HAST Year 11 Mathematical Reasoning free practice questions with answers
Read the opening questions and their worked answers from paper 1 of our 20-paper HAST Year 11 Mathematical Reasoning set, then download the 4-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
Topics: Mathematics: fractions; Mathematics: estimation; Mathematics: ratios.
- Mixed to improper: (whole × denominator + numerator) over the same denominator.
- To estimate, round each number to one significant figure, then calculate.
- A ratio a : b splits a total into a + b equal parts: find the value of one part first.
Read the text of this sample
Work through the questions in order. If a question stalls you, move on and come back. Then check your work against the worked solutions.
1. Write 4 A B C D
2. Estimate 936 × 97 by rounding each number to its leading digit (first digit).
A 900,000
B 90,000
C 1,000
D 9,000
3. A prize of $130 is divided between two people in the ratio 5 : 8. What is the larger share, in dollars?
A 80
B 65
C 90
D 50 5 8 as an improper fraction. 37 4 28 8 37 8 9 8 MATHEMATICAL REASONING — 35 QUESTIONS Multiple choice · 40 minutes
1. Write 4
Correct answer: C —
• Whole × bottom: 4 × 8 = 32.
• Add the top: 32 + 5 = 37.
• The bottom stays 8:
• Why the other options are wrong:
• A (
• B (
• D (
2. Estimate 936 × 97 by rounding each number to its leading digit (first digit). [Estimation]
Correct answer: B — 90,000
• Round 936 to 900 and 97 to 100.
• 900 × 100 = 90000.
• Why the other options are wrong:
• A (900,000): This is the correct answer (90,000) multiplied by 10: a scaling factor was applied (or a factor missed) that the working above does not use.
• C (1,000): Multiply, don't add.
• D (9,000): This is the correct answer (90,000) divided by 10: a scaling factor was applied (or a factor missed) that the working above does not use. 5 8 as an improper fraction. [Fractions]
37 8 37 4 ): The denominator stays the same. 28 8 ): Whole × denominator, then add the top. 9 8 ): Multiply the whole number by the denominator first. 37 8 .
3. A prize of $130 is divided between two people in the ratio 5 : 8. What is the larger share, in dollars? [Ratios]
Correct answer: A — 80
• The ratio 5 : 8 means the prize is split into 5 + 8 = 13 equal parts.
• One part is $130 ÷ 13 = $10.
• The smaller share has 5 parts: 5 × $10 = $50. The larger share has 8 parts: 8 × $10 = $80.
• The larger share: $80.
• Why the other options are wrong:
• B (65): The shares are not equal; they are in the ratio 5 : 8.
• C (90): This is the correct answer (80) plus 10: an extra 10 was added at the end of the calculation (an off-by-10 error).
• D (50): That is a different share from the one asked for.
Your sample is downloading. Liked it? HAST Year 11 Mathematical Reasoning Paper 1 is the full paper: 35 multiple-choice questions in 40 minutes (4 options each, no calculator), with a worked solution for every question.
Get Paper 1 for A$11.99See all 20 papers from A$11.99More free HAST Entry Tests samples
Questions about this sample
What is in the HAST Year 11 Mathematical Reasoning free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 4-page PDF; this page shows the opening pages.
How many full HAST Year 11 Mathematical Reasoning papers are there?
20 original papers for students preparing for Year 11 entry (HAST (High Achievers Selection Test)). Each is 35 multiple-choice questions in 40 minutes (4 options each, no calculator), with a worked solution for every question. Papers start at A$11.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.