VWO / HAVO Centraal Examen (Netherlands) · Mathematics

Mathematics for VWO and HAVO

39 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 39 questions

What is the derivative of $f (x) = x^{3}$ with respect to $x$ ?
What is the value of $lo g_{2} 8$ ?
Solve the equation $2 x + 5 = 17$ .
What is the derivative of $g (x) = sin x$ ?
A line passes through the points $(1, 2)$ and $(3, 8)$ . What is its slope?
What is $e^{l n 5}$ ?
What is the period of the function $y = sin (2 x)$ ?
What is the median of the data set $3, 7, 1, 9, 5$ ?
What is the derivative of $f (x) = x^{2} e^{x}$ ?
Solve $3^{x} = 81$ .
Solve $lo g_{3} x + lo g_{3} (x - 2) = 1$ for $x$ .
What are the coordinates of the vertex of the parabola $y = x^{2} - 6 x + 5$ ?
What is the derivative of $f (x) = ln (3 x)$ for $x > 0$ ?
Calculate $\int_{0}^{2} 3 x^{2} d x$ .
A fair coin is tossed three times. What is the probability of exactly two heads?
Which values of $x$ in the interval $[0, 2 π]$ satisfy $sin x = \frac{1}{2}$ ?
What is the derivative of $h (x) = (2 x + 1)^{5}$ ?
A culture of $200$ bacteria doubles every $3$ hours. How many bacteria are there after $9$ hours?
For a normal distribution, roughly what fraction of values lie within two standard deviations of the mean?
What is the domain of $f (x) = x - 4$ in the real numbers?
The function $f (x) = x^{3} - 3 x$ has a stationary point at $x = - 1$ . What kind of point is it?
What is $lo g_{10} 2 + lo g_{10} 50$ ?
In how many ways can a committee of $3$ people be chosen from a group of $6$ people?
The vectors $a = (23)$ and $b = (3 - 2)$ are given. What is true about them?
What is the equation of the tangent line to $y = x^{2}$ at the point where $x = 3$ ?
What is the expected value of the number shown when a fair six-sided die is thrown once?
What is the sum of the first $10$ terms of the arithmetic sequence $3, 7, 11, 15, \dots$ ?
What is the sum of the infinite geometric series $4 + 2 + 1 + \frac{1}{2} + \dots$ ?
Which expression equals $sin 2 x$ ?
For $x \geq 0$ , find the maximum value of $f (x) = x e^{- x}$ .
Solve $e^{2 x} - 5 e^{x} + 6 = 0$ .
A rectangle has a perimeter of $40$ m. What is the greatest area it can have, and what are its sides?
Calculate $\int_{0}^{π /2} sin x cos x d x$ .
A fair die is rolled $4$ times. What is the probability of at least one six?
What is the area of the region enclosed by the graphs of $y = x$ and $y = x^{2}$ ?
Solve $2 cos^{2} x - 3 cos x + 1 = 0$ for $0 \leq x < 2 π$ .
Solve $2 lo g x = lo g (x + 6)$ for $x$ , using logarithms with the same base.
A bag holds $5$ red and $3$ blue balls. Two balls are drawn without replacement. What is the probability that both are red?
For $f (x) = \frac{x}{x ^{2} + 1}$ , at which values of $x$ is $f^{'} (x) = 0$ ?

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