GANITA MANJARI · GRADE 9 · PART II · CHAPTER 9
Think first. Use AI purposefully. Verify always.
01 · DISCOVER
A learner tests 3, 5 and 7 and guesses that every prime is odd. What example has been missed?
Claim: for every positive integer n, n² + n + 5 is prime. Think of a test value first.
02 · UNDERSTAND
A counterexample satisfies the starting condition but fails the conclusion. One such example disproves an “always” claim. Many successful checks do not prove every possible case.
03 · KEY IDEAS
04 · VISUALISE
Claim → permitted test value → condition met → conclusion fails → counterexample.
05 · METHOD / REASONING
Read the claim → think → choose a permitted example → check the condition → test the conclusion → conclude.
06 · ORIGINAL AIMS WORKED EXAMPLE
Claim: every positive multiple of 7 is odd.
07 · AIMS METHOD
Why does 18 disprove “Every multiple of 3 is a perfect square”?
18 = 3 × 6 but lies strictly between and , so it is not a square.
08 · PRACTICE SPRINT
Ten original AIMS questions: 3 Warm-up, 4 Build, 2 Think and 1 Challenge.
Start Practice Sprint →Check & Feedback: incorrect answers receive a conceptual hint and another attempt; correct answers include reasoning.
TEXTBOOK CONNECTION
Ganita Manjari · Grade 9 · Part II · Chapter 9. Use your textbook for the complete questions. These are topic references and original AIMS guidance, not reproduced exercises.
Exercise Practice
Source page 6 · TEST
Divisibility by 24 versus divisibility by 4 and 6
A shared multiple of 4 and 6 need not contain every factor required by 24.
Test the reverse separately rather than multiplying the two divisors blindly.
Exercise Practice
Source page 6 · TEST
Prime-generating claims with square and exponential expressions
Seek a permitted input giving a composite result and show a nontrivial factorisation.
The third source expression has an exponent on 4; it is not 4 times n.
Exercise Practice
Source page 6 · TEST
Prime claims involving powers of 2
Keep the prime/even input restrictions and check the powers accurately.
Do not confuse an exponent with multiplication; supporting small cases are not a proof.
