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UCE (O-Level) Geometry — practice questions

Explore 49 free Geometry questions in UCE (O-Level) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry questions and exercises with answers

Showing questions 1–30 of 49.

A sailor in a boat looks up at the top of a cliff. What is the angle between the line of sight and the horizontal called?Read the answer and worked solution →An observer stands on top of a cliff and looks down at a boat below. What is the angle between the line of sight and the horizontal called?Read the answer and worked solution →Which result is used alongside the three trigonometric ratios to solve two-dimensional problems?Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Sort each statement by which idea it describesRead the answer and worked solution →Complete the arc length relationRead the answer and worked solution →

Worked practice questions

A sailor in a boat looks up at the top of a cliff. What is the angle between the line of sight and the horizontal called?

  1. The angle of depression
  2. The angle of reflection
  3. The angle of rotation
  4. The angle of elevation
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Correct answer: D. The angle of elevation

1. The top of the cliff sits above the horizontal plane through the sailor's eyes. 2. The angle of elevation is the angle formed by the line of sight and the horizontal plane for an object above it. 3. The cliff can be treated as a vertical line, which gives a right-angled triangle. 4. In trigonometry the angle of inclination means the same thing as the angle of elevation. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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An observer stands on top of a cliff and looks down at a boat below. What is the angle between the line of sight and the horizontal called?

  1. The angle of depression
  2. The angle of elevation
  3. The angle of incidence
  4. The angle of inclination
Show answer and solution

Correct answer: A. The angle of depression

1. The boat sits below the horizontal plane through the observer's eyes. 2. The angle of depression is the angle formed by the line of sight and the horizontal plane for an object below it. 3. The angle of elevation from the boat back up to the observer has the same size. 4. The angle of inclination is another name for the angle of elevation, so it names the upward case. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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Which result is used alongside the three trigonometric ratios to solve two-dimensional problems?

  1. The mid-point theorem
  2. The theorem of Pythagoras
  3. The remainder theorem
  4. The factor theorem rule
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Correct answer: B. The theorem of Pythagoras

1. The three trigonometric ratios are sine, cosine and tangent. 2. Each ratio links one angle to two of the three sides of a right-angled triangle. 3. Sometimes a problem gives two sides and needs the third one before a ratio can be used. 4. The theorem of Pythagoras supplies that missing third side. 5. These three ratios and the theorem of Pythagoras together solve two-dimensional problems. 6. The mid-point theorem belongs to geometry of triangles and says nothing about angles in a right-angled triangle. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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