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Grade 12 Mathematics entrance exam, 2018 E.C. (2026), version 4

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 4; the others are listed further down.

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  • 2018 E.C. (2026), version 4

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  • 56 questions with answers

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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 one of the following statement is true about the set of integers?

  1. A.Integers only include positive numbers and Zero.
  2. B.Every integer is rational number
  3. C.The set of integers included irrational numbers
  4. D.Every integer is also a whole number
Show the answer and explanation

Answer: B Every integer is rational number

Why

Every integer zz can be expressed as a fraction z/1z/1 where both the numerator and denominator are integers, which satisfies the definition of a rational number.

Question 2

Which of the following number is an irrational number?

  1. A.π
  2. B.-7
  3. C.0.222...
  4. D.√25
Show the answer and explanation

Answer: A π

Why

The number π\pi is a well-known transcendental, irrational number, whereas −7-7, 0.222...=2/90.222... = 2/9, and 25=5\sqrt{25} = 5 are all rational numbers.

Question 3

A gardener wants to build a square flower bed with an area of 45 square feet. Between which two whole numbers on a tape measure will side length fall?

  1. A.8 and 9
  2. B.5 and 6
  3. C.6 and 7
  4. D.7 and 8
Show the answer and explanation

Answer: C 6 and 7

Why

The side length of the square is 45\sqrt{45}. Since 62=366^2 = 36 and 72=497^2 = 49, the value of 45\sqrt{45} lies between the whole numbers 6 and 7.

Question 4

Which of the following square roots represent a rational number?

  1. A.√0.25
  2. B.√10
  3. C.√0.1
  4. D.√2
Show the answer and explanation

Answer: A √0.25

Why

0.25=0.5=1/2\sqrt{0.25} = 0.5 = 1/2, which is a terminating decimal and thus a rational number, whereas 10\sqrt{10}, 0.1\sqrt{0.1}, and 2\sqrt{2} are irrational.

Question 5

A student solves a system of linear equations in two variables and finds x = 4. Then he concludes that the solution to the system is 4. Which evaluation is correct?

  1. A.The conclusion is correct only if the system has no solution
  2. B.The conclusion is correct because x is independent variable
  3. C.The conclusion is correct if the student used substitution method.
  4. D.The conclusion is incorrect because the solution must be in ordered pair form.
Show the answer and explanation

Answer: D The conclusion is incorrect because the solution must be in ordered pair form.

Why

A system of linear equations in two variables (typically xx and yy) requires a solution in the form of an ordered pair (x,y)(x, y), rather than just a single coordinate value.

Question 6

What is the solution set for |x² - 5| = 4?

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

Answer: A {-3,-1,1,3}

Why

Solving ∣x2−5∣=4|x^2 - 5| = 4 yields two cases: x2−5=4  ⟹  x=±3x^2 - 5 = 4 \implies x = \pm 3, and x2−5=−4  ⟹  x=±1x^2 - 5 = -4 \implies x = \pm 1. Thus, the solution set is {−3,−1,1,3}\{-3, -1, 1, 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 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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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 56 of its questions, each with its answer and an explanation that points back to the textbook.

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