Algebra Problems Year 8  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 113 Input Output Express Relationships Describe the rule connecting the dual Inputs to the Output Symbols, Mapping, Table, Relationship, Function 87, 115 Brackets Order of operations, Brackets The difference that the placing of brackets makes! Brackets, Associative, Commutative 123 Bad Dog! Construct and solve simple equations Cheery the Dog has just swallowed Sweety the Cat - how heavy were they each beforehand?! Like Terms, Solve, Equation 114, 150, 158 The Sum of r 3 Formulae, Proof 13 + 23 + 33 ... from a really simple diagram Formulae, Tn, Predict, Verify 117 Three Numbers Simplify expressions Find the original numbers, given the sums of the three taken in pairs Simplify, Solve, Equation 55, 117, 121 Prime Time Algebraic expressions, Proof Can you show that all Primes are of the form '6n+1' or '6n-1', no squares divided by 5 give remainder 2 or 3 etc? Formula, General term 105, 110, 120 Large Perfect Squares Algebraic expressions, Calculations This is based on the idea of squaring a bracket and the first few problems would be a nice 'long' multiplication revision puzzle Partition, Multiply out, Square,  Verify 109, 161 Funny Functions Functions, Complex calculations, Analyzing the Calculator functions 'SQRT' and 'INT', looking at associativity etc Brackets, Associative 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 53, 145 Factor Squares Prime Factors, Sequences Does the sequence 6, 12, 24,... contain any square numbers? Prime factor decomposition 149 Parking Meters Sequences, Spreadsheets A mixture of dollars and quarters make up \$29.50 - how many coins of each type, 43 in total? Calculate, Sequence 154, 262 The Knockout Tournament Sequences, Organizing Data How many games are needed in a tournament for 100 teams? How many byes etc? Predict, Generate, Verify 30, 144 Shelf Tidying Sequences, Justify methods How quickly can you put the Star Trek videos back in order? Sequence, Proof 155 Pick A Shape Generate sequence, Find nth term Pick's Theorem for Areas on a dotty grid Formula, Generate Tn, Proof 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 161, 165, 203 Graphic Convergence Linear Equations, Elimination A mapping for x and y sends points to a convergent 'invariant point' - nice, visual, algebraic exercise Unknown, Expression, Substitute, Solution 173, 81,193 Leg It Ratios, Travel graphs, Similar Triangles Two runners are racing over 100m - how much start (or handicap) is needed to make the race a 'fair' one? Distance, Time, Speed, Ratio 173, 81,193 Lap Times Ratios, Travel graphs, Similar triangles Two friends are running round a track at different speeds - how often do they pass each other? Distance, Time, Speed, Ratio 175 Die Hard Graphs, Sequencing The old Jugs problem, with a 'graphical' hint Coordinates, Graph, Sequence