SF0001 Introductory Course in Mathematics 5.0 credits

1. Numeric calculations
   Different types of calculations, fractions, exponentiation
2. Algebra
   Algebraic expressions, linear expressions, quadratic expressions
3. Roots and logarithms
   Roots, root equations, logarithms, logarithm equations
4. Trigonometry
   Angles and circles, trigonometric functions, trigonometric relationships, trigonometric equations
5. Written account and communication
   How to write about math, individual assignments

The course, which is a bridge between high school and higher education, consists of four main parts and hand in assignments. The sections go through some of the basic knowledge important to have fully updated for upcoming higher education studies. The course is web based and flexible, i.e. the student studies in a pace that suits him or her best.

After the course the student should be able to;

• Decide which one of two logarithmic xpressions is bigger based on a comparison of base/argument
• Simplify algebraic expressions and process these with the rules of squares
• Solve algebraic equations which after simplification or by using logarithms lead to first degree equations
• Solve second degree equations by completing the square and know how to check the solution
• Factorize second degree expressions and know how to solve factorized or almost factorized second degree equations
• Decide on the smallest/largest value a second degree expression can take
• Solve simple root equations by the use of squares and know why the solution has to be proven
• Convert between the formulas y=kx+m and ax+by+c=0
• Sketch straight lines from the equation
• Solve geometric problems that contain straight lines
• Sketch the graph for second degree functions with the help of completing the square
• Sketch areas that are given by linear differences and decide the area of these
• Formulate and use the Pythagorean theorem
• State the values of cos, sin and tan for the standard angles 0°, 30°, 45°, 60° and 90° by heart
• Solve trigonometric problems that involve orthogonal triangles
• Convert degrees, radians and circuits and be aware of the terms unit circle, tangent, radius, diameter, periphery, chord and arc
• Decide the values of sin, cos and tan for arguments that can be reduced to the default angles I one of the squares
• Sketch the graph for cos, sin and tan
• Calculate the area and circumference of circular sectors
• Calculate the distance between two points of a plane
• Sketch circles by completing the square in their equations
• Solve geometrical problems with the help of the law of Area, the law of Sinus and the law of Cosine
• Derive trigonometric relationships from symmetry in the unit circle
• Simplify trigonometric expressions with the help of the trigonometric relationships
• Solve trigonometric base equations
• Solve trigonometric equations that can be transformed back into trigonometric base equations.

General requirements: Completed upper secondary education including documented proficiency in Swedish corresponding to Swedish 3/Swedish B  and English corresponding to English 6/English A.

Specific requirements: Knowledge of Mathematics corresponding to Mathematics 3B/C.

The course material will be published on the internet and is freely accessible for course participants.

If the course is discontinued, students may request to be examined during the following two academic years.

• INL1 - Assignment, 5.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The last day to submit assigments is the day before the start of the fall semester at KTH and the last day to supplement submitted assignments is two weeks after that date. 

All computer tests and assignments passed.

Tommy Ekola

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

This course has been closed since spring 2018
The course will be available in the future as a MOOC (mass open open course).More info can be found on summermat.se.

Those who have completed or been registered to the course SF1651 will not be admitted to this course since both courses have the same content and level.

The course is part of a collaboration between a number of Swedish universities and colleges in the joint project sommarmatte.se. You should therefore not apply for this course if you already are admitted to or have completed any of the courses: MA101A at HS Gävle, MA0014 at HS Dalarna, ETE500 at Linköping University.