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Mathematics entrance exam, 2018 E.C. (2026)

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.

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  • Both streams

    Who sits it

  • 2018 E.C. (2026)

    Exam year

  • 58 questions with answers

    In this set

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

Question 1

Consider the data: 11, 13, 15, 17, 19, 21. Which one of the following is the mean deviation from the mean?

  1. A.4
  2. B.3.5
  3. C.4.5
  4. D.3
Show the answer and explanation

Answer: D 3

Why

The mean of the data is (11+13+15+17+19+21)/6 = 16. The absolute deviations from the mean are 5, 3, 1, 1, 3, and 5, which sum to 18; dividing this sum by 6 yields a mean deviation of 3.

Question 2

Consider the quadrilateral ABCD where A=(0,0), B=(-1,1)), C=(0,2) and D=(2,2). Which one of the following is true?

  1. A.CD is perpendicular to AB.
  2. B.BC is parallel to AD.
  3. C.CD is perpendicular to BE.
  4. D.AB is parallel to CD.
Show the answer and explanation

Answer: B BC is parallel to AD.

Why

The slope of BC is (2 - 1) / (0 - (-1)) = 1, and the slope of AD is (2 - 0) / (2 - 0) = 1. Since their slopes are equal and they are on distinct lines, BC is parallel to AD.

Question 3

Consider the greatest integer function defined by \(f(x)=[x-1]\). Which of the following sets is the domain of f?

  1. A.The set of rational numbers.
  2. B.The set of integers.
  3. C.The set of real numbers.
  4. D.The set of natural numbers.
Show the answer and explanation

Answer: C The set of real numbers.

Why

The greatest integer function [u] is defined for all real numbers u. Therefore, the domain of f(x) = [x - 1] is the set of all real numbers (R).

Question 4

Which one of the following relations is a function?

  1. A.R={(x,y):x,y\in R and \(y^2=x\)}
  2. B.R={(x,y):x,y\in R and |y|=x}
  3. C.R={(x,y):x,y\in R and \(y=x^2\)}
  4. D.\(R=\{(x,y):x,y\in R \text{ and } y^4=x\}\)
Show the answer and explanation

Answer: C R={(x,y):x,y\in R and \(y=x^2\)}

Why

A relation is a function if each input x corresponds to exactly one output y. In y = x^2, each real number x yields exactly one real number y, whereas in the other options, a single positive x-value yields two distinct y-values.

Question 5

Which one of the following is a source of cash loan?

  1. A.Non-government organization to alleviate public problems.
  2. B.Investors involved in home construction for a community.
  3. C.Group of investors committed to drilling out underground water.
  4. D.A money line group investing in health improvement sectors.
Show the answer and explanation

Answer: A Non-government organization to alleviate public problems.

Why

Non-governmental organizations (NGOs) are recognized formal institutions that provide micro-credit or cash loans to alleviate public and socio-economic problems in community development.

Question 6

What is the average rate of change of \(y=f(x)\) with respect to x on the interval \([a,b]\)?

  1. A.\(\frac{f(b)+f(a)}{2}\)
  2. B.\(\frac{b-a}{f(b)-f(a)}\)
  3. C.\(\frac{f(b)-f(a)}{2}\)
  4. D.\(\frac{f(b)-f(a)}{b-a}\)
Show the answer and explanation

Answer: D \(\frac{f(b)-f(a)}{b-a}\)

Why

The average rate of change of a function f over an interval [a, b] is defined as the change in the function values divided by the change in the input, which is given by the formula (f(b) - f(a)) / (b - a).

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Mathematics papers from other years

2017 E.C. (2025)2016 E.C. (2024)2014 E.C. (2022)2013 E.C. (2021)2005 E.C. (2013)

Revise Mathematics before you sit this paper

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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 58 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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