Using the chain rule within product rule problems

Identifying the correct rule to use

An introduction to using the quotient rule

Identifying the correct rule to use

Identifying the correct rule to use

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Quotient and remainder, polynomial division.

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Identifying the correct rule to use

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

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A simultaneous equations question with integers only

This is a test only

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

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ratio test question

Oefeningen:

BASIS: Maak een extra "part" aan, waar om het product van de twee breuken gevraagd wordt.

BASIS: Zoek uit waar typische_fout voor dient (bij de variabelen) en hoe die typische fout dan effectief gesignaleerd wordt.

GEMIDDELD: Zorg dat geen/enkel (jouw keuze) noemers voorkomen die geen gemeenschappelijke deler hebben. (Hint: gcd(a,b) kan een hulp zijn, met een for-loop.)

1) Voer de vraag zelf uit als leerling

2) Randomiseer deze vraag. Vervang de concrete getalletjes door willekeurig getrokken variabelen, maar zorg dat de vraagstelling en modeloplossing nog mooi eruit zien.

3) Controleer of de willekeurige getallen altijd even moeilijk zijn, of de randomisatie soms significant moeilijker is. Indien ze moeilijker is, beperk die gevallen bij Variable Testing.

Quadratic factorisation that does not rely upon pattern matching.

One could also use the pattern matching syntax to check automatically; this is programatically harder.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Question requires students to determine if the smallest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the smallest angle and to know that smallest angle is oppositeshortest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Question requires students to determine if the largest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the largest angle and to know that largest angle is opposite longest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

A simple test of definitions, properties and transform tables. Useful for retrieval practice.

Shows different ways to load a geogebra applet.