2022 - JAMB Mathematics Past Questions and Answers - page 1

To solve the equation \(\frac{1}{8}^{k+2}\) = 1, we need to find the value of k.

Here's how:

1. Recognize that any non-zero number raised to the power of 0 equals 1. Therefore, for \(\frac{1}{8}^{k+2}\) to equal 1, the exponent (k+2) must be equal to 0.
2. Set the exponent equal to 0: k + 2 = 0
3. Solve for k: Subtract 2 from both sides of the equation: k = -2

1. Convert the binary number \(101_{two}\) to decimal: \(101_{two} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5\)
2. Cube the decimal equivalent: \(5^3 = 5 \times 5 \times 5 = 125\)
3. Convert the result (125) back to binary.
   • \(125 \div 2 = 62\) remainder 1
   • \(62 \div 2 = 31\) remainder 0

• we can express the diagram as E' n F n G'
• sets E and G are present in the Universal Set but are not included in the expression
• the shaded portion in the diagram is set F

S=HH, HT, TH, TT

We can get the result by subtracting the probability of getting no heads with 1.

That is, the probability of getting at least one head = 1 minus the probability of getting no heads:
 P=1−1/4

= 3/4

= 0.75

To find the value of x,

6 = \(\frac{2 + 5 + x+1 + x+2 + 7 + 9}{6}\)

6 * 6 = 2 + 5 + x+1 + x+2 + 7 + 9

36 = 2x + 26

36 - 26 = 2x

10 = 2x

x = 5

median = \(\frac{7+6}{2}\)

= 6.5

sin θ = \(\frac{opp}{hyp}\) → \(\frac{-3}{5}\)

opp = -3, hyp = 5

using Pythagoras' formula:

hyp\(^2\) = adj\(^2\) + opp\(^2\)

adj\(^2\) = hyp\(^2\) - opp\(^2\)

adj\(^2\) = 5\(^2\) - 3\(^2\) → 25 - 9

adj\(^2\) = 16

adj = 4

cos θ = \(\frac{adj}{hyp}\) → \(\frac{4}{5}\)

In the third quadrant, cos θ is negative

=> - \(\frac{4}{5}\)

Rationalizing the denominator using conjugates with the numerator an integer, \({3+√2}\)

 \(\frac{1}{3-√2}\)

=> \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

=  \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)

=  \(\frac{3+√2}{9 - 2}\) →  \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) +  \(\frac{√2}{7}\)

Using the Pythagoras theorem,

Hyp\(^2\) = adj\(^2\) + opp\(^2\)

5\(^2\) = opp\(^2\) + 3\(^2\) 

5\(^2\) - 3\(^2\) = adj\(^2\)

4 = adj

Hence, length of the chord = 2 * 4 = 8cm

\(\frac{28 * 360}{100}\) 

= 100.8º

Volume of a rectangular pyramid, v = \(\frac{length * width * height}{3}\) or \(\frac{area * height}{3}\)

v = \(\frac{24 * 7.5}{3}\) → \(\frac{180}{3}\)

= 60cm\(^3\)