number
Natural numbers: all rational and irrational numbers
Integer: whole number
Prime number: divisible by itself. 1 is not prime number
Rational number: can be written as fraction
Irrational number: cannot be written as fraction
Integer: whole number
Prime number: divisible by itself. 1 is not prime number
Rational number: can be written as fraction
Irrational number: cannot be written as fraction
HCF and LCM: solve by branching or Venn diagram
Sets
Ratio and Proportion
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\[Direct:y=kx\]
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\[Indirect:y=\frac{k}{x}\]
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Percentages
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\[Simple\: interest:I=\frac{PRT}{100}\]
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\[Compound\: interest:A=P(1+\frac{R}{100})^{n}\]
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algebra and graphs
\[Quadratic\: formula:x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\]
Sequences
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\[Linear:a+(n-1)d\]
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\[Quadratic:an^{2}+bn+c\]
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coordinate geometry
\[Equation: y=mx+c;\: y-y_{1}=m(x-x_{1})\]
\[Gradient: m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
\[mid\: point=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\]
\[distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]
geometry
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Similarity
AAA length same ratio |
Congruency
RHS, SAS, ASA |
Rectangle: opposite sides parallel equal, all angles 90, diagonals bisect each other
Parallelogram: opposite sides parallel equal, opposite angles equal, diagonals bisect each other
Trapezium: one pair sides parallel
Kite: adjacent side equal, diagonals perpendicular to each other
Polygons
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\[Exterior\: angles=\frac{360}{n}\]
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\[Interior\: angles=\frac{180(n-2)}{n}\]
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mensuration
Area
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\[Triangle=\frac{1}{2}b\times h\]
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\[Parallelogram=b\times h\]
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\[Trapezium=\frac{1}{2}(a+b)\times h\]
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\[Area\: Circle=\pi r^{2}\]
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\[Circumference\: Circle=2\pi r\]
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Volume and Surface Area
\[Cylinder:V=\pi r^{2}h;\: SA=2\pi rh+2\pi r^{2}\]
\[Cone:V=\frac{1}{3}\pi r^{2}h;\: SA=\pi rl+\pi r^{2}\]
\[Sphere:V=\frac{4}{3}\pi r^{3};\: SA=4\pi r^{2}\]
trigonometry
\[Pythagoras\: theorem:a^{2}+b^{2}=c^{2}\]
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\[sinx=\frac{opposite}{hypotenuse}\]
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\[cosx=\frac{adjacent}{hypotenuse}\]
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\[tanx=\frac{opposite}{adjacent}\]
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\[Sine\: rule:\frac{a}{sina}=\frac{b}{sinb}=\frac{c}{sinc}\]
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\[Cosine\: rule:a^{2}=b^{2}+c^{2}-2bc\: cosa\]
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\[Area\: of\: triangle=\frac{1}{2}absinc\]
vectors and transformation
\[Parallel\: vector:k\binom{a}{b}is\: parallel\: to\binom{a}{b}\]
\[Magnitude\: of\: vector:|x|=\sqrt{a^{2}+b^{2}}\]
Transformation
Reflection: require equation of mirror line
Rotation: require centre of rotation (draw lines of same length from a guessed point to a similar point on object and image)
angle (measure the angle)
rotation (clockwise or anticlockwise)
Translation: give the translation vector
Rotation: require centre of rotation (draw lines of same length from a guessed point to a similar point on object and image)
angle (measure the angle)
rotation (clockwise or anticlockwise)
Translation: give the translation vector
\[\binom{x}{y}\]
Enlargement: state scale factor K and centre of enlargement
\[Scale\: factor\: K=\frac{image}{object}\]
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\[K<0:object\: image\: opposite\: side\: of\: centre\]
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\[K>0:object\: image\: same\: side\: of\: centre\]
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probability
\[Probability=\frac{event\: possible\: outcomes}{total\: outcomes}\]
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\[OR\: Rule:P(A\: or\: B)=P(A)+P(B)\]
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\[AND\: Rule:P(A\: and\: B)=P(A)\times P(B)\]
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Condition probability
\[P(A|B)\: is\: A\: given\: B=\frac{P(A\cap B)}{P(B)}\]
statistics
Histogram
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\[Class\: width=Interval\]
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\[Frequency\: density=Height\]
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\[Frequency=Class\: width\times Frequency\: density\]
\[Position\: of\: median=\frac{n+1}{2}\]
