2005 - JAMB Mathematics Past Questions and Answers - page 1

If 13_m + 24_m = 41_m
1 * m¹ + 3 ⁰ + 2 * m¹ + 4 * m⁰ = 4 * m¹ + 1 * m⁰
1 * m + 3 * 1 + 2 * m + 4 * 1 = 4 * m + 1 * 1
m + 3 + 2m + 4 = 4m + 1
3m + 7 = 4m + 1
4m -3m = 7 - 1
m = 6

\(\frac{321_4}{23_4}\=\frac{(3\times4^{2})+(2\times4^{1})+(1\times4^{0})}{(2\times4^{0})+(3\times4^{0})}\=\frac{3\times16+2\times4+1\times1}{2\times4+3\times1}\=\frac{48+8+1}{8+3}\=\frac{57}{11}=5\hspace{1mm}remainder\hspace{1mm}2\∴r=2_{10} \ Now\hspace{1mm}convert\hspace{1mm}2_{10} \hspace{1mm}to\hspace{1mm}base\hspace{1mm}4\\frac{4}{2} = 2\\frac{4}{0}=0\hspace{1mm}or\hspace{1mm}2\∴r=2\)

3¹/₂ - (2¹/₃ * 1¹/₄) + ³/₅
= ⁷/₂ - (⁷/₃ * ⁵/₄) + ³/₅
= ⁷/₂ - ³⁵/₁₂ + ³/₅
= L.C.M = 60
= (210 - 175 + 36)/60
= ⁷¹/₆₀
= 1¹¹/₆₀

\(I = N4.50, P = N150,T=2\frac{1}{2}\hspace{1mm}years\I=\frac{P\times T\times R}{100}\4.50=\frac{150 \times 2\frac{1}{2} \times R}{100}\\frac{4.50}{1}=\frac{150 \times 5 \times R}{100\times 2}\4.50\times 4 = 15R\R=\frac{4.50\times5}{15}\R = \frac{6}{5}\Again\hspace{1mm}I\hspace{1mm}=\frac{P\times T \times R}{100}\=\frac{250\times 1 \times 6}{100\times 2\times 5}\=\frac{3}{2}=N1.50\)

Let x = the number of oranges
The 1^st received ¹/₃ of x = ¹/₃x
∴Remainder = x - ¹/₃x = ^2x/₃
The 2^nd received ²/₃ of ^2x/₃ = ²/₃ * ^2x/₃ = ^4x/₃
The 3^rd received 12 oranges
∴¹/₃x + ^4x/₉ + 12 = x
(3x + 4x + 108)/9 = x
3x + 4x + 108 = 9x
7x + 108 = 9x
9x - 7x = 108
2x = 108
x = 54 oranges

\(\frac{81^{\frac{3}{4}}-27^{\frac{1}{3}}}{3 \times 2^3} = \frac{(3^{3-\frac{3}{4}}-3^{3-\frac{3}{4}})}{3\times 2^3}\=\frac{3^3 - 3}{3 \times 8}\=\frac{27-3}{24}\=\frac{24}{24}\=1\)

Log₁₀2 = 0.3010 and Log₁₀3 = 0.4771
Log₁₀4.5 = Log₁₀4¹/₂
= Log₁₀⁹/₂
= Log₁₀9 - Log₁₀2
= log₁₀3² - Log₁₀2
= 2Log₁₀3 - Log₁₀2
= 2(0.4771) - 0.3010
= 0.9542 - 0.3010
= 0.6532

\(\frac{(\sqrt{12}-\sqrt{3})}{(\sqrt{12}+\sqrt{3})}=\frac{\sqrt{4\times 3}-\sqrt{3}}{\sqrt{4\times 3}+\sqrt{3}}\=\frac{2\sqrt{3}-\sqrt{3}}{2\sqrt{3}+\sqrt{3}}\=\frac{\sqrt{3}}{3\sqrt{3}}\=\frac{1}{3}\)

Two games played only = 5 + 7 + 3
= 15

m = 3, p = -3, q = 7 and r = 5/2
m(p+q+r) = 3(-3 + 7 + ⁵/₂)
= 3(4 + ⁵/₂)
= 3(4 + 2¹/₂)
= 3 * 6¹/₂
= 3 * ¹³/₂
= ³⁹/₂
= 19.50