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Date	November Example questions	Marks available	6	Reference code	EXN.1.SL.TZ0.3
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Find	Question number	3	Adapted from	N/A

Question

The following table shows the probability distribution of a discrete random variable $X$ where $x = 1, 2, 3, 4$ .

Find the value of $k$ , justifying your answer.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

uses $\sum P (X = x) (= 1)$ (M1)

$k^{2} + (7 k + 2) + (- 2 k) + (3 k^{2}) (= 1)$

$4 k^{2} + 5 k + 1 (= 0)$ A1

EITHER

attempts to factorize their quadratic M1

$(k + 1) (4 k + 1) = 0$

OR

attempts use of the quadratic formula on their equation M1

$k = \frac{- 5 \pm \sqrt{5^{2} - 4 (4) (1)}}{8} (= \frac{- 5 \pm 3}{8})$

THEN

$k = - 1, - \frac{1}{4}$ A1

rejects $k = - 1$ as this value leads to invalid probabilities, for example, $P (X = 2) = - 5 < 0$ R1

so $k = - \frac{1}{4}$ A1

Note: Award R0A1 if $k = - \frac{1}{4}$ is stated without a valid reason given for rejecting $k = - 1$ .

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » SL 2.6—Quadratic function

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