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S5 Maths: Trigonometric Graphs and Transformations: Paper 2 (intermediate)
S5 Maths: Trigonometric Graphs and Transformations: Paper 2 (intermediate)
Ten combined items: changing amplitude and period together, finding extreme values with a vertical shift, and turning an inside constant into a shift.
Direct answers Items 1-3: 4, 120 degrees, 720 degrees. Items 4-6: maximum 4 and negative 2, maximum 7 and 3, left by 30 degrees. Items 7-9: 90 degrees, vertical stretch of 3, negative 3. Item 10: the period is 180 degrees.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S5 Maths: Trigonometric Graphs and Transformations |
| Level | Intermediate |
02 Questions (10 items)
- FoundationWhat is the amplitude of y = 4 cos 3x?
- FoundationWhat is the period of y = 4 cos 3x in degrees?
- FoundationWhat is the period of y = 2 sin(x/2) in degrees?
- IntermediateFind the maximum and minimum of y = 1 + 3 sin x.
- IntermediateFind the maximum and minimum of y = 5 – 2 cos x.
- IntermediateHow is the graph of y = sin(2x + 60 degrees) shifted from y = sin 2x?
- ChallengeWhat is the period of y = tan 2x in degrees?
- ChallengeGoing from y = sin x to y = 3 sin x, what happens to the graph?
- ChallengeWhat is the maximum value of y = sin x – 4?
- Error redoA student says y = cos 2x has period 360 degrees because cos x does. What is wrong, and what is the period?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 4 | The 4 in front of cosine is the amplitude. |
| 2 | 120 degrees | The multiplier on x is 3, and 360 divided by 3 is 120 degrees. |
| 3 | 720 degrees | The multiplier is one half, so 360 divided by one half gives 720 degrees. |
| 4 | Maximum 4, minimum negative 2 | The sine part runs from negative 3 to 3, and adding 1 gives maximum 4 and minimum negative 2. |
| 5 | Maximum 7, minimum 3 | cos x runs from negative 1 to 1, times negative 2 gives 2 to negative 2, and adding 5 gives 7 and 3. |
| 6 | Left by 30 degrees | Factor out the 2 to get sin 2(x + 30 degrees), and a plus means 30 degrees to the left. |
| 7 | 90 degrees | The basic tangent period is 180 degrees, and dividing by 2 gives 90 degrees. |
| 8 | It is stretched vertically by a factor of 3 | The outside factor 3 multiplies every y value by 3, which is a vertical stretch. |
| 9 | Negative 3 | Sine peaks at 1 and the graph moves down 4, so the maximum is negative 3. |
| 10 | The 2 on x halves the period, so the period is 180 degrees | The period depends only on the multiplier of x, and 2 turns 360 degrees into 180 degrees. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Rewrite each function as y equals a constant plus amplitude times the trig function of a multiple of x plus a shift.Tutor Registration →
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