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Curaçao Eindexamen VSBO-TKL - independent subject foundations study materials
Curaçao Eindexamen VSBO-TKL - independent subject foundations study resources

Curaçao Eindexamen VSBO-TKL - independent subject foundations practice questions

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Question 1Lower-secondary number, algebra, geometry and data

Simplify the square root expression: $A = \sqrt{75} - 2\sqrt{27} + \sqrt{48}$. What is the resulting exact value?

  1. $5\sqrt{3}$
  2. $3\sqrt{3}$ Correct answer.
  3. $\sqrt{3}$
  4. $7\sqrt{3}$

Explanation

Factoring each radicand by perfect squares: $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$; $2\sqrt{27} = 2\sqrt{9 \times 3} = 2(3\sqrt{3}) = 6\sqrt{3}$; $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$. Combining the terms yields $A = 5\sqrt{3} - 6\sqrt{3} + 4\sqrt{3} = (5 - 6 + 4)\sqrt{3} = 3\sqrt{3}$.

Question 2Lower-secondary number, algebra, geometry and data

Rationalize the denominator of the fraction $F = \frac{6}{\sqrt{5} - 1}$. What is the simplified expression?

  1. $\frac{6(\sqrt{5} + 1)}{6}$
  2. $3(\sqrt{5} - 1)$
  3. $\frac{3(\sqrt{5} + 1)}{2}$ Correct answer.
  4. $\frac{3\sqrt{5} - 3}{4}$

Explanation

Multiplying the numerator and denominator by the conjugate $(\sqrt{5} + 1)$: $F = \frac{6(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)} = \frac{6(\sqrt{5} + 1)}{(\sqrt{5})^2 - 1^2} = \frac{6(\sqrt{5} + 1)}{5 - 1} = \frac{6(\sqrt{5} + 1)}{4}$. Simplifying by dividing numerator and denominator by 2 gives $\frac{3(\sqrt{5} + 1)}{2}$.

Question 3Lower-secondary number, algebra, geometry and data

Expand and simplify the algebraic expression: $E(x) = (2x - 3)^2 - (x + 1)(2x - 3)$.

  1. $2x^2 - 13x + 6$
  2. $4x^2 - 11x + 12$
  3. $2x^2 - 7x + 6$
  4. $2x^2 - 11x + 12$ Correct answer.

Explanation

Expanding $(2x - 3)^2 = 4x^2 - 12x + 9$. Expanding $(x + 1)(2x - 3) = 2x^2 - 3x + 2x - 3 = 2x^2 - x - 3$. Subtracting the two expressions: $E(x) = (4x^2 - 12x + 9) - (2x^2 - x - 3) = 4x^2 - 12x + 9 - 2x^2 + x + 3 = (4-2)x^2 + (-12+1)x + (9+3) = 2x^2 - 11x + 12$.

Question 4Lower-secondary number, algebra, geometry and data

Completely factorize the algebraic expression: $P(x) = (3x - 2)^2 - 16$.

  1. $3(x - 2)(3x + 2)$ Correct answer.
  2. $(3x - 6)(3x - 2)$
  3. $(3x + 2)(3x - 2)$
  4. $9(x - 2)(x + 2)$

Explanation

Using the difference of two squares identity $a^2 - b^2 = (a - b)(a + b)$ with $a = 3x - 2$ and $b = 4$: $P(x) = [(3x - 2) - 4][(3x - 2) + 4] = (3x - 6)(3x + 2)$. Factoring out 3 from the first binomial $(3x - 6) = 3(x - 2)$ gives $P(x) = 3(x - 2)(3x + 2)$.

Question 5Lower-secondary number, algebra, geometry and data

Solve the zero-product equation in $\mathbb{R}$: $(2x - 5)(3x + 4) = 0$.

  1. $S = \left\{ \frac{4}{3}, -\frac{5}{2} \right\}$
  2. $S = \left\{ -\frac{4}{3}, \frac{5}{2} \right\}$ Correct answer.
  3. $S = \left\{ \frac{5}{2}, \frac{4}{3} \right\}$
  4. $S = \left\{ -\frac{5}{2}, -\frac{4}{3} \right\}$

Explanation

A product of factors equals zero if and only if at least one factor is zero: $2x - 5 = 0 \implies 2x = 5 \implies x = 5/2$; or $3x + 4 = 0 \implies 3x = -4 \implies x = -4/3$. Thus the solution set is $S = \{-4/3, 5/2\}$.

Question 6Lower-secondary number, algebra, geometry and data

Solve the first-degree inequality in $\mathbb{R}$: $3x - 7 \le 5x + 5$.

  1. $S = ]-\infty, -6]$
  2. $S = [6, +\infty[$
  3. $S = [-6, +\infty[$ Correct answer.
  4. $S = ]-\infty, 6]$

Explanation

Subtracting $5x$ from both sides: $3x - 5x - 7 \le 5 \implies -2x - 7 \le 5$. Adding 7 gives $-2x \le 12$. Dividing both sides by $-2$ reverses the inequality symbol: $x \ge \frac{12}{-2} \implies x \ge -6$. In interval notation, $S = [-6, +\infty[$.

Question 7Lower-secondary number, algebra, geometry and data

Solve the system of two linear equations in $\mathbb{R} \times \mathbb{R}$: $$\begin{cases} 2x + 3y = 21 \\ 5x - y = 10 \end{cases}$$

  1. $(x, y) = (5, 3)$
  2. $(x, y) = (2, 5)$
  3. $(x, y) = (3, 4)$
  4. $(x, y) = (3, 5)$ Correct answer.

Explanation

From the second equation, express $y = 5x - 10$. Substitute into the first equation: $2x + 3(5x - 10) = 21 \implies 2x + 15x - 30 = 21 \implies 17x = 51 \implies x = 3$. Then $y = 5(3) - 10 = 15 - 10 = 5$. Thus $(x, y) = (3, 5)$. Checking: $2(3)+3(5)=6+15=21$ and $5(3)-5=10$.

Question 8Lower-secondary number, algebra, geometry and data

Let $ABC$ be a right-angled triangle at $A$ such that $AB = 8\text{ cm}$ and $AC = 6\text{ cm}$. Let $H$ be the orthogonal projection of $A$ on the hypotenuse $[BC]$. Calculate the length of the height $AH$.

  1. $4.8\text{ cm}$ Correct answer.
  2. $5.0\text{ cm}$
  3. $4.0\text{ cm}$
  4. $3.6\text{ cm}$

Explanation

By Pythagoras theorem, $BC = \sqrt{AB^2 + AC^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\text{ cm}$. The area of triangle $ABC$ can be calculated in two ways: $\text{Area} = \frac{AB \times AC}{2} = \frac{BC \times AH}{2}$. Thus $AB \times AC = BC \times AH \implies 8 \times 6 = 10 \times AH \implies AH = \frac{48}{10} = 4.8\text{ cm}$.

Question 9Lower-secondary number, algebra, geometry and data

A triangle has side lengths $7\text{ cm}$, $24\text{ cm}$, and $25\text{ cm}$. According to the converse of Pythagoras' theorem (réciproque de Pythagore), what can be concluded?

  1. The triangle is isosceles because $25 - 24 = 1$.
  2. The triangle is right-angled because $7^2 + 24^2 = 49 + 576 = 625 = 25^2$. Correct answer.
  3. The triangle is obtuse because $25^2 > 7^2 + 24^2$.
  4. The triangle is equilateral because all side lengths are integers.

Explanation

Calculating the square of the longest side: $25^2 = 625$. The sum of the squares of the other two sides: $7^2 + 24^2 = 49 + 576 = 625$. Since $25^2 = 7^2 + 24^2$, by the converse of Pythagoras' theorem, the triangle is strictly right-angled.

Question 10Lower-secondary number, algebra, geometry and data

In a triangle $ABC$, point $M$ lies on $[AB]$ and point $N$ lies on $[AC]$ such that $(MN)$ is parallel to $(BC)$. Given $AB = 12\text{ cm}$, $AM = 4\text{ cm}$, and $BC = 15\text{ cm}$, what is the length of segment $[MN]$?

  1. $4\text{ cm}$
  2. $6\text{ cm}$
  3. $5\text{ cm}$ Correct answer.
  4. $7.5\text{ cm}$

Explanation

According to Thales' theorem: $\frac{AM}{AB} = \frac{AN}{AC} = \frac{MN}{BC}$. Substituting known values: $\frac{4}{12} = \frac{MN}{15} \implies \frac{1}{3} = \frac{MN}{15} \implies MN = \frac{15}{3} = 5\text{ cm}$.

Question 11Lower-secondary number, algebra, geometry and data

In triangle $RST$, point $P$ belongs to segment $[RS]$ and point $Q$ belongs to segment $[RT]$ in the same order. If $RP = 3\text{ cm}$, $RS = 7.5\text{ cm}$, $RQ = 4\text{ cm}$, and $RT = 10\text{ cm}$, are lines $(PQ)$ and $(ST)$ parallel?

  1. No, because $7.5 - 3 \neq 10 - 4$.
  2. No, because $3 \times 4 \neq 7.5 \times 10$.
  3. It is impossible to determine without knowing the angle at vertex $R$.
  4. Yes, because the ratios $\frac{RP}{RS} = \frac{3}{7.5} = 0.4$ and $\frac{RQ}{RT} = \frac{4}{10} = 0.4$ are equal in the same order. Correct answer.

Explanation

According to the converse of Thales' theorem (réciproque du théorème de Thalès), since the points $R, P, S$ and $R, Q, T$ are aligned in the same order and $\frac{RP}{RS} = \frac{3}{7.5} = \frac{2}{5} = 0.4$ while $\frac{RQ}{RT} = \frac{4}{10} = \frac{2}{5} = 0.4$, the ratios are equal, proving that $(PQ) \parallel (ST)$.

Question 12Lower-secondary number, algebra, geometry and data

In a right-angled triangle $EFG$ at $E$, the hypotenuse is $FG = 15\text{ cm}$ and $\cos(\widehat{EFG}) = 0.6$. Calculate the length of adjacent side $EF$ and the length of opposite side $EG$.

  1. $EF = 9\text{ cm}$ and $EG = 12\text{ cm}$ Correct answer.
  2. $EF = 12\text{ cm}$ and $EG = 9\text{ cm}$
  3. $EF = 6\text{ cm}$ and $EG = 9\text{ cm}$
  4. $EF = 10\text{ cm}$ and $EG = 11\text{ cm}$

Explanation

By definition, $\cos(\widehat{EFG}) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{EF}{FG} \implies EF = FG \times \cos(\widehat{EFG}) = 15 \times 0.6 = 9\text{ cm}$. Using Pythagoras theorem: $EG = \sqrt{FG^2 - EF^2} = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12\text{ cm}$.

Question 13Lower-secondary number, algebra, geometry and data

Let $\alpha$ be an acute angle such that $\cos(\alpha) = \frac{4}{5}$. Calculate $\tan(\alpha)$.

  1. $\frac{4}{3}$
  2. $\frac{3}{4}$ Correct answer.
  3. $\frac{3}{5}$
  4. $\frac{5}{4}$

Explanation

Using the fundamental trigonometric identity $\cos^2(\alpha) + \sin^2(\alpha) = 1$: $\sin^2(\alpha) = 1 - \left(\frac{4}{5}\right)^2 = 1 - \frac{16}{25} = \frac{9}{25} \implies \sin(\alpha) = \frac{3}{5}$. Then $\tan(\alpha) = \frac{\sin(\alpha)}{\cos(\alpha)} = \frac{3/5}{4/5} = \frac{3}{4} = 0.75$.

Question 14Lower-secondary number, algebra, geometry and data

A student obtained the following grades on four test papers with coefficients (weights): Grade 8 (coeff 2), Grade 10 (coeff 3), Grade 12 (coeff 4), and Grade 16 (coeff 1). What is the weighted mean average (moyenne pondérée)?

  1. $11.50 / 20$
  2. $10.50 / 20$
  3. $11.00 / 20$ Correct answer.
  4. $12.00 / 20$

Explanation

The weighted sum of scores is: $(8 \times 2) + (10 \times 3) + (12 \times 4) + (16 \times 1) = 16 + 30 + 48 + 16 = 110$. The total sum of coefficients is $2 + 3 + 4 + 1 = 10$. The weighted mean is $\bar{x} = \frac{110}{10} = 11.00$.

Question 15Lower-secondary number, algebra, geometry and data

Consider the ordered statistical dataset of 8 scores: $5, 8, 9, 12, 14, 17, 19, 21$. What are the median (médiane) and the range (étendue) of this dataset?

  1. Median = 12 and Range = 16
  2. Median = 13.5 and Range = 21
  3. Median = 14 and Range = 15
  4. Median = 13 and Range = 16 Correct answer.

Explanation

With $N = 8$ (even), the median is the arithmetic mean of the 4th and 5th values: $\text{Median} = \frac{12 + 14}{2} = 13$. The range is the difference between the maximum and minimum values: $\text{Range} = 21 - 5 = 16$.

Question 16Lower-secondary number, algebra, geometry and data

In an orthonormal coordinate system $(O, \vec{i}, \vec{j})$, let points be $A(2, -1)$ and $B(-3, 4)$. What are the coordinates of vector $\vec{AB}$ and its exact Euclidean norm $\|\vec{AB}\|$?

  1. $\vec{AB}(-5, 5)$ and $\|\vec{AB}\| = 5\sqrt{2}$ Correct answer.
  2. $\vec{AB}(5, -5)$ and $\|\vec{AB}\| = 5\sqrt{2}$
  3. $\vec{AB}(-1, 3)$ and $\|\vec{AB}\| = \sqrt{10}$
  4. $\vec{AB}(-5, 5)$ and $\|\vec{AB}\| = 50$

Explanation

Vector coordinates: $\vec{AB} = (x_B - x_A, y_B - y_A) = (-3 - 2, 4 - (-1)) = (-5, 5)$. The norm is $\|\vec{AB}\| = \sqrt{(-5)^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$.

Question 17Lower-secondary number, algebra, geometry and data

In the Cartesian plane, find the coordinates of midpoint $I$ of line segment $[AB]$ where $A(6, -4)$ and $B(-2, 8)$.

  1. $I(4, 4)$
  2. $I(2, 2)$ Correct answer.
  3. $I(8, -12)$
  4. $I(2, 6)$

Explanation

The midpoint formula is $I\left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right) = I\left(\frac{6 + (-2)}{2}, \frac{-4 + 8}{2}\right) = I\left(\frac{4}{2}, \frac{4}{2}\right) = I(2, 2)$.

Question 18Lower-secondary number, algebra, geometry and data

Determine the reduced equation (équation réduite) of the straight line $(D)$ passing through points $A(1, 3)$ and $B(4, 9)$.

  1. $y = 2x + 3$
  2. $y = 3x$
  3. $y = 2x + 1$ Correct answer.
  4. $y = \frac{1}{2}x + \frac{5}{2}$

Explanation

Slope $m = \frac{y_B - y_A}{x_B - x_A} = \frac{9 - 3}{4 - 1} = \frac{6}{3} = 2$. The line has equation $y = 2x + p$. Substituting $A(1, 3)$: $3 = 2(1) + p \implies p = 3 - 2 = 1$. Thus $y = 2x + 1$. Checking $B(4, 9)$: $2(4) + 1 = 9$ (verified).

Question 19Lower-secondary number, algebra, geometry and data

In the plane, line $(D_1)$ has equation $y = -\frac{2}{3}x + 4$. What is the slope (coefficient directeur) of any line $(D_2)$ perpendicular to $(D_1)$?

  1. $-\frac{3}{2}$
  2. $-\frac{2}{3}$
  3. $\frac{2}{3}$
  4. $\frac{3}{2}$ Correct answer.

Explanation

Two non-vertical lines are perpendicular if and only if the product of their slopes equals $-1$: $m_1 \times m_2 = -1$. Here, $-\frac{2}{3} \times m_2 = -1 \implies m_2 = \frac{-1}{-2/3} = \frac{3}{2}$.

Question 20Lower-secondary number, algebra, geometry and data

A regular pyramid has a square base with side length $a = 6\text{ cm}$ and a height $h = 10\text{ cm}$. What is its volume $V$?

  1. $120\text{ cm}^3$ Correct answer.
  2. $360\text{ cm}^3$
  3. $60\text{ cm}^3$
  4. $180\text{ cm}^3$

Explanation

The area of the square base is $\text{Base} = a^2 = 6^2 = 36\text{ cm}^2$. The volume of a pyramid is $V = \frac{1}{3} \times \text{Base} \times h = \frac{1}{3} \times 36 \times 10 = 12 \times 10 = 120\text{ cm}^3$.

Question 21Lower-secondary number, algebra, geometry and data

A cone of revolution has a base radius $R = 6\text{ cm}$ and a height $H = 12\text{ cm}$. It is cut by a plane parallel to the base at a scale reduction factor $k = \frac{1}{2}$. What is the exact volume $V'$ of the small reduced cone?

  1. $72\pi\text{ cm}^3$
  2. $18\pi\text{ cm}^3$ Correct answer.
  3. $36\pi\text{ cm}^3$
  4. $144\pi\text{ cm}^3$

Explanation

The total volume of the initial cone is $V = \frac{1}{3}\pi R^2 H = \frac{1}{3}\pi (6^2)(12) = \frac{1}{3}\pi (36)(12) = 144\pi\text{ cm}^3$. Under a linear reduction factor $k = 1/2$, volumes are scaled by $k^3 = (1/2)^3 = 1/8$. Thus $V' = k^3 V = \frac{1}{8} \times 144\pi = 18\pi\text{ cm}^3$.

Question 22Lower-secondary number, algebra, geometry and data

Calculate the exact volume $V$ of a solid sphere of radius $r = 3\text{ cm}$.

  1. $12\pi\text{ cm}^3$
  2. $108\pi\text{ cm}^3$
  3. $36\pi\text{ cm}^3$ Correct answer.
  4. $27\pi\text{ cm}^3$

Explanation

The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. Substituting $r = 3\text{ cm}$: $V = \frac{4}{3}\pi (3^3) = \frac{4}{3}\pi (27) = 4 \times 9\pi = 36\pi\text{ cm}^3$.

Question 23Lower-secondary number, algebra, geometry and data

A BEPC preparation manual initially priced at $25,000\text{ FCFA}$ receives a $20\%$ discount, after which a $5\%$ municipal tax is applied to the discounted price. What is the final price paid by the student?

  1. $21,250\text{ FCFA}$
  2. $20,000\text{ FCFA}$
  3. $22,500\text{ FCFA}$
  4. $21,000\text{ FCFA}$ Correct answer.

Explanation

Applying the $20\%$ discount: $\text{Discounted Price} = 25,000 \times (1 - 0.20) = 25,000 \times 0.80 = 20,000\text{ FCFA}$. Applying the $5\%$ tax to the discounted price: $\text{Final Price} = 20,000 \times (1 + 0.05) = 20,000 \times 1.05 = 21,000\text{ FCFA}$.

Question 24Lower-secondary number, algebra, geometry and data

A bag contains 4 red balls, 6 green balls, and 10 white balls, all identical to the touch. A ball is drawn at random. What is the probability of drawing a ball that is NOT white?

  1. $\frac{1}{2}$ (or $0.50$) Correct answer.
  2. $\frac{1}{4}$ (or $0.25$)
  3. $\frac{3}{10}$ (or $0.30$)
  4. $\frac{3}{5}$ (or $0.60$)

Explanation

Total number of balls $= 4 + 6 + 10 = 20$. The number of favorable outcomes (balls that are not white, i.e., red or green) is $4 + 6 = 10$. The probability is $P(\text{not white}) = \frac{10}{20} = \frac{1}{2} = 0.50$.

Question 25Lower-secondary number, algebra, geometry and data

Given the approximation $2.236 < \sqrt{5} < 2.237$, find the framing (encadrement) of the expression $A = 3\sqrt{5} - 4$.

  1. $6.708 < A < 6.711$
  2. $2.708 < A < 2.711$ Correct answer.
  3. $2.236 < A < 2.237$
  4. $0.708 < A < 0.711$

Explanation

Multiplying the inequality by $3 > 0$: $3 \times 2.236 < 3\sqrt{5} < 3 \times 2.237 \implies 6.708 < 3\sqrt{5} < 6.711$. Subtracting 4 from all parts: $6.708 - 4 < 3\sqrt{5} - 4 < 6.711 - 4 \implies 2.708 < A < 2.711$.

Question 26Markets, macroeconomic models and development evidence

In economics, how are 'primary needs' (primaire behoeften / basisbehoeften) distinguished from 'secondary needs' (secundaire behoeften / luxebehoeften)?

  1. Primary needs are essential for human survival such as food, potable water, basic clothing, and shelter; secondary needs enhance comfort and personal enjoyment Correct answer.
  2. Primary needs can only be purchased with credit cards, while secondary needs are paid in cash
  3. Primary needs are provided completely free by the government to all residents
  4. Primary needs only include luxury sports cars and overseas vacations

Explanation

Primary needs (basisbehoeften) are fundamental goods and services indispensable for biological survival, including food, clean water, shelter, and basic medical care. Secondary needs (luxebehoeften) improve quality of life and social comfort, such as entertainment, smartphones, and fashion items.

Question 27Markets, macroeconomic models and development evidence

What occurs in a competitive local market when the price of fresh red snapper at the floating market is set below the equilibrium market price?

  1. A shortage (excess demand) occurs, where the quantity demanded by buyers exceeds the quantity supplied by fishermen Correct answer.
  2. A surplus (excess supply) occurs, with unsold fish piling up on the docks
  3. Consumer demand drops to zero immediately
  4. Fishermen triple their daily catch without incurring additional costs

Explanation

When price is held below equilibrium, lower prices stimulate higher consumer demand while simultaneously reducing sellers' incentive to supply, creating a market shortage (tekort / excess demand).

Question 28Markets, macroeconomic models and development evidence

Under Curaçao labor legislation, what is the legal definition and purpose of the statutory minimum wage (wettelijk minimumloon)?

  1. The legally mandated minimum hourly or monthly wage an employer must pay an employee to ensure a basic social subsistence level Correct answer.
  2. The maximum amount an executive may earn in the private banking sector
  3. A voluntary bonus paid only during national holidays
  4. An hourly wage that only applies to government civil servants

Explanation

The statutory minimum wage (Landsverordening minimumlonen) establishes a legal wage floor below which no employer may contractually pay adult workers, protecting vulnerable employees from exploitation and ensuring a basic standard of living.

Question 29Markets, macroeconomic models and development evidence

Why is an open island economy such as Curaçao described as having a high 'import quota' (invoerquote)?

  1. Because the total value of imported goods represents a very high percentage of the island's Gross Domestic Product Correct answer.
  2. Because the island strictly prohibits all foreign commercial container ships from docking
  3. Because the government imposes a zero-quota limit allowing no foreign goods onto the island
  4. Because domestic factories produce all consumer electronics and vehicles locally

Explanation

The import quota is the value of imports expressed as a percentage of GDP: (Imports / GDP) * 100%. Small island economies lack domestic heavy industry, agriculture, and raw materials, resulting in high import quotas often exceeding 50-70% of national output.

Question 30Markets, macroeconomic models and development evidence

A consumer purchases an electrical appliance on an installment hire-purchase plan (huurkoop). The cash price is Cg 1,200. Under the installment plan, the buyer pays an immediate deposit (aanbetaling) of Cg 300 and 12 monthly payments of Cg 90 each. How much extra credit cost (interest and financing fees) does the consumer pay compared to buying in cash?

  1. Cg 180 Correct answer.
  2. Cg 300
  3. Cg 80
  4. Cg 1,380

Explanation

Total installment cost = Deposit + (12 * Monthly payment) = Cg 300 + (12 * Cg 90) = Cg 300 + Cg 1,080 = Cg 1,380. Financing credit cost = Total installment cost - Cash price = Cg 1,380 - Cg 1,200 = Cg 180.

Question 31Markets, macroeconomic models and development evidence

In basic commercial bookkeeping, what are the two main sides of a balance sheet (balans), and which types of accounts belong on each side?

  1. Left side: Assets (Activa / Bezittingen); Right side: Liabilities and Equity (Passiva / Schulden en Eigen Vermogen) Correct answer.
  2. Left side: Revenues; Right side: Costs
  3. Left side: Debits; Right side: Bank transfers only
  4. Left side: Taxes owed; Right side: Cash in cash register

Explanation

A balance sheet presents the financial position at a specific moment: the left side (Activa/Debet) lists company assets (fixed and current assets), while the right side (Passiva/Credit) lists claims against those assets (equity and short/long-term liabilities). Total Activa must always equal total Passiva.

Question 32Markets, macroeconomic models and development evidence

A retail business in Willemstad purchases commercial merchandise for Cg 4,000 on credit from a local distributor. In double-entry bookkeeping, what is the correct journal entry to record this transaction?

  1. Debit: Inventory / Merchandise (Voorraad goederen) Cg 4,000; Credit: Accounts Payable / Creditors (Crediteuren) Cg 4,000 Correct answer.
  2. Debit: Accounts Payable (Crediteuren) Cg 4,000; Credit: Bank Cg 4,000
  3. Debit: Cash (Kas) Cg 4,000; Credit: Sales Revenue (Omzet) Cg 4,000
  4. Debit: Accounts Receivable (Debiteuren) Cg 4,000; Credit: Inventory Cg 4,000

Explanation

Purchasing inventory on credit increases the asset Inventory (Voorraad goederen, debited on the Activa side) and increases the liability Accounts Payable (Crediteuren, credited on the Passiva side) by Cg 4,000.

Question 33Recording, costing, organization and business decisions

A household in Buena Vista prepares a monthly family budget. Net monthly family income is Cg 3,400. Fixed monthly expenses (rent, electricity, water, insurance) total Cg 1,850, and household grocery spending is Cg 950. How much money remains available for incidental and recreational expenses?

  1. Cg 600 Correct answer.
  2. Cg 800
  3. Cg 1,550
  4. Cg 450

Explanation

Total planned expenditures = Fixed expenses (Cg 1,850) + Groceries (Cg 950) = Cg 2,800. Remaining discretionary budget = Total Net Income (Cg 3,400) - Total planned expenditures (Cg 2,800) = Cg 600.

Question 34Recording, costing, organization and business decisions

A customer takes out a personal consumer loan of Cg 5,000 from a commercial bank in Willemstad to purchase a scooter. The loan has a simple annual interest rate of 8.0% and must be fully repaid with interest after exactly one year. What is the total amount the customer must pay back?

  1. Cg 5,400 Correct answer.
  2. Cg 5,800
  3. Cg 4,600
  4. Cg 5,080

Explanation

Annual interest = Principal * Interest rate = Cg 5,000 * 0.08 = Cg 400. Total repayment = Principal + Interest = Cg 5,000 + Cg 400 = Cg 5,400.

Question 35Recording, costing, organization and business decisions

A supermarket in Salinja sells an imported kitchen blender with a retail price of Cg 150.00 excluding 6% OB. What is the total final price the consumer must pay at the cash register including OB?

  1. Cg 159.00 Correct answer.
  2. Cg 156.00
  3. Cg 165.00
  4. Cg 141.00

Explanation

OB amount = Cg 150.00 * 0.06 = Cg 9.00. Total consumer price = Cg 150.00 + Cg 9.00 = Cg 159.00.

Question 36Recording, costing, organization and business decisions

A souvenir shop in Punda purchases handmade ceramic mugs for Cg 12.00 each from a local artisan. The shop applies a profit markup of 50% on the purchase cost (inkoopprijs) to establish its selling price excluding OB. What is the selling price excluding OB?

  1. Cg 18.00 Correct answer.
  2. Cg 24.00
  3. Cg 16.00
  4. Cg 15.00

Explanation

Markup amount = Purchase Cost * Markup % = Cg 12.00 * 0.50 = Cg 6.00. Selling price = Purchase Cost + Markup = Cg 12.00 + Cg 6.00 = Cg 18.00.

Question 37Recording, costing, organization and business decisions

Over the course of a financial year, an electronics retailer reports an average inventory value (gemiddelde voorraad) of Cg 40,000. Total Cost of Goods Sold (Inkoopwaarde van de omzet - IWO) during that year was Cg 240,000. What is the inventory turnover rate (omloopsnelheid van de voorraad)?

  1. 6.0 times per year Correct answer.
  2. 4.0 times per year
  3. 8.0 times per year
  4. 0.17 times per year

Explanation

Inventory turnover rate = Cost of Goods Sold (IWO) / Average Inventory = Cg 240,000 / Cg 40,000 = 6.0 times per year. This means the store sells and replaces its entire stock on average 6 times annually.

Question 38Recording, costing, organization and business decisions

If an electronics retailer has an inventory turnover rate of 6.0 times per year, what is the average inventory holding period in days (gemiddelde opslagduur / omlooptijd in dagen), assuming a standard 360-day commercial year?

  1. 60 days Correct answer.
  2. 30 days
  3. 90 days
  4. 120 days

Explanation

Average holding period in days = 360 days / Inventory turnover rate = 360 / 6.0 = 60 days. On average, merchandise remains in the warehouse for 60 days before being sold.

Question 39Electrical circuits, machines and digital logic

If an electric winch performs 18,000 Joules of work in 30 seconds to haul a fishing boat up a ramp, what is the power output (vermogen P) of the winch motor?

  1. 600 W (0.60 kW) Correct answer.
  2. 540,000 W
  3. 60 W
  4. 18,030 W

Explanation

Power is the rate at which work is done: P = W / t = 18,000 J / 30 s = 600 Watts (W), or 0.60 kW.

Question 40Electrical circuits, machines and digital logic

An electric kettle connected to a 240 V mains electrical outlet in a workshop has a heating element with an internal resistance of 20 Ohms. Using Ohm's law (V = I * R), what current flows through the kettle element when operating?

  1. 12 A Correct answer.
  2. 4,800 A
  3. 0.083 A
  4. 220 A

Explanation

By Ohm's law: Current I = Voltage / Resistance = V / R = 240 V / 20 Ohms = 12 Amperes (A).

Question 41Electrical circuits, machines and digital logic

At the wind farms of Tera Kòrá and Playa Kanoa in Curaçao, kinetic wind energy is converted into electrical energy. What key electrical component inside the nacelle of a wind turbine generates alternating current (AC) from the rotational motion of the rotor shaft?

  1. An electrical generator (generator) Correct answer.
  2. A storage battery bank
  3. A diesel injection pump
  4. An electric heating element

Explanation

The wind turns the turbine rotor blades and main shaft (usually through a gearbox), spinning an electromagnetic generator (generator) which uses electromagnetic induction to convert rotational kinetic energy into alternating electric current (AC) fed into the Aqualectra grid.

Question 42Electrical circuits, machines and digital logic

A 24 V DC industrial heating element has a measured electrical resistance of 8 Ω. Calculate the electric current (I) flowing through the element and the thermal power (P) dissipated.

  1. I = 1.5 A and P = 36 W
  2. I = 3 A and P = 72 W Correct answer.
  3. I = 4 A and P = 96 W
  4. I = 0.33 A and P = 8 W

Explanation

According to Ohm's Law and Joule's Power Law: 1. Current: I = V / R = 24 V / 8 Ω = 3 A. 2. Power: P = V · I = 24 V · 3 A = 72 W (or P = I² · R = 3² · 8 = 9 · 8 = 72 W).

Question 43Electrical circuits, machines and digital logic

In a direct current circuit, two 6 Ω resistors are connected in parallel with each other. This parallel group is then connected in series with a 5 Ω resistor across a 16 V DC power supply. What is the total equivalent resistance (R_eq) of the circuit and the voltage drop across the 5 Ω resistor (V_5)?

  1. R_eq = 17 Ω and V_5 = 4.7 V
  2. R_eq = 11 Ω and V_5 = 7.3 V
  3. R_eq = 8 Ω and V_5 = 10 V Correct answer.
  4. R_eq = 4 Ω and V_5 = 20 V

Explanation

1. Equivalent resistance of the parallel branch: R_p = (6 · 6) / (6 + 6) = 36 / 12 = 3 Ω. 2. Total equivalent circuit resistance: R_eq = R_p + R_series = 3 + 5 = 8 Ω. 3. Total circuit current: I_total = V_source / R_eq = 16 V / 8 Ω = 2 A. 4. Voltage drop across the 5 Ω resistor: V_5 = I_total · 5 Ω = 2 A · 5 Ω = 10 V.

Question 44Electrical circuits, machines and digital logic

At an electrical circuit junction (node), currents entering the node are I₁ = 4.0 A and I₂ = 2.5 A. A third branch carries current I₃ = 1.8 A directed away from the node. According to Kirchhoff's Current Law (KCL), what is the magnitude and direction of current I₄ in the fourth branch connected to this node?

  1. I₄ = 4.7 A leaving the node Correct answer.
  2. I₄ = 8.3 A entering the node
  3. I₄ = 4.7 A entering the node
  4. I₄ = 3.3 A leaving the node

Explanation

Kirchhoff's Current Law states that the algebraic sum of currents entering a node equals the sum of currents leaving: ∑I_in = ∑I_out. Sum of known entering currents: I₁ + I₂ = 4.0 + 2.5 = 6.5 A. Known leaving current: I₃ = 1.8 A. Since entering exceeds leaving (6.5 > 1.8), I₄ must be leaving the node: 6.5 A = 1.8 A + I₄ ⇒ I₄ = 6.5 - 1.8 = 4.7 A leaving the node.

Question 45Electrical circuits, machines and digital logic

A series R-L circuit consists of a non-inductive resistor R = 30 Ω and an inductive coil with inductive reactance X_L = 40 Ω connected to a 100 V (RMS), 50 Hz AC voltage source. What is the total impedance (Z), the RMS current (I), and the power factor (cos φ) of the circuit?

  1. Z = 70 Ω, I = 1.43 A, cos φ = 0.43 leading
  2. Z = 10 Ω, I = 10 A, cos φ = 1.0
  3. Z = 50 Ω, I = 2 A, cos φ = 0.8 lagging
  4. Z = 50 Ω, I = 2 A, cos φ = 0.6 lagging Correct answer.

Explanation

1. Impedance of series R-L circuit: Z = √(R² + X_L²) = √(30² + 40²) = √(900 + 1600) = √2500 = 50 Ω. 2. RMS Current: I = V / Z = 100 V / 50 Ω = 2 A. 3. Power factor: cos φ = R / Z = 30 / 50 = 0.6. Since the circuit is inductive, current lags voltage, so the power factor is 0.6 lagging (επαγωγικός).

Question 46Electrical circuits, machines and digital logic

In electric power transformers, where do iron core losses (απώλειες σιδήρου: δινορρεύματα και υστέρηση) occur, and how are eddy current losses effectively minimized in practical manufacturing?

  1. They occur in the ferromagnetic core; eddy currents are reduced by assembling the core from thin, insulated silicon-steel laminations. Correct answer.
  2. They occur in the copper windings; eddy currents are reduced by using thicker solid copper bars.
  3. They occur in the external oil radiator; eddy currents are reduced by adding ceramic coolant.
  4. They occur in the porcelain bushings; eddy currents are reduced by increasing high-voltage insulation.

Explanation

Core losses occur in the magnetic core due to alternating magnetic flux: hysteresis losses (magnetic domain friction) and eddy current losses (induced circular currents). Eddy current losses are proportional to lamination thickness squared (t²); therefore, they are suppressed by laminating the core with thin sheets of silicon alloy steel insulated with varnish.

Question 47Electrical circuits, machines and digital logic

What is the truth table output sequence for a 2-input NAND logic gate for input combinations (A, B) = (0, 0), (0, 1), (1, 0), and (1, 1)?

  1. 0, 0, 0, 1
  2. 1, 0, 0, 0
  3. 1, 1, 1, 0 Correct answer.
  4. 0, 1, 1, 0

Explanation

A NAND gate performs an AND operation followed by an inversion: Y = ¬(A · B). For (0, 0): ¬(0 · 0) = ¬0 = 1. For (0, 1): ¬(0 · 1) = ¬0 = 1. For (1, 0): ¬(1 · 0) = ¬0 = 1. For (1, 1): ¬(1 · 1) = ¬1 = 0. Therefore, the outputs are 1, 1, 1, 0.

Question 48Electrical circuits, machines and digital logic

In a digital combinational Half-Adder (ημιαθροιστής) circuit with single-bit inputs A and B, which logic gates generate the Sum (S) and Carry (C) outputs respectively?

  1. Sum S = A + B (OR), Carry C = A ⊕ B (XOR)
  2. Sum S = A · B (AND), Carry C = A + B (OR)
  3. Sum S = A ⊙ B (XNOR), Carry C = A + B (OR)
  4. Sum S = A ⊕ B (XOR), Carry C = A · B (AND) Correct answer.

Explanation

Binary single-bit addition produces: 0 + 0 = 0 (Sum 0, Carry 0) 0 + 1 = 1 (Sum 1, Carry 0) 1 + 0 = 1 (Sum 1, Carry 0) 1 + 1 = 10₂ (Sum 0, Carry 1). The Sum output matches the XOR function: S = A ⊕ B. The Carry output matches the AND function: C = A · B.

Question 49Electrical circuits, machines and digital logic

A capacitor with capacitance C = 100 μF (100 × 10⁻⁶ F) is connected to a 50 Hz sinusoidal AC electrical line. Calculate its capacitive reactance (χωρητική αντίσταση, X_C). (Use π ≈ 3.1416).

  1. X_C ≈ 31.83 Ω Correct answer.
  2. X_C ≈ 15.92 Ω
  3. X_C ≈ 63.66 Ω
  4. X_C ≈ 314.16 Ω

Explanation

The formula for capacitive reactance is: X_C = 1 / (2π · f · C). Given f = 50 Hz and C = 100 × 10⁻⁶ F = 10⁻⁴ F: 2π · f = 2 · 3.1416 · 50 = 314.16 rad/s. X_C = 1 / (314.16 · 10⁻⁴) = 10,000 / 314.16 ≈ 31.83 Ω.

Question 50Engineering models, drawings, evidence and project decisions

A service van travels from Willemstad to Westpunt, covering a distance of 45 kilometers in 45 minutes (0.75 hours). What is the average speed of the vehicle in kilometers per hour (km/h)?

  1. 60 km/h Correct answer.
  2. 45 km/h
  3. 33.75 km/h
  4. 90 km/h

Explanation

Average speed v = distance / time = s / t = 45 km / 0.75 h = 60 km/h (or 45 km in 45 min = 1 km per minute * 60 minutes = 60 km/h).