Year 12 ICAS Mathematics 5-Question Sample

Question 1 of 5 Chance and data

In a two-events problem from a west-side study-group worksheet, two counters are drawn without replacement. What is the probability that both are red?

Counters in a bag

Colour	Count
Red	5
Blue	8
Total	13

A $\frac{5}{39}$ B $\frac{25}{169}$ C $\frac{5}{13}$ D $\frac{10}{39}$

Question 2 of 5 Chance and data

In a restricted-sample problem from a blue-team lesson-starter slide, a student is known to be from the robotics club. What is the probability that the student passed the trial?

Trial outcome by group

Group	Passed	Not passed	Total
Robotics club	20	10	30
Other students	20	6	26

A $\frac{1}{2}$ B $\frac{5}{7}$ C $\frac{2}{3}$ D $\frac{1}{3}$

Question 3 of 5 Number and arithmetic

In an investment-balance problem from a west-side holiday-homework booklet, an account compounds annually. Which amount is closest to the balance after 2 years?

Investment details

Starting amount	Annual rate	Years
$1000	6%	2

A $1,120.00 B $2,560.00 C $1,060.00 D $1,123.60

Question 4 of 5 Number and arithmetic

For an exact-value check from a blue-team skills-checkpoint sheet, simplify $\sqrt{98}+\sqrt{72}$.

A $\sqrt{170}$ B $13\sqrt{2}$ C $42\sqrt{2}$ D $14\sqrt{2}$

Question 5 of 5 Chance and data

In a box-plot question from a west-side study-group worksheet, use the box-plot summary. Which comparison is best supported?

Box plot summary

Class	Minimum	Q1	Median	Q3	Maximum
A	29	39	47	55	69
B	30	40	51	63	76

A Class B has the higher median and the larger interquartile range. B Class A has the higher median and the larger interquartile range. C The two classes have the same median, but Class A has the larger spread. D Class A must have the highest mean because its minimum is smaller.

Year 12 Mathematics sample

Answer the sample questions

In a two-events problem from a west-side study-group worksheet, two counters are drawn without replacement. What is the probability that both are red?

In a restricted-sample problem from a blue-team lesson-starter slide, a student is known to be from the robotics club. What is the probability that the student passed the trial?

In an investment-balance problem from a west-side holiday-homework booklet, an account compounds annually. Which amount is closest to the balance after 2 years?

For an exact-value check from a blue-team skills-checkpoint sheet, simplify \(\sqrt{98}+\sqrt{72}\).

In a box-plot question from a west-side study-group worksheet, use the box-plot summary. Which comparison is best supported?