Algebra Problems Extension                                                           

To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problem-and-solution Word document.

Examples Page Ref  Problem Title Objectives Ref Description Key Words
114, 150, 158 The Sum of r 3 Formulae, Proof, Index Laws 13 + 23 + 33 ... from a really simple diagram Formulae, Tn, Predict, Verify 
115, 150 Paper Sizes Trial + Improvement, Similarity A3, A4 paper etc  Forming equations
120, 239 Simpson's Rule and the Volume of a Sphere Formulae This exercise leads the pupil through applications of Simpson’s rule to the formula for the volume of a sphere. It is intriguing that all these volumes are  given exactly by the rule.   Cubic expression, Formulae, Like terms
108, 120 Continued Square Roots Quadratic Equations,  Trial + Improvement Easy answers to nasty-looking types Subject of the formula, Iteration, Factorize
105, 110, 120 Large Perfect Squares Algebraic expressions, Calculations 1111≤ etc - These are all based on the idea of squaring a bracket  Partition, Multiply out, Square,  Verify
119, 127 A Whole Diophantine Algebraic expressions Solve some unusual Simultaneous Equations for Integer solutions only - adding and factorising a little... Simultaneous Equations, Linear Expressions
121 Target Practice Algebraic expressions Prove a simple result about  rings on a circular target Multiply out, Square
121, 186, 189 How Many Triangles Triangles, Algebraic expressions How many different triangles can you make with rods of 6 different lengths ? Good  exercise in algebraic manipulation. Formulae, Tn, Predict, Verify 
121, 281, 285 Domino Match Probability, Sample Space,  Rearranging Algebra What's the likelihood of any 2 dominoes matching each other ? Nice algebraic cancelling ... Formulae, Take out common factors
127 Simultaneous Equations Simultaneous Equations Symmetric, but nasty-looking, Simultaneous Equations yield beautifully simple answers if an intelligent approach is taken to their 'adding and subtracting'.  Factorize, Simultaneous Equations
127, 139, 141 Diophantine Pairs  Equations, Linear Expressions Finding all the Integer solutions to an Equation Change Subject, Linear Expression
91, 127, 189 The Magic of Pythagoras Forming and Simultaneous Equations, Elimination This Problem is a variation on the Well in the Courtyard problem... and has a lovely, surprising answer ! Simultaneous Equations
133, 141, 151, 159 Peachy Pyramids Use ICT to explore non-linear sequences Exploring the beautiful square fruit pyramids that are seen on greengrocers' stalls Spreadsheet, Sequence, Formula, Squares, ICT
133, 141, 151, 159 Plummy Pyramids Use ICT to explore non-linear sequences Exploring the more-complex rectangular fruit pyramids that are seen on greengrocers' stalls Spreadsheet, Sequence, Formula, Squares, ICT
129 Absolute Equations Simultaneous Equations Introducing the |x| notation, and solving simple equations using it Simultaneous Equations, Graphical method
57, 91, 133 Power Twins Index Laws, Powers 2 4 = 4 2 - find some more examples !  Index Laws, Power, Exponent
133, 227, 234 Overlapping Squares 1 Graphs, Trial + Improvement This problem offers an element of surprise in that the equation of the locus of possible solutions isnít the straight line that pupils may well expect... Graphs, Subject of the formula, Reciprocal
119, 171 Swap It and See Complex expressions Why is (0.43^2 + 0.57) equal to (0.57^2 + 0.43)? Brackets, Quadratic graphs, 
143, 119 Perfect Cubes Complex expressions Can both (n + 3) and (n^2 + 3) be perfect cubes? Expand Brackets, Tn, 
149, 161 Toffee Maths Function, Linear sequence A fold-on-itself process that shows up the nature of 'Chaos', using a simple iterative function  Rationals + Irrationals, Iterative Processes, Mappings, Spreadsheets
150, 175 Graphical Convergence Functions, Graphs, Proof A mapping for x and y sends points to a convergent 'invariant point' - nice, visual, algebraic exercise    Sequence, Convergent, Predict, Verify
108, 150 Funny Functions Functions, Calculators, Proof Analyzing the Calculator functions 'SQRT' and 'INT', looking at associativity etc   Brackets, Associative, Mappings
109, 151, 155 PC Plod... Generate non-linear sequences How many ways can a policeman patrol a grid of streets ? Sequence, Pascal's triangle, Notation
 

 

 

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Last modified: June 18, 2007