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Grade 12 Mathematics entrance exam, 2017 E.C. (2025), natural stream

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2017 E.C. Every question comes with the correct answer and a worked explanation. This is the natural stream paper. The other stream sat a different Mathematics paper the same year, listed further down.

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  • Natural science stream

    Who sits it

  • 2017 E.C. (2025), natural stream

    Exam year

  • 50 questions with answers

    In this set

Try questions from this paper

Answer each question yourself before opening the answer. The explanations point to the exact place in the textbook, so you know which page to reread when you miss one.

Question 1

Which one of the following function is NOT a power function?

  1. A.f(x)=x−35f(x) = x^{-\frac{3}{5}}
  2. B.f(x)=2x32f(x) = \sqrt{2} x^{\frac{3}{2}}
  3. C.f(x)=πx5f(x) = \pi x^5
  4. D.f(x)=(3)xf(x) = (\sqrt{3})^x
Show the answer and explanation

Answer: D f(x)=(3)xf(x) = (\sqrt{3})^x

Why

A power function is defined as f(x)=kxaf(x) = k x^a where the variable is in the base. Since f(x)=(3)xf(x) = (\sqrt{3})^x has the variable in the exponent, it is an exponential function, not a power function.

Question 2

Let f(x)=(1−2x)12f(x) = (1 - 2x)^\frac{1}{2}. Then what is the values of f′(x)f'(x)?

  1. A.11−2x\frac{1}{\sqrt{1 - 2x}}
  2. B.−121−2x\frac{-1}{2} \sqrt{1 - 2x}
  3. C.121−2x\frac{1}{2} \sqrt{1 - 2x}
  4. D.−11−2x-\frac{1}{\sqrt{1 - 2x}}
Show the answer and explanation

Answer: D −11−2x-\frac{1}{\sqrt{1 - 2x}}

Why

Using the chain rule, the derivative of f(x)=(1−2x)1/2f(x) = (1 - 2x)^{1/2} is f′(x)=12(1−2x)−1/2⋅ddx(1−2x)=12(1−2x)−1/2⋅(−2)=−11−2xf'(x) = \frac{1}{2}(1 - 2x)^{-1/2} \cdot \frac{d}{dx}(1 - 2x) = \frac{1}{2}(1 - 2x)^{-1/2} \cdot (-2) = -\frac{1}{\sqrt{1 - 2x}}.

Question 3

Which of the following statement describes the difference between scalar and vector quantities?

  1. A.Physical quantities that only have direction are scalars, while that have only magnitude are vectors.
  2. B.Physical quantities that only have magnitude are scalars, while that have both magnitude and direction are vectors.
  3. C.Physical quantities that only have magnitude are vectors, while that have both magnitude and direction are scalars.
  4. D.Physical quantities that only have direction are vectors, while that have both magnitude and direction are scalars.
Show the answer and explanation

Answer: B Physical quantities that only have magnitude are scalars, while that have both magnitude and direction are vectors.

Why

By definition, scalar quantities possess only magnitude, whereas vector quantities possess both magnitude and a specific direction in space.

Question 4

Consider the following data: 1, 3, 7, 9, 11, 13, 18, 28. Then the coefficient of mean deviation about the median is equal to:

  1. A.14\frac{1}{4}
  2. B.85\frac{8}{5}
  3. C.58\frac{5}{8}
  4. D.12\frac{1}{2}
Show the answer and explanation

Answer: C 58\frac{5}{8}

Why

The median of the ordered data set is 1010. The sum of the absolute deviations about the median is 9+7+3+1+1+3+8+18=509+7+3+1+1+3+8+18 = 50, giving a mean deviation of 6.256.25. Dividing this by the median yields the coefficient of mean deviation: 6.25/10=0.625=5/86.25 / 10 = 0.625 = 5/8.

Question 5

Which one of the following is an irrational number?

  1. A.3.40003.4000
  2. B.0.04\sqrt{0.04}
  3. C.1.16222...1.16222...
  4. D.29\sqrt{29}
Show the answer and explanation

Answer: D 29\sqrt{29}

Why

Terminating decimals, repeating decimals, and square roots of perfect squares are all rational numbers. Since 2929 is not a perfect square, its square root is an irrational number.

Question 7

Which one of the following statements defines favorable outcomes in a random experiment?

  1. A.The outcomes that insure the occurrence of a particular result.
  2. B.The outcomes containing all sample elements.
  3. C.The outcomes containing only one sample element.
  4. D.The outcomes that have equal chance of being chosen.
Show the answer and explanation

Answer: A The outcomes that insure the occurrence of a particular result.

Why

Favorable outcomes are those outcomes in the sample space of a random experiment that correspond to the occurrence of a specific desired event.

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The other Mathematics papers of 2017 E.C.

2017 E.C. (2025)2017 E.C. (2025), version 12017 E.C. (2025), version 22017 E.C. (2025), version 4

Mathematics papers from other years

2018 E.C. (2026)2018 E.C. (2026), social stream2018 E.C. (2026), version 12018 E.C. (2026), version 22018 E.C. (2026), version 32018 E.C. (2026), version 42018 E.C. (2026), version 52018 E.C. (2026), version 62016 E.C. (2024)2016 E.C. (2024), natural stream2016 E.C. (2024), social stream2016 E.C. model exam2015 E.C. (2023)2015 E.C. (2023), natural stream2015 E.C. (2023), social stream2014 E.C. (2022)2014 E.C. (2022), social stream2013 E.C. (2021)2013 E.C. (2021), version 12011 E.C. (2019)2009 E.C. (2017)2008 E.C. (2016)2007 E.C. (2015)2006 E.C. (2014)2005 E.C. (2013)

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Are these the real 2017 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2017 E.C. (2025). Our set holds 50 of its questions, each with its answer and an explanation that points back to the textbook.

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Can I download the Mathematics 2017 E.C. paper as a PDF?

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