Separable 1st order ODE with exponentials

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

Write fractions as sums of unit fractions

Questions on powers, the laws of indices, and exponential growth.

Intorduction to proof and existence statements.

Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.

Simple inequalities - finding values of x

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.

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

Zwei Läden verkaufen verschiedenfärbige Sweatshirts.

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

What is the function of the given graph?

Try to solve some simultaneous equations using matrix inverses.

Verschiedene Fragen zu Anzahlen von Teilmengen.

Questions which ask the student to intepret vector diagrams in order to write out the components in terms of base vectors. Also addition and subtraction of vectors and vector magnitude.

This question introduces base vectors i and j and asks the student to interpret a JSXGraph diagram to write four vectors in terms of the base vectors. Further parts ask the student to add vectors and find a magnitude.

This question asks the student to interpret a JSXGraph diagram to write three vectors in terms of the base vectors. Each vector has both a horizontal and vertical component. Further parts ask the student to add vectors and find a magnitude. 

Find angular speed and reaction force of a swinging pendulum.

Linear combinations of $2 \times 2$ matrices. Three examples.

Linear combinations of $2 \times 2$ matrices. Three examples.

Cofactors Determinant and inverse of a 3x3 matrix.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Integrate Paris Law equation to estimate life to failure.