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100+ Free Mathematics Advanced Practice Questions

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Key Facts: Mathematics Advanced Exam

Drill Finland Ylioppilastutkinto mathematics advanced skills with 100 original English MCQs: functions, algebra, geometry, probability, modeling, and calculus ideas. Official exam is a 6-hour digital constructed-response paper (max 120 points).

Sample Mathematics Advanced Practice Questions

Try these sample questions to test your Mathematics Advanced exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Let f(x) = 3x^2 - 5x + 2. What is f(2)?
A.4
B.6
C.8
D.12
Explanation: Substitute x = 2: f(2) = 3(2)^2 - 5(2) + 2 = 3·4 - 10 + 2 = 12 - 10 + 2 = 4.
2The quadratic f(x) = x^2 - 6x + 5 has roots at:
A.x = 1 and x = 5
B.x = -1 and x = -5
C.x = 2 and x = 3
D.x = 0 and x = 6
Explanation: Factor x^2 - 6x + 5 = (x - 1)(x - 5). Setting each factor to zero gives roots x = 1 and x = 5. The quadratic formula with Δ = 36 - 20 = 16 yields the same roots: (6 ± 4)/2.
3What is the vertex of the parabola y = x^2 - 4x + 7?
A.(2, 3)
B.(2, 7)
C.(-2, 3)
D.(4, 7)
Explanation: For y = ax^2 + bx + c the vertex abscissa is x = -b/(2a) = 4/2 = 2. Then y = 2^2 - 4·2 + 7 = 4 - 8 + 7 = 3. Completing the square gives y = (x - 2)^2 + 3, confirming vertex (2, 3).
4The domain of f(x) = 1/(x - 3) is all real x except:
A.x = 3
B.x = 0
C.x = 1
D.x = -3
Explanation: A rational function is undefined where the denominator is zero. Solving x - 3 = 0 gives the excluded value x = 3. Every other real number is in the domain.
5Simplify (x^2 - 9)/(x - 3) for x ≠ 3.
A.x + 3
B.x - 3
C.x^2 - 3
D.9
Explanation: Difference of squares: x^2 - 9 = (x - 3)(x + 3). Cancelling the common factor (x - 3) for x ≠ 3 leaves x + 3.
6If f(x) = 2^x, what is f(3)?
A.8
B.6
C.9
D.4
Explanation: By definition of exponential powers, 2^3 = 2·2·2 = 8, so f(3) = 8.
7log_2(16) equals:
A.4
B.2
C.8
D.16
Explanation: log_2(16) is the exponent that produces 16 when the base is 2. Since 2^4 = 16, log_2(16) = 4.
8sin(π/6) equals:
A.1/2
B.√3/2
C.√2/2
D.1
Explanation: The standard special-angle value is sin(π/6) = sin(30°) = 1/2.
9cos(π/3) equals:
A.1/2
B.√3/2
C.0
D.√2/2
Explanation: The standard special-angle value is cos(π/3) = cos(60°) = 1/2.
10The range of f(x) = e^x is:
A.(0, ∞)
B.(-∞, ∞)
C.[0, ∞)
D.(-∞, 0)
Explanation: The exponential e^x is positive for every real x. As x → -∞, e^x → 0 but never reaches 0; as x → ∞, e^x → ∞. Therefore the range is the open interval (0, ∞).

About the Mathematics Advanced Practice Questions

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