2022 - JAMB Mathematics Past Questions and Answers - page 2

Tn = a + (n-1)d

10th term = 32

32 = 3/2 + 9d 

9d = 32 - 3/2

9d = 61/2

d = 61/18

T4 = 3/2 + 3(61/18)

T4 = 3/2 + 61/6 → 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