Correct Answer: A. 30

Explanation

\(1 + \sqrt [3]{x-3} = 4\)

= \(\sqrt[3]{x - 3} = 4 - 1\)

\(\sqrt[3]{x - 3} = 3 \)

take the cube of both sides

= x - 3 = 27

x = 27 + 3

∴ x = 30

Correct Answer: C. 7x - 2

Explanation

\(7x^2 + 33x - 10\)

\(7x^2 + 35x - 2x - 10\)

7x (x + 5) - 2 (x + 5)

(7x - 2) (x + 5)

Correct Answer: D. -2 ? x< 4

Explanation

(a)

Antilog of \(\bar{1}.2207 = 0.1663\)

(b) \(\log_{10} y + 3 \log_{10} x = 2\)

\(\log_{10} y + \log_{10} x^{3} = 2\)

\(\log_{10} (yx^{3}) = 2\)

\(yx^{3} = 10^{2}\)

\(yx^{3} = 100\)

\(y = \frac{100}{x^{3}}\)

(c) \(3x - 2y = 21 .... (1)\)

\(4x + 5y = 5 ..... (2)\)

Multiply (1) by 4 and (2) by 3,

\(12x - 8y = 84 .... (1a)\)

\(12x + 15y = 15 ... (2a)\)

(1a) - (2a),

\(- 8y - 15y = 84 - 15\)

\(- 23y = 69 \implies y = -3\)

\(3x - 2y = 21 \implies 3x - 2(-3) = 21\)

\(3x + 6 = 21 \implies 3x = 15\)

\(x = 5\)

Correct Answer: B. 61.33

Explanation

Step 1: Find the sum of the values... (2+5+10+77+241+3)/3=368 Step 2: Find how many numbers are given... There are 6 numbers. Step 3: To find the mean, divide the sum by how many numbers.... 368/6=61.33

Explanation

(a)(i) Mean = \(\frac{\sum fx}{\sum f} = \frac{167}{32}\)

= \(5.21875 \approxeq 5.22\)

(ii) By inspection, the average of the numbers in the 16th and 17th position give the median

= \(\frac{5 + 5}{2} = 5\)

(iii) Mode = 7 marks having the largest frequency.

(b) Students who scored at least 8 marks = Those who scored 8, 9, 10.

Total number of students that scored at least 8 = 3 + 2 + 1 = 6.

\(%age = \frac{6}{32} \times 100% = 18.75%\)

Correct Answer: D. 6

Explanation

The mode is the occurrence with the highest frequency which, from the table, is 45 (the occurrence of obtaining a 6).

Correct Answer: C. 3200 πkm

Explanation

P(67°W, 0°N)

Q(67°W 90°N), R = 6400km

Distance PQ =

90/360 x 2 x 6400 π

= 3200πkm

Correct Answer: C. \(\frac{2x^{\frac{7}{2}}}{7} + c\)

Explanation

\(x^{2}\sqrt{x} \equiv x^{2}. x^{\frac{1}{2}} = x^{\frac{5}{2}}\)

\(\implies \frac{\mathrm d y}{\mathrm d x} = x^{\frac{5}{2}}\)

\(y = \int x^{\frac{5}{2}} \mathrm d x\)

= \(\frac{x^{\frac{5}{2} + 1}}{\frac{5}{2} + 1} + c\)

= \(\frac{2x^{\frac{7}{2}}}{7} + c\)

Explanation

(a) since the curved surface areas were the same, it was expected that they have 5 x 12\(pi\) = 6 \(\pi\)l and solving for the slant height to get l = 10 cm.

Then by the use of Pythagoras theorem, the height of the second cone is h\(^2\) = 10\(^2\) - 6\(^2\) and when simplified will result in h = 8 cm.

(b(i), they were to find BA = \(\begin{pmatrix} 3 & -2 \\4 & 1\end{pmatrix}\) \(\begin{pmatrix} 2 & 5 \\ -1 & -3\end{pmatrix}\) = \(\begin{pmatrix} 8 & 21 \\ 7 & 17 \end{pmatrix}\)

(b)(ii), the determinant of BA = (8 x 17) - (21 x 7) = 136 - 147 = -11