2024 - JAMB Mathematics Past Questions and Answers - page 5

The function given is y = -3 - 2x + x². To find the minimum value of the function, we need to differentiate it with respect to x, which gives:

dy/dx = -2 + 2x. Setting dy/dx = 0 to find the critical point:

-2 + 2x = 0, which simplifies to x = 1.

Therefore, the value of x that gives the minimum value of the function is 1.

The pipe has an external radius of 11 cm and the metal thickness is 10 cm. Therefore, the internal radius is 11 - 10 = 1 cm. The area of the metal is the surface area of the pipe, which is given by the formula:

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

Substitute the values into the formula to calculate the area of the metal used in making the pipe. The correct value is 21π cm².

The formula for the sum of the interior angles of a polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

Setting (n - 2) × 180° = 1080°, we solve for n:

\(\frac{(n - 2) 180}{180}\) = \(\frac{1080}{180}\)

(n - 2) = 6
n = 6 + 2 = 8

The polygon has 8 sides, so the correct answer is 8.

∑f = 2 + 2 + 8 + 4 + 4

= 20

\(\frac{d}{dx} [\log (4x^3 - 2x)]\) ... (1)

Let u = 4x\(^3\) - 2x.

\(\frac{\mathrm d}{\mathrm d x} (\log (4x^3 - 2x)) = (\frac{\mathrm d}{\mathrm d u})(\frac{\mathrm d u}{\mathrm d x})\)

\(\frac{\mathrm d}{\mathrm d u} (\log u)\) = \(\frac{1}{u}\)

\(\frac{\mathrm d u}{\mathrm d x} = 12x^2 - 2\)

\(\therefore \frac{d}{dx} [\log (4x^3 - 2x)] = \frac{12x^2 - 2}{u}\)

= \(\frac{12x^2 - 2}{4x^3 - 2x}\)

To subtract the numbers 243₆ - 243₅, we first convert each of them to base 10:

243₆ = 2 × 6² + 4 × 6 + 3 = 72 + 24 + 3 = 99

243₅ = 2 × 5² + 4 × 5 + 3 = 50 + 20 + 3 = 73

The difference in base 10 is 99 - 73 = 26. Therefore, the answer is 26.

2\(^{x + y}\) = 16 ; 4\(^{x - y}\) = \(\frac{1}{32}\).

\(\implies 2^{x + y} = 2^4\)

\(x + y = 4 ... (1)\)

\(2^{2(x - y)} = 2^{-5} \)

\(2^{2x - 2y} = 2^{-5}\)

\(\implies 2x - 2y = -5 ... (2)\)

Solving the equations (1) and (2) simultaneously gives:

x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\)

The range of a set of numbers is the difference between the largest and smallest values. The given numbers are: 4, 9, 6, 3, 2, 8, 10, and 11.

The largest number is 11, and the smallest number is 2. Therefore, the range is:

Range = 11 - 2 = 9.

Thus, the range is 9.

To express the product of 0.0014 × 0.011 in standard form, we first calculate the product:

0.0014 × 0.011 = 0.0000154

Now, we express this number in standard form as 1.54 × 10⁻⁵.

Thus, the answer is 1.54 x 10⁻⁵.

We are given the following details:

• Principal amount (\(P\)) = N525
• Amount (\(A\)) = N588
• Time (\(t\)) = 3 years
• We need to find the rate of interest per annum (\(r\))

Step 1: Recall the formula for simple interest:

The formula for simple interest is:

\( A = P + \left( \frac{P \times r \times t}{100} \right) \)

Where:

• \(A\) = Amount after interest
• \(P\) = Principal amount
• \(r\) = Rate of interest per annum
• \(t\) = Time in years

Step 2: Substitute the known values into the formula:

\( 588 = 525 + \left( \frac{525 \times r \times 3}{100} \right) \)

Step 3: Solve for \(r\):

First, subtract 525 from both sides:

\( 588 - 525 = \frac{525 \times r \times 3}{100} \)

\( 63 = \frac{525 \times r \times 3}{100} \)

Next, multiply both sides by 100 to eliminate the denominator:

\( 6300 = 525 \times r \times 3 \)

Now, divide both sides by 525 and 3 to isolate \(r\):

\( r = \frac{6300}{525 \times 3} = \frac{6300}{1575} \)

Finally, simplify the right-hand side:

\( r = 4 \)