 Course offering missing for current semester as well as for previous and coming semesters

## Content and learning outcomes

### Course contents

Part of course: Exam 1

• Numbers and numerical calculations, formulas, units.
• Plan and space geometry, trigonometry of right triangles.
• Algebra: Polynomials, rational expressions, solving equations, linear inequalities.
• Functions of: Linear functions, linear equations, polynomial functions, exponential and power functions, scientific notation and logarithms. Solving equations

Part of course: Exam 2

• Changes in speeds and derivatives, chain rule (introduction). Curves and derivatives, extreme values, maximum and minimum value.
• Arithmetical and geometrical sequences and sums

### Intended learning outcomes

OVERALL GOALS
The student will be given a basic understanding of and skills in mathematics, needed to be able to understand the mathematics courses, as part of the college and engineering programs.

Part of course: Exam 1

The student will after the course to:

• deal with numerical calculations with real numbers, written in different ways
• manage formulas
• calculate the correct devices enter perimeter and area for a few simple areas and areas and volumes of some simple cells
• using key rates and know the concepts of classical geometry
• apply trigonometry in right triangles
• simplify and transform algebraic polynomial expressions
• solve equations of the first and second degree, linear inequalities, root equations and also polynomial equations of higher degree by factoring or by substitution
• simplify and use rational expressions and solve equations containing rational expressions
• interpret and use the powers and logarithms with real exponents, and master the relevant laws such as counting the solution of equations
• explain the characteristics of linear and some non-linear functions
• work with linear equations in different forms, solve systems of equations using algebraic methods, and interpret the solution from the graphical view
• determine the maximum and minimum points by using the symmetry of the quadratic function
• set up, interpret, and illustrate linear functions, power functions and exponential functions as models of real events in different areas
• use their skills in problem solving and in their study subjects

Part of course: Exam 2

The student will after the course to:

• explain, illustrate, use and interpret the concept of changing coefficients and derivatives of a function and use these to describe the characteristics of a function and its graph
• derive and use the rules of differentiation for some basic power functions, exponential functions and use the chain rule
• describe why and how the number e is introduced
• to draw conclusions about a function's derivative and estimate the value of the derivative when the function is given by its graph
• use the relationship between a function's graph and its derivatives in different application contexts
• use mathematical models of various kinds, including those based on arithmetic and geometrical progressions

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Basic qualifications for university studies and Mathematics B from high school or equivalent.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Natur o Kultur
Ma4000 CD ISBN 978-91-27-41704-5
Formler och tabeller ISBN 978-91-27-72279-8

Konvergenta
Matematik-1000 övningsuppgifter i matematik på gymnasienivå kurs C, D och E. ISBN: 9197370800

## Examination and completion

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

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 6,0 fup, betygsskala: A, B, C, D, E, FX, F
• TEN2 - Examination, 6,0 fup, betygsskala: A, B, C, D, E, FX, 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.

When the written test is given bonus points can be counted, but only at the regular exam.

### Other requirements for final grade

The final score is calculated as described in course-PM is based on all parts.
Written exam

Required reports, oral and / or in writing, of the selected data continuously during the course.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Examiner Per Ahlén

### Ethical approach

• 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.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web ML0012

### Offered by

ITM/Sustainable Production Development

### Main field of study

No information inserted

### Education cycle

Pre-university level