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S4 Maths: Sine Rule and Cosine Rule (Paper 4 (error clinic))
S4 Maths: Sine Rule and Cosine Rule (Paper 4 (error clinic))
Paper 4 (error clinic): ten questions on the sine rule and the cosine rule with answers and one-line notes.
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: S4 Maths: Sine Rule and Cosine Rule |
| Level | S4 |
02 Questions (10 items)
- FoundationIn triangle ABC, A = 45 degrees, B = 60 degrees and a = 6 cm. Find b.
- FoundationTwo sides are 3 cm and 4 cm with an included angle of 90 degrees. Find the third side.
- FoundationA triangle has sides 5 cm and 8 cm with an included angle of 90 degrees. Find its area.
- IntermediateTwo sides are 9 cm and 6 cm with an included angle of 50 degrees. Find the third side.
- IntermediateAn isosceles triangle has sides 5 cm, 5 cm and 8 cm. Find the base angle A opposite the other 5 cm side.
- IntermediateIn triangle ABC, b = 14 cm, B = 42 degrees and C = 98 degrees. Find c.
- ChallengeA triangle has area 24 cm squared with two sides of 8 cm. Find the two possible included angles.
- ChallengeA triangle has sides 6 cm, 7 cm and 7 cm. Find its area.
- ChallengeIn triangle ABC, a = 9 cm, b = 11 cm and A = 40 degrees. Find all possible B and the number of solutions.
- Error redoIn a triangle A = 50 degrees, B = 60 degrees and a = 10 cm. Find b. A student starts with the cosine rule and gets stuck. Which rule applies and what is b?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | b = 7.348 cm. | b is 6 times sin 60 degrees divided by sin 45 degrees. |
| 2 | The third side is 5 cm. | cos 90 degrees is 0, so this is just Pythagoras and c squared is 25. |
| 3 | The area is 20 cm squared. | sin 90 degrees is 1, so the area is 5 times 8 halved. |
| 4 | The third side is 6.898 cm. | c squared is 81 + 36 minus 108 times cos 50 degrees, about 47.6. |
| 5 | A = 36.87 degrees. | cos A is 64 over 80, that is 0.8. |
| 6 | c = 20.719 cm. | c is 14 times sin 98 degrees divided by sin 42 degrees. |
| 7 | C = 48.59 degrees or 131.41 degrees. | sin C is 48 over 64, so an acute and an obtuse angle both work. |
| 8 | The area is 18.974 cm squared. | With s = 10 the area is the square root of 10 times 4 times 3 times 3. |
| 9 | B = 51.779 degrees or 128.221 degrees, giving two triangles. | sin B is about 0.786, and 40 plus 128.2 stays under 180. |
| 10 | b = 11.305 cm, from the sine rule b = 10 times sin 60 degrees divided by sin 50 degrees. | With two angles and one side there is no included angle, so the sine rule applies. |
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.
Ask what you hold first: three sides, two sides with the included angle, or two angles with a side. Use the sine rule for two angles and a side, and the cosine rule when the included angle is known. When a sine rule gives an angle, check whether 180 degrees minus it is still valid, because that gives a second triangle. For the area, take half the product of two sides times the sine of the included angle.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.
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