Mathematics (Core), 1985, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1985

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

21 - 30 of 47 Questions

#	Question	Ans
21.	Solve the following equation \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\) A. (\(\frac{5}{2}\), 1) B. (5, -4) C. (2, 1) D. (1, \(\frac{-5}{2}\)) E. (\(\frac{-5}{2}\), 1) Show Content Detailed Solution \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\) \(\frac{2}{2r - 1}\) - \(\frac{1}{r + 2}\) = \(\frac{5}{3}\) \(\frac{2r + 4 - 2r + 1}{2r - 1 (r + 2)}\) = \(\frac{5}{3}\) \(\frac{5}{(2r + 1)(r + 2)}\) = \(\frac{5}{3}\) 5(2r - 1)(r + 2) = 15 (10r - 5)(r + 2) = 15 10r² + 20r - 5r - 10 = 15 10r² + 15r = 25 10r² + 15r - 25 = 0 2r² + 3r - 5 = 0 (2r² + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5) (r	D
22.	Solve the simultaneous equations 2x - 3y = 10, 10x - 6y = 5 A. x = 2\(\frac{1}{2}\), y = 3\(\frac{1}{2}\) B. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) C. x = 2\(\frac{1}{4}\), y = 3\(\frac{1}{2}\) D. x = 2\(\frac{1}{3}\), y = 3\(\frac{1}{2}\) E. x = 2\(\frac{1}{3}\), y = 2\(\frac{1}{2}\) Show Content Detailed Solution 2x - 3y = -10; 10x - 6y = -5 2x - 3y = -10 x 2 10x - 6y = 5 4x - 6y = -20 .......(i) 10x - 6y = 5.......(ii) eqn(ii) - eqn(1) 6x = 15 x = \(\frac{15}{6}\) = \(\frac{5}{2}\) x = 2\(\frac{1}{2}\) Sub. for x in equ.(ii) 10(\(\frac{5}{2}\)) - 6y = 5 y = 3\(\frac{1}{2}\)	A
23.	If f(x - 2) = 4x² + x + 7, find f(1) A. 12 B. 27 C. 7 D. 46 E. 17 Show Content Detailed Solution f(x - 2) = 4x² + x + 7 x - 2 = 1, x = 3 f(x - 2) = f(1) = 4(3)² + 3 + 7 = 36 + 10 = 46	D
24.	In \(\bigtriangleup\) XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = \(\theta\). Find cos\(\theta\)^o A. \(\frac{4}{39}\) B. \(\frac{43}{39}\) C. \(\frac{209}{3}\) D. \(\frac{43}{78}\) Show Content Detailed Solution cos\(\theta\) = \(\frac{13^2 + 9^2 - 11^2}{2(13)(9)}\) = \(\frac{169 + 81 - 21}{26 \times 9}\) cos\(\theta\) = \(\frac{129}{26 \times 9}\) = \(\frac{43}{78}\)	D
25.	Find the missing value in the table below \(\begin{array}{c\|c} x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y = 4 - 3x - x^3 & 80 & & 18 & 8 & 4 & 0 & -10 & -32 \end{array}\) A. -32 B. -14 C. 40 D. 22 E. 37 Show Content Detailed Solution When x = -3, y = 4 - 3(3) - (-3)3 = 4 + 9 + 27 = 13 + 27 = 40	C
26.	The number of goals scored by a football team in 20 matches is shown below \(\begin{array}{c\|c} \text{No. of goals} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{No. of matches} & 3 & 5 & 7 & 3 & 1 & 0 \end{array}\) What are the values of the mean and the mode respectively? A. (1.75, 5) B. (1.75, 2) C. (1.75, 1) D. (65, 74) Show Content Detailed Solution \(\begin{array}{c\|c}x & f & fx\\ \hline 0 & 3 & 0\\ 1 & 5 & 5\\ 2 & 7 & 14\\ 3 & 4 & 12\\4 & 1 & 4\\5 & 0 & 0\end{array}\) \(\sum{f}\) = 20 \(\sum fx\) = 35 Mean = \(\frac{\sum fx}{\sum f}\) = \(\frac{35}{20}\) = \(\frac{7}{4}\) = 1.75 Mode = 2 = 1.75, 2	B
27.	If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides? A. \(\sqrt{2}\) B. \(\frac{1}{2}\) C. 22 D. 1 E. 2 - 1 Show Content Detailed Solution 45^o = \(\frac{x}{2}\), Since 45^o = \(\frac{1}{\sqrt{2}}\) x = 2 x \(\frac{1}{\sqrt{2}}\) = \(\frac{2\sqrt{2}}{2}\) = \(\sqrt{2}\)	A
28.	If two fair coins are tossed, what is the probability of getting at least one head? A. \(\frac{1}{4}\) B. \(\frac{1}{2}\) C. 1 D. \(\frac{43}{78}\) E. \(\frac{3}{4}\) Show Content Detailed Solution Prob. of getting at least one head Prob. of getting one head + prob. of getting 2 heads = \(\frac{1}{4}\) + \(\frac{2}{4}\) = \(\frac{3}{4}\)	E
29.	The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is? A. 234.00 cm³ B. 526.50 cm³ C. 166.00 cm³ D. 687cm³ Show Content Detailed Solution Let x represent total vol. 2 : 3 = 2 + 3 = 5 \(\frac{3}{5}\)x = 351 x = \(\frac{351 \times 5}{3}\) = 585 Volume of smaller block = \(\frac{2}{5}\) x 585 = 234.00cm\(^3\)	A
30.	The bearing of a bird on a tree from a hunter on the ground is N72oE. What is the bearing of the hunter from the birds? A. S 18^o W B. S 72^o W C. S 72^o E D. S 27^o E E. S 27^o W Show Content Detailed Solution B = Bird ; H = Hunter. Bearing of the hunter from the bird = S 72° W.	B

21.	Solve the following equation \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\) A. (\(\frac{5}{2}\), 1) B. (5, -4) C. (2, 1) D. (1, \(\frac{-5}{2}\)) E. (\(\frac{-5}{2}\), 1) Show Content Detailed Solution \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\) \(\frac{2}{2r - 1}\) - \(\frac{1}{r + 2}\) = \(\frac{5}{3}\) \(\frac{2r + 4 - 2r + 1}{2r - 1 (r + 2)}\) = \(\frac{5}{3}\) \(\frac{5}{(2r + 1)(r + 2)}\) = \(\frac{5}{3}\) 5(2r - 1)(r + 2) = 15 (10r - 5)(r + 2) = 15 10r² + 20r - 5r - 10 = 15 10r² + 15r = 25 10r² + 15r - 25 = 0 2r² + 3r - 5 = 0 (2r² + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5) (r	D
22.	Solve the simultaneous equations 2x - 3y = 10, 10x - 6y = 5 A. x = 2\(\frac{1}{2}\), y = 3\(\frac{1}{2}\) B. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\) C. x = 2\(\frac{1}{4}\), y = 3\(\frac{1}{2}\) D. x = 2\(\frac{1}{3}\), y = 3\(\frac{1}{2}\) E. x = 2\(\frac{1}{3}\), y = 2\(\frac{1}{2}\) Show Content Detailed Solution 2x - 3y = -10; 10x - 6y = -5 2x - 3y = -10 x 2 10x - 6y = 5 4x - 6y = -20 .......(i) 10x - 6y = 5.......(ii) eqn(ii) - eqn(1) 6x = 15 x = \(\frac{15}{6}\) = \(\frac{5}{2}\) x = 2\(\frac{1}{2}\) Sub. for x in equ.(ii) 10(\(\frac{5}{2}\)) - 6y = 5 y = 3\(\frac{1}{2}\)	A
23.	If f(x - 2) = 4x² + x + 7, find f(1) A. 12 B. 27 C. 7 D. 46 E. 17 Show Content Detailed Solution f(x - 2) = 4x² + x + 7 x - 2 = 1, x = 3 f(x - 2) = f(1) = 4(3)² + 3 + 7 = 36 + 10 = 46	D
24.	In \(\bigtriangleup\) XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = \(\theta\). Find cos\(\theta\)^o A. \(\frac{4}{39}\) B. \(\frac{43}{39}\) C. \(\frac{209}{3}\) D. \(\frac{43}{78}\) Show Content Detailed Solution cos\(\theta\) = \(\frac{13^2 + 9^2 - 11^2}{2(13)(9)}\) = \(\frac{169 + 81 - 21}{26 \times 9}\) cos\(\theta\) = \(\frac{129}{26 \times 9}\) = \(\frac{43}{78}\)	D
25.	Find the missing value in the table below \(\begin{array}{c\|c} x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y = 4 - 3x - x^3 & 80 & & 18 & 8 & 4 & 0 & -10 & -32 \end{array}\) A. -32 B. -14 C. 40 D. 22 E. 37 Show Content Detailed Solution When x = -3, y = 4 - 3(3) - (-3)3 = 4 + 9 + 27 = 13 + 27 = 40	C

26.	The number of goals scored by a football team in 20 matches is shown below \(\begin{array}{c\|c} \text{No. of goals} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{No. of matches} & 3 & 5 & 7 & 3 & 1 & 0 \end{array}\) What are the values of the mean and the mode respectively? A. (1.75, 5) B. (1.75, 2) C. (1.75, 1) D. (65, 74) Show Content Detailed Solution \(\begin{array}{c\|c}x & f & fx\\ \hline 0 & 3 & 0\\ 1 & 5 & 5\\ 2 & 7 & 14\\ 3 & 4 & 12\\4 & 1 & 4\\5 & 0 & 0\end{array}\) \(\sum{f}\) = 20 \(\sum fx\) = 35 Mean = \(\frac{\sum fx}{\sum f}\) = \(\frac{35}{20}\) = \(\frac{7}{4}\) = 1.75 Mode = 2 = 1.75, 2	B
27.	If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides? A. \(\sqrt{2}\) B. \(\frac{1}{2}\) C. 22 D. 1 E. 2 - 1 Show Content Detailed Solution 45^o = \(\frac{x}{2}\), Since 45^o = \(\frac{1}{\sqrt{2}}\) x = 2 x \(\frac{1}{\sqrt{2}}\) = \(\frac{2\sqrt{2}}{2}\) = \(\sqrt{2}\)	A
28.	If two fair coins are tossed, what is the probability of getting at least one head? A. \(\frac{1}{4}\) B. \(\frac{1}{2}\) C. 1 D. \(\frac{43}{78}\) E. \(\frac{3}{4}\) Show Content Detailed Solution Prob. of getting at least one head Prob. of getting one head + prob. of getting 2 heads = \(\frac{1}{4}\) + \(\frac{2}{4}\) = \(\frac{3}{4}\)	E
29.	The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is? A. 234.00 cm³ B. 526.50 cm³ C. 166.00 cm³ D. 687cm³ Show Content Detailed Solution Let x represent total vol. 2 : 3 = 2 + 3 = 5 \(\frac{3}{5}\)x = 351 x = \(\frac{351 \times 5}{3}\) = 585 Volume of smaller block = \(\frac{2}{5}\) x 585 = 234.00cm\(^3\)	A
30.	The bearing of a bird on a tree from a hunter on the ground is N72oE. What is the bearing of the hunter from the birds? A. S 18^o W B. S 72^o W C. S 72^o E D. S 27^o E E. S 27^o W Show Content Detailed Solution B = Bird ; H = Hunter. Bearing of the hunter from the bird = S 72° W.	B