Year 9 Maths • AC9M9N01 • Authored homework
Real numbers, exact values and inequalities
Work with real numbers by comparing rational and irrational values, using exact forms such as π and square roots, estimating when useful, and representing inequalities correctly. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Classify 7/8, √25, √30, 0.125, π and -4 as rational or irrational where appropriate.
Write an exact expression for the circumference of a circle with radius 6 cm, then give a decimal approximation.
Estimate √50 to one decimal place and explain why it is between 7 and 8.
Place √2, 1.5, 3/2 and π/2 in ascending order.
Explain the difference between an exact value and an approximation.
Solve x + 4 < 11 and show the solution on a number line.
Write an inequality for “n is at least 12”.
Round 7π to two decimal places and explain why the exact form may be better.
Correct this misconception: “Every decimal is irrational.”
Give a real-world situation where an inequality is more useful than a single number.
Part B
Long-answer questions
A circular table has diameter 1.2 m. Find the exact circumference in terms of π and an approximate circumference to the nearest centimetre.
Compare √45 and 6.7 without using a calculator as your only explanation. Show reasoning.
A container must hold at least 2.5 L but less than 3 L. Write and graph an inequality for the capacity c.
Solve 3x - 5 ≥ 16, then test two values to check your solution set.
Explain why √49 is rational but √50 is irrational, using definitions and examples.
A student says 22/7 and π are the same because calculators give close answers. Evaluate the claim.
Use a number line to show an interval of possible values for a measurement rounded to 8.4 cm to the nearest tenth.
Create and solve a practical problem that needs an exact value first and a rounded answer at the end.
Write a full solution to a problem involving real numbers, inequalities and approximation, including a reasonableness check.
Explain how exact values, approximations and inequalities can all be useful in measurement or design.
Part C
Research and understanding task
Find one real situation involving a measurement limit, tolerance, design size or circular measurement. Create a problem using exact values or inequalities, solve it, and explain the meaning of the answer.