PRE CALCULUS Advanced Topics 4 ā Questions and Answers
Question 1: What is the dot product of vectors u = āØ2, ā1ā© and v = āØ4, 3ā©?
- 5 (Correct answer)
- 11
- ā5
- 8
Correct answer: 5
u Ā· v = (2)(4) + (ā1)(3) = 8 ā 3 = 5.
Question 2: What is the period of the function f(x) = sin(3x)?
- 2Ļ/3 (Correct answer)
- 3Ļ
- 6Ļ
- 2Ļ
Correct answer: 2Ļ/3
The period of sin(bx) is 2Ļ/b, so for b=3 the period is 2Ļ/3.
Question 3: Which test can confirm that a power series converges?
- Ratio Test (Correct answer)
- Horizontal Line Test
- Vertical Line Test
- Symmetry Test
Correct answer: Ratio Test
The Ratio Test evaluates lim|aāāā/aā| and determines convergence when the limit is less than 1.
Question 4: The eccentricity of an ellipse satisfies which condition?
- 0 < e < 1 (Correct answer)
- e = 1
- e > 1
- e = 0
Correct answer: 0 < e < 1
For an ellipse, the eccentricity e = c/a lies strictly between 0 and 1.
Question 5: What is the value of iā“ where i = ā(ā1)?
- 1 (Correct answer)
- ā1
- i
- āi
Correct answer: 1
iĀ²=ā1, so iā“=(iĀ²)Ā²=(ā1)Ā²=1.
Question 6: Which of the following is the general term of the sequence 2, 6, 18, 54, ā¦?
- 2Ā·3^(nā1) (Correct answer)
- 3Ā·2^(nā1)
- 2n+4
- 6nā4
Correct answer: 2Ā·3^(nā1)
The sequence has first term 2 and common ratio 3, giving aā = 2Ā·3^(nā1).
Question 7: Which of the following describes an even function?
- f(āx) = f(x) for all x (Correct answer)
- f(āx) = āf(x) for all x
- f(x+p) = f(x) for some p
- f(x) = f(x+1)
Correct answer: f(āx) = f(x) for all x
A function is even if f(āx)=f(x), meaning its graph is symmetric about the y-axis.
PRE CALCULUS Advanced Topics 4
What is the dot product of vectors u = āØ2, ā1ā© and v = āØ4, 3ā©?