-y -- * F * d - I

\ .A

IB Math SL- 2nd ~Lar t e r Benchmark /

1. The following Venn diagram set U and the sets A and

I I U I

I

(a) Shadethe area in the diagram whlch represents the set B n A'.

n(U) = 100, A(A) = 30, n(B) = 50, n(A u B) = 65.

(b) Findn(BnA1). n ~ b n ~ ' ) z.35

(c) An eleinent is selected at random from U. What is the probability that this element is i n B n A ' ? 7

I

Working: , nlA) =

DO' z% 3r ~(ps ~ 3 5 - 3s - r 00 \ \

I

(Total 4 marks)

IB Math SL- 2nd Quarter Benchmark Name

2. The table below shows the subjects studied by 210 students at a college.

(a) -is selected at random. Let A be the event the s tude~t studies Art.

1 Let B be the event the student is in Year 2. e c b w '. L t b

(i) ~ i n d P(A).

I

(ii) Find the probability that the student is a Year 2 Art student.

(iii) Are the events A and B independent? Justify your answer. I (6)

@) Given fistory studf: t isaselected at random, calculate the probability that the stu,en::f:, year I .p [ S-6

(c) Two students are selected a the probability that one student is in Year 1, and the other, in Year 2.

I (4) I (Total 12 marks)

3. A painter has 12 tins of paint. Seven tins are red and five tins are yellow. Two tins are chosen at random. Calculate the probability that both tins are the same colour.

(Total 6 marks)

ANSWER SHEET 1 . FEUILLE DE REPONSES HO JA DE RESPUESTAS

Please complete the boxes/Veuillez remplir les casesklene 10s recuadros

Question Question Pregunta

Examiner Examinateur Examinador

l a , a I

8

IB Math SL- 2nd Quarter Benchmark Name

4. Given the following frequency distribution, find

(a) the median;

(b) the mean.

Number ( x )

Frequency (n

(Total 4 marks)

Working: , I r r / f ' / f

/ r f / / / / ,I, -l ,5i,%,S,%, '01 '0

'-I L2 2 J

5 5

5. Differentiate with respect to x:

(a) (x2+1l2'

(b) ln(3x-1).

2 5 4 3 4 2

U I

8 3 lo

2

I Working: , I

4 5 6 7 8 1 0

Answers:

(a>

.................................................................. (b)

...................................................... (b) & 3 x 4 (Total 4 marks)

IB Math SL- 2nd Quarter Benchmark Name

6. The curve y = f ( x ) passes through the point (2,6).

d~ Given that - = 3x2 - 5 , find y in terms of x. dx