Mathematics (Core), 2009, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2009

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

1 - 10 of 50 Questions

#	Question	Ans
1.	If 55\(_x\) + 52\(_x\) = 77\(_{10}\) find X A. 5 B. 6 C. 7 D. 10 Show Content Detailed Solution 5 \(\times\) x\(^1\) + 5 \(\times\) x\(^0\) + 5 \(\times\) x\(^1\) + 2 \(\times\) x\(^0\) = 77 (change all to base 10) 5x + 5 + 5x + 2 = 77 10x + 7 = 77 10x = 77-7 10x = 70 x = 70/10 x = 7 There is an explanation video available below.	C
2.	Simplify \(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}\) A. 4 B. 4¹/₆ C. 4⁵/₆ D. 5¹/₆ Show Content Detailed Solution \(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}=5\left(\frac{1-9+6}{12}\right)\\ 5\left(\frac{-2}{12}\right)\\ =4\left(\frac{12-2}{12}\right)\) (carry one from 5 and call it 12) \(4\frac{10}{12}\\ =4\frac{5}{6}\) There is an explanation video available below.	C
3.	Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures. A. 6.24 B. 3.22 C. 2.78 D. 2.13 Show Content Detailed Solution \(\frac{81.81 + 99.44}{20.09 + 36.16}\\ =\frac{181.25}{56.25}\\ =\frac{18125}{5625}\\ \frac{29}{9}\\ =3\frac{2}{9}\\ ≅ 3.22\) There is an explanation video available below.	B
4.	A man bought a second-hand photocopying machine for N34,000. He serviced it at a cost of N2,000 and then sold it at a profit of 15%. What was the selling price? A. N37,550 B. N40,400 C. N41,400 D. N42,400 Show Content Detailed Solution C.P = N34000 + N2000 = N36000 Gain = 100 + 15 = 115% S.P = \(\frac{115}{100}\times \frac{N3600}{1}\) = N41400 There is an explanation video available below.	C
5.	A student spent 1/5 of his allowance on books, 1/2 of remainder on food and kept the rest for contingencies. What fraction was kept? A. ⁷/₁₅ B. ⁸/₁₅ C. ²/₅ D. ⁴/₅ Show Content Detailed Solution Let his allowance = y. \(Books = \frac{y}{5}\) \(Remainder: y - \frac{y}{5} = \frac{4y}{5}\) \(Food: \frac{1}{2} \times \frac{4y}{5} = \frac{2y}{5}\) \(Contingencies: \frac{4y}{5} - \frac{2y}{5} = \frac{2y}{5}\) Therefore, he kept \(\frac{2}{5}\) of his allowance for contingencies. There is an explanation video available below.	C
6.	If log\(_{10}\)2 = 0.3010 and log\(_{10}\)7 = 0.8451, evaluate log\(_{10}\)280 A. 3.4471 B. 2.4471 C. 1.4471 D. 1.4071 Show Content Detailed Solution Log 2 = 0.3010, Log 7 = 0.8451 ∴Log 280 = Log 28 x 10 = Log 7x4x10 =Log7 + Log4 + Log10 = Log7 + Log2\(^2\) + Log10 = Log7 + 2Log2 + Log10 = 0.8451 + 2(0.3010) + 1 = 0.8451 + 0.6020 + 1 = 2.4471 There is an explanation video available below.	B
7.	Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\) A. 17-√7 B. 4-√7 C. 15+√7 D. 7-√7 Show Content Detailed Solution \(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\ =\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\ =\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\ =\frac{8-2\sqrt{7}}{2}\) Factorize then divide by 2 \(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\) There is an explanation video available below.	B
8.	If x = {n\(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, find x \(\cap\) y. A. {5,10} B. {5, 10, 15} C. {2, 5, 10} D. {5, 10, 15, 20} Show Content Detailed Solution X = {n(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5} Implies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5 Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5} Put X = 1, 2, 3, 4, and 5 Y = {5, 10, 15, 20, 25} X \(\cap\) Y = {2, 5, 10, 17, 26} \(\cap\) {5, 10, 15, 20, 25} = {5, 10} There is an explanation video available below.	A
9.	I.S∩T∩W=S II. S ∪ T ∪ W = W III. T ∩ W = S If S⊂T⊂W, which of the above statements are true? A. I and II B. I and III C. II and III D. I, II and III Show Content Detailed Solution If S \(\subset\) T \(\subset\) W, S \(\cap\) T \(\cap\) W = S is true since S \(\cap\) T = S and S \(\cap\) W = S. S \(\cup\) T \(\cup\) W = W is also true. S \(\cup\) T = T and T \(\cup\) W = W. However, to say that T \(\cap\) W = S is not very true mathematically. Instead, it is safe to say S \(\subset\) (T \(\cap\) W). There is an explanation video available below.	A
10.	If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t? A. \(\frac{p^2 t}{s^3}\) B. \(\frac{p^3 t}{s^3}\) C. \(\frac{p^3 t}{s^2}\) D. \(\frac{p^ t}{s^3}\) Show Content Detailed Solution \(p =\sqrt{\frac{rs^3}{t}}\\= p^2 =\frac{rs^3}{t}\\ tp^2 = rs^3\\ r = \frac{p^2 t}{s^3}\) There is an explanation video available below.	A

1.	If 55\(_x\) + 52\(_x\) = 77\(_{10}\) find X A. 5 B. 6 C. 7 D. 10 Show Content Detailed Solution 5 \(\times\) x\(^1\) + 5 \(\times\) x\(^0\) + 5 \(\times\) x\(^1\) + 2 \(\times\) x\(^0\) = 77 (change all to base 10) 5x + 5 + 5x + 2 = 77 10x + 7 = 77 10x = 77-7 10x = 70 x = 70/10 x = 7 There is an explanation video available below.	C
2.	Simplify \(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}\) A. 4 B. 4¹/₆ C. 4⁵/₆ D. 5¹/₆ Show Content Detailed Solution \(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}=5\left(\frac{1-9+6}{12}\right)\\ 5\left(\frac{-2}{12}\right)\\ =4\left(\frac{12-2}{12}\right)\) (carry one from 5 and call it 12) \(4\frac{10}{12}\\ =4\frac{5}{6}\) There is an explanation video available below.	C
3.	Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures. A. 6.24 B. 3.22 C. 2.78 D. 2.13 Show Content Detailed Solution \(\frac{81.81 + 99.44}{20.09 + 36.16}\\ =\frac{181.25}{56.25}\\ =\frac{18125}{5625}\\ \frac{29}{9}\\ =3\frac{2}{9}\\ ≅ 3.22\) There is an explanation video available below.	B
4.	A man bought a second-hand photocopying machine for N34,000. He serviced it at a cost of N2,000 and then sold it at a profit of 15%. What was the selling price? A. N37,550 B. N40,400 C. N41,400 D. N42,400 Show Content Detailed Solution C.P = N34000 + N2000 = N36000 Gain = 100 + 15 = 115% S.P = \(\frac{115}{100}\times \frac{N3600}{1}\) = N41400 There is an explanation video available below.	C
5.	A student spent 1/5 of his allowance on books, 1/2 of remainder on food and kept the rest for contingencies. What fraction was kept? A. ⁷/₁₅ B. ⁸/₁₅ C. ²/₅ D. ⁴/₅ Show Content Detailed Solution Let his allowance = y. \(Books = \frac{y}{5}\) \(Remainder: y - \frac{y}{5} = \frac{4y}{5}\) \(Food: \frac{1}{2} \times \frac{4y}{5} = \frac{2y}{5}\) \(Contingencies: \frac{4y}{5} - \frac{2y}{5} = \frac{2y}{5}\) Therefore, he kept \(\frac{2}{5}\) of his allowance for contingencies. There is an explanation video available below.	C

6.	If log\(_{10}\)2 = 0.3010 and log\(_{10}\)7 = 0.8451, evaluate log\(_{10}\)280 A. 3.4471 B. 2.4471 C. 1.4471 D. 1.4071 Show Content Detailed Solution Log 2 = 0.3010, Log 7 = 0.8451 ∴Log 280 = Log 28 x 10 = Log 7x4x10 =Log7 + Log4 + Log10 = Log7 + Log2\(^2\) + Log10 = Log7 + 2Log2 + Log10 = 0.8451 + 2(0.3010) + 1 = 0.8451 + 0.6020 + 1 = 2.4471 There is an explanation video available below.	B
7.	Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\) A. 17-√7 B. 4-√7 C. 15+√7 D. 7-√7 Show Content Detailed Solution \(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\ =\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\ =\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\ =\frac{8-2\sqrt{7}}{2}\) Factorize then divide by 2 \(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\) There is an explanation video available below.	B
8.	If x = {n\(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, find x \(\cap\) y. A. {5,10} B. {5, 10, 15} C. {2, 5, 10} D. {5, 10, 15, 20} Show Content Detailed Solution X = {n(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5} Implies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5 Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5} Put X = 1, 2, 3, 4, and 5 Y = {5, 10, 15, 20, 25} X \(\cap\) Y = {2, 5, 10, 17, 26} \(\cap\) {5, 10, 15, 20, 25} = {5, 10} There is an explanation video available below.	A
9.	I.S∩T∩W=S II. S ∪ T ∪ W = W III. T ∩ W = S If S⊂T⊂W, which of the above statements are true? A. I and II B. I and III C. II and III D. I, II and III Show Content Detailed Solution If S \(\subset\) T \(\subset\) W, S \(\cap\) T \(\cap\) W = S is true since S \(\cap\) T = S and S \(\cap\) W = S. S \(\cup\) T \(\cup\) W = W is also true. S \(\cup\) T = T and T \(\cup\) W = W. However, to say that T \(\cap\) W = S is not very true mathematically. Instead, it is safe to say S \(\subset\) (T \(\cap\) W). There is an explanation video available below.	A
10.	If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t? A. \(\frac{p^2 t}{s^3}\) B. \(\frac{p^3 t}{s^3}\) C. \(\frac{p^3 t}{s^2}\) D. \(\frac{p^ t}{s^3}\) Show Content Detailed Solution \(p =\sqrt{\frac{rs^3}{t}}\\= p^2 =\frac{rs^3}{t}\\ tp^2 = rs^3\\ r = \frac{p^2 t}{s^3}\) There is an explanation video available below.	A