Studentereksamen STX (Denmark) · Mathematics

Advanced Mathematics, Vectors, Calculus and Statistics

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

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

All 57 questions

In mathematics, what is the vertex of the parabola defined by the quadratic function $f (x) = x^{2} - 6 x + 8$ ?
In mathematics, what is the doubling time $T_{2}$ for the exponential growth model $f (x) = 150 \cdot 1.0 5^{x}$ ?
In mathematics, what is the half-life $T_{1/2}$ of a decaying substance modeled by $N (t) = 800 \cdot 0.8 5^{t}$ ?
In mathematics, if a power function $f (x) = b \cdot x^{a}$ passes through $(1, 4)$ and $(2, 32)$ , what is the exponent $a$ ?
In mathematics, what is the exact solution to the exponential equation $4 \cdot e^{2 x} = 28$ ?
In mathematics, what is the domain of the real logarithmic function $f (x) = ln (3 x - 12)$ ?
In mathematics, what is the discriminant $d$ of the quadratic equation $2 x^{2} - 5 x + 3 = 0$ and how many real roots exist?
In mathematics, what is the solution set to the rational inequality $\frac{x - 3}{x + 2} < 0$ ?
In mathematics, if $f (x) = 2 x - 5$ and $g (x) = x^{2} + 1$ , what is the composite function value $(g \circ f) (3)$ ?
In mathematics, what is the inverse function $f^{- 1} (x)$ for the bijective function $f (x) = 3 x + 9$ ?
In mathematics, what is the value of $lo g_{10} (0.001)$ ?
In mathematics, for the linear model $y = a x + b$ , what is the slope $a$ of the line passing through $(- 1, 4)$ and $(3, 16)$ ?
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, which transformation maps the graph of $y = f (x)$ to $y = f (x - 4) + 2$ ?
In mathematics, what is the solution to the system of linear equations $2 x + y = 11$ and $x - y = 1$ ?
In mathematics, if a population grows by 4 percent each year, what is the annual growth factor $a$ ?
In mathematics, what are the roots of the cubic equation $x^{3} - 4 x = 0$ ?
In mathematics, what is the value of $\sum_{k = 1}^{5} (2 k - 1)$ ?
In mathematics, what is the range of the real exponential function $f (x) = 3^{x} - 5$ ?
In mathematics, what is the derivative $f^{'} (x)$ of the function $f (x) = 5 x^{4} - 3 x^{2} + 7 x - 9$ ?
In mathematics, what is the slope of the tangent line to the curve $y = x^{3} - 2 x + 4$ at the point where $x = 2$ ?
In mathematics, what is the equation of the tangent line to $f (x) = x^{2} + 3 x$ at the point $x_{0} = 1$ ?
In mathematics, what is the derivative of the product function $f (x) = x^{2} \cdot e^{x}$ ?
In mathematics, what is the derivative of the quotient function $f (x) = \frac{x ^{2}}{x + 1}$ for $x \neq = - 1$ ?
In mathematics, using the chain rule, what is the derivative of $f (x) = ln (x^{2} + 4)$ ?
In mathematics, what are the local extrema of the polynomial function $f (x) = 2 x^{3} - 3 x^{2} - 12 x + 5$ ?
In mathematics, what is the inflection point of the cubic polynomial function $f (x) = x^{3} - 6 x^{2} + 9 x + 2$ ?
In mathematics, what is the value of the definite integral $\int_{1}^{3} (3 x^{2} - 2 x + 1) d x$ ?
In mathematics, what is the exact area of the region bounded by $y = x^{2}$ and $y = 4$ ?
In mathematics, what is the volume of revolution obtained by rotating $y = x$ around the x-axis for $0 \leq x \leq 4$ ?
In mathematics, what is the general antiderivative $\int (e^{3 x} + cos (2 x)) d x$ ?
In mathematics, what is the value of the definite integral $\int_{1}^{e} \frac{1}{x} d x$ ?
In mathematics, what is the second derivative $f^{''} (x)$ of $f (x) = x^{4} - 2 x^{3} + 5 x$ ?
In mathematics, which condition guarantees that a continuous function $f (x)$ on $[a, b]$ has an absolute maximum and minimum?
In mathematics, if $\frac{d y}{d x} = 2 x y$ with initial condition $y (0) = 3$ and $y > 0$ , what is the explicit solution $y (x)$ ?
In mathematics, what is the rate of change of the area of a circle $A = π r^{2}$ with respect to radius $r$ when $r = 5$ cm?
In mathematics, what is the average value of $f (x) = 6 x - 2$ on the interval $[0, 4]$ ?
In mathematics, for what value of $x$ does the curve $f (x) = \frac{1}{3} x^{3} - x$ have horizontal tangent lines?
In mathematics, what is the dot product $u \cdot v$ of vectors $u = (3 - 4)$ and $v = (25)$ ?
In mathematics, what is the length (magnitude) $∣ a ∣$ of the 3D vector $a = 2 - 3 6$ ?
In mathematics, two vectors $a = (4 k)$ and $b = (6 - 8)$ are orthogonal if and only if $k$ equals what value?
In mathematics, what is the determinant $det (a, b)$ of $a = (25)$ and $b = (31)$ ?
In mathematics, what is the cross product $u \times v$ of $u = 100$ and $v = 010$ in standard 3D coo…
In mathematics, what is the equation of the plane through $(1, 2, - 1)$ with normal vector $n = 2 - 3 4$ ?
In mathematics, what is the distance from the point $P (2, 3)$ to the line with equation $3 x - 4 y + 1 = 0$ ?
In mathematics, what is the center and radius of the circle with equation $(x - 5)^{2} + (y + 2)^{2} = 49$ ?
In mathematics, what is the cosine of the angle $θ$ between vectors $u = (12)$ and $v = (21)$ ?
In mathematics, in a triangle with side lengths $a = 5$ , $b = 7$ , and enclosed angle $C = 6 0^{\circ}$ , what is the length of side $c$ by the Law of Cosines?
In mathematics, what is the probability of rolling a sum of 7 when two fair six-sided dice are rolled simultaneously?
In mathematics, in a binomial distribution with $n = 100$ trials and success probability $p = 0.2$ , what is the expected value $μ$ and standard deviation $σ$ ?
In mathematics, in how many distinct ways can 3 students be chosen from a group of 8 students to form a committee?
In mathematics, if events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ , what is $P (A \cup B)$ ?
In mathematics, what is the median of the data set ${4, 8, 3, 9, 12, 7, 5, 11}$ ?
In mathematics, in a standard normal distribution $Z \sim N (0, 1)$ , approximately what percentage of observations lie within 2 standard deviations of the mean?
In mathematics, what is the degrees of freedom for a chi-squared ( $χ^{2}$ ) test of independence on a contingency table with 4 rows and 3 columns?
In mathematics, if $v = (- 3 4)$ , what is the unit vector $\overset{v}{^}$ pointing in the same direction?
In mathematics, what is the formula for the sample variance $s^{2}$ of $n$ observations $x_{1}, x_{2}, \dots, x_{n}$ ?

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