Further Mathematics Questions & Answers - Free Online Practice

311.

Which of the following quadratic curves will not intersect with the x- axis?

$y = 2 - 4x - x^{2}$

$y = x^{2} - 5x -1$

$y = 2x^{2} - x - 1$

$y = 3x^{2} - 2x + 4$

View answer & explanation

Correct answer is D

The criterion for the quadratic curve to intersect the x- axis is $b^{2} > 4ac$ .

312.

If $2\log_{4} 2 = x + 1$ , find the value of x.

-2

-1

View answer & explanation

Correct answer is C

$2\log_{4} 2 = x + 1$

$\log_{4} 2^{2} = \log_{4} 4 = 1$

$x + 1 = 1 \implies x = 0$

313.

The polynomial $2x^{3} + x^{2} - 3x + p$ has a remainder of 20 when divided by (x - 2). Find the value of constant p.

-6

-8

View answer & explanation

Correct answer is B

Remainder for f(2) = 20.

$f(2) = 2(2^{3}) + 2^{2} - 3(2) + p = 20$

$16 + 4 - 6 + p = 20$

$14 + p = 20$

$p = 6$

314.

If $f(x) = 2x^{2} - 3x - 1$ , find the value of x for which f(x) is minimum.

$\frac{3}{2}$

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{2}{3}$

View answer & explanation

Correct answer is C

$y = 2x^{2} - 3x - 1$

$\frac{\mathrm d y}{\mathrm d x} = 4x - 3 = 0$ (At turning point)

$4x = 3 \implies x = \frac{3}{4}$

315.

The sum of the first n terms of a linear sequence is $S_{n} = n^{2} + 2n$ . Determine the general term of the sequence.

n + 1

2n + 1

3n + 1

4n + 1

View answer & explanation

Correct answer is B

$S_{n} = \frac{n}{2}(2a + (n - 1) d = n^{2} + 2n$

$n(2a + (n - 1) d = 2n^{2} + 4n$

$2an + n^{2}d - nd = 2n^{2} + 4n$

$n^{2}d = 2n^{2}$

$d = 2$

$(2a - d) n = 4n$

$2a - d = 4 \implies 2a = 4 + d = 4 + 2 = 6$

$a = 3$

$T_{n} = a + (n - 1)d$

= $3 + (n - 1)2 = 3 + 2n - 2 = 2n + 1$

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