Explanation

(a)

Correct Answer: C. 18years

Explanation

Let Mr Manu be x years old and Adu be y years old.

But Mr Manu is four times as old as Adu then, x = 4y.

7 years ago, the sum of their ages was 76.

( x - 7) + ( y - 7) = 76

x + y - 14 = 76

x + y = 76 + 14 = 90

But x = 4y

Therefore, 4y + y = 90

5y = 90

y = \(\frac{90}{5}\)

y = 18

Therefore Adu is 18 years old.

Correct Answer: C. II, IV

Explanation

Let's look at each statement. I. Always search for the middle number This is false, because what happens if the number set is jumbled. To find median, it's important to oragnize in increasing or decreasing order. II. Always arrange in increasing or decreasing order before searching for the middle number As explained in statement one explanation, this is true. III. Once arranged, if the set has an even number, just take the two middle numbers and subtract them and divide by two This s false, because once there is an even number set, you need to ADD the middle numbers and divide it by two. Essentially, the new value represents the middle of the set. IV. Once arranged, if the set has an even number, just take the two middle numbers and add them and divide by two This is true based on statement three explanation.

Correct Answer: C. 18

Correct Answer: C. \(\frac{3}{5}\)

Explanation

pr. (More than one pet)

= \(\frac{\text{No. of students with > 1 pet}}{\text{total no. of students}}\)

= \(\frac{5 + 10 + 3}{30}\)

= \(\frac{18}{30}\)

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

Explanation

(a) Let \(u = (x - 3)\) and \(v = (x^{2} + 5)\).

\(y = uv\)

\(\frac{\mathrm d u}{\mathrm d x} = 1 ; \frac{\mathrm d v}{\mathrm d x} = 2x\)

From the product rule,

\(\frac{\mathrm d y}{\mathrm d x} = v \frac{\mathrm d u}{\mathrm d x} + u \frac{\mathrm d v}{\mathrm d x}\)

\(\frac{\mathrm d y}{\mathrm d x} = (x^{2} + 5)(1) + (x - 3)(2x)\)

= \(x^{2} + 5 + 2x^{2} - 6x\)

= \(3x^{2} - 6x + 5\)

(b)(i) \(f(x) = x^{3} + ax^{2} + bx + 3\)

Since \((x + 1)^{2}\) is a factor, then \(f(-1) = 0\).

\(\therefore f(-1) = (-1)^{3} + a(-1)^{2} + b(-1) + 3\)

\(0 = -1 + a - b + 3 \implies a - b = -2 ... (1)\)

When the leading coefficient is 1, the possible rational zeros are the factors of the constant term. Since we already have 2 out of the three zeros of the polynomial, the third one will be (x + 3). [Check for yourself using the long division method].

\(\therefore f(-3) = 0\)

\(f(-3) = (-3)^{3} + a(-3)^{2} + b(-3) + 3\)

\(-27 + 9a - 3b + 3 = 0 \implies 9a - 3b = 24 ... (2)\)

From (1), \(a = -2 + b\)

\(\therefore 9(-2 + b) - 3b = 24\)

\(-18 + 9b - 3b = 24 \implies 6b = 42\)

\(b = 7 \implies a = -2 + 7 = 5\)

(a, b) = (5, 7).

(ii) We already have the three factors of the polynomial as \((x + 1)^{2}; (x + 3)\).

Hence the zeros of f(x) are -1, -1 and -3.

Correct Answer: C. loss of 10%

Explanation

s.p = N6900

%profit = 15%

%profit = \(\frac{s.p - c.p}{c.p}\) x 100%

15% = \(\frac{6900 - c.p}{c.p}\) x 100%

\(\frac{15}{100}\)c.p = N6900 - c.p

0.15 c.p = N6900 - c.p

1.15c.p + c.p = N6900

c.p = \(\frac{6900}{1.15}\)

= 6000.00

Now new S.P = N6600

profit = s.p - c.p = 6000 - 6600

= 600

%profit = \(\frac{600}{6600}\) x 100%

= 10%

Correct Answer: D. 7cm

Explanation

Volume = \(\frac{1}{3}\) x 9 x 5 x h

105 = \(\frac{1}{3}\) x 9 x 5 x h

\(\frac{105}{15} = \frac{15h}{15}\)

h = 7cm

Correct Answer: B. 14 cm

Correct Answer: A. 3