Correct Answer: B. 10

Correct Answer: D. 30.63

Explanation

34.624

+ 9.83

--------------

44.454

-------------

75.0785

_

44.454

------------

30.6245

-----------

30.63 to 2d.p

Correct Answer: C. 1 - 6x

Correct Answer: B. 12

Explanation

(a) \(\frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x}\)

\(x^{3} - 4x^{2} + 3x = x(x^{2} - 4x + 3)\)

\(x^{2} - 4x + 3 = (x - 1)(x - 3)\)

\(\therefore x^{3} - 4x^{2} + 3x = x(x - 1)(x - 3)\)

\(\implies \frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x} = \frac{A}{x} + \frac{B}{x - 1} + \frac{C}{x - 3}\)

\(\implies \frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x} = \frac{A(x - 1)(x - 3) + B(x)(x - 3) + C(x)(x - 1)}{x(x - 1)(x - 3)}\)

Equating, we have

\(2x^{2} - 5x + 1 = A(x - 1)(x - 3) + B(x)(x - 3) + C(x)(x - 1) \)

Let x = 1, we have

\(2 - 5 + 1 = -2B \implies B = 1\)

Let x = 3, we have

\(18 - 15 + 1 = 6C \implies C = \frac{4}{6} = \frac{2}{3}\)

Let x = 0, we have

\(0 - 0 + 1 = 3A \implies A = \frac{1}{3}\)

\(\therefore \frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x} = \frac{1}{3x} + \frac{1}{x - 1} + \frac{2}{3(x - 3)}\)

(b) \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24\)

\(\implies (x - 3)(12 - 2x + 8) - (-4)(30 - 5x - 4) + 3(-20 - 4) = -24\)

\((x - 3)(20 - 2x) + 4(26 - 5x) - 72 + 24 = 0\)

\(20x - 2x^{2} - 60 + 6x + 104 - 20x - 48 = 0\)

\(-2x^{2} + 6x - 4 = 0\)

\(2x^{2} - 6x + 4 = 0\)

\(2x^{2} - 4x - 2x + 4 = 0 \implies 2x(x - 2) - 2(x - 2) = 0\)

\((2x - 2)(x - 2) = 0 \implies \text{x = 1 or 2}\).

Correct Answer: A. 2/11

Correct Answer: B. x varies inversely as ?y

Explanation

\(y \propto \frac{1}{x^2}\)

\(y = \frac{k}{x^2}\)

\(x^2 = \frac{k}{y}\)

\(x = \frac{\sqrt{k}}{\sqrt{y}}\)

Since k is a constant, then \(\sqrt{k}\) is also a constant.

\(\therefore x \propto \frac{1}{\sqrt{y}}\)

Correct Answer: B. 1977

Explanation

(a) it will take 1 boy 10m days and when 4 more boys are added, it will take 8(m + 4) days. Since the rate of consumption was the same, then 10m = 8m + 32 and when solves, m = 16

(b) Let x be the number. so that \(\frac{5}{6}\)x = 10 + \(\frac{1}{2}\)x and multiplying through by 6 to get 5x = 60 + 2x. This was solved to get x = 20

(c) Let the gradient be m = \(\frac{\frac{1}{2} - (\frac{1}{2})}{2 - (-1)} = \frac{2}{3}\). The equation of the lines is y - y\(_1\) = m(x - x\(_1\)). Sunstituting for x\(_1\) and y\(_1\)

y - (\(\frac{-1}{2}\)) = \(\frac{1}{2}\)(x - (-1)) and this can be simplified to y = \(\frac{1}{3}x - \frac{1}{6}\) or 2x - 6y - 1 = 0

Correct Answer: C. ?11/4

Explanation

The mean is the average of all the numbers in the data set. Add the numbers provided. 9+(?6)+(?3)+(?11)=?11 Divide this value by four. ?11/4 The answer is: ?11/4