin y - 2\sin x \sin y\) = \(\sin^{2} x + \sin^{2} y ... (2)\) Recall: \(\sin x = \cos (90 - x) ... (a)\) From (1), \(y = 90 - x ... (b)\) Putting (a) and (b) in (2), we have \(\sin^{2} x + \sin^{2} y \equiv \cos^{2} (90 - x) + \sin^{2} (90 - x)\) = 1 There is an explanation video available below.	A
10.	A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much income tax expenses does he pay each year? A. 15 B. 50 C. 70 D. 25 Show Content Detailed Solution His annual salary = N2000 His allowances = N600 So his taxable income = Annual salary − allowance = N2000 − N600 = N1400 He pay at 5% Then, his allowance income tax 5/100 × 1400 = N70 There is an explanation video available below.	C

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