GANITA MANJARI · GRADE 9 · PART II · CHAPTER 9

APS–3M

Think first. Use AI purposefully. Verify always.

Original AIMS written questions. Attempt on paper before comparing reasoning. No automatic marking.

3-mark reasoning

Give a false/false pair using multiples of 8 and 15. Justify both verdicts.

Your approach, or a note of what you attempted on paper

3-mark reasoning

Disprove: a product is square only if both positive integer factors are square.

Your approach, or a note of what you attempted on paper

3-mark reasoning

Explain odd positive factor count → perfect square without relying on a list of examples.

Your approach, or a note of what you attempted on paper

3-mark reasoning

Compare the two equal-area right triangles with legs 3,8 and 4,6. Is either direction of area/congruence justified?

Original AIMS diagrams: perpendicular legs 3,8 and 4,6. Use the perpendicular leg lengths to compare area and shape.

Your approach, or a note of what you attempted on paper

3-mark reasoning

A learner claims every number $n^{2}$ + n + 7 is prime for positive integer n. Find and verify a counterexample.

Your approach, or a note of what you attempted on paper

3-mark reasoning

A rectangle is known to have equal diagonals. Explain why this does not prove every equal-diagonal quadrilateral is a rectangle.

Your approach, or a note of what you attempted on paper