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
Simpsons 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 isn�t 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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