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Grade 12 Mathematics entrance exam, 2018 E.C. (2026), version 6

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. The 2018 E.C. exam went out in several versions. This page holds version 6; the others are listed further down.

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  • Both streams

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  • 2018 E.C. (2026), version 6

    Exam year

  • 51 questions with answers

    In this set

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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 of the following is true about the relation between the set of integers (Z), positive rational numbers (Q⁺) and rational numbers (Q)?

  1. A.Z ⊆ Q⁺
  2. B.Z ∩ Q⁺ = Q⁺
  3. C.Q⁺ ∪ Z ⊆ Q
  4. D.Z = Q⁺
Show the answer and explanation

Answer: C Q⁺ ∪ Z ⊆ Q

Why

Since both the set of positive rational numbers (Q⁺) and the set of integers (Z) are subsets of the set of rational numbers (Q), their union is also a subset of Q.

Question 2

Which of the following is true?

  1. A.the set of irrational numbers are closed under multiplication
  2. B.the sum of two irrational numbers is always irrational
  3. C.the product of two irrational numbers is rational
  4. D.the set of rational numbers is closed under addition and multiplication
Show the answer and explanation

Answer: D the set of rational numbers is closed under addition and multiplication

Why

The set of rational numbers is closed under both addition and multiplication because adding or multiplying any two rational numbers always results in a rational number.

Question 3

If the system { x + by = 10, ax + 2y = 20 } has infinite solutions, then values of a and b respectively?

  1. A.2 and 1
  2. B.-1 and 2
  3. C.1 and 2
  4. D.1 and 1
Show the answer and explanation

Answer: A 2 and 1

Why

For the system to have infinitely many solutions, the equations must be dependent, which means 1/a = b/2 = 10/20 = 1/2, giving a = 2 and b = 1.

Question 4

The sum of two numbers is 75, two-third of larger number is 10 more than the smaller. What are the numbers?

  1. A.30 and 45
  2. B.35 and 40
  3. C.24 and 51
  4. D.25 and 50
Show the answer and explanation

Answer: C 24 and 51

Why

Letting the numbers be x and y (with x > y), we have x + y = 75 and (2/3)x = y + 10. Solving this system yields the larger number as 51 and the smaller as 24.

Question 5

Which of the following is the solution set of 1 - 2|x+2| = 6?

  1. A.{}
  2. B.{1/2,9/2}
  3. C.{5,9}
  4. D.{-4}
Show the answer and explanation

Answer: A {}

Why

Isolating the absolute value gives |x+2| = -2.5, which has no solution because the absolute value of a real number is always non-negative.

Question 6

The solution set of |5 - 3x| + 9 > 17 is:

  1. A.(-∞, -1] ∪ [13/3, ∞)
  2. B.(-∞, 13/3) ∪ (-1, ∞)
  3. C.(-1, ∞)
  4. D.(-∞, -1) ∪ (13/3, ∞)
Show the answer and explanation

Answer: D (-∞, -1) ∪ (13/3, ∞)

Why

The inequality |5 - 3x| > 8 simplifies to 5 - 3x > 8 or 5 - 3x < -8, which yields x < -1 or x > 13/3, corresponding to the interval (-∞, -1) ∪ (13/3, ∞).

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The other Mathematics papers of 2018 E.C.

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 5

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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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 51 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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