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Sample Suriname Eindexamen HAVO Practice Questions
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1Differentiate f(x) = 3x³ - 5x² + 7x - 4.
A.9x² - 10x + 7
B.9x² - 5x + 7
C.6x² - 10x + 7
D.9x³ - 10x² + 7x
Explanation: Apply d(xⁿ)/dx = nxⁿ⁻¹ to each polynomial term. The derivatives are 9x², -10x, 7 and 0, giving f′(x) = 9x² - 10x + 7.
2What is the turning point of f(x) = x² - 6x + 8, and what type of extremum is it?
A.Maximum at (3, -1)
B.Minimum at (-3, 35)
C.Minimum at (3, -1)
D.Minimum at (4, 0)
Explanation: Completing the square gives f(x) = (x - 3)² - 1. The square is nonnegative, so the minimum is -1 at x = 3.
3A population follows N(t) = N₀(1.04)^t, with t in years. Using ln 2 = 0.693 and ln 1.04 = 0.0392, what is its approximate doubling time?
A.25.0 years
B.17.7 years
C.12.5 years
D.0.0566 years
Explanation: Doubling requires (1.04)^t = 2. Taking logarithms gives t = ln 2/ln 1.04 = 0.693/0.0392 ≈ 17.7 years.
4Solve log₁₀(x) + log₁₀(x - 3) = 1 over the real numbers.
A.x = -2 and x = 5
B.x = 2
C.x = 10
D.x = 5 only
Explanation: Both logarithms require x > 3. Combining them gives x(x - 3) = 10, or (x - 5)(x + 2) = 0. Only x = 5 satisfies the logarithmic domain.
5In a normal distribution with mean 170 cm and standard deviation 8 cm, approximately what percentage lies between 162 cm and 178 cm?
A.68%
B.95%
C.50%
D.99.7%
Explanation: The interval runs from one standard deviation below the mean to one above it. The normal-distribution empirical rule places approximately 68% of observations in this interval.
6How many different committees of three can be selected from twelve students, if committee members have no distinct roles?
A.1,320
B.36
C.72
D.220
Explanation: Because roles and order do not matter, use combinations. The count is 12 × 11 × 10/(3 × 2 × 1) = 220.
7For an acute angle θ, cos θ = 0.60. What is sin θ?
A.0.40
B.0.80
C.0.64
D.0.36
Explanation: The identity sin²θ + cos²θ = 1 gives sin²θ = 1 - 0.36 = 0.64. Sine is positive for an acute angle, so sin θ = 0.80.
8Which equation describes a circle centred at (2, -3) with radius 4?
A.(x + 2)² + (y - 3)² = 16
B.(x - 2)² + (y + 3)² = 4
C.(x - 2)² + (y + 3)² = 16
D.(x - 2)² + (y - 3)² = 16
Explanation: A circle with centre (h, k) and radius r satisfies (x - h)² + (y - k)² = r². Substituting h = 2, k = -3 and r = 4 gives (x - 2)² + (y + 3)² = 16.
9Find the inverse function of f(x) = 2x - 5 on the real numbers.
A.(x + 5)/2
B.(x - 5)/2
C.2x + 5
D.1/(2x - 5)
Explanation: Starting with y = 2x - 5, solve for x to obtain x = (y + 5)/2. Interchanging the input and output names gives f⁻¹(x) = (x + 5)/2.
10SRD 10,000 earns 6% interest compounded annually, with no deposits, withdrawals or fees. What is the balance after two years?
A.SRD 11,200
B.SRD 10,600
C.SRD 11,236
D.SRD 12,360
Explanation: Annual compounding multiplies the balance by 1.06 each year. After two years it is 10,000 × 1.06² = SRD 11,236, including interest on the first year's interest.
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