Mathematics Advanced Reference Sheet (NSW)

The formula for simple interest is on the Reference Sheet.

• True

• False

There are two versions of the formula for finding the arc length given on the Reference Sheet.

• True

• False

The formula $A=4\pi r^2$  is given on the Reference Sheet. This formula is for finding:

• The surface area of a hemi-sphere.

• The surface area of a sphere.

• The surface area of a pyramid.

• The surface area of a cylinder.

Which of the following formulae are not given on the Reference Sheet?

(multiple answers!)

•  $\left(x-h\right)^2+\left(y-k\right)^2=r^2$  

•  $y-y_1=m\left(x-x_1\right)$  

•  $\tan A=\frac{\sin A}{\cos A}$  

•  $FV=PV\left(1+r\right)^n$  

Which of these formulae IS given on the Reference Sheet.

• $\cos\left(90\degree-x\right)=\sin x$

• $\cos^2x+\sin^2x=1$

• $\tan^2x+1=\sec^2x$

• $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Approximately what percentage of scores have z-scores between −2 and 2?

(a)  

Which of these is given on the Reference Sheet?

• $y=e^x$ $\frac{dy}{dx}=e^x$

• $y=e^{ax}+b$ $\frac{dy}{dx}=ae^{ax+b}$

• $y=e^{f\left(x\right)}$ $\frac{dy}{dx}=f'\left(x\right)e^{f\left(x\right)}$

Which trigonometric ratio does not have its integral explicitly stated on the Reference Sheet.

• $\sin x$

• $\cos x$

• $\tan x$

• $\sec^2x$

 $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}$  is the

• chain rule

• product rule

• quotient rule

• 30 cm rule

If  $y=\frac{u}{v}$  then

•  $\frac{dy}{dx}=\frac{u\frac{dv}{dx}-v\frac{du}{dx}}{v^2}$  

•  $\frac{dy}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$