Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30

• A. x = 3 or 7, y = 12 or 8
• B. x = 6 or 1, y = 11 or 5
• C. x = 2 or 5, y = 15 or 6
• D. x = 1 or 5, y = 10 or 7

Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).

• A. 15
• B. 17
• C. 20
• D. 23

Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\)

• A. x(x²-1)
• B. 3x(x²-1)
• C. 3x²-1
• D. 7x⁶-5x⁴

Consider the following statements:

X: Benita is polite

y: Benita is neat

z: Benita is intelligent

Which of the following symbolizes the statement: "Benita is neat if and only if she is neither polite nor intelligent"?

• A. y? ~x v z
• B. y? ~x v ~z
• C. y? ~x ^ ~z
• D. y? ~x ^ z

A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x : 3 < x < 9} are subsets of the universal set U = {2, 3, 4, 5, 6, 7, 8, 9}. Find

(a) \(A \cap (B' \cap C')\) ;

(b) \((A \cup B) \cap (B \cup C)\).

Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)

• A. 10\(\sqrt{3}\)
• B. 18\(\sqrt{3}\)
• C. 14\(\sqrt{3}\)
• D. 7\(\sqrt{3}\)

The temperature in a chemical plant was -5^oC at 2.00 am. The temperature fell by 6^oC and then rose again by 7^oC. What was the final temperature?

• A. -6^oC
• B. -4^oC
• C. 4^oC
• D. 8^oC

(a) Using logarithm table, evaluate \(\frac{\sqrt[3]{1.376}}{\sqrt[4]{0.007}}\) correct to three significant figure.

(b) Without using Mathematical tables, find the value of \(\frac{\log 81}{\log \frac{1}{3}}\).

A plane figure with ten sides and ten angles

• A. hexagon
• B. octagon
• C. decagon
• D. pentagon

Find the gradient of the line passing through the points (-2, 0) and (0, -4)

• A. 2
• B. -4
• C. -2
• D. 4