**31. **If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.

**A.**12**B.**8**C.**9**D.**16

**Correct Option: Answer is C**

\(p \propto \frac{1}{\sqrt{q}}\)

\(\implies p = \frac{k}{\sqrt{q}}\)

when p = 3, q = 16.

\(3 = \frac{k}{\sqrt{16}}\)

\(k = 3 \times 4 = 12\)

\(\therefore p = \frac{12}{\sqrt{q}}\)

when p = 4,

\(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\)

\(\sqrt{q} = 3 \implies q = 3^2 \)

\(q = 9\)

**32. **Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.

**A.**43.6% loss**B.**35% profit**C.**63.2% profit**D.**28% loss

**Correct Option: Answer is A**

200 mangoes at 4 for N2.50

\(\implies\) Total cost price = \(\frac{200}{4} \times N 2.50\)

= N 125.00

Since 30 mangoes got spoilt \(\implies\) Left over = 200 – 30

= 170 mangoes

170 mangoes at 2 for N 2.40

\(\implies\) Total selling point = \(\frac{170}{2} \times N 2.40\)

= N 204.00

Profit : N (204.00 – 125.00) = N 79.00

% profit = \(\frac{79}{125} \times 100%\)

= 63.2% profit.

**33. **The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.

**A.**19%**B.**20%**C.**25%**D.**16.3%

**Correct Option: Answer is A**

p>S.I = \(\frac{PRT}{100}\)

\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\)

\(x = \frac{4890 \times 100}{8550 \times 3}\)

\(x = 19.06%\)

\(x \approxeq 19%\)

**34**. Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)

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

**Correct Option: Answer is D**

81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)

= \((\sqrt[4]{81})^{-3} \times \sqrt{25} \times (\sqrt[5]{243})^2\)

= \(\frac{5 \times 3^2}{3^{3}}\)

= \(\frac{5}{3}\)

**35**. Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.

**A.**46.2**B.**43.1**C.**534**D.**431

**Correct Option: Answer is B**

**36. **If S = (4t + 3)(t – 2), find ds/dt when t = 5 secs.

**A.**50 units per sec**B.**35 units per sec**C.**22 units per sec**D.**13 units per sec

**Correct Option: Answer is B**

**37. **The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is

**A.**31°**B.**30°**C.**26°**D.**48°

**Correct Option: Answer is B**

Since there are 4 angles given, the polygon is a quadrilateral.

Sum of angle in a quadrilateral = 360°

$\therefore $ 2x + 5x + x + 4x = 360°

12x = 360°

x = 30°

**38. **The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?

**A.**15.5%**B.**18.2%**C.**14.8%**D.**16.7%

**Correct Option: Answer is D**

Actual weight = 0.18g

Error = 0.21g – 0.18g

= 0.03g

% error = 0.030.18×100

= 16.7%

**39. **Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.

**A.**1.3**B.**2.5**C.**4.6**D.**3.2

**Correct Option: Answer is D**

\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)

= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\)

= \((\frac{600}{32} \times \frac{84}{2000})^{-1}\)

= \((\frac{63}{80})^{-1}\)

= \(\frac{80}{63}\)

= 1.3 (to 1 decimal place)

**40. **If 2\(^{x + y}\) = 16 and 4\(^{x – y} = \frac{1}{32}\), find the values of x and y.

**A.**x = \(\frac{3}{4}\), y = \(\frac{11}{4}\)**B.**x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)**C.**x = \(\frac{2}{3}\), y = \(\frac{4}{5}\)**D.**x = \(\frac{2}{3}\), y = \(\frac{13}{4}\)

**Correct Option: Answer is B**

2\(^{x + y}\) = 16 ; 4\(^{x – y}\) = \(\frac{1}{32}\).

\(\implies 2^{x + y} = 2^4\)

\(x + y = 4 … (1)\)

\(2^{2(x – y)} = 2^{-5} \)

\(2^{2x – 2y} = 2^{-5}\)

\(\implies 2x – 2y = -5 … (2)\)

Solving the equations (1) and (2) simultaneously, we have

x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\)