Form 3 Trigonometric Ratios Practice
Form 3 · 20 practice questions with instant marking and worked solutions.
Trigonometric Ratios is an important part of the Form 3 mathematics curriculum. This topic develops choosing trigonometric ratios, degree mode, bearings and 3-D contexts. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.
A reliable approach to Trigonometric Ratios has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.
The twenty original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Trigonometric Ratios; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample.
Effective revision is more than recording a score. After completing the Trigonometric Ratios set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.
Trigonometric Ratios should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.
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0 / 20 answered
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1 BasicIn a right triangle, the side opposite θ is 5 and the adjacent side is 12. Find $\tan\theta$. Choose the correct answer.
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2 BasicIn a right triangle, the side opposite θ is 6 and the adjacent side is 8. Find $\tan\theta$. Give the numerical value only.
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3 BasicIn a right triangle, the side opposite θ is 8 and the adjacent side is 15. Find $\tan\theta$. Show the essential working and give the numerical value.
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4 BasicIn Trigonometric Ratios, the value of $\tan\theta=\frac{3}{4}$ is 1. Is this statement true?
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5 StandardIn a right triangle, the side opposite θ is 10 and the adjacent side is 24. Find $\tan\theta$. Choose the correct answer.
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6 StandardIn a right triangle, the side opposite θ is 12 and the adjacent side is 16. Find $\tan\theta$. Give the numerical value only.
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7 StandardIn a right triangle, the side opposite θ is 16 and the adjacent side is 30. Find $\tan\theta$. Show the essential working and give the numerical value.
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8 StandardIn Trigonometric Ratios, the value of $\tan\theta=\frac{6}{8}$ is 3/4. Is this statement true?
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9 AdvancedIn a right triangle, the side opposite θ is 15 and the adjacent side is 36. Find $\tan\theta$. Choose the correct answer.
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10 AdvancedIn a right triangle, the side opposite θ is 18 and the adjacent side is 24. Find $\tan\theta$. Give the numerical value only.
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11 AdvancedIn a right triangle, the side opposite θ is 24 and the adjacent side is 45. Find $\tan\theta$. Show the essential working and give the numerical value.
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12 AdvancedIn Trigonometric Ratios, the value of $\tan\theta=\frac{9}{12}$ is 1. Is this statement true?
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13 ChallengingIn a right triangle, the side opposite θ is 20 and the adjacent side is 48. Find $\tan\theta$. Choose the correct answer.
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14 ChallengingIn a right triangle, the side opposite θ is 24 and the adjacent side is 32. Find $\tan\theta$. Give the numerical value only.
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15 ChallengingIn a right triangle, the side opposite θ is 32 and the adjacent side is 60. Find $\tan\theta$. Show the essential working and give the numerical value.
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16 ChallengingIn Trigonometric Ratios, the value of $\tan\theta=\frac{12}{16}$ is 3/4. Is this statement true?
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17 EliteIn a right triangle, the side opposite θ is 25 and the adjacent side is 60. Find $\tan\theta$. Choose the correct answer.
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18 EliteIn a right triangle, the side opposite θ is 30 and the adjacent side is 40. Find $\tan\theta$. Give the numerical value only.
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19 EliteIn a right triangle, the side opposite θ is 40 and the adjacent side is 75. Find $\tan\theta$. Show the essential working and give the numerical value.
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20 EliteIn Trigonometric Ratios, the value of $\tan\theta=\frac{15}{20}$ is 1. Is this statement true?
The report lists what you got wrong and why. Only you can see it.
Common mistakes
Common mistakes in Trigonometric Ratios
This topic needs particular care with choosing trigonometric ratios, degree mode, bearings and 3-D contexts. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.
Keep missing the same type?
Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.