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S5 Maths: Trigonometric Graphs and Transformations: Paper 1 (basics)
S5 Maths: Trigonometric Graphs and Transformations: Paper 1 (basics)
Ten items to build the base: extreme values and periods of sine, cosine and tangent, plus vertical stretch and horizontal shift.
Direct answers Items 1-3: 1, negative 1, 360 degrees. Items 4-6: 3, 180 degrees, 3. Items 7-9: 180 degrees, right by 30 degrees, reflection in the x-axis. Item 10: the period stays 360 degrees and the 2 only changes the amplitude.
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 | Basic |
02 Questions (10 items)
- FoundationWhat is the maximum value of y = sin x?
- FoundationWhat is the minimum value of y = sin x?
- FoundationWhat is the period of y = sin x in degrees?
- IntermediateWhat is the amplitude of y = 3 sin x?
- IntermediateWhat is the period of y = sin 2x in degrees?
- IntermediateWhat is the maximum value of y = cos x + 2?
- ChallengeWhat is the period of y = tan x in degrees?
- ChallengeGoing from y = sin x to y = sin(x – 30 degrees), which way does the graph move and by how much?
- ChallengeGoing from y = sin x to y = -sin x, what happens to the graph?
- Error redoA student says y = 2 sin x has period 720 degrees because of the 2 in front. What is wrong, and what is the period?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1 | The peak of a sine wave is at 90 degrees, where the value is 1. |
| 2 | Negative 1 | The trough of a sine wave is at 270 degrees, where the value is negative 1. |
| 3 | 360 degrees | A sine graph repeats every 360 degrees, so the period is 360 degrees. |
| 4 | 3 | The amplitude is the multiplier in front of sine, so it is 3. |
| 5 | 180 degrees | The 2 in front of x halves the period, and 360 divided by 2 is 180 degrees. |
| 6 | 3 | cos x peaks at 1 and the whole graph moves up 2, so the maximum is 3. |
| 7 | 180 degrees | A tangent graph repeats every 180 degrees, so its period is 180 degrees. |
| 8 | Right by 30 degrees | A minus inside the bracket moves the graph to the right by 30 degrees. |
| 9 | It is reflected in the x-axis | A minus sign changes the sign of every y value, so the graph flips over the x-axis. |
| 10 | The 2 changes the amplitude only; the period stays 360 degrees | Only a multiplier on x changes the period, while a multiplier outside changes the amplitude. |
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 down amplitude, period and shift before answering each item.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.