Have you always been fighting to understand mathematics or have you never got the necessary routine to carry out basic mathematical manipulations? This is your opportunity to change that. BasalMat is a free study activity you should consider, if you are determined to improve your basic mathematical skills that are required by the mathematical courses on your first year of study.
Maybe you are in doubt whether the activity is aimed at you. To find out, you can take this test, which you should be able to complete without the use of any aids and only with a few or no mistakes. The answers can be found here. If you had more than a couple of mistakes, or used more than two hours to complete the test, and are you determined to work with your basic mathematical skills, then you should consider following the BasalMat free study activity. If you need another test, you can find one here. It is a bit more difficult and without answers.
BasalMat is planed so that students with both A and B level from high school can attend. The activity consists of 7 lectures of which 5 are common for the two levels and 2 are split into an A and a B level. In Aalborg, BasalMat is in Danish while it is in English in both Esbjerg and Copenhagen. A part of the material used in Aalborg is also in English.
This course is to be passed by active participation. Active participation means that you max may be absent from one of the seven lectures.
Lecture  Topic  Content  Objective 

1  Calculations with numbers  Introduction to numbersets  specially the rational and irrational numbers. Orders of operation, exponents, radicals and fractions. 

2  Reduction  The students mus learn to reduce expressions with one or more unknown. Also recuctions that include taking the square of a binomial or factorization is included. 

3  Solving equations  Solving linear and quadratic equations. 

4  Functions  Functions and inverse functions 

5A  Differential og integral calculus  Rules for differentiation og integration 

5B  Differential calculus  Rules for finding derivatives 

6A  Differential equations  Solution of linear differential equations 

6B  Integral calculus  Rules for integration 

7  Problem solving  Problem solving 

Press "Lecture 1" to see the materials for lecture 1, and similar for the other lectures.
Topic 
Khan Academy 
Khan Academy exercises 
Webmatematik (Danish) 
Defining derivatives 
slopeofalinesecanttoacurve calculusderivatives1newhdversion derivativeintuitionmodule 
derivative_intuition  differenskvotientogdifferentialkvotient 
Derivatives 
powerrule derivativepropertiesandpolynomialderivatives derivativesofsinxcosxtanxexandlnx 
power_rule special_derivatives 
aflededefunktioner regnereglerfordifferentialkvotienter 
Area calculations  areabetweenacurveandanaxis 
bestemtintegralogareal arealmellemtofunktioner 

Optimization 
minimizingsumofsquares minimizingthecostofastoragecontainer 
optimization  optimering 
Topic 
Khan Academy 
Khan Academy exercises 
Webmatematik (Danish) 
Introduction to differential equations 
differentialequationintroduction findingparticularlinearsolutiontodifferentialequation 
hvaderdifferentialligninger goreprove 

Separable differential equations 
separabledifferentialequationsintroduction particularsolutiontodifferentialequationexample 
losningertildifferentialligninger eksponentielvakst inhomogenelineareforsteordensdifferentialligninger separationafvariable 

Modeling  newtonslawofcooling 
Topic 
Khan Academy 
Khan Academy exercises 
Webmatematik (Danish) 
Rules of integration and indefinite integrals 
antiderivativesandindefiniteintegrals indefiniteintegralsofxraisedtoapower antiderivativeofhairierexpression basictrigandexponentialantiderivatives 
antiderivatives indefiniteintegrals 
stamfunktion ubestemtintegral integreredefunktioner regnereglerforintegraler 
Definite integrals and area determination 
areaunderratenetchange simpleriemannapproximationusingrectangles riemannsumsandintegrals connectingthefirstandsecondfundamentaltheoremsofcalculus definiteintegralsandnegativearea integratingfunctionsums 
areaunderaratefunctionequalsnetchange areabetweenacurveandanaxis evaluatingdefiniteintegrals propertiesofintegrals 
bestemtintegralogareal arealmellemtofunktioner 
Press "Lecture 1" to see the exercises for lecture 1, and similar for the other lectures.
Exercise 5. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 5. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 7. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 6. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 6. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 4. A $300$ m long fence must enclose a rectangular area. Determine the lenght of the sides in the rectangle, so that the area is as large as possible.
Exercise 5. A $300$ m long fence must enclose a rectangular area. One side is along a river, so the fence is only needed on three sides. Determine the lenght of the sides in the rectangle, so that the area is as large as possible.
Exercise 6.An open box must have a quadratic bottom and a volume of $5000 cm^3$. Determine the side length of the bottom of the box and the height, so that the surface area is as small as possible.
Exercise 7.A rectangle is inscribed into a halfcircle with radius 12 m. Determine the length and width of the rectangle, so its area is as large as possible.
Exercise 8. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 5. Find the constants $a$ and $b$ so the function $f(x)=ax+b$ is a solution for the differential equation $y'y=2x3$.
Exercise 6. Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.
Exercise 6: Calculate the area bounded by the graph of the function $f(x)=9x^2$ and the first coordinate axis.
Exercise 7: Calculate the area bounded by the graphs of the functions $$f(x)=\frac{1}{4}x^2  2\quad \mbox{ and } \quad g(x)=x+1.$$
Exercise 8: Get together with another student that has finished the above exercises. Make $2 \times 5$ exercises of the same type as above and solve the exercises made by the other student. You have to be able to solve your own exercises, so you can give a hint to the other student if he/she cannot solve your exercises.