Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers of x.

• A. \(10x^{3}k^{2}\)
• B. \(5x^{3}k^{2}\)
• C. \(-5x^{2}k^{3}\)
• D. \(-10x^{2}k^{3}\)

Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.

• A. k = 5, r = -1
• B. k = 5, r = 2
• C. k = 2, r = -5
• D. k = -1, r = 5

The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms

• A. nth = 3
• B. nth = 4
• C. nth = 5
• D. nth = 6

Make x the subject of the relation d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)

• A. x = \(\frac{6 + 12}{d^2 + y}\)
• B. x = \(\frac{12}{d^2 - y}\)
• C. x = \(\frac{12}{y} - 2d^2\)
• D. x = \(\frac{12}{2d^2 + y}\)

Add all the even numbers from 15 to 20

• (a) 55
• (b) 34
• ( c)54
• (d) 64

Calculate the length of an arc of a circle diameter 14 cm, which substends an angle of 90° at the center of the circle

• A. 7π/2 cm
• B. 7π cm
• C. 14π cm
• D. 7π/4 cm

In a class of 40 students, 25 speak Hausa, 16 speak Igbo, 21 speak Yoruba and each of the students speak at least one of the these three languages. If 8 speak Hausa and Igbo, 11 speak Hausa and Yoruba and 6 speak Igbo and Yoruba.

(a) Draw a Venn diagram to illustrate the information, using x to represent the number of students that speak all three languages.

(b) calculate the value of x.

Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity

• A. p
• B. p -1
• C. p/(p-1)
• D. p/(p+1)

If x - 1 and x + 1 are both factors of the equation x³ + px² + qx + 6 = 0, evaluate p and q

• A. -6, -1
• B. 6, 1
• C. 1, -1
• D. 6, -6

Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)

• A. \(\frac{3}{2}\)
• B. \(\frac{1}{2}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{5}{3}\)