2007 - JAMB Mathematics Past Questions and Answers - page 7

x₁₀ = 1214₅

= x₁₀ = 1 x 5³ + 2 x 5² + 1 * 5¹ + 4 x 5⁰

= 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1

= 125 + 50 + 5 + 4

= 184

(\frac{(0.5652 - 0.4375)^2}{0.04}\

\frac{(0.5625+0.4375)(0.5625-0.4375)}{0.04}\

\frac{1.000\times 0.125}{0.04}\

=3.125\

=3.13)

2(3^2x-1) = 162

3^2x-1 = 162/2

3^2x-1 = 81

3^2x-1 = 3²

2x - 1 = 4 (equating the indices)

2x = 5
⁵/₂

x =

(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\

=\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\

=\frac{3}{5} \div \frac{6}{7}\

=\frac{3}{5} \times \frac{7}{6}\

=\frac{7}{10})

log₁₀12.5 = log₁₀ 12¹/₂

= log₁₀²⁵/₂

= log₁₀25 - log₁₀2

= log₁₀5² - log₁₀2

= 2log₁₀5 - log₁₀2

= 2log₁₀¹⁰/₂ - log₁₀2

= 2(1-x)- x

= 2 - 2x – x

= 2 – 3x

5% profit = 100 + 5 = 105%

26% profit = 100 + 26 = 126%

∴ 105% → N60,000

1% → 60000/15

126% = 1000/105 x 126/1

=N72,000

P = {1, 3, 5, 7, 9, 11}

Q = {2, 4, 6, 8, 1, 12}

P∩Q = {1, 3, 5, 7, 9, 11}∩{2, 4, 6, 8, 1, 12}

= {} = ∅

1011²₂ - 101²₂ = (1x2³ + 0x2² + 1x2¹ + 1x2⁰)² - (1x2² + 0x2¹ + 1x2²)²

(1x8 + 0x4 + 1x2 + 1x1) ² - (1x4 + 0x2 + 1x1) ²)

= (8 + 0 + 2 + 1) ² - (4 + 0 + 1) ²

= 11² - 5²

= 16 x 6 = 96

96₁₀ to base 2

2/96 = 48 R 0

2/48 = 24 R 0

2/24 = 12 R 0

2/12 = 6 R 0

2/6 = 3 R 0

2/3 = 1 R 1

2/1 = 0 R 1

1100000₂

All the perfect squares < 40

X = {1, 4, 9, 16, 25, 36}

All the odd numbers from 1 to 15

Y = {1, 3, 5, 7, 9, 11, 13, 15}

X ∩ Y = {1, 9}

Length of an arc = θ/360 x 2πr

90/360 x 2 x π x 7

= ^7π/₂