(a) Using a scale of 2 cm to 30° on the x- axis, 2 cm to 0.2 units on the y- axis, on the same graph sheet, draw the graphs of \(y = \sin 2x\) and \(y = \cos x\) for \(0° \leq x \leq 210°\) at intervals of 30°.

(b) Using the graphs in (a), find the truth set of :

(i) \(\sin 2x = 0\) ; (ii) \(\sin 2x - \cos x = 0\).

A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

• A. N16,200
• B. N1,4,200
• C. N12,000
• D. N8000.

Let p be a probability function on set S, where S = (a₁, a₂, a₃, a₄). Find P(a₁) if P(a₂) = \(\frac{1}{3}\), p(a₃) = \(\frac{1}{6}\) and p(a₄) = \(\frac{1}{5}\)

• A. \(\frac{7}{3}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{3}{10}\)

Find the quadratic equation whose roots are \(\frac{2}{3} and \frac{- 3}{4}\)

• A. \(12y^2 - y - 6 = 0\)
• B. \(12y^2 - y + 6 = 0\)
• C. \(12y^2 + y - 6 = 0\)
• D. \(y^2 + y - 6 = 0\)

In how many ways can 3 seats be occupied if 5 people are willing to sit?

• A. 60
• B. 20
• C. 5
• D. 120

Which of the following fractions is the highest?

• (a) 3/4
• (b) 7/9
• ( c) 2/3
• (d) 12/15

A trader made a loss of 10% on a motorcycle he sold for N54,000: How much should he have sold the motorcycle to avoid any loss?

• a. N56,000
• b. N58,000
• c. N60,000
• d. N62,000

y is inversely proportional to x and y = 4 when x = 1/2. Find x when y = 10.

• A. 2
• B. 10
• C. 1/5
• D. 1/10

If S = (x : x² = 9, x > 4), then S is equal to

• A. 4
• B. {0}
• C. ∅
• D. {∅}

From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number

• A. \(\frac{1}{5}\)
• B. \(\frac{2}{5}\)
• C. \(\frac{3}{5}\)
• D. \(\frac{4}{5}\)