📄 Maths Cheat Sheet – Page 1 (Equations & Linear Relationships)

🟦 Equations

• 1-step:

  X+to=b⇒x=b-to,tox=b⇒x=b/tox + a = b \Rightarrow x = ba, \quad ax = b \Rightarrow x = b/ax+to=b⇒x=b-to ,to x=b⇒x=b / a

• 2-step:

  Tox+b=c⇒x=(c-b)/toax + b = c \Rightarrow x = (cb)/ato x+b=c⇒x=( c-b ) / a

• Brackets:

  • Expand:to(b+c)=tob+toca(b+c) = ab + aca ( b+c )=ab+a c

  • Factorise:tob+toc=to(b+c)ab + ac = a(b+c)ab+a c=a ( b+c )

• Fractions: Clear denominators first

• Check: Substitute back

Worked Example (Rectangle):

• l=w+3, P=14l = w+3, \, P=14l=w+3 ,P=14

2((w+3)+w)=14⇒4w+6=14⇒w=2⇒l=52((w+3)+w)=14 \Rightarrow 4w+6=14 \Rightarrow w=2 \Rightarrow l=52 (( w+3 )+w )=14⇒4 w+6=14⇒w=2⇒l=5

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🟩 Linear Relationships

• Equation of a line: and=mx+cy=mx+cand=m x+c

  • m=m =m= gradient (slope = rise ÷ run)

  • c=c =c= y-intercept (where line crosses y-axis)

• Gradient formula:

M=and2-and1x2-x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2-x1and2-and1​

• Slope meaning:

  • Positive → line rises ↑

  • Negative → line falls ↓

  • Zero → horizontal —

  • Undefined → vertical |

• How to find slope: rise/run between 2 points

• How to find y-intercept: putx=0x=0x=0 OR substitute a point intoand=mx+cy=mx+cand=m x+c

• Distance formula: (x2-x1)2+(and2-and1)2\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}( x2-x1)2+( and2-and1)2​

• Midpoint formula: (x1+x22,and1+and22)\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)(2x1+ x2​,2and1+ and2​)

• Parallel lines: same slope

• Perpendicular lines: slopes × = −1

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🟩 Cartesian Plane Tips

• Axes: x horizontal, y vertical, origin (0,0)

• Quadrants: I(+,+), II(−,+), III(−,−), IV(+,-)

• Plot line: start at y-int (0,c), use slope, draw line

• Tips: label points, use ruler, check coordinates

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📄 Maths Cheat Sheet – Page 2 (Geometric Figures & Angles)

🟥 Geometric Figures

Congruence & Similarity

• Congruent = same shape & size

• Triangle congruence: SSS, SAS, AAS, RHS

• Triangle similarity: AAA

Triangles:

• Angles sum = 180°

• Exterior angle = sum of opposite interior angles

• Types:

  • Isosceles → 2 sides & angles equal

  • Equilateral → all sides & angles 60°

  • Right → Pythagoras:to2+b2=c2a^2+b^2=c^2to2+b2=c2

Quadrilaterals (angles sum = 360°):

• Parallelogram → opp sides // & =, opp angles =

• Rectangle → 4 right angles, opp sides =

• Rhombus → all sides =, diagonals ⟂

• Square → rectangle + rhombus

• Trapezium → 1 pair of parallel sides

Circles:

• Angle in semicircle = 90°

• Angle at center = 2 × angle at circumference

• Tangent ⟂ radius

Transformations:

• Rotation = turn around a point

• Translation = slide

• Reflection = flip over a line

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🔺 Z, F, T Angles

• Z-angle (alternate angles) → equal, opposite sides of transversal

• F-angle (corresponding angles) → equal, same relative position

• T-angle (co-interior) → sum = 180°

How to solve:

1. Z → set alternate angles equal → solve

2. F → set corresponding angles equal → solve

3. T → sum of co-interior angles = 180° → solve