2022 - JAMB Mathematics Past Questions and Answers - page 2

To solve this problem, we need to find the common difference (d) of the arithmetic progression (AP) and then calculate the 4th term.

1. Find the common difference (d):
   The formula for the nth term of an AP is given by: a_n = a + (n - 1)d
   Where:
   • a_n is the nth term
   • a is the first term
   • n is the term number
   • d is the common difference
   
   We are given that the 10th term (a₁₀) is 32, and the first term (a) is 3/2. So, we can write:
   32 = 3/2 + (10 - 1)d
   32 = 3/2 + 9d
   9d = 32 - 3/2
   9d = 64/2 - 3/2
   9d = 61/2
   d = 61/18
2. Find the 4th term:
   Now we can find the 4th term (a₄) using the formula:
   a₄ = a + (4 - 1)d
   a₄ = 3/2 + 3 * (61/18)
   a₄ = 3/2 + 61/6
   a₄ = 9/6 + 61/6
   a₄ = 70/6
   a₄ = 35/3

Therefore, the 4th term of the AP is 35/3.

In the third quadrant where the tangent of any angle is positive.

The sine and cosine of any angle between 180 and 270 degrees are negative.

ZOOLOGY has 7 letters in total, with O repeated thrice hence,

\(\frac{7!}{3!}\) → \(\frac{7*6*5*4*3*2*1}{3*2*1}\)

= 840ways

To find the integral of (2x+1)^3, we can use the power rule for integration and the chain rule. 1. **Power Rule:** The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. 2. **Apply the rule:** In this case, we have ∫(2x+1)^3 dx. Let u = 2x + 1. Then du/dx = 2, which means dx = du/2. 3. **Substitute and Integrate:** Substitute u and dx in the integral: ∫u^3 (du/2) = (1/2)∫u^3 du Applying the power rule:

To find the product AB, we need to perform matrix multiplication. Matrix A is a 3x2 matrix, and Matrix B is a 2x2 matrix. The resulting matrix will therefore be a 3x2 matrix. Here's how to calculate the elements of the resulting matrix: 1. **Element (1,1):** (2 \* 3) + (1 \* 4) = 6 + 4 = 10 2. **Element (1,2):** (2 \* 2) + (1 \* 2) = 4 + 2 = 6 3. **Element (2,1):** (2 \* 3) + (3 \* 4) = 6 + 12 = 18

Given r = \( \sqrt \frac{3v}{\pi h} \)

Square both sides:

r\(^2\) = \(\frac{3v}{πh}\)

cross multiply

3v = r\(^2\) * πh

v = \(\frac{πr^2h}{3}\)

To find the determinant of a 2x2 matrix, we use the formula: det(A) = ad - bc, where A = \\(\\begin{pmatrix} a & b \\ c & d \\end{pmatrix}\\) In this case, the matrix A is \\(\\begin{pmatrix} 2 & 3 \\ 1 & 3 \\end{pmatrix}\\). So, a = 2, b = 3, c = 1, and d = 3. det(A) = (2 * 3) - (3 * 1) = 6 - 3 = 3

Log\(_2\) 8√2 => Log\(_2\) √128 

=> Log\(_2\) 128\(^\frac{1}{2}\)

= \(\frac{1}{2}\) * (Log\(_2\) 128) 

=> \(\frac{1}{2}\) * (Log\(_2\) 2\(^7\))

=  7 * \(\frac{1}{2}\) * (Log\(_2\) 2)

where (Log\(_2\) 2) = 1 

=>  7 * \(\frac{1}{2}\) * 1

= \(\frac{7}{2}\) or 3.5

A circle.

Numerator: 96 => 37.5% of 96 = 36

decrease by 36 => 96 - 36

new numerator = 60

Denominator: 50 => 20% of 50 = 10

decrease by 10 => 50 - 10 = 40

new denominator = 40

the new fraction = \(\frac{60}{40}\) or 1.5