Vitnemål Eksamen (Norway) · Mathematics (Vitnemål Norway)

Algebra, Functions, Calculus and Probability

79 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 79 questions

Solve the equation $5 x + 3 = 28$ .
Write $3^{2} \cdot 3^{3}$ as a single power of 3.
What is the slope of the line through the points $(1, 2)$ and $(3, 8)$ ?
Solve $x^{2} - 7 x + 12 = 0$ .
An arithmetic sequence has $a_{1} = 5$ and difference $d = 3$ . What is $a_{20}$ ?
A geometric sequence has $a_{1} = 3$ and ratio $q = 2$ . What is the sum of the first 6 terms?
Evaluate $l g 1000 + lo g_{2} 8$ .
A circle has diameter 10. What is its circumference?
What is the value of $sin 9 0^{\circ} + cos 0^{\circ}$ ?
Find the derivative of $f (x) = x^{4} - 2 x^{2}$ .
Find the derivative of $g (x) = e^{2 x}$ .
Find the derivative of $h (x) = (x^{2} + 1)^{3}$ .
Evaluate $\int_{0}^{2} (2 x + 3) d x$ .
A card is drawn at random from a standard deck of 52 cards. What is the probability that it is a heart?
Find the dot product of $a = [2, 3]$ and $b = [1, - 4]$ .
What is the length of the vector $[3, 4]$ ?
Solve $3^{x} = 81$ .
The numbers $4, 7, 7, 10, 12$ are measurements. What is their mean?
A fair coin is tossed three times. What is the probability of exactly two heads?
Solve the inequality $∣2 x - 1∣ < 5$ .
A price of 500 kroner is raised by 20 percent, and the new price is then lowered by 20 percent. What is the final price?
What is the vertex of the parabola $y = x^{2} + 6 x + 5$ ?
Solve the system $2 x + y = 7$ and $x - y = 2$ .
What is the area of a triangle with sides 5, 12 and 13?
Simplify $\frac{x ^{2} - 9}{x - 3}$ for $x \neq = 3$ .
Solve $ln x = 2$ .
A deposit of 10 000 kroner earns 5 percent interest per year, added to the account each year. How much is there after two years?
Solve $sin x = \frac{1}{2}$ for $0 \leq x \leq 2 π$ .
What is the local minimum value of $f (x) = x^{3} - 12 x$ ?
What is the sum of the infinite series $12 + 4 + \frac{4}{3} + \dots$ ?
What is the area of the region between the graphs of $y = 4$ and $y = x^{2}$ ?
Three fair dice are thrown. What is the probability of getting at least one six?
The vectors $a = [1, 2]$ and $b = [k, - 3]$ are perpendicular. What is $k$ ?
Solve $e^{2 x} - 5 e^{x} + 6 = 0$ .
A farmer has 100 m of fence and builds a rectangular pen against a long straight wall, so only three sides need fencing. What is the largest area?
What is the equation of the tangent line to $y = ln x$ at the point where $x = e$ ?
In mathematics, what is the slope of the linear function $f (x) = - \frac{3}{4} x + 5$ ?
In mathematics, what are the real roots of the quadratic equation $x^{2} - 7 x + 12 = 0$ ?
In mathematics, what is the exact value of $lo g_{10} (1000) - ln (e^{4})$ ?
In mathematics, what is the solution set of $ln (x + 2) + ln (x - 2) = ln (5)$ for $x > 2$ ?
In mathematics, what is the first derivative $f^{'} (x)$ of $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ ?
In mathematics, what is the derivative $f^{'} (x)$ of the function $f (x) = (x^{2} + 1) e^{x}$ ?
In mathematics, what is the derivative $f^{'} (x)$ of $f (x) = \frac{2 x}{x + 1}$ for $x \neq = - 1$ ?
In mathematics, what is the derivative $f^{'} (x)$ of $f (x) = ln (x^{2} + 4)$ ?
In mathematics, what is the equation of the tangent line to the curve $y = x^{2}$ at the point where $x = 3$ ?
In mathematics, what is the exact value of the definite integral $\int_{1}^{3} (3 x^{2} - 2 x) d x$ ?
In mathematics, what is the area enclosed between the parabola $y = 4 - x^{2}$ and the line $y = 0$ ?
In mathematics, if a fair six-sided die is rolled 5 times, what is the probability of obtaining exactly two sixes?
In mathematics, in how many distinct ways can a committee of 3 students be chosen from a group of 8 candidates?
In mathematics, given $P (A) = 0.4$ , $P (B) = 0.5$ , and $P (A \cap B) = 0.2$ , what is the conditional probability $P (A ∣ B)$ ?
In mathematics, what is the scalar (dot) product of the vectors $u = [3, - 4]$ and $v = [2, 5]$ ?
In mathematics, for what value of $k$ are the 2D vectors $a = [k, 3]$ and $b = [4, - 6]$ orthogonal?
In mathematics, what is the exact value of $sin (\frac{π}{3}) + cos (\frac{π}{6})$ ?
In mathematics, what are the solutions to $2 cos (x) - 1 = 0$ in the interval $x \in [0, 2 π)$ ?
In mathematics, in an arithmetic sequence with first term $a_{1} = 5$ and common difference $d = 3$ , what is the 10th term $a_{10}$ ?
In mathematics, what is the sum of the convergent infinite geometric series $\sum_{n = 0}^{\infty} 8 (\frac{1}{3})^{n}$ ?
In mathematics, a radioactive substance decays according to $N (t) = N_{0} e^{- 0.05 t}$ , where $t$ is in years; what is its half-life $T_{1/2}$ ?
In mathematics, an initial deposit of $10, 000$ NOK grows with an annual interest rate of $4%$ ; what is the capital after $3$ years compounded annually?
In mathematics, what are the coordinates and nature of the stationary point of $f (x) = x^{3} - 3 x$ for $x > 0$ ?
In mathematics, what is the $x$ -coordinate of the inflection point of $f (x) = x^{3} - 6 x^{2} + 9 x - 4$ ?
In mathematics, if every data value in a sample is multiplied by 3, how does the sample standard deviation change?
In mathematics, in a normal distribution with mean $μ = 50$ and standard deviation $σ = 5$ , what percentage of data falls within the interval $[45, 55]$ ?
In mathematics, what is the indefinite integral $\int 2 x e^{x^{2}} d x$ ?
In mathematics, what is the Euclidean distance between the points $A (- 1, 3)$ and $B (3, 6)$ ?
In mathematics, what is the magnitude (length) of the vector $v = [6, - 8]$ ?
In mathematics, what is the cosine of the angle $θ$ between vectors $u = [1, 2]$ and $v = [2, 1]$ ?
In mathematics, in a triangle with side $a = 8$ , opposite angle $A = 3 0^{\circ}$ , and angle $B = 4 5^{\circ}$ , what is side $b$ by the Law of Sines?
In mathematics, in a triangle with sides $a = 5$ , $b = 7$ , and included angle $C = 6 0^{\circ}$ , what is the length of side $c$ ?
In mathematics, what is the horizontal asymptote of the rational function $f (x) = \frac{6 x ^{2} - 5}{2 x ^{2} + 3 x - 1}$ as $x \to \infty$ ?
In mathematics, what is the vertical asymptote of $f (x) = \frac{x + 4}{2 x - 6}$ ?
In mathematics, what is the limit $lim_{x \to \infty} \frac{4 x ^{2} + 9}{3 x - 1}$ ?
In mathematics, in how many different orders can 4 books be arranged on a shelf?
In mathematics, what is the derivative $\frac{d}{d x} (tan x)$ for $x \neq = \frac{π}{2} + k π$ ?
In mathematics, what is $lo g_{2} (32)$ ?
In mathematics, what is the radius of the circle defined by $(x - 3)^{2} + (y + 5)^{2} = 49$ ?
In mathematics, what is the vertex of the parabola $y = 2 x^{2} - 8 x + 11$ ?
In mathematics, what is the solution $(x, y)$ to the system $2 x + y = 7$ and $x - y = 2$ ?
In mathematics, what is the solution set of $∣2 x - 5∣ = 9$ ?
In mathematics, if the probability of rain on any given autumn day is $0.35$ , what is the probability that it does not rain?

Keep practising

More Vitnemål Eksamen (Norway) topics

Literature, Language and Text Analysis78 questions
Norwegian and Nordic History78 questions
Realfagsmatematikk R2: Kalkulus, Vektorer og Differensiallikninger43 questions
Integrasjonsteknikker og geometriske anvendelser6 questions
Trigonometriske funksjoner og harmoniske svingninger6 questions
Vektorer i rommet og romgeometri6 questions
Differensiallikninger og rekker6 questions

All Vitnemål Eksamen (Norway) 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 Stúdentspróf (Iceland)37 questions
Algebra, Functions, Calculus and Probability for Ylioppilastutkinto (Finnish Matriculation)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 Vitnemål Eksamen (Norway) test?

Take a mock test Vitnemål Eksamen (Norway) hub