Algebra Problems Year 9
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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 
1^{3}
+ 2^{3} + 3^{3} ... from a really simple diagram 
Formulae,
T_{n}, 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 nastylooking, 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 nonlinear 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 nonlinear sequences 
Exploring
the morecomplex 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
foldonitself 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 
Coordinates,
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 



































