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112年 - 112-1 國立南科國際實驗高級中學正式教師甄選試題_雙語部:數學專業能力#114450
> 申論題
2. Given an angle
θ
，the solution of equation
Please find the solution of equation
相關申論題
1. Given a polynomial f(x) whose degree is no less than 3. The remainders of f(x) being divided by (x − a)(x − b), (x − b)(x − c), (x − a)(x − c) are −x − 5, 4x, 3x + 3 respectively. Find the remainder of f(x) being divided by (x − a)(x − b)(x − c).
#488889
2. How many nonnegative integer solutions are there to the equation x + 2y + 3z = 17?
#488890
3. Find the largest possible volume of the tetrahedron PQRS, where P(1,0,0), Q(0,2,0), R(0,0,3) and S lies on the unit sphere centered at the origin.
#488891
4. The parametric curve (x, y) = (2 cos θ , 2 sin θ + 3 cos θ), 0 ≤ θ ≤ 2π represents an ellipse. Find the foci that lie in the first quadrant.
#488892
5. Let f(x) = x(x − 1)(x − 2) … (x − 2023) and g(x) = f(f(x)). Calculate g ′ (1).
#488893
6. Find all a such that both of equations x2 + αx + 1996 = 0 and x 2 + 1996x + α= 0 has two integer roots.
#488894
7. Appling Gram-Schmidt method, it can decomposition vector = (3, −4) and = (4,3), α, β are real number. Please find the 2 × 2 matrix P, such that .
#488895
8. If the distribution of discrete random variable X is ,where p is positive real number, please find the variance Var(X) of X.
#488896
1. There was a class of 41 people divided into three groups A, B, and C, and the average score of subject natural’s test was 89.7 points; the average score of group A was 89.8 points; the average score of A, B combination was 88.5 points; the average score of A and C combination was 91 points, and how many people were in each of groups A, B and C?
#488897
3. As figure 1, two 3 by 4 rectangles overlap in such a way that their sides are perpendicular. If the area and perimeter of the shaded region are 22 and 20 respectively, compute length AB.
#488899
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