Two variables x and y are such that \(\frac{dy}{dx}\) = 4x - 3 and y = 5 when x = 2. Find y in terms of x

• A. 2x² - 3x + 5
• B. 2x² - 3x + 3
• C. 2x² - 3x
• D. 4

A die has four of it's faces coloured white and the remaining two coloured black. What is the probability that when the die is thrown two consecutive time, the top face will be white in both cases?

• A. \(\frac{2}{3}\)
• B. \(\frac{1}{9}\)
• C. \(\frac{4}{9}\)
• D. \(\frac{1}{36}\)

Find the area bounded by the curve y = 3x² - 2x + 1, the ordinates x = 1 and x = 3 and the x-axis

• A. 24
• B. 22
• C. 21
• D. 20

\(\begin{array}{c|c} \text{Class Interval} & Frequency & \text{Class boundaries} & Class Mid-point \\ \hline 1.5 - 1.9 & 2 & 1.45 - 1.95 & 1.7\\ 2.0 - 2.4 & 21 & 1.95 - 2.45 & 2.2\\ 2.5 - 2.9 & 4 & 2.45 - 2.95 & 2.7 \\ 3.0 - 2.9 & 15 & 2.95 - 3.45 & 3.2\\ 3.5 - 3.9 & 10 & 3.45 - 3.95 & 3.7\\ 4.0 - 4.4 & 5 & 3.95 - 4.45 & 4.2\\ 4.5 - 4.9 & 3 & 4.45 - 4.95 & 4.7\end{array}\)

Find the mode of the distribution above to find the mode of the distribution.

• A. 3.2
• B. 3.3
• C. 3.7
• D. 4.2

Evaluate \(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)

• A. 27
• B. 1
• C. 1/3
• D. 1/8

Find the area bounded by the curve y = 3x\(^2\) - 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.

• A. 27°
• B. 30°
• C. 54°
• D. 108°

Convert 3.1415926 to 5 decimal places

• A. 3.14160
• B. 3.14159
• C. 0.31415
• D. 3.14200

\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)

Find the standard deviation of the data using the table above

• A. 5
• B. \(\sqrt{6}\)
• C. \(\frac{5}{3}\)
• D. \(\sqrt{5}\)

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR

• A. x + 2y - 1= -0
• B. 2x + y - 3 = 0
• C. x - 2y - 3 = 0
• D. 2x + y - 1 = 0

Use the graph of the curve y = f(x)to solve the inequality f(x) ≤ 0

• A. -1 ≥ x ≥ 1, x ≥ 2
• B. x ≤ -1, 1 ≥ x ≥ 2
• C. x ≥ -1, 1 ≥ x ≥ 2
• D. x ≥ 2, -1 ≥ x ≥ 1