One-way ANOVA example

Students are given the equations of two lines in the form y=mx+b and asked if they are parallel.

The line equations are randomised.

The answer is yes or no. There is a 1 in 6 chance of the lines being parallel.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Students are shown an exponential function formula and asked to identify the correct graph, given an exponential, a hyperbola, a parabola and a line.

Students are shown an exponential graph and asked to choose the correct formula for the graph.

Students are given a formula for compound interest and asked to evaluate it for given initial investment values.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

Solving a quadratic equation of the form $ax^2+bx+c=0$.

Given random graph of cirlce, write locus in complex form. centre in 1st quadrant

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Paired t-test to see if there is a difference between times taken to complete a task.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown an infographic, and need to calculate a percentage from the information supplied. There are 7 different versions of this question.

Made for my TALMO talk. This demonstrates how you can use a part with no marks as an oracle to perform calculations, to help the student check their working.

Questions shown in my presentation for the Teaching And Learning Mathematics Online session, 16th November 2022.

Omvormen van formules

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

Calculating a section of a sector of a circle when given the arc length and angle of the sector of the circle. This question requires the use of the formulas to find the area of a sector of a circle and to find the area of a triangle. 

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\cos(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\cos(\theta)-B\sin(\theta)$ to $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\sin(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $af(x)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $af(x)$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $af(x)$.