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Grade 12 Mathematics entrance exam, 2015 E.C. (2023), social stream

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2015 E.C. Every question comes with the correct answer and a worked explanation. This is the social stream paper. The other stream sat a different Mathematics paper the same year, listed further down.

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  • Social science stream

    Who sits it

  • 2015 E.C. (2023), social stream

    Exam year

  • 44 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 9

Which one of the following defines a prime number?

  1. A.It is a natural number where one of its factors is 33.
  2. B.It is a natural number that has exactly two distinct factors.
  3. C.It is an odd natural number that has only two factors.
  4. D.It is a natural number that has an odd number of factors.
Show the answer and explanation

Answer: B It is a natural number that has exactly two distinct factors.

Why

A prime number is defined as a natural number greater than 1 that has exactly two distinct positive divisors (factors): 1 and itself.

Question 10

Which one of the following is a vector quantity?

  1. A.Temperature of a room.
  2. B.Floor area of a classroom.
  3. C.Speed of a motorbike.
  4. D.Force to push a car.
Show the answer and explanation

Answer: D Force to push a car.

Why

Force is a vector quantity because it has both magnitude and direction, whereas temperature, area, and speed are scalar quantities.

Question 13

Which one of the following is true for the values of the trigonometric functions for the indicated angles?

  1. A.sin⁡(5π2)=−1\sin\left(\frac{5\pi}{2}\right)=-1
  2. B.tan⁡(−3π)=−1\tan(-3\pi)=-1
  3. C.cos⁡(−3π2)=0\cos\left(-\frac{3\pi}{2}\right)=0
  4. D.tan⁡(7π)=−1\tan(7\pi)=-1
Show the answer and explanation

Answer: C cos⁡(−3π2)=0\cos\left(-\frac{3\pi}{2}\right)=0

Why

Since cosine is an even function, cos⁡(−3π2)=cos⁡(3π2)=0\cos(-\frac{3\pi}{2}) = \cos(\frac{3\pi}{2}) = 0. The other options are incorrect: sin⁡(5π2)=1\sin(\frac{5\pi}{2}) = 1, and tan⁡(−3π)=tan⁡(7π)=0\tan(-3\pi) = \tan(7\pi) = 0.

Question 14

Which one of the following is true about the function f(x)=cos⁡xf(x) = \cos x?

  1. A.Domain of ff is [−1,1][-1,1].
  2. B.It is periodic with period 2π2\pi.
  3. C.Range of ff is {y∣y∈R}\{y|y\in\mathbb{R}\}.
  4. D.The difference between its maximum and minimum values is 2π2\pi.
Show the answer and explanation

Answer: B It is periodic with period 2π2\pi.

Why

The function f(x)=cos⁡xf(x) = \cos x is a fundamental trigonometric function with a domain of R\mathbb{R}, a range of [−1,1][-1, 1], and a periodic nature of period 2π2\pi.

Question 15

If the polynomial f(x)=x4−9x2+22f(x) = x^4 - 9x^2 + 22 is divided by x−2x - 2, which one of the following are the quotient and remainder respectively?

  1. A.x3−2x2−5x+10x^3 - 2x^2 - 5x + 10 and 22
  2. B.x3−2x2−5x+10x^3 - 2x^2 - 5x + 10 and −2-2
  3. C.x3+2x2−5x−10x^3 + 2x^2 - 5x - 10 and −2-2
  4. D.x3+2x2−5x−10x^3 + 2x^2 - 5x - 10 and 22
Show the answer and explanation

Answer: D x3+2x2−5x−10x^3 + 2x^2 - 5x - 10 and 22

Why

Using synthetic division or polynomial long division to divide x4−9x2+22x^4 - 9x^2 + 22 by x−2x - 2 yields a quotient of x3+2x2−5x−10x^3 + 2x^2 - 5x - 10 and a remainder of 22.

Question 16

Consider the graph of f(x)=log⁡5(x+3)f(x) = \log_5(x + 3) which is shown below. Which one of the following is NOT true about the function ff?

  1. A.The domain of ff is the set of all real numbers greater than −3-3.
  2. B.The x-intercept of the graph of ff is −2-2.
  3. C.The y-axis is a vertical asymptote of the graph of ff.
  4. D.The function increases as the value of xx increases.
Show the answer and explanation

Answer: C The y-axis is a vertical asymptote of the graph of ff.

Why

The vertical asymptote of the logarithmic function f(x)=log⁡5(x+3)f(x) = \log_5(x + 3) occurs where the argument equals zero, which is at the line x=−3x = -3, not the y-axis (x=0x = 0).

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The other Mathematics papers of 2015 E.C.

2015 E.C. (2023)2015 E.C. (2023), natural stream

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 62017 E.C. (2025)2017 E.C. (2025), natural stream2017 E.C. (2025), version 12017 E.C. (2025), version 22017 E.C. (2025), version 42016 E.C. (2024)2016 E.C. (2024), natural stream2016 E.C. (2024), social stream2016 E.C. model exam2014 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 2015 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2015 E.C. (2023). Our set holds 44 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 2015 E.C. paper as a PDF?

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