Correct Answer: D. 3x²-7x-6=0

Explanation

\(x = -\frac{2}{3} \implies x + \frac{2}{3} = 0\)

\(x = 3 \implies x - 3 = 0\)

\(\implies (x - 3)(x + \frac{2}{3}) = 0\)

\(x^2 - 3x + \frac{2}{3}x - 2 = 0\)

\(x^2 - \frac{7}{3}x - 2 = 0\)

\(3x^2 - 7x - 6 = 0\)

Correct Answer: B. 11.4 N

Explanation

\(m=4.56kg;t=16s;v_1=(10ms^{-1},060^o);v_2=(50ms^{-1},060^o)\)

Notice that there is no change in the direction of the velocity

So,we don't need to write it in a vector form

\(a=\frac{?v}{t}=\frac{50 - 10}{16}\)

\(a=\frac{40}{16}=2.5ms^{-2}\)

F = ma = 4.56 x 2.5

∴ F = 11.4 N

Correct Answer: C. 4

Correct Answer: D. \(x^2 + 3x - 40=0\)

Explanation

Equation with roots -8 and 5: (x + 8)(x - 5) = 0

\(x^2 - 5x + 8x - 40 = 0\)

\(x^2 + 3x - 40 = 0\)

Correct Answer: D. 20

Correct Answer: C. 1.8

Explanation

Mean = \(\frac{24}{8} = 3\)

Standard deviation = \(\sqrt{\frac{26}{8}}\)

= \(\sqrt{3.25}\)

= 1.802 \(\approeq\) 1.8

Correct Answer: B. \(-\frac{2}{5}\)

Explanation

\(S_{\infty} = \frac{a}{1 - r}\) (Sum to infinity of a GP)

\(250 = \frac{350}{1 - r} \implies 250(1 - r) = 350\)

\(350 = 250 - 250r \implies 350 - 250 = -250r\)

\(250r = -100 \implies r = \frac{-100}{250} = -\frac{2}{5}\)

Correct Answer: A. \(-\frac{1}{2}\)

Explanation

sin 210 = - sin (210 - 180) = - sin 30

= -1/2

Explanation

(a) Using long division

(x + 2)(2x\(^2\) + 7x - 15)

(x + 2)(2x - 3)(x - 5)

zeros of g (x) are;

x + 2 =0, 2x - 3 = 0

x + 5 = 0, x = -2

x = \(\frac{5}{2}\) and x = -5

(b) 3(2^\(^x\)) + 3\(^{y - 2}\) = 25 .......x1

2\(^x\) - 3\(^{y + 1}\) = -19 .........x3

3(2\(^x\)) + 3\(^{y - 2}\) = 25

3\(^{y - 2}\) + 3(3\(^{y + 1}\)) = 82

\(\frac{3^y}{9} + \frac{3^y}{1}\) = 82

\(\frac{3^y + 9(3^y)}{9}\) = 82

3\(^y\) + 9(3\(^y)\)) = 82 x 9

let p = 3y

p + qp = 738

\(\frac{10p}{10} = \frac{738}{10}\)

p = 73.8, 3\(^y\) = 73.8

log3\(^y\) = log 73.8

\(\frac{y log 3}{log 3} = \frac{log 73.8}{\log 3}\)

y = 3.9

from

2\(^x\) + 3\(^{y + 1}\) = - 19

2\(^x\) + 3\(^{3.9 + 1}\) = - 19

2\(^x\) + 3\(^{4 - 9}\) = - 19

2\(^x\) - 217.7 = - 19

2\(^x\) = 198.71

log 2\(^x\) = log 198.71

\(\frac{x \log 2}{log 2} = \frac{log 198.71}{log 2}\)

x = 7.6

Explanation

(a)

(b)(i) Lower quartile, \(Q_{1} = 32.5\)

Upper quartile, \(Q_{3} = 53.0\)

Semi-interquartile range = \(\frac{1}{2} (Q_{3} - Q_{1})\)

= \(\frac{1}{2} (53.0 - 32.5) = \frac{1}{2} (20.5)\)

= \(10.25\)

(ii) Number of students that passed with distinction = (80 - 74)

= 6 students

Percentage = \(\frac{6}{80} \times 100% = 7.5%\)