Stage 9 - Q1 - 2 marks
Calculate exactly and simplify.
Hint
Convert the mixed number to an improper fraction before squaring.
Stage 9 - Q2 - 2 marks
Calculate exactly and simplify.
Hint
Convert the mixed number to an improper fraction before squaring.
Stage 9 - Q3 - 2 marks
Calculate exactly and simplify.
Hint
Follow the operation order and keep fractions exact.
Stage 9 - Q4 - 2 marks
Calculate exactly and simplify.
Hint
Follow the operation order and keep fractions exact.
Stage 9 - Q5 - 4 marks
A rectangle is \(3\frac{1}{6}\) m by \(3\) m. Estimate its area using half-unit benchmarks, then find the exact area.
Hint
An estimate checks size; it does not replace the exact calculation.
Stage 9 - Q6 - 4 marks
A square has side \(3\frac{1}{4}\) cm. Estimate and then calculate its exact area.
Hint
Square the full mixed number, not its parts separately.
Stage 9 - Q7 - 3 marks
A pupil writes \((4\frac13)^2=\frac{145}{9}\). Explain and correct the error.
Hint
Compare with the square of a nearby whole number.
Stage 9 - Q8 - 4 marks
Compare \((\frac{5}{2}+\frac{2}{3})^2\) with \((\frac{5}{2})^2+(\frac{2}{3})^2\). State the larger expression and difference.
Hint
A square of a sum includes more than two squared terms.
Stage 9 - Q9 - 4 marks
A square has area \(9\) square cm. Find its positive side length and check by squaring.
Hint
Use the fact that the numerator and denominator are perfect squares.
Stage 9 - Q10 - 5 marks
Challenge: Two squares have sides \(\frac{7}{2}\) cm and \(\frac{2}{3}\) cm. A third square has side equal to the sum. Find how much greater the third area is than the first two combined, then explain a rule that works for any positive a and b.
Hint
A square built from the two side lengths contains two cross rectangles.