Math Revision

Trigonometry

100

Recall the 3 Trigonometric Ratios

SOH - Sin = Opposite / Hypotenuse

CAH - Cos = Adjacent / Hypotenuse

TOA - Tan = Opposite / Adjacent

200

TRUE/FALSE: You can use the SINE rule for right angled triangles

False

300

State the COSINE rule for finding sides

c² = a² + b² - 2ab cosC

400

Convert 240^o into its simplest radian form

4pi / 3

500

A non-right angled triangle is shown with one side 3cm and another side 4cm. The angle between the two sides is 135^o. Find the area of this triangle corrected to 2 decimal places

4.24cm²

Functions

100

If variables x and y are in indirect proportion and k is the constant of proportionality, then the equation is written as…

y = k/x

200

Solve |2x – 1| = 3

x = 2 and x = -1

300

State the co-ordinates and the radius of (x–2)² + (y+3)² = 16

Co-ordinates = (2, -3)

Radius = 4

400

Find the composite function f(g(x)) given: f(x) = x² and g(x) = x² + 4

x⁴+8x²+16

500

Sketch (x+2)³

man idk

Calculus

100

State the gradient-intercept formula

y=mx+b

200

State the first principle formula

f’(x)=lim as h>0 f(x+h) - f(x) / h

300

Differentiate: y = (2x²-3x+1)⁴

y’ = (16x-12)(2x²-3x+1)³

OR

y’ = (4x-3) x 4(2x²-3x+1)³

400

Derive: (sqrtx + x)⁴, and find f’(3)

f’(x) = (1/2x^-1/2 + 1) x 4(x^1/2 + x)³

f’(3) = 546.20

500

Find the equation of the tangent to the curve f(x) = x² + 1 at (-1, 1) and find the equation of the normal at the same point

Tangent: y=-2x-1

Normal: y=1/2x + 1/2