Practice Flashcards: National 5 Mathematics: geometry and trigonometry | Zestly

Question 1

Pythagoras' Theorem

Accepted Answer

For a right-angled triangle with hypotenuse $c$ and sides $a, b$: $a^2 + b^2 = c^2$. Example: $3^2 + 4^2 = 5^2$.

Question 2

Area of a triangle (trigonometry)

Accepted Answer

Area $= \frac{1}{2}ab \sin(C)$. Example: $\frac{1}{2} 	imes 4 	imes 5 	imes \sin(30^\circ) = 5$.

Question 3

Sine Rule

Accepted Answer

$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$. Example: If $a=10, A=30^\circ, B=45^\circ$, then $b = \frac{10 \sin(45^\circ)}{\sin(30^\circ)} \approx 14.1$.

Question 4

Cosine Rule (side)

Question 5

Cosine Rule (angle)

Question 6

Arc length

Question 7

Area of a sector

Question 8

Volume of a cone

Question 9

Volume of a sphere

Question 10

Volume scale factor

Question 11

Trigonometric identity

Question 12

Converse of Pythagoras