Mathematics (Core), 1997, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1997

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

1 - 10 of 45 Questions

#	Question	Ans
1.	Evaluate 64.764\(^2\) - 35.236\(^2\) correct to 3 significant figures A. 2960 B. 2950 C. 2860 D. 2850 Show Content Detailed Solution (64.764 - 35.236)(64.764 + 35.236) = 29.528 x 100 = 2950 to 3 sig. fig.	B
2.	Find the value of (0.006)³ + (0.004)³ in standard form A. 2.8 x 10^-9 B. 2.8 x 10^-7 C. 2.8 x 10^-8 D. 2.8 x 10^-6 Show Content Detailed Solution (0.006)³ + (0.004)³ = 2.16 x 10^-7 (2.16 + 0.64) x 10^-7 = 2.8 x 10^-7	B
3.	Given that log_a2 = 0.693 and log_a3 = 1.097, find log_a 13.5 A. 1.404 B. 1.790 C. 2.598 D. 2.790 Show Content Detailed Solution log_a 13.5 = log_a \(\frac{27}{2}\) = 3log_a 3 - log²_a = 3 x 1.097 - 0.693 = 2.598	C
4.	If 8^{\(\frac{x}{2}\)} = (2^{\(\frac{3}{8}\)})(4\(\frac{3}{4}\)), find x A. \(\frac{3}{8}\) B. \(\frac{3}{4}\) C. \(\frac{4}{5}\) D. \(\frac{5}{4}\) Show Content Detailed Solution 8^{\(\frac{x}{2}\)} = 2^{\(\frac{3}{8}\)}2^{2 x \(\frac{3}{4}\)} 2^{\(\frac{3x}{2}\)} = 2^{\(\frac{3}{4}\)} ^{\(\frac{3x}{2}\)} = \(\frac{15}{8}\) \(\frac{2 \times 15}{3 \times 8}\) = \(\frac{5}{4}\)	D
5.	Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\) A. \(\frac{19 + 4\sqrt{25}}{11}\) B. \(\frac{19 + 4\sqrt{15}}{11}\) C. \(\frac{19 + 2\sqrt{15}}{11}\) D. \(\frac{19 + 2\sqrt{15}}{19}\) Show Content Detailed Solution \(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\) = \(\frac{5 + 12\sqrt{15}}{33}\) =\(\frac{19 + 4\sqrt{15}}{11}\)	B
6.	Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years A. 6% B. 8% C. 10% D. 12% Show Content Detailed Solution 1 = \(\frac{PRT}{100}\) 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\)% = 8%	B
7.	If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩( Y ∪ Z) A. (p, o, u, r) B. (s, p, d, r) C. (s, p, n, e) D. (n, d, u) Show Content Detailed Solution \(Y \cup Z\) = \({s, e, n, o, u, p, r}\) \(X \cap (Y \cup Z)\) = \({p, e, n}\)	C
8.	A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo? A. 0 B. 9 C. 11 D. 20 Show Content Detailed Solution Let the number of students that speak Hausa and Igbo be represented by H and I respectively. n(H only) = 80 - 9 = 71. n(I only) = 20 - 9 = 11. n(neither H nor I) = 100 - (71 + 9 + 11) = 100 - 91 = 9 students.	B
9.	If the function f(fx) = x³ + 2x² + qx - 6 is divisible by x + 1, find q A. -5 B. -2 C. 2 D. 5 Show Content Detailed Solution x + 1 = 0, x = -1; f(x) = x³ + 2x² + qx - 6 0 = -1 + 2 - q - 6 q = -5	A
10.	Solve the simultaneous equations \(\frac{2}{x} - {\frac{3}{y}}\) = 2, \(\frac{4}{x} + {\frac{3}{y}}\) = 10 A. x = \(\frac{3}{2}\), y = \(\frac{3}{2}\) B. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) C. x = \(\frac{-1}{2}\), y = \(\frac{-3}{2}\) D. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) Show Content Detailed Solution \(\frac{2}{x} - {\frac{3}{y}}\) = 2.....(1) \(\frac{4}{x} + {\frac{3}{y}}\) = 10 ... (2) (1) + (2): \(\frac{6}{x}\) = 12 \(\to\) x = \(\frac{6}{12}\) x = \(\frac{1}{2}\) put x = \(\frac{1}{2}\) in equation (i) = 4 - \(\frac{3}{y}\) = 2 = 4 - 2 = \(\frac{3}{y}\) therefore y = \(\frac{3}{2}\)	B

1.	Evaluate 64.764\(^2\) - 35.236\(^2\) correct to 3 significant figures A. 2960 B. 2950 C. 2860 D. 2850 Show Content Detailed Solution (64.764 - 35.236)(64.764 + 35.236) = 29.528 x 100 = 2950 to 3 sig. fig.	B
2.	Find the value of (0.006)³ + (0.004)³ in standard form A. 2.8 x 10^-9 B. 2.8 x 10^-7 C. 2.8 x 10^-8 D. 2.8 x 10^-6 Show Content Detailed Solution (0.006)³ + (0.004)³ = 2.16 x 10^-7 (2.16 + 0.64) x 10^-7 = 2.8 x 10^-7	B
3.	Given that log_a2 = 0.693 and log_a3 = 1.097, find log_a 13.5 A. 1.404 B. 1.790 C. 2.598 D. 2.790 Show Content Detailed Solution log_a 13.5 = log_a \(\frac{27}{2}\) = 3log_a 3 - log²_a = 3 x 1.097 - 0.693 = 2.598	C
4.	If 8^{\(\frac{x}{2}\)} = (2^{\(\frac{3}{8}\)})(4\(\frac{3}{4}\)), find x A. \(\frac{3}{8}\) B. \(\frac{3}{4}\) C. \(\frac{4}{5}\) D. \(\frac{5}{4}\) Show Content Detailed Solution 8^{\(\frac{x}{2}\)} = 2^{\(\frac{3}{8}\)}2^{2 x \(\frac{3}{4}\)} 2^{\(\frac{3x}{2}\)} = 2^{\(\frac{3}{4}\)} ^{\(\frac{3x}{2}\)} = \(\frac{15}{8}\) \(\frac{2 \times 15}{3 \times 8}\) = \(\frac{5}{4}\)	D
5.	Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\) A. \(\frac{19 + 4\sqrt{25}}{11}\) B. \(\frac{19 + 4\sqrt{15}}{11}\) C. \(\frac{19 + 2\sqrt{15}}{11}\) D. \(\frac{19 + 2\sqrt{15}}{19}\) Show Content Detailed Solution \(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\) = \(\frac{5 + 12\sqrt{15}}{33}\) =\(\frac{19 + 4\sqrt{15}}{11}\)	B

6.	Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years A. 6% B. 8% C. 10% D. 12% Show Content Detailed Solution 1 = \(\frac{PRT}{100}\) 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\)% = 8%	B
7.	If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩( Y ∪ Z) A. (p, o, u, r) B. (s, p, d, r) C. (s, p, n, e) D. (n, d, u) Show Content Detailed Solution \(Y \cup Z\) = \({s, e, n, o, u, p, r}\) \(X \cap (Y \cup Z)\) = \({p, e, n}\)	C
8.	A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo? A. 0 B. 9 C. 11 D. 20 Show Content Detailed Solution Let the number of students that speak Hausa and Igbo be represented by H and I respectively. n(H only) = 80 - 9 = 71. n(I only) = 20 - 9 = 11. n(neither H nor I) = 100 - (71 + 9 + 11) = 100 - 91 = 9 students.	B
9.	If the function f(fx) = x³ + 2x² + qx - 6 is divisible by x + 1, find q A. -5 B. -2 C. 2 D. 5 Show Content Detailed Solution x + 1 = 0, x = -1; f(x) = x³ + 2x² + qx - 6 0 = -1 + 2 - q - 6 q = -5	A
10.	Solve the simultaneous equations \(\frac{2}{x} - {\frac{3}{y}}\) = 2, \(\frac{4}{x} + {\frac{3}{y}}\) = 10 A. x = \(\frac{3}{2}\), y = \(\frac{3}{2}\) B. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) C. x = \(\frac{-1}{2}\), y = \(\frac{-3}{2}\) D. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) Show Content Detailed Solution \(\frac{2}{x} - {\frac{3}{y}}\) = 2.....(1) \(\frac{4}{x} + {\frac{3}{y}}\) = 10 ... (2) (1) + (2): \(\frac{6}{x}\) = 12 \(\to\) x = \(\frac{6}{12}\) x = \(\frac{1}{2}\) put x = \(\frac{1}{2}\) in equation (i) = 4 - \(\frac{3}{y}\) = 2 = 4 - 2 = \(\frac{3}{y}\) therefore y = \(\frac{3}{2}\)	B