Test whether a student knows the monotonic sequence theorem.

Integration by susbtitution, no hint given

First test

No description given

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Test di ingresso su geometria analitica (retta e parabola) e disequazioni

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

This question tests learner's knowledge of the inverse matrix method for a 2x2 matrix.

This question tests students knowledge of basic matrix arithmetic.

No description given

No description given

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

No description given

This question tests a student's ability to raise a negative base to a negative exponent.

This question tests a student's ability to raise 1 to a negative exponent.

This question tests a student's ability to raise a positive base to a negative exponent and then take the negative. The base and the exponent have the same absolute value.

This question tests a student's ability to raise a positive base to a negative exponent and then take the negative.

This question tests a student's ability to raise a positive base to a negative exponent.

This question tests a student's ability to raise a negative base to an exponent of -1.

This question tests a student's ability to raise a positive base to an exponent of -1.

This question tests a student's ability to divide one fraction by another (at least one of the numerators will be negative).

This question tests a student's ability to divide one fraction by another.

This question tests a student's ability to multiply two fractions. Some of the numerators or denominators will be negative.

This question tests a student's ability to multiply two fractions.

This question tests a student's ability subtract one fraction from another with different denominators (at least one of them is negative).

This question tests a student's ability to subtract one fraction from another with different denominators.

This question tests a student's ability to add two fractions with different denominators (at least one of them is negative).