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Grade 12 Mathematics entrance exam, 2018 E.C. (2026), social stream

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2018 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

  • 2018 E.C. (2026), social stream

    Exam year

  • 40 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

What is the solution set of 5x2=25x\sqrt{5^{x^2}} = 25^x?

  1. A.∅
  2. B.0{0}
  3. C.2{\sqrt{2}}
  4. D.0,4{0,4}
Show the answer and explanation

Answer: D 0,4{0,4}

Why

Equating exponents of base 5 gives x2/2=2xx^2/2 = 2x, which simplifies to x2−4x=0x^2 - 4x = 0, giving solutions x=0x = 0 and x=4x = 4.

Question 2

In an experiment of rolling a die, what is the probability of getting 1 or 5?

  1. A.16\frac{1}{6}
  2. B.13\frac{1}{3}
  3. C.23\frac{2}{3}
  4. D.14\frac{1}{4}
Show the answer and explanation

Answer: B 13\frac{1}{3}

Why

The outcomes for rolling a 1 or a 5 are {1, 5}, and since there are 6 total possible outcomes, the probability is 2/6 = 1/3.

Question 3

Which one of the following pairs of lines are perpendicular to each other?

  1. A.l1:y=2x−1l_1:y=2x-1 and l2:y=12x+1l_2:y=\frac{1}{2}x+1
  2. B.l1:y=1l_1:y=1 and l2:y=−2l_2:y=-2
  3. C.l1:y=3x+1l_1:y=3x+1 and l2:y=−3x+4l_2:y=-3x+4
  4. D.l1:x=3l_1:x=3 and l2:y=1l_2:y=1
Show the answer and explanation

Answer: D l1:x=3l_1:x=3 and l2:y=1l_2:y=1

Why

A vertical line (x = 3) and a horizontal line (y = 1) are perpendicular to each other because they intersect at a 90-degree angle.

Question 4

Suppose that a person has 4 jackets and 5 trousers. In how many different ways can the person dress?

  1. A.20
  2. B.16
  3. C.9
  4. D.25
Show the answer and explanation

Answer: A 20

Why

By the fundamental counting principle, the number of ways to choose one jacket and one pair of trousers is 4 * 5 = 20.

Question 5

Consider the following grouped data as shown in the table below. Which one of the following is the variance of the above data? Value Frequency 1-5 4 6-10 5 11-15 6 16-20 5

  1. A.60
  2. B.29.5
  3. C.59
  4. D.28.5
Show the answer and explanation

Answer: D 28.5

Why

The midpoints of the classes are 3, 8, 13, and 18 with mean 11, and using the population variance formula gives 570 / 20 = 28.5.

Question 7

Which of the following statements defines a prime number?

  1. A.It is a natural number that is a product of two distinct numbers.
  2. B.It is a natural number that has more than two factors.
  3. C.It is a natural number that is a factor of all numbers.
  4. D.It is a natural number that has exactly two distinct factors.
Show the answer and explanation

Answer: D 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 factors: 1 and itself.

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The other Mathematics papers of 2018 E.C.

2018 E.C. (2026)2018 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 6

Mathematics papers from other years

2017 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 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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All Grade 12 Mathematics papersAll papers of 2018 E.C.Every subject and year

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Are these the real 2018 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2018 E.C. (2026). Our set holds 40 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 2018 E.C. paper as a PDF?

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