18N.2.SL.TZ0.T_2

pestleMathematicsAASLPaper 218N· sl-5-5-integration-introduction-areas-between-curve-and-x-axissource ↗

160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.

A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.

Set S represents those students who are taught in Spanish.

Set B represents those students who study Biology.

Set M represents those students who study Mathematics.

A student from the school is chosen at random.

Find the number of students in the school that are taught in Spanish.

[2]

a.i.

Find the number of students in the school that study Mathematics in English.

[2]

a.ii.

Find the number of students in the school that study both Biology and Mathematics.

[2]

a.iii.

Write down $n\left( {S \cap \left( {M \cup B} \right)} \right)$ .

[1]

b.i.

Write down $n\left( {B \cap M \cap S'} \right)$ .

[1]

b.ii.

Find the probability that this student studies Mathematics.

[2]

c.i.

Find the probability that this student studies neither Biology nor Mathematics.

[2]

c.ii.

Find the probability that this student is taught in Spanish, given that the student studies Biology.

[2]

c.iii.

Markscheme / solution

10 + 40 + 28 + 17 (M1)

= 95 (A1)(G2)

Note: Award (M1) for each correct sum (for example: 10 + 40 + 28 + 17) seen.

[2 marks]

a.i.

20 + 12 (M1)

= 32 (A1)(G2)

Note: Award (M1) for each correct sum (for example: 10 + 40 + 28 + 17) seen.

[2 marks]

a.ii.

12 + 40 (M1)

= 52 (A1)(G2)

Note: Award (M1) for each correct sum (for example: 10 + 40 + 28 + 17) seen.

[2 marks]

a.iii.

78 (A1)

[1 mark]

b.i.

12 (A1)

[1 mark]

b.ii.

$\frac{{100}}{{160}}$ $\left( {\frac{5}{8}{\text{,}}\,\,0.625{\text{,}}\,\,62.5\,{\text{% }}} \right)$ (A1)(A1) (G2)

Note: Throughout part (c), award (A1) for correct numerator, (A1) for correct denominator. All answers must be probabilities to award (A1).

[2 marks]

c.i.

$\frac{{42}}{{160}}$ $\left( {\frac{{21}}{{80}}{\text{,}}\,\,0.263\,\,\left( {0.2625} \right){\text{,}}\,\,26.3\,{\text{% }}\,\,\left( {26.25\,{\text{% }}} \right)} \right)$ (A1)(A1) (G2)

Note: Throughout part (c), award (A1) for correct numerator, (A1) for correct denominator. All answers must be probabilities to award (A1).

[2 marks]

c.ii.

$\frac{{50}}{{70}}$ $\left( {\frac{5}{7}{\text{,}}\,\,0.714\,\,\left( {0.714285 \ldots } \right){\text{,}}\,\,71.4\,{\text{% }}\,\,\left( {71.4285 \ldots \,{\text{% }}} \right)} \right)$ (A1)(A1) (G2)

Note: Throughout part (c), award (A1) for correct numerator, (A1) for correct denominator. All answers must be probabilities to award (A1).

[2 marks]

c.iii.

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

c.iii.