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S3 Maths: Equations of Straight Lines (Paper 3 (challenge))
S3 Maths: Equations of Straight Lines (Paper 3 (challenge))
Paper 3 (challenge): ten straight-line questions 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: S3 Maths: Equations of Straight Lines |
| Level | S3 |
02 Questions (10 items)
- FoundationThe point (k, 7) lies on the line through (1, 1) and (3, 7). Find k.
- FoundationGive the slope and both intercepts of 2x – 3y + 6 = 0.
- FoundationFind, in general form, the line through (2, -1) perpendicular to 3x + y = 5.
- IntermediateFind the equation of the line through (1, 4) and (5, -4).
- IntermediateFind the intersection of 2x + y = 7 and x – y = 2.
- IntermediateA triangle has vertices A(0, 0), B(6, 0) and C(2, 4). Find the line containing the altitude from C to AB.
- ChallengeThe points (1, 2), (3, 8) and (5, k) are collinear. Find k.
- ChallengeFor y = mx + 3, what is m if it is parallel to y = 2x – 1, and if it is perpendicular?
- ChallengeFind the area of the triangle formed by 4x – 3y = 24 and the two axes.
- Error redoWrite y – 3 = 2(x – 1) in the general form Ax + By + C = 0.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | k = 3 | The slope is 6 over 2, which is 3, so the line is y = 3x – 2, and 3k – 2 = 7 gives k = 3. |
| 2 | Slope 2/3, y-intercept 2, x-intercept -3 | Rearranging gives y = (2/3)x + 2, and setting y = 0 gives 2x + 6 = 0, so the x-intercept is -3. |
| 3 | x – 3y – 5 = 0 | The given line has slope -3, so the perpendicular slope is 1/3; substituting (2, -1) gives c = -5/3, and multiplying by 3 gives x – 3y – 5 = 0. |
| 4 | y = -2x + 6 | The slope is -4 minus 4 over 5 minus 1, which is -2, and substituting (1, 4) gives c = 6. |
| 5 | (3, 1) | Adding the two equations gives 3x = 9, so x = 3, and substituting back into x – y = 2 gives y = 1. |
| 6 | x = 2 | AB lies on the x-axis, so the perpendicular through C is vertical at the x value of C, which is 2. |
| 7 | k = 14 | The slope of the first two points is 6 over 2, which is 3, so the line is y = 3x – 1 and at x = 5 the value is 14. |
| 8 | Parallel m = 2; perpendicular m = -1/2 | Parallel means the same slope, 2; perpendicular means the slopes multiply to -1, so m is the negative reciprocal -1/2. |
| 9 | 24 square units | The x-intercept is 6 and the y-intercept is -8, so the area is 6 times 8 divided by 2, which is 24. |
| 10 | 2x – y + 1 = 0 | Expanding the right side gives y – 3 = 2x – 2, and rearranging gives 2x – y + 1 = 0. |
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.
Start every straight-line question by writing down what you are given: two points, a point with a slope, or an equation. For slope from two points, subtract the y values and the x values in the same order, because swapping the order flips the sign. Once you have the slope, use y = mx + c and substitute the known point to find c. To convert Ax + By + C = 0 into slope-intercept form, isolate y so the slope is -A/B. Parallel lines share the same slope, perpendicular slopes multiply to -1, and that pair of facts settles most reasoning questions. Finish by substituting your answer back and checking that the intercepts match the graph.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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