Selectividad / EvAU (Spain) · Mathematics

Calculus, Algebra, Geometry and Probability

35 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 35 questions

What is $lim_{x \to 0} \frac{s i n 3 x}{x}$ ?
What is the derivative of $f (x) = ln (x^{2} + 1)$ ?
Evaluate $\int_{0}^{3} 2 x d x$ .
What is the determinant of $(2314)$ ?
If $P (A) = 0.5$ , $P (B) = 0.4$ and $P (A \cap B) = 0.2$ , what is $P (A \cup B)$ ?
For $f (x) = x^{3} - 3 x$ , at which value of $x$ does $f$ have a local minimum?
Find $\int x e^{x} d x$ .
What is the horizontal asymptote of $f (x) = \frac{3 x ^{2} + 1}{x ^{2} - 4}$ ?
Let $A = (1021)$ . What is the entry in the first row, second column of $A^{5}$ ?
For which value of $k$ are the vectors $(1, 2, 3)$ and $(k, - 1, 0)$ perpendicular?
What is the area of the parallelogram spanned by $u = (1, 2, 0)$ and $v = (3, 1, 0)$ ?
Which equation gives the plane through $(1, 0, 0)$ , $(0, 1, 0)$ and $(0, 0, 1)$ ?
What is the distance from the point $(1, 1, 1)$ to the plane $x + 2 y + 2 z = 0$ ?
If $X \sim B (3, \frac{1}{2})$ , what is $P (X = 2)$ ?
If $X \sim N (50, 4)$ (mean 50, standard deviation 4), which standard normal probability equals $P (X \leq 58)$ ?
What is the rank of $(1224)$ ?
A system of three equations in three unknowns has $rank (A) = 2$ and $rank (A^{*}) = 3$ , where $A^{*}$ is the augmented matrix. What can be said?
What is the inverse of $(1011)$ ?
What is $lim_{x \to 1} \frac{x ^{2} - 1}{x - 1}$ ?
What is the equation of the tangent line to $y = x^{2}$ at the point where $x = 1$ ?
Which point lies on the line $(x, y, z) = (1, 2, 3) + t (2, 0, - 1)$ ?
A random sample of $n = 100$ has mean $50$ and the population standard deviation is $σ = 10$ . What is the margin of error of the 95% confidence interval for the mean (using $z = 1.96$ )?
The function $f (x) = {x + 1 a x - 1 x < 2 x \geq 2$ is continuous at $x = 2$ . What is $a$ ?
Find the inflection point of $f (x) = x^{3} - 6 x^{2} + 9 x + 1$ .
What is the area of the region under $y = x^{2}$ between $x = 0$ and $x = 3$ ?
A farmer has 100 m of fencing and builds a rectangular pen with a wall on one side, so only three sides need fence. What is the largest possible area?
Machine A makes 60% of a factory's items and 2% of them are defective; machine B makes the other 40% and 5% of them are defective. An item is picked at random and found defective. What is the probabil…
What is the area of the region enclosed by $y = x$ and $y = x^{2}$ ?
The matrix $A = 105216340$ has $det A = 1$ . What is $det (2 A)$ ?
For which value(s) of $a$ is $det 111 1 a 1 11 a$ equal to zero?
What is the distance from the point $P (2, 1, 2)$ to the line through the origin with direction $d = (1, 2, 2)$ ?
Find $\int x ln x d x$ for $x > 0$ .
What is $lim_{x \to 0} \frac{e ^{x} - 1 - x}{x ^{2}}$ ?
The tangent to $f (x) = x^{3} - 3 x$ at $x = 2$ crosses the $y$ -axis at which point?
What is the derivative of $f (x) = e^{2 x}$ ?

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