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. 

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Original: https://numbas.mathcentre.ac.uk/question/11698/equation-of-a-straight-line/ by Newcastle University Mathematics and Statistics,

translated to German, added Parts b), c), d), e)

This is a set of questions for students to practice identifying parabolas, hyperbolas and exponentials.

There are also a few questions asking students to draw graphs, and to evaluate the curves at specific points.

10 questions are selected from a larger pool. 

In the first question students are asked to identify the type of a graph.

In the second question students are asked to identify the type of an equation.

Then next 6 questions are basic questions about evaluating points on a curve or matching curves and equations.

The last 2 questions are applications - e.g. compound interest, displayed as an equation, a table or a graph.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.

The line parameters and the given point are randomised.

Students are shown a graph and, in the context of a word problem, are asked to find the gradient and the y-intercept, to read points from the graph, and to identify the correct equation for the graph.

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.

Find the stationary points of a cubic which has 2 turning points.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Divide $ f(x)=x ^ 4 + ax ^ 3 + bx^2 + cx+d$ by $g(x)=x^2+p $ so that:
$\displaystyle \frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}$

Find a regression equation.

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

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

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

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Find $g(x)$.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

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

Differentiate

\[ \sqrt{a x^m+b})\]

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.