Algebra is a core part of GCSE Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.
Key concepts
ExpandingMultiplying out the brackets in an expression
FactorisingThe reverse of expanding — putting brackets back
Single bracketOne bracket like 3(x + 4) to multiply out
Double bracketTwo brackets multiplied, like (x+2)(x+3)
Common factorA number or letter that divides every term
FOILFirst, Outer, Inner, Last — order for double brackets
Linear equationAn equation where the highest power of x is 1
Simultaneous equationsTwo equations solved together for two unknowns
EliminationAdding or subtracting equations to remove a variable
Substitution methodPutting one equation into the other to solve
Forming an equationTurning a worded problem into algebra
Balance methodDoing the same operation to both sides
VariableA letter standing for an unknown number
ExpressionNumbers and letters combined, with no equals sign
Common mistakes to avoid
Questions where students often pick the tempting wrong answer — make sure you know the right one:
Fully factorise 6x + 9.✗ 3(2x + 9), by only dividing the first term by the common factor. ✓ 3(2x + 3) — take out the common factor 3.
Expand 3 - (x - 4).✗ 3 - x - 4 = -1 - x, by only applying the minus to the first term inside. ✓ 7 - x — the minus sign outside the bracket changes the sign of every term inside (3 - x + 4).
When solving 3x = 12, what do you do to both sides?✗ Subtract 3 from both sides because 3 was multiplying x. ✓ Divide both sides by 3 to get x = 4.
What is the value of x^0 (for x not equal to zero)?✗ x^0 equals 0 because raising something to the zero gives nothing. ✓ 1 — any non-zero number to the power of zero equals 1.
What does x^(1/2) mean?✗ x^(1/2) means x divided by 2 — half of x. ✓ The square root of x (the positive root when x is positive).
Practise Algebra — free games
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