Study Mathematics notes on Solid Geometry, Circle Theorem for Form 1-3. Useful for revision, homework, and exam preparation in Malaysia.
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NOTES AND FORMULAE SPM MATHEMATICS
FORM 1-3 NOTES
1. SOLID GEOMETRY
(a) Area and perimeter
Triangle
\[
\begin{aligned}
A | =\frac{1}{2} \times \text { base × height } | =\frac{1}{2} b h
\end{aligned}
\]
Trapezium
\[
\begin{array}{l}
A=\frac{1}{2} \text { (sum of two }
\text { parallel sides) × height }
\quad=\frac{1}{2}(a+b) \times h
\end{array}
\]
Circle
Area $=\pi r^{2}$
Circumference $=2 \pi r$
Sector
\[
\text { Area of sector }=\frac{\theta}{360} \times
\]
Length of $\operatorname{arc}=$
\[
\frac{\theta}{360} \times 2 \pi r
\]
Cylinder
Curve surface area
\[
=2 \pi r h
\]
Sphere
Curve surface area $=$
\[
4 \pi r^{2}
\]
(b)
Cube:
\[
\mathrm{V}=x \times x \times x=x^{3}
\]
Cuboid:
\[
\begin{aligned}
\mathrm{V} | =l \times b \times h | =l b h
\end{aligned}
\]
Cylinder
\[
V=\pi r^{2} h
\]
Prism
$V=$ Area of cross section × length
Sphere
\[
V=\frac{4}{3} \pi r^{3}
\]
Pyramid
\[
\begin{array}{c}
V=\frac{1}{3} \times \text { base area × }
\text { height }
\end{array}
\]
2. CIRCLE THEOREM
Angle at the centre $=2 \times$ angle at the circumference
\[
x=2 y
\]
Angles in the same segment are equal $x=y$
Sum of opposite angles of a cyclic quadrilateral $=180^{\circ}$
\[
a+b=180^{\circ}
\]
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
\[
b=a
\]
Angle between a tangent and a radius $=90^{\circ}$
\[
\angle O P Q=90^{\circ}
\]
Angle in a semicircle
\[
\angle A C B=90^{\circ}
\]
Cone
\[
V=\frac{1}{3} \pi r^{2} h
\]
zefry@sas.edu.my
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