This mini-lesson covers Algebra & Graphs for Cambridge IGCSE Mathematics (0580): algebraic manipulation, equations, simultaneous & quadratic equations, inequalities, sequences, functions and graphs of functions (Extended content included).
Honest heads-up: these games test recall of methods and results, not full algebraic working. In the exam, show every line.
Answer as you go and collect โญ stars. Press Start.
Expand brackets carefully, then collect like terms. Factorise by taking out the highest common factor, or expand a double bracket with a grid / FOIL.
Sign care: (x โ 4)(x + 4) = xยฒ โ 16, a difference of two squares โ the middle terms cancel.
Do the same to both sides to keep the balance. Undo operations in reverse order (inverse of + is โ, of ร is รท).
Solve 3x + 4 = 19.
3x = 15 โ x = 5
Two equations, two unknowns. Eliminate a variable by adding or subtracting (make coefficients match), or substitute.
x + y = 10 and x โ y = 4. Add: 2x = 14 โ x = 7. Then y = 3.
Solution: x = 7, y = 3 (check: 7+3 = 10 โ)
Solve xยฒ + bx + c = 0 by factorising (find two numbers that multiply to c and add to b), or use the quadratic formula.
xยฒ โ 7x + 12 = 0 โ (x โ 3)(x โ 4) = 0 โ x = 3 or x = 4
Solve like an equation, but reverse the inequality sign whenever you multiply or divide by a negative number.
Solve 2x + 1 < 11 โ 2x < 10 โ x < 5.
Watch the flip: โx < 3 becomes x > โ3 (divide by โ1, flip the sign).
For a linear (arithmetic) sequence the nth term is dn + (a โ d), where d is the common difference and a is the first term.
5, 8, 11, 14โฆ d = 3, first term 5, so nth term = 3n + 2.
Check n = 1: 3(1) + 2 = 5 โ
Tap a sequence, then its correct nth-term rule.
A function f(x) is a rule; f(3) means substitute x = 3. The inverse fโปยน(x) undoes it. Recognise graph shapes: linear (straight), quadratic (parabola), cubic, reciprocal (y = 1/x) and exponential.
f(x) = 2x + 5. Then f(4) = 2(4) + 5 = 13.
Sort each equation by its graph shape. Tap it, then its box.
Manipulation: expand double brackets; factorise; difference of two squares.
Equations: keep the balance; simultaneous by elimination/substitution.
Quadratics: factorise or use x = [โb ยฑ โ(bยฒโ4ac)]/2a.
Inequalities: flip the sign when รท or ร by a negative.
Sequences: linear nth term dn + (a โ d).
Functions & graphs: f(x) substitution; recognise linear/quadratic/cubic/reciprocal/exponential shapes.
You've covered the Algebra & Graphs essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.
You've worked through Algebra & Graphs for Cambridge IGCSE Mathematics (0580). ๐
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