How did algebra develop and why do we use it?

Key questions

  1. 1

    How do we recognise and work with different types of equations and inequalities?

  2. 2

    How can we manipulate algebraic expressions involving surds, indices, and fractions?

  3. 3

    How are equations formed and what do they mean?

  4. 4

    How can algebra be used to generalise our thinking?

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Resource type Title
Many ways problem Two-way algebra
Many ways problem Which is bigger?


Resource type Title
Fluency exercise Equation Sudoku
Fluency exercise Multiple manipulations
Package of problems Index issues
Package of problems Nested surds
Problem requiring decisions Real-world problems?
Food for thought $n^5 - n$
Food for thought Comparing continued fractions
Food for thought Powerful fractions

Review questions

Title Ref
Can we factorise $(x+y)^6 - (x-y)^6$ completely? R9404
Can we find the dimensions of this rectangle? R6127
Can we find the radii of two circles given two clues? R7032
Can we fully factorise $x^4+4y^4$? R8219
Can we list all $p/q$ between $0$ and $1$ if $2 \le q \le 5$? R9354
Can we prove that, for a triangle, $4(s-b)(s-c) \le a^2$? R8056
Can we prove these bounds for this fraction involving surds? R7077
Can we prove these inequalities involving $a, b, c$ and $d$? R7865
Can we show this surd is less than $6$? R5701
Can we simplify these expressions involving indices? R8779
Can we simplify these algebraic fractions? R5364
Can we solve these equations in $x, y, z, a$ and $b$? R6155
Can we solve these simultaneous equations of degree 1 and 2? R6797
Can we solve these two equations involving $x,y,1/x$ and $1/y$? R6694
Given that $a, b > 0$, can we prove that $a/b + b/a \ge 2$? R7354
Given these power facts, can we show $z^6=cx$? R9160
How long was the walk to Glastonbury Tor? R6121
If these equations have an infinity of solutions, how are $a$ and $b$ related? R6327
If we know the area-sum and the perimeter-sum, what are the sides? R5505
When do these simultaneous equations have a positive solution? R8158
When is the inequality $x^4<8x^2+9$ satisfied? R9603
When is this product of powers an integer? R6983