Ylioppilastutkinto (Finnish Matriculation) · Mathematics

Algebra, Functions, Calculus and Probability

37 practice questions, each with the answer and an explanation.

Practise Algebra, Functions, Calculus and Probability now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 37 questions

Solve $5 x + 3 = 2 x + 18$ .
Differentiate $f (x) = 3 x^{2} - 5 x + 1$ .
What is $lo g_{3} 81$ ?
What is the distance between the points $(1, 2)$ and $(4, 6)$ ?
A triangle has base 10 and height 6. What is its area?
Solve $x^{2} = 49$ .
Find $\int 4 x^{3} d x$ .
What is the equation of the line through $(2, 5)$ with slope $- 3$ ?
Differentiate $f (x) = ln (2 x + 1)$ .
Evaluate $\int_{1}^{e} \frac{1}{x} d x$ .
Solve $sin x = \frac{1}{2}$ for $0 \leq x \leq 2 π$ .
What is the unit vector in the direction of $v = (3, 4)$ ?
An arithmetic sequence has $a_{3} = 7$ and $a_{8} = 22$ . What is $a_{20}$ ?
Three of 10 tickets are winning tickets. Two tickets are drawn without replacement. What is the probability that neither wins?
A game pays 6 euros with probability $\frac{1}{6}$ and costs 1 euro otherwise. What is the expected gain per game?
Factor $x^{3} - 4 x$ completely.
Solve $e^{2 x} = 5$ .
Every value in a data set is increased by 10. What happens to the mean and the standard deviation?
What are the centre and radius of the circle $x^{2} + y^{2} - 6 x + 4 y - 12 = 0$ ?
1000 euros is invested at 4% annual interest, compounded yearly. What is the value after 3 years?
Find $lim_{x \to 0} \frac{s i n 3 x}{x}$ .
Solve the inequality $∣2 x - 3∣ < 5$ .
What is the coefficient of $x^{2}$ in the expansion of $(1 + 2 x)^{5}$ ?
For $f (x) = x^{3} - 3 x^{2}$ , on which interval is $f$ decreasing?
From a point 60 m from the foot of a tower, the angle of elevation of its top is $3 0^{\circ}$ . How tall is the tower?
A box without a lid is made from a $12 \times 12$ sheet by cutting a square of side $x$ from each corner and folding up the sides. What is the largest possible volume?
What is the area of the region between $y = 4 - x^{2}$ and $y = x + 2$ ?
The region under $y = x$ for $0 \leq x \leq 4$ is rotated about the $x$ -axis. What is the volume?
One person in 100 has a condition. A test is positive for 95% of those who have it and for 5% of those who do not. A person tests positive. About how likely is the person to have the condition?
What is the local maximum value of $f (x) = x^{2} e^{- x}$ ?
Find $\int x e^{x} d x$ .
A sequence has $a_{1} = 2$ and $a_{n + 1} = 3 a_{n} - 1$ . What is $a_{4}$ ?
What is $\sum_{k = 1}^{\infty} 0. 6^{k}$ ?
Which tangent lines to $y = x^{2}$ pass through the point $(0, - 4)$ ?
Solve $2 cos^{2} x - cos x - 1 = 0$ for $0 \leq x < 2 π$ .
What is the area of the triangle with vertices $(0, 0)$ , $(4, 1)$ and $(2, 5)$ ?
How many different arrangements are there of the letters of the word FINNISH?

Keep practising

More Ylioppilastutkinto (Finnish Matriculation) topics

Advanced Calculus, Vectors, Geometry and Probability43 questions
General Mathematics: Algebra, Functions, Geometry and Financial Math43 questions
Finnish Literature, Textual Analysis, and Language Structure42 questions
Finnish History: From the Middle Ages to the Modern Era42 questions
Language, Epic and Modern Literature36 questions
From Swedish Rule to the European Union36 questions
Funktiot, raja-arvot ja differentiaalilaskenta6 questions
Integraalilaskenta ja pinta-alat6 questions

All Ylioppilastutkinto (Finnish Matriculation) practice →

Algebra, Functions, Calculus and Probability in other exams

Algebra, Functions, Calculus and Probability for Brandos Atestatas (Lithuania)93 questions
Algebra, Functions, Calculus and Probability for Vitnemål Eksamen (Norway)79 questions
Algebra, Functions, Calculus and Probability for Stúdentspróf (Iceland)37 questions
Algebra, Functions, Calculus and Probability for Riigieksamid (Estonian State Exams)36 questions
Algebra, Functions, Calculus and Probability for CESS & Examen d'entrée (Belgium)34 questions

Ready for the full Ylioppilastutkinto (Finnish Matriculation) test?

Take a mock test Ylioppilastutkinto (Finnish Matriculation) hub