Questions: Proof and iteration
Pick a question type. Each time you get new numbers. Free ones are marked free.
Algebraic proof
- Show an identity: a difference of squaresShow that, 3 marks, free, Higher tier
- Which expression is always odd?Choose, 1 mark, free, Higher tier
- The sum of consecutive integersShow that, 3 marks, free, Higher tier
- The square of an odd numberShow that, 3 marks, free, Higher tier
- Find unknowns in an identityFind, 2 marks, free, Higher tier
- Is it always a multiple?Choose, 2 marks, free, Higher tier
- The difference of consecutive squaresChoose, 1 mark, free, Higher tier
- Prove a sum is a multiple of 3Prove, 3 marks, free, Higher tier
- Why is n(n + 1) even?Choose, 1 mark, free, Higher tier
- Which statement is an identity?Choose, 1 mark, free, Higher tier
- Show a difference of squares is linearShow that, 2 marks, free, Higher tier
Counterexamples
- A counterexample about primesFind, 1 mark, free, Higher tier
- If a > b, is a² > b²?Choose, 1 mark, free, Higher tier
- Is the sum of two primes even?Choose, 1 mark, free, Higher tier
- When does a prime formula fail?Find, 2 marks, free, Higher tier
- Always true, sometimes true or never true?Choose, 1 mark, free, Higher tier
- Prove the sum of two odd numbers is evenProve, 3 marks, free, Higher tier
- Is 1/x always smaller than x?Choose, 1 mark, free, Higher tier
- The first value that breaks a ruleFind, 2 marks, free, Higher tier
- Up and down by the same percentageShow that, 2 marks, free, Higher tier
- Choose the right algebra for a proofChoose, 1 mark, free, Higher tier
Roots by a change of sign
- Values either side of a rootWork out, 3 marks, Plus, Higher tier
- Which interval contains the root?Choose, 2 marks, Plus, Higher tier
- A table of values to find a sign changeComplete, 2 marks, Plus, Higher tier
- Narrow the intervalChoose, 2 marks, Plus, Higher tier
- A root to 1 decimal place by decimal searchFind, 3 marks, Plus, Higher tier
- The whole number just below the rootFind, 2 marks, Plus, Higher tier
- Estimate a root from a graphEstimate, 1 mark, Plus, Higher tier
- When a sign change can misleadChoose, 1 mark, Plus, Higher tier
- No sign change does not mean no rootChoose, 1 mark, Plus, Higher tier
Iteration
- One step of an iterationWork out, 2 marks, Plus, Higher tier
- Three steps of an iterationWork out, 3 marks, Plus, Higher tier
- Iterate to a rootFind, 3 marks, Plus, Higher tier
- Which equation does the iteration solve?Choose, 1 mark, Plus, Higher tier
- Show that an equation can be rearrangedShow that, 2 marks, Plus, Higher tier
- A simple iteration with exact valuesWork out, 2 marks, Plus, Higher tier
- Where does an iteration end up?Find, 2 marks, Plus, Higher tier
- An iteration for a square rootWork out, 2 marks, Plus, Higher tier
- Why an iteration finds a rootExplain, 2 marks, Plus, Higher tier
- Check a root by substitutionWork out, 3 marks, Plus, Higher tier
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