SIMAK UI · Basic Mathematics (Matematika Dasar)

Calculus, Analytic Geometry and Probability

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

Practise Calculus, Analytic Geometry and Probability now

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

All 25 questions

Evaluate the limit: $lim_{x \to 0} \frac{s i n ( 3 x )}{t a n ( 5 x )}$ .
Find the equation of the tangent line to the curve $y = x^{3} - 3 x + 2$ at the point $(2, 4)$ .
Evaluate the definite integral $\int_{0}^{2} (3 x^{2} - 2 x + 1) d x$ .
A circle has equation $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ . What are its center and radius?
Find the maximum area of a rectangle with perimeter 40 meters.
Evaluate the limit $lim_{x \to 1} \frac{x + 3 - 2}{x - 1}$ .
Find the area bounded by the parabola $y = x^{2}$ and the line $y = 2 x$ .
What is the perpendicular distance from the point $(1, - 2)$ to the line $3 x - 4 y + 5 = 0$ ?
If $f (x) = ln (x^{2} + 1)$ , find the second derivative $f^{''} (0)$ .
Two fair six-sided dice are tossed. What is the probability that the sum of the faces is greater than 9?
Find all inflection points of the cubic curve $y = 2 x^{3} - 6 x^{2} + 4 x - 1$ .
Evaluate the integral $\int x e^{2 x} d x$ .
A committee of 4 people is chosen at random from 5 men and 4 women. What is the probability that the committee consists of 2 men and 2 women?
Find the equation of the circle tangent to both the $x$ -axis and $y$ -axis with radius 4 in the fourth quadrant.
Evaluate the limit: $lim_{x \to \infty} (x^{2} + 4 x - x)$ .
Find the derivative $\frac{d y}{d x}$ at $(1, 1)$ for the curve implicitly defined by $x^{2} + x y + y^{2} = 3$ .
A random variable $X$ has probability density function $f (x) = k x$ for $0 \leq x \leq 4$ , and 0 elsewhere. Find the constant $k$ and the expected value $E [X]$ .
Find the volume of the solid generated by revolving the region bounded by $y = x$ , $y = 0$ , and $x = 4$ about the $x$ -axis.
The line $y = m x + 2$ is tangent to the parabola $y = x^{2}$ . Find the possible values of the slope $m$ .
If events $A$ and $B$ are independent with $P (A) = 0, 4$ and $P (B) = 0, 5$ , find $P (A \cup B)$ .
Find the coordinates of the local minimum point of the function $f (x) = x^{3} - 6 x^{2} + 9 x + 1$ .
Evaluate the improper integral $\int_{1}^{\infty} \frac{1}{x ^{3}} d x$ .
Find the eccentricity of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ .
Two cards are drawn successively without replacement from a standard 52-card deck. What is the probability that both cards are Aces?
If the position of a particle along the $x$ -axis is given by $s (t) = t^{3} - 6 t^{2} + 9 t$ , at what times $t > 0$ is the particle momentarily at rest?

Keep practising

Ready for the full SIMAK UI test?

Take a mock test SIMAK UI hub

Calculus, Analytic Geometry and Probability

Practise Calculus, Analytic Geometry and Probability now

All 25 questions

Keep practising

More SIMAK UI topics

Ready for the full SIMAK UI test?