VWO / HAVO Centraal Examen (Netherlands) · Mathematics

Geometry, Vectors and Trigonometry

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

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All 10 questions

What is the dot product of the vectors $u = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ and $v = 5 \hat{i} + \hat{j} - 2 \hat{k}$ ?
What is the angle between the positive x-axis and the line $y = 3 x + 4$ in degrees?
In triangle $A B C$ , side $a = 7$ , side $b = 5$ , and angle $C = 6 0^{\circ}$ . Using the law of cosines, what is the exact length of side $c$ ?
What is the cross product $a \times b$ of $a = 100$ and $b = 010$ in right-handed 3D space?
What are the center and radius of the sphere with Cartesian equation $x^{2} + y^{2} + z^{2} - 4 x + 6 y - 2 z - 11 = 0$ ?
What is the exact value of $sin (7 5^{\circ})$ derived from the sum-of-angles formula $sin (4 5^{\circ} + 3 0^{\circ})$ ?
What is the equation of the plane passing through the point $(1, 2, 3)$ with normal vector $n = 2 - 1 4$ ?
What is the distance between the two parallel planes $2 x - 2 y + z = 5$ and $2 x - 2 y + z = - 4$ ?
What is the perimeter of a regular hexagon inscribed in a circle of radius $R = 6$ cm?
What is the transformation matrix representing a counter-clockwise rotation by $9 0^{\circ}$ ( $\frac{π}{2}$ radians) about the origin in $R^{2}$ ?

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