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Explore: Maths in the Real World

All questions are real maths problems set in Sport, Science and Art contexts — difficulty matched to your grade!

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Study Notes & Materials

Key concepts, formulas and examples for every topic. Select a grade and click Load.

Showing Grade 7 notes. Select a different grade and click Load Materials for other grades (requires JavaScript on Cloudflare Pages).

x=
Algebra Basics
Algebra uses pronumerals (letters) to represent unknown numbers. Solve equations using inverse operations.
Key Facts
x+5=12 → x=12-5=7 (inverse operations)
3x+2x=5x (like terms: add coefficients)
2(x+3)=2x+6 (expand: multiply each term)
y=3x+1, x=4 → y=3(4)+1=13 (substitute)
Worked Examples
Solve 2x=14 → x=7
Simplify 4a+3b-2a = 2a+3b
Expand 3(2x-5) = 6x-15
If y=2x-1 and x=5, y=9
/
Linear Patterns
A linear pattern increases/decreases by a constant amount each step (common difference d).
Key Facts
nth term: T(n) = a + (n-1)d
a = first term, d = common difference
Positive d = increasing, Negative d = decreasing
Graph of linear pattern = straight line
Worked Examples
3,7,11,15: d=4, T(n)=4n-1
20,15,10,5: d=-5, T(n)=25-5n
10th term of 2,5,8: T(10)=2+9×3=29
100th term of 3,7,11: T(100)=3+99×4=399
ang
Angles
Angles measure the turn between two lines. Key angle rules apply at intersections and in triangles.
Key Facts
Acute < 90°, Right = 90°, Obtuse 90°-180°
Straight angle = 180°, Reflex > 180°
Angles in triangle add to 180°
Angles on a straight line add to 180°
Vertically opposite angles are equal
Worked Examples
Triangle: 50°+70°+?=180° → ?=60°
Supplementary: 120°+?=180° → ?=60°
Complementary: 35°+?=90° → ?=55°
Co-interior angles: add to 180°

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