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

Paper Info

Year :

1997

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

31 - 40 of 45 Questions

#	Question	Ans
31.	In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ. A. √23cm B. √13cm C. 2√5cm D. 2√3cm Show Content Detailed Solution (XZ)² = 3² + 4² - 2 x 3 x 4 cos60^o = 25 - 24\(\frac{1}{2}\) XZ = √13cm	B
32.	Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x A. \(\frac{2 + 2}{3x^3}\) B. 2 + \(\frac{1}{6x}\) C. 2 - \(\frac{2}{3x^3}\) D. \(\frac{1}{5}\) Show Content Detailed Solution \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) let y = 3x² y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\) Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\) \(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x^-3 = 2 - \(\frac{2}{3x^3}\)	C
33.	\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to A. -sin(6x - 2) B. -sin(3x² - 2x)dx C. (6x - 2) sin(3x² - 2x) D. -(6x - 2)sin(3x² - 2x) Show Content Detailed Solution Let \(3x^{2} - 2x = u\) \(y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u\) \(\frac{\mathrm d u}{\mathrm d x} = 6x - 2\) \(\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u\) = \(- (6x - 2) \sin (3x^{2} - 2x)\)	D
34.	Integrate \(\frac{1}{x}\) + cos x with respect to x A. -\(\frac{1}{x^2}\) + sin x + k B. x + sin x - k C. x - sin x + k D. -\(\frac{1}{x^2}\) - sin x + k Show Content Detailed Solution \(\int \frac{1}{x} + \cos x = ln x - \sin x + k\)	C
35.	If \(y = x(x^4 + x + 1)\), evaluate \(\int \limits_{0} ^{1} y \mathrm d x\). A. \(\frac{11}{12}\) B. 1 C. \(\frac{5}{6}\) D. zero Show Content Detailed Solution \(y = x(x^{4} + x + 1) = x^{5} + x^{2} + x\) \(\int \limits_{0} ^{1} (x^{5} + x^{2} + x) \mathrm d x = \frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}\) = \([\frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}]_{0} ^{1}\) = \(\frac{1}{6} + \frac{1}{3} + \frac{1}{2}\) = \(1\)	B
36.	\(\begin{array}{c\|c} Age & 20 & 25 & 30 & 35 & 40 & 45\\ \hline Number of people & 3 & 5 & 1 & 1 & 2 & 3\end{array}\) Find the median age of the frequency distribution in the table above. A. 20 B. 25 C. 30 D. 35	B
37.	Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60 A. 2 B. 3 C. 4 D. 6 Show Content Detailed Solution Range : 10 - 2 = 8 Variance = \(\frac{\sum d^{2}}{n}\) = \(\frac{60}{10}\) = 6 8 - 6 = 2.	A
38.	In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana? A. \(\frac{17}{30}\) B. \(\frac{11}{30}\) C. \(\frac{6}{30}\) D. \(\frac{5}{30}\) Show Content Detailed Solution P_grape or P_banana = \(\frac{6}{30}\) + \(\frac{11}{30}\) = \(\frac{17}{30}\)	A
39.	A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number A. \(\frac{5}{11}\) B. \(\frac{1}{2}\) C. \(\frac{6}{11}\) D. \(\frac{7}{10}\) Show Content Detailed Solution n(even numbers between 10 and 20 inclusive) = 6 n(numbers between 10 and 20) = 11 P(even) = \(\frac{6}{11}\)	C
40.	Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 A. 2 B. 3 C. \(\sqrt{10}\) D. \(\sqrt{11}\) Show Content Detailed Solution x = \(\frac{\sum x}{N}\) = \(\frac{0}{11}\) = 0 \(\begin{array}{c\|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}\) S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\) = \(\sqrt{\frac{110}{11}}\) = \(\sqrt{10}\)	C

31.	In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ. A. √23cm B. √13cm C. 2√5cm D. 2√3cm Show Content Detailed Solution (XZ)² = 3² + 4² - 2 x 3 x 4 cos60^o = 25 - 24\(\frac{1}{2}\) XZ = √13cm	B
32.	Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x A. \(\frac{2 + 2}{3x^3}\) B. 2 + \(\frac{1}{6x}\) C. 2 - \(\frac{2}{3x^3}\) D. \(\frac{1}{5}\) Show Content Detailed Solution \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) let y = 3x² y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\) Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\) \(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x^-3 = 2 - \(\frac{2}{3x^3}\)	C
33.	\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to A. -sin(6x - 2) B. -sin(3x² - 2x)dx C. (6x - 2) sin(3x² - 2x) D. -(6x - 2)sin(3x² - 2x) Show Content Detailed Solution Let \(3x^{2} - 2x = u\) \(y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u\) \(\frac{\mathrm d u}{\mathrm d x} = 6x - 2\) \(\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u\) = \(- (6x - 2) \sin (3x^{2} - 2x)\)	D
34.	Integrate \(\frac{1}{x}\) + cos x with respect to x A. -\(\frac{1}{x^2}\) + sin x + k B. x + sin x - k C. x - sin x + k D. -\(\frac{1}{x^2}\) - sin x + k Show Content Detailed Solution \(\int \frac{1}{x} + \cos x = ln x - \sin x + k\)	C
35.	If \(y = x(x^4 + x + 1)\), evaluate \(\int \limits_{0} ^{1} y \mathrm d x\). A. \(\frac{11}{12}\) B. 1 C. \(\frac{5}{6}\) D. zero Show Content Detailed Solution \(y = x(x^{4} + x + 1) = x^{5} + x^{2} + x\) \(\int \limits_{0} ^{1} (x^{5} + x^{2} + x) \mathrm d x = \frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}\) = \([\frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}]_{0} ^{1}\) = \(\frac{1}{6} + \frac{1}{3} + \frac{1}{2}\) = \(1\)	B

36.	\(\begin{array}{c\|c} Age & 20 & 25 & 30 & 35 & 40 & 45\\ \hline Number of people & 3 & 5 & 1 & 1 & 2 & 3\end{array}\) Find the median age of the frequency distribution in the table above. A. 20 B. 25 C. 30 D. 35	B
37.	Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60 A. 2 B. 3 C. 4 D. 6 Show Content Detailed Solution Range : 10 - 2 = 8 Variance = \(\frac{\sum d^{2}}{n}\) = \(\frac{60}{10}\) = 6 8 - 6 = 2.	A
38.	In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana? A. \(\frac{17}{30}\) B. \(\frac{11}{30}\) C. \(\frac{6}{30}\) D. \(\frac{5}{30}\) Show Content Detailed Solution P_grape or P_banana = \(\frac{6}{30}\) + \(\frac{11}{30}\) = \(\frac{17}{30}\)	A
39.	A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number A. \(\frac{5}{11}\) B. \(\frac{1}{2}\) C. \(\frac{6}{11}\) D. \(\frac{7}{10}\) Show Content Detailed Solution n(even numbers between 10 and 20 inclusive) = 6 n(numbers between 10 and 20) = 11 P(even) = \(\frac{6}{11}\)	C
40.	Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 A. 2 B. 3 C. \(\sqrt{10}\) D. \(\sqrt{11}\) Show Content Detailed Solution x = \(\frac{\sum x}{N}\) = \(\frac{0}{11}\) = 0 \(\begin{array}{c\|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}\) S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\) = \(\sqrt{\frac{110}{11}}\) = \(\sqrt{10}\)	C