Mathematics (Core), 2010, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2010

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

1 - 10 of 49 Questions

#	Question	Ans
1.	Evaluate \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\) A. ¹/₃ B. 3 C. 6 D. ¹/₆ Show Content Detailed Solution \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}=\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\\ =\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\\ =\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\\ =\frac{2}{3}\times \frac{1}{2}\\ =\frac{1}{3}\) There is an explanation video available below.	A
2.	Rationalize \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\) A. (3 √ 15 +11) / 2 B. 3 √ 15 -11 C. (3 √ 15 -11) / 2 D. 3 √ 15 +11 Show Content Detailed Solution \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\) = \((\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}})(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}})\) = \(\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}\) = \(\frac{3\sqrt{15} + 11}{2}\) There is an explanation video available below.	A
3.	Express the product of 0.21 and 0.34 in standard form A. 7.14 x 10^-3 B. 7.14 x 10^-2 C. 7.14 x 10^-1 D. 7.14 x 10^-4 Show Content Detailed Solution 0.21 x 0.34 = 0.0714 = 7.14 x 10-2 There is an explanation video available below.	B
4.	In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers? A. 10 B. 5 C. 15 D. 20 Show Content Detailed Solution Let C n G = X n C only = 40 - x n G only = 30 - x 40 - X + 30 - X + X = 50 70 - X = 50 X = 70 - 50 X = 20 There is an explanation video available below.	D
5.	Factorize completely \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}\) A. \(\frac{x(x-5)}{2(x+2)}\) B. \(\frac{x(x-5)}{2(x-2)}\) C. \(\frac{x(x+5)}{2(x+2)}\) D. \(\frac{x^{2} + 4}{2x+4}\) Show Content Detailed Solution \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8} = \frac{x(x^{2} + 3x - 10)}{2(x^{2} - 4)}\) = \(\frac{x(x^{2} - 2x + 5x - 10)}{2(x - 2)(x + 2)}\) = \(\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}\) = \(\frac{x(x + 5)}{2(x + 2)}\) There is an explanation video available below.	C
6.	If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64 A. 12 B. 6 C. 3 D. 5 Show Content Detailed Solution y ∝ √x y = K√x K = y/√x = 3/√16 = 3/4 y = 3/4√x = 3/4√64 when x = 64 = 3/4 x 8/1 = 6 There is an explanation video available below.	B
7.	If x y* = x + y2, find then value of (23)5 A. 36 B. 25 C. 11 D. 55 Show Content Detailed Solution x y* = x + y2 2 * 3 = 2 + 32 = 2 + 9 = 11 (2 * 3) * 5 = 11 + 52 = 11 + 25 = 36 There is an explanation video available below.	A
8.	If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true? A. q = 18 B. p <1 C. p = 18 D. q < 1 Show Content Detailed Solution If 18(p + q) = (18 + p)q then 18p + 18q = 18q + pq 18p = pq \(\implies\) q = 18. There is an explanation video available below.	A
9.	If \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\), find the value of x A. 3 B. 4 C. 5 D. 2 Show Content Detailed Solution \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\) x x 7 - 2 x 3 = 15 7x - 6 = 15 7x = 15+6 7x = 21 x = 21/7 x = 3 There is an explanation video available below.	A
10.	From the diagram above, find x A. 65^o B. 50^o C. 75^o D. 55^o Show Content Detailed Solution ∠RTS = 90o (∠ in semi circle) ∠UTS = 25o (∠ in alternate segment) X + 90 + 25 = 180(sum of ∠s on a str line) X + 115 = 180 X = 180 - 115 X = 65o There is an explanation video available below.	A

1.	Evaluate \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\) A. ¹/₃ B. 3 C. 6 D. ¹/₆ Show Content Detailed Solution \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}=\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\\ =\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\\ =\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\\ =\frac{2}{3}\times \frac{1}{2}\\ =\frac{1}{3}\) There is an explanation video available below.	A
2.	Rationalize \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\) A. (3 √ 15 +11) / 2 B. 3 √ 15 -11 C. (3 √ 15 -11) / 2 D. 3 √ 15 +11 Show Content Detailed Solution \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\) = \((\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}})(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}})\) = \(\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}\) = \(\frac{3\sqrt{15} + 11}{2}\) There is an explanation video available below.	A
3.	Express the product of 0.21 and 0.34 in standard form A. 7.14 x 10^-3 B. 7.14 x 10^-2 C. 7.14 x 10^-1 D. 7.14 x 10^-4 Show Content Detailed Solution 0.21 x 0.34 = 0.0714 = 7.14 x 10-2 There is an explanation video available below.	B
4.	In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers? A. 10 B. 5 C. 15 D. 20 Show Content Detailed Solution Let C n G = X n C only = 40 - x n G only = 30 - x 40 - X + 30 - X + X = 50 70 - X = 50 X = 70 - 50 X = 20 There is an explanation video available below.	D
5.	Factorize completely \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}\) A. \(\frac{x(x-5)}{2(x+2)}\) B. \(\frac{x(x-5)}{2(x-2)}\) C. \(\frac{x(x+5)}{2(x+2)}\) D. \(\frac{x^{2} + 4}{2x+4}\) Show Content Detailed Solution \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8} = \frac{x(x^{2} + 3x - 10)}{2(x^{2} - 4)}\) = \(\frac{x(x^{2} - 2x + 5x - 10)}{2(x - 2)(x + 2)}\) = \(\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}\) = \(\frac{x(x + 5)}{2(x + 2)}\) There is an explanation video available below.	C

6.	If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64 A. 12 B. 6 C. 3 D. 5 Show Content Detailed Solution y ∝ √x y = K√x K = y/√x = 3/√16 = 3/4 y = 3/4√x = 3/4√64 when x = 64 = 3/4 x 8/1 = 6 There is an explanation video available below.	B
7.	If x y* = x + y2, find then value of (23)5 A. 36 B. 25 C. 11 D. 55 Show Content Detailed Solution x y* = x + y2 2 * 3 = 2 + 32 = 2 + 9 = 11 (2 * 3) * 5 = 11 + 52 = 11 + 25 = 36 There is an explanation video available below.	A
8.	If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true? A. q = 18 B. p <1 C. p = 18 D. q < 1 Show Content Detailed Solution If 18(p + q) = (18 + p)q then 18p + 18q = 18q + pq 18p = pq \(\implies\) q = 18. There is an explanation video available below.	A
9.	If \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\), find the value of x A. 3 B. 4 C. 5 D. 2 Show Content Detailed Solution \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\) x x 7 - 2 x 3 = 15 7x - 6 = 15 7x = 15+6 7x = 21 x = 21/7 x = 3 There is an explanation video available below.	A
10.	From the diagram above, find x A. 65^o B. 50^o C. 75^o D. 55^o Show Content Detailed Solution ∠RTS = 90o (∠ in semi circle) ∠UTS = 25o (∠ in alternate segment) X + 90 + 25 = 180(sum of ∠s on a str line) X + 115 = 180 X = 180 - 115 X = 65o There is an explanation video available below.	A