Hello! This test an extra opportunity to complete some practice questions on the material we have covered so far. Your results will NOT count towards your final grade, and there is no time limit to complete the test. You can check your answers as you go along, and even try new examples of the same type. Full solutions are also available for most questions. If there are any questions you don't understand, take a photo and we can discuss it in class or at a one-to-one appointment. 

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

This question applies a rewriting rule to the student's answer and correct answer, to interpret chained inequalities $a<b<c$ and $a>b>c$ as $(a<b) \wedge (b<c)$ and $(a>b) \wedge (b>c)$ respectively.

This is a work-around until the parser interprets chained relations this way automatically.

No description given

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

Students are given a line equation in the form y=mx+b and asked to graph it.

m and b are randomised.

The question is not auto-marked, students need to "reveal answers" to see a sample graph that they can compare to their own.

This question demonstrates how to link a GeoGebra object to the answer to a part.

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 $g(x)$.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Solve for $x$: $a\cosh(x)+b\sinh(x)=c$. There are two solutions for this example.

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

Differentiate $ (ax+b)^m(cx+d)^n$ using the product rule. The answer will be of the form $(ax+b)^{m-1}(cx+d)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.

Differentiate $ x ^ m(ax+b)^n$ using the product rule. The answer will be of the form $x^{m-1}(ax+b)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.

Differentiate $ x ^m \sqrt{a x+b}$.
The answer is in the form $\displaystyle \frac{x^{m-1}g(x)}{2\sqrt{ax+b}}$
for a polynomial $g(x)$. Find $g(x)$.

Finding areas under graphs using definite integration.

Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

Elementary examples of multiplication and powers of complex numbers. Four parts.

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

First part: Express  $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d},\;a=-c$. Numerator is an integer.

Second part: $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d}+ \frac{r}{sx+t}$ as single fraction