Theory

UNFINISHED Log Laws - Yr 11+. Proof - UNFINISHED!

Questions

Choose "+"s or "-"s to make this equation true - Multi-part question which scales in difficulty. Appropriate for any year level. Easiest problem just requires knowledge of addition and subtraction, hardest problem requires summation notation.

Word puzzles - Yr 7+. Knowledge of pronumerals, distributive law.

Two digit numbers magic trick - Yr 7+. Knowledge of place value and algebra.

Absolute value graphical question - Yr 7+. Knowledge of pronumerals, multiples, trial and error method.

Exponents puzzle - Yr 7+. Knowledge of pronumerals, exponents.

Absolute value graphical question - Yr 7+. Knowledge of place value, pronumerals. Word problem.

Factors and maximisation puzzle - Yr 7+. Knowledge of factors.

Word problem: bricklayer rates - Yr 7+. Cases.

Prime factorisation - Yr 7+. Knowledge of factors.

Multiples of 3 puzzle - Yr 8+. Knowledge of divisibility tests, place value, algebra (solving equations). Should be very comfortable with pronumerals.

Ages puzzle - Yr 8+. Word problem, interpreting an answer with a context.

Rectangle puzzle - two approaches - Yr 8+. Proof by trial and error as well as a factorisation trick.

Test-scoring problems - Yr 8+. Algebra, word problems, trial and error.

Difference of squares puzzle - dealing with sqrts - Yr 9+. Knowledge of difference of squares identity.

Difference of squares when working with large numbers - Yr 9+. Knowledge of difference of squares. "No calculator" problem.

Difference of squares puzzle with slight twist - Yr 9+. Knowledge of the difference of squares identity, and ability to find factors of integers.

How many digits? - Yr 9+. Knowledge of index laws, prime factorisation.

Ratio word problem - Yr 9+. Simultaneous equations.

Nested roots - Yr 9+. Solid understaning of index laws required.

Powers of x+1/x type puzzles - Yr 9+. Knowledge of distributive law, expansion/factorisation.

Proportion word problem - Yr 9+. Simultaneous equations.

Factorisation trick - Yr 9+.

Which integers can be expresed as a difference of squares? - Yr 9+.

Difference of squares - divisors - Yr 9+.

Powers of a fraction - Yr 10+. Knowledge of index laws, prime factorisation.

Integer solutions to quadratic inequality - Yr 10+. Knowledge of quadratic inequalities, factorisation, graphing.

Difference of squares puzzle - Yr 10+. Knowledge of the difference of squares identity, ability to solve simultaneous equations.

Equation of a circle - Yr 10+. Knowledge of the equation of a circle and how to solve inequalities.

Factorial puzzle - Yr 10+. Knowledge of factorial notation, quadratic equations.

Factorial divisibility problem - Yr 10+. Knowledge of factorial notation, prime factorisation.

Easy factorial question - Yr 10+. Knowledge of factorial notation. NOTE - add some more to this question.

Ordered pairs satisfying an equation - Yr 10+. Quadratic equations.

Prove that no integer solutions exist - Yr 10+. Factorisation.

Tricky simultaneous equations problem - Yr 10+. Knowledge of simultaneous equations, difference of squares.

Symmetry in simultaneous equations - Yr 10+.

Various short problems - Yr 10+.

Tricky inequality - Yr 10+. Quadratic inequalities, exponents.

Logarithms - intensity of light problem - Yr 11+. Knowledge of exponential and log functions.

Log and square root problems - Yr 11+.

Slightly longer log puzzles - Yr 11+.

Tricky sum of cubes question - Yr 11+. Knowledge of sum of cubes factorisation.

Log change of base problem - Yr 11+. Knowledge of log laws.

Super hard logs question - Yr 11+. Knowledge of logarithms, completing the square, trial and error.

Telescoping sums - Yr 11+.

Absolute value graphical question - Yr 11+. Knowledge of absolute value function, graphical methods.

Quadratic sum of roots maxima problem - Yr 11+. Knowledge of sum of roots of quadratic

Tricky difference of squares - Yr 11+. Knowledge of polynomials, relationship between zeros and coefficients.

Tricky summation - Yr 11+. Knowledge of summation notation, some basic summation results and techniques (eg grouping methods)

Two summation questions - Yr 11+. Knowledge of summation notation and sum from 1 to n.

Tricky critical points problem - Yr 11+. Uses algebra not calculus.

Diophantine equation problem using absolute value - Yr 11+.

Log puzzle (domain trick) - Yr 11+. Quadratics.

Sum of consecutive integers is a perfect square - Yr 11+. Summation notation, trial and error.

Variety of problems on sequences and series - Yr 11+.

Sequence problem - Yr 11+. Induction.

Geometric progression puzzle - Yr 11+.

Logarithms and quadratics - Yr 11+.

Quick funny log puzzle - Yr 11+.

Prime puzzle - Yr 11+. Knowledge of factorisation of difference of cubes, quadratics.

Log question - Yr 11+.

When is this expression an integer? - Yr 12. Quadratic equation, proof by contradiction.

Complex numbers Argand diagram question - Yr 12. Distances on the Argand diagram, quadratic equations, cubic factorisation.

Prove both numbers can't be real - Yr 12+. Knowledge of quadratics, complex numbers.

Inequalities problems - Yr 12+. Includes AM-GM and Cauchy-Schwartz.

Induction to find a closed form - Yr 12+. Series, proof by induction.

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