Algebra Problems Year 9  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 57, 115 Huge Powers Index Laws How to compare the relative sizes of numbers as huge as 2 800 and 3 600 ? Power, Index laws 115, 150 Paper Sizes Trial + Improvement, Similarity A3, A4 paper etc Trial + Improvement 115, 151, 159 The Sum of r 3 Formulae, Proof, Index Laws 13 + 23 + 33 ... from a really simple diagram Formulae, Tn, Predict, Verify 59, 105, 110, 121 Large Perfect Squares Algebraic expressions, Calculations 1111² etc - These are all based on the idea of squaring a bracket Partition, Multiply out, Square,  Verify 120, 240 Simpson's Rule and the Volume of a Sphere Using 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 123, 127 High But Friendly Simultaneous Equations Linear Equations, Elimination Simultaneous equations in 5 unknowns ... but easy to guess their relative sizes and hence solve (honest!) Unknown, Expression, Substitute, Solution 125, 139, 151 How Hot Is That? Linear Equations, Formulae, Graphs, Spreadsheets How good is F =2C+30 at approximating temperature conversions? Substitute, Formulae, Equation 126 Simultaneous Equations 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 91, 127, 189 The Magic of Pythagoras Forming and Solving Simultaneous Equations, Elimination This Problem is a variation on the Well in the Courtyard problem... and has a lovely, surprising answer, as all the unwanted terms 'cancel out' ! 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 133, 227 Overlapping Squares 1 Graphs, Trial + Improvement This problem offers an element of surprise in that the equation of the locus of possible solutions isn’t the straight line that pupils may well expect... Graphs, Subject of the formula, Reciprocal 29, 135, 237 Athletics Track Equations, Formulae, Circles, Spreadsheets Designing an 'oval' running track, with bend radii, staggers etc. An algebraic and/or spreadsheet approach. Algebraic expressions, Subject of the formula 149, 161 Toffee Maths Function, Linear sequence A fold-on-itself process that shows up the nature of 'Chaos', using a simple iterative function Flow chart, Transform, Mapping 150, 175 Graphical Convergence Functions, Graphs, Proof A mapping for x and y sends points to a convergent 'invariant point' - nice, visual, algebraic exercise Unknown, Expression, Substitute, Solution 155 Pick A Shape Generate sequence, Find nth term Pick's Theorem for Areas on a dotty grid Formula, Generate Tn, Proof 109, 161 Funny Functions Functions, Complex calculations, Analyzing the Calculator functions 'SQRT' and 'INT', looking at associativity etc Brackets, Associative 161, 165, 203 Graphic Convergence Co-ordinates, Mappings A pair of mappings for x and y lead to a convergent sequence of points, which can also be viewed as a combination of transformations - quite pretty. Mapping, Consecutive, Sequence, Predict, Verify