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NSC / Matric Geometry — practice questions

Explore 48 free Geometry questions in NSC / Matric 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 48.

Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?Read the answer and worked solution →When solving a trigonometric equation, what is the CAST diagram used for?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 →Match each identity to its nameRead the answer and worked solution →

Worked practice questions

Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?

  1. The functions are always positive
  2. The functions repeat periodically
  3. The functions have no maximum
  4. The functions are not continuous
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Correct answer: B. The functions repeat periodically

1. Sine, cosine and tangent all repeat their values after a fixed interval of angle. 2. So once one angle satisfies an equation, adding whole periods to it gives more angles that also satisfy it. 3. Subtracting whole periods works in the same way and gives negative angles. 4. That is why a general solution is written with a whole number of periods added on. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_

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When solving a trigonometric equation, what is the CAST diagram used for?

  1. To find the size of the reference angle
  2. To find the period of the function
  3. To find where the ratio is positive
  4. To find the value of the amplitude
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Correct answer: C. To find where the ratio is positive

1. A calculator returns only one angle, called the reference angle, for a given ratio. 2. But the same ratio has the same sign in two of the four quadrants. 3. The CAST diagram records which trigonometric ratios are positive in each quadrant. 4. It is therefore used to decide which quadrants the solutions lie in. 5. The reference angle itself comes from the calculator, not from the diagram. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_

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Complete the definition of conditional probability

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Missing parts
  1. Answer
    P(F)
    Choices
    1. P(F)
    2. P(E)
    3. P(E ∪ F)
  2. Answer
    not zero
    Choices
    1. not zero
    2. equal to 1
    3. less than P(E)
  3. Answer
    0 and 1
    Choices
    1. 0 and 1
    2. −1 and 1
    3. 0 and P(F)
Complete the statement
P(E|F) is defined as P(E ∩ F) divided by {0}, and it is only defined when P(F) is {1}. Its value always lies between {2}.
The definition the whole chapter is built on, including the condition that makes it meaningful. Source: syllabus Maths Part II, Ch 13 Probability.

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