2024 - JAMB Mathematics Past Questions and Answers - page 3

Simplify the expression: \(\frac{2x^3 + 2x}{x} = 2x^2 + 2\)

Integrate term by term:

• \(\int 2x^2 dx = \frac{2x^3}{3}\)
• \(\int 2 dx = 2x\)

Therefore, the integral is: \(\frac{2x^3}{3} + 2x + k\), where k is the constant of integration.

Given: P = N525, A = N588, t = 3 years. Find r.

Simple interest formula: A = P + (P x r x t) / 100

Substitute values: 588 = 525 + (525 x r x 3) / 100

63 = (525 x r x 3) / 100

6300 = 525 x r x 3

r = 6300 / (525 x 3) = 4%

(x₁, y₁) = (0,5)

(x₂, y₂) = (5,0)

Using the two-point formula:

\(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\)

\(\frac{y - 5}{0 - 5} = \frac{x - 0}{5 - 0}\)

\(\frac{y - 5}{-5} = \frac{x}{5}\)

Multiply both sides by 5:

y - 5 = -x

Thus: x + y = 5

or y = -x + 5

Given 8x^{-2} = 2/25, rewrite as 8 / x^2 = 2 / 25. Cross-multiply:

8 * 25 = 2 * x^2 → 200 = 2x^2

Divide both sides by 2: x^2 = 100. Taking square root: x = 10

To convert the decimal number 27 to base 3, we repeatedly divide by 3 and record the remainders:

1. 27 ÷ 3 = 9, remainder 0
2. 9 ÷ 3 = 3, remainder 0
3. 3 ÷ 3 = 1, remainder 0
4. 1 ÷ 3 = 0, remainder 1

Reading the remainders from bottom to top, we get 1000. Therefore, $27_{10} = 1000_3$. However, since none of the options given matched with our solution, let's calculate the correct answer. The question seems to have a typo. Let's convert 27 (base 10) to base 3.

We divide 27 by 3:

• 27 / 3 = 9, remainder 0
• 9 / 3 = 3, remainder 0
• 3 / 3 = 1, remainder 0
• 1 / 3 = 0, remainder 1

So, reading the remainders from the bottom up, we get $1000_3$. Since this option is not available, we can assume the question has an error.

Since y varies directly as \(w^2\):

\(y = k w^2\)

Given y = 8, w = 2:

\(8 = k(4)\)

\(k = 2\)

Now substitute w = 3:

\(y = 2(3^2) = 18\)

The sum of the ratio is:

\(5 + 3 + 2 = 10\)

The highest share corresponds to 5 parts:

\(40 = \frac{5}{10}T\)

Solve for T:

\(T = \frac{40 \times 10}{5} = 80\)

The smallest share is 2 parts:

\(\frac{2}{10} \times 80 = 16\) apples

The common ratio \( r \) of a G.P. is the ratio of the second term to the first term:

\[ r = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}} \]

Rationalize by multiplying numerator and denominator by \( \sqrt{10} - \sqrt{5} \):

\[ r = \frac{(\sqrt{10} + 2\sqrt{5})(\sqrt{10} - \sqrt{5})}{(\sqrt{10} + \sqrt{5})(\sqrt{10} - \sqrt{5})} = \frac{\sqrt{50}}{5} = \sqrt{2} \]

The common ratio is \( \sqrt{2} \).

The external radius is 11 cm and the thickness of the metal is 10 cm. Hence, the internal radius is 11 - 10 = 1 cm. The surface area of the metal is:

Surface area = 2π x (external radius + internal radius) x height

Substituting values gives the area as 21π cm².

The determinant of the left-hand side is:

The determinant of the right-hand side is:

Equate both sides:

Solve for x: