Start learning →

NSC / Matric Integral Calculus — practice questions

Explore 22 free Integral Calculus questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Integral Calculus with Quill →

Integral Calculus questions and exercises with answers

Showing questions 1–22 of 22.

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 arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead 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 →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead 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
Show answer and solution

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_

Open this question →

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
Show answer and solution

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_

Open this question →

Complete the arc length relation

Read exercise and reference answers
Missing parts
  1. Answer
    rθ
    Choices
    1. rθ
    2. r/θ
    3. θ/r
Complete the statement
In a circle of radius r, an arc of length l subtends an angle of θ radians, and these are related by l = {0}.
The definition of radian measure, from the first summary bullet. Source: syllabus Maths, Ch 3 Trigonometric Functions.

Open this exercise →

How to practise

  1. Choose a Integral Calculus question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Sequences and SeriesBinomial TheoremCorrelation and RegressionGeometryLinear ProgrammingMeanMedianPermcomb