Class 11 Mathematics · Chapter 11 · Test 3
Maximum/Minimum Values and Applications
43 MCQs Covers maximum and minimum values of a + b sin(cθ + d) and their reciprocals, plus amplitude, period and shifts.
43 questions · 35 min · 43 marks
Want to try first? Take the free Mathematics test: Complex Number Operations
Sample questions
The first 5 of 43. Try each one, then tap to see the answer.
Question 1
For f(θ) = a + b sin θ, the maximum value is:
- Aa − |b|
- Ba + |b|
- C|a| + b
- Da·b
Show answerHide answer
Answer: B
Since sin θ ≤ 1, the maximum is M = a + |b| (when b sin θ is largest).
Question 2
For f(θ) = a + b sin θ, the minimum value is:
- Aa + |b|
- B|a| − b
- C−a
- Da − |b|
Show answerHide answer
Answer: D
The minimum is m = a − |b|.
Question 3
The amplitude of f(θ) = a + b sin θ can be found using:
- A(M − m)/2
- B(M + m)/2
- CM·m
- DM/m
Show answerHide answer
Answer: A
M − m = 2|b|, so the amplitude |b| = (M − m)/2.
Question 4
In f(θ) = a + b sin(cθ + d), the constant a represents:
- Athe phase shift
- Bthe period
- Cthe vertical shift
- Dthe amplitude
Show answerHide answer
Answer: C
a moves the graph up or down without changing its shape or period.
Question 5
In f(θ) = a + b sin(cθ + d), the constant d produces:
- Aa vertical shift
- Ba phase shift (horizontal translation)
- Ca change in amplitude
- Da change in period
Show answerHide answer
Answer: B
d shifts the wave left (if d > 0) or right (if d < 0).
More tests in Trigonometric Functions and their Graphs
Practise with a free account
Save your scores, see which chapters need work, and keep a notebook of every question you got wrong.