Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$. Solution involves the inverse trigonometric function $\arcsin$.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

No description given

No description given

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

No description given

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

No description given

No description given

No description given

Differentiate $ (a+bx) ^ {m} \sin(nx)$

More work on differentiation with trigonometric functions

No description given

Calculate the local extrema of a function ${f(x) = e^{x/C1}(C2sin(x)-C3cos(x))}$

The graph of f(x) has to be identified.

The first derivative of f(x) has to be calculated. 

The min max points have to be identified using the graph and/or calculated using the first derivative method.  Requires solving trigonometric equation

No description given

No description given

No description given

Calculation of the length and alternative form of the parameteric representation of a curve, involving trigonometric functions.

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$. Solution involves the inverse trigonometric function $\arcsin$.

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

Differentiate $ (a+bx) ^ {m} \sin(nx)$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

No description given

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.)

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.