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##### 預微積分/三角函數 （時間限制：40 分鐘）

##### 年終評估

1. Suppose that the 𝑥-intercepts of the graph of 𝑦 = 𝑓( 𝑥) are (-9,0) and (2,0). what are the 𝑥-intercepts of the graph of 𝑦 =5𝑓 (𝑥+4 )?

(−13, 2 and (−2, 1)

(−13, 0) and (−2, 0)

(2, 0) and (−2, 0)

(−10,0) and (2, 0)

2. Suppose 𝑓 is an odd function. What is an equivalent expression for 𝑓(−𝑥 )?

f(x)

–f(-x)

–f(x)

None of the above

3. A farmer is fencing a triangular field. The sides of the field are 45 yards, 53 yards, and 72 yards respectively. In order to make the fence perfect, the farmer needs to know the angle opposite the shortest side. Find this angle to the nearest degree.

36°

39°

49°

19°

4. Convert − 11𝜋/ 9 to degrees and write it as the least possible positive coterminal angle

240°

80°

40°

140°

5. Find the largest possible angle in a triangle with sides 𝑎 = 1 and 𝑏 = 2 and ∠𝐴 = 10°, where side 𝑎 is opposite of ∠𝐴. Round to the nearest degree.

150°

80°

60°

160°

6. Determine the solution set of the equation log 𝑥−2 =1−log 𝑥+1 .

4,-3

4

-3

no solution

7. The graph of which function has a period of 𝜋 and an amplitude of 𝜋

𝑦=1/2𝜋sin2𝑥

𝑦=𝜋sin𝑥

𝑦=2𝜋sin2𝑥

𝑦=𝜋sin2𝑥

8. Convert 29.411° to 𝐷°𝑀'𝑆" (degrees, minutes, seconds). Round to the nearest second.

29°24'40"

29°14'40"

19°24'40"

29°14'44"

9. Write and simplify the fifth term of the expansion of (x + 1)^8

70x⁴

35x⁴

70𝑥³

80𝑥³

10. There are 9 boys and 11 girls in a Grade 12 English class. In how many ways can 5 students be chosen for a group project if the group must have 3 female members and 2 male members?

940 ways

540 ways

9540 ways

5940 ways

11. What are the real zeros of the function (𝑥) = 𝑥³ + 6𝑥² − 13𝑥 − 42 ?

7, 3, 1

−7, 3, 1

−7, 3, −2

None of the above

12. How long will it take for 1000 to double, in an investment, when interest is compounded continuously at the rate of 5.8% per annum. Round your answer to the nearest year.

9

10

11

12

13. Find the measure of a central angle θ that is subtended by the arc of length π and has a radius of 4. Express angle θ in degrees.

θ = 45 degrees

θ = 75 degrees

θ = 90 degrees

θ = 120 degrees

14. A ball is thrown in the air. After t seconds, the ball is at an altitude of h(t) = 12−3(t−2)² feet above the ground. What is the highest altitude above the ground that the ball will reach?

8 feet

2 feet

10 feet

12 feet

15. Only one of the following statements is true about the rational function f(x) = 1/x . Which is that statement?

y → ∞ as x → ∞ and y → ∞ as x → −∞

y → ∞ as x → ∞ and y → −∞ as x → −∞

the function has a horizontal asymptote

the function has no vertical asymptote

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