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S5 Maths: Trigonometric Graphs and Transformations: Paper 4 (error replay)
S5 Maths: Trigonometric Graphs and Transformations: Paper 4 (error replay)
Ten items on the usual slips: swapping amplitude and period, reversing the shift direction, and the undefined point of tangent at 90 degrees.
Direct answers Items 1-3: maximum 6 and negative 6, 90 degrees, maximum 3 and 1. Items 4-6: undefined, left by 60 degrees, maximum 1 and negative 1. Items 7-9: amplitude 3 with period 180 degrees, maximum 4 and 2, one point. Item 10: the direction is wrong and the shift is 90 degrees to the right.
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 | Error replay |
02 Questions (10 items)
- FoundationFind the maximum and minimum of y = 6 cos x.
- FoundationWhat is the period of y = sin 4x in degrees?
- FoundationFind the maximum and minimum of y = 2 + cos x.
- IntermediateWhat is the value of y = tan x at x = 90 degrees?
- IntermediateGoing from y = sin x to y = sin(x + 60 degrees), which way does the graph move and by how much?
- IntermediateFind the maximum and minimum of y = -cos x.
- ChallengeFind the amplitude and period of y = 3 sin 2x.
- ChallengeFind the maximum and minimum of y = cos 2x + 3.
- ChallengeBetween 0 and 360 degrees, how many maximum points does y = sin x have?
- Error redoA student says y = sin(x – 90 degrees) moves 90 degrees to the left. What is wrong, and what is the correct direction?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Maximum 6, minimum negative 6 | cos x runs from negative 1 to 1, and multiplying by 6 gives 6 and negative 6. |
| 2 | 90 degrees | The multiplier on x is 4, and 360 divided by 4 is 90 degrees. |
| 3 | Maximum 3, minimum 1 | cos x runs from negative 1 to 1, and adding 2 gives 3 and 1. |
| 4 | Undefined | 90 degrees is an asymptote of the tangent graph, since cos 90 degrees is 0 and division by 0 is undefined. |
| 5 | Left by 60 degrees | A plus inside the bracket moves the graph to the left by 60 degrees. |
| 6 | Maximum 1, minimum negative 1 | The minus sign flips the graph vertically but does not change the size of the extreme values. |
| 7 | Amplitude 3, period 180 degrees | The outside 3 is the amplitude and the 2 on x makes the period 360 divided by 2, which is 180 degrees. |
| 8 | Maximum 4, minimum 2 | cos 2x still runs from negative 1 to 1, and adding 3 gives 4 and 2. |
| 9 | One | Sine reaches its maximum of 1 only at 90 degrees, so there is a single maximum point. |
| 10 | The direction is wrong; the minus inside moves the graph 90 degrees to the right | A plus shifts left and a minus shifts right, so subtracting 90 degrees moves the graph to the right. |
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.
Write one line for each slip, such as treating the amplitude as the period.Tutor Registration →
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