Mathematics 4024 · O Level · Cumulative frequency diagrams

Cumulative frequency diagrams — practice question

Six hundred candidates sat a mathematics examination made up of two papers. Each paper was marked out of 100. The diagram presents the cumulative frequency curves for Paper 1 and Paper 2 on the same grid.
(a(i)(a))[1]

Use the cumulative frequency curve for Paper 1 to estimate the median.

(a(i)(b))[2]

From the cumulative frequency curve for Paper 1, estimate the interquartile range.

(a(i)(c))[1]

Use the cumulative frequency curve for Paper 1 to estimate how many candidates scored more than $45$.

(a(ii))[1]

A candidate gained $60$ on Paper 1. Using both graphs, estimate that candidate’s mark on Paper 2.

(a(iii))[1]

State, with a reason, which paper you think was the more difficult.

(b(i))[1]

Find the value of $x$.

(b(ii))[1]

Find the probability that the total value of the two coins chosen is $40$ cents.

(b(iii))[2]

Find the probability that the total value of the two coins chosen is $\$1.20$.

(b(iv))[2]

At a car park, the fee is $\$1.40$. Amira selects three coins, one after another. Find the probability that the total value of the three coins is $\$1.40$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $40$ to $41$

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