Matematik 3c
Derivatives, integrals and trigonometry: the course that starts calculus.
Matematik 3c is where calculus begins: limits, derivatives and a first look at integrals, together with polynomials and trigonometry in any triangle. In Gy25 it is called Matematik – fortsättning, nivå 1c.
Overview
For many students, 3c is the most interesting maths course in upper secondary school, because it introduces the derivative: a way of measuring how fast something changes at a single moment. With it you can find the highest and lowest points of a graph, describe motion and solve optimisation problems. The course also takes a first look at integrals, which turn the question around and add up change.
The new ideas are powerful, but most of the difficulty in 3c comes from algebra. Simplifying rational expressions, handling powers and solving equations quickly decide whether a calculus problem goes smoothly. Trigonometry in any triangle, with the sine, cosine and area rules, is a separate part of the course and often appears on the national test. Students who can explain in words what a derivative means, and not only how to calculate one, usually do well on the reasoning questions.
What you learn
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Algebra
Polynomials, rational expressions and their simplification.
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Limits and derivatives
What a derivative is, and the rules for working it out.
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Using derivatives
Rates of change, sketching graphs, and finding maximum and minimum values.
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Integrals
Antiderivatives, and integrals as areas under a curve.
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Trigonometry
The sine, cosine and area rules in any triangle.
How it's scored
Your teacher sets the grade (A–F) from everything you have shown during the course. The national test is weighed in specially, but it doesn't decide the grade on its own.
How to prepare
- Understand what a derivative means, not just the rules: many test questions ask you to explain.
- Practise without a calculator: the national test has parts where you can't use one.
- Work through old national tests that have been released, under the real time limits.
- Keep the algebra from 2c sharp: most mistakes in calculus are algebra mistakes.
Official pages
Dates, registration and fees change from year to year, so check them on the official pages.