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Grade 12 Mathematics entrance exam, 2018 E.C. (2026), version 3

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 3; the others are listed further down.

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  • 2018 E.C. (2026), version 3

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Question 1

Which of the following statement defines an arithmetic progression?

  1. A.It is a sequence in which the ratio between consecutive terms is a positive constant.
  2. B.It is a sequence in which the difference between consecutive terms is a non-zero constant.
  3. C.It is a sequence in which the difference between consecutive terms is a constant.
  4. D.It is a sequence in which the ratio between consecutive terms is a non-zero constant.
Show the answer and explanation

Answer: C It is a sequence in which the difference between consecutive terms is a constant.

Why

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is a constant (which can be positive, negative, or zero). Option B is incorrect because the common difference can be zero (e.g., the constant sequence 5, 5, 5, ...).

Question 2

The simplified form of the expression (√32 + √48) / (√8 + √12) is equal to:

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

Answer: D 2

Why

Simplifying the radicals gives numerator 42+43=4(2+3)4\sqrt{2} + 4\sqrt{3} = 4(\sqrt{2} + \sqrt{3}) and denominator 22+23=2(2+3)2\sqrt{2} + 2\sqrt{3} = 2(\sqrt{2} + \sqrt{3}). Dividing them yields 4/2=24/2 = 2.

Question 4

Which one of the following pairs of numbers are irrational numbers between 11 and 13?

  1. A.√120 and √168
  2. B.3+√81 and 2√37
  3. C.2+√112 and 3√17
  4. D.√125 and √175
Show the answer and explanation

Answer: C 2+√112 and 3√17

Why

Since 112=12111^2 = 121 and 132=16913^2 = 169, we want irrational numbers whose square lies between 121 and 169. For option C, 2+1122 + \sqrt{112} is approximately 2+10.58=12.582 + 10.58 = 12.58, and 317=1533\sqrt{17} = \sqrt{153} is approximately 12.3712.37; both are irrational numbers in the open interval (11,13)(11, 13).

Question 5

If a polynomial function f(x)=x³+ax²+bx+3 is divided by x+2 the remainder is 15 and x-1 is a factor of f(x), then what are the values of a and b respectively?

  1. A.-6,2
  2. B.6,2
  3. C.2,6
  4. D.2,-6
Show the answer and explanation

Answer: D 2,-6

Why

Using the Remainder Theorem, f(1)=1+a+b+3=0  ⟹  a+b=−4f(1) = 1 + a + b + 3 = 0 \implies a + b = -4, and f(−2)=−8+4a−2b+3=15  ⟹  2a−b=10f(-2) = -8 + 4a - 2b + 3 = 15 \implies 2a - b = 10. Solving this system of equations yields a=2a = 2 and b=−6b = -6.

Question 7

Which of the following ordered pairs gives the coordinates of the point that divides a line segment with endpoints A(-1,5) and B(5,2) in the ratio 1:2?

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

Answer: D (1,4)

Why

Using the section formula x=mx2+nx1m+nx = \frac{mx_2 + nx_1}{m+n} and y=my2+ny1m+ny = \frac{my_2 + ny_1}{m+n} with ratio 1:21:2 and endpoints A(−1,5)A(-1,5), B(5,2)B(5,2) gives x=1(5)+2(−1)3=1x = \frac{1(5) + 2(-1)}{3} = 1 and y=1(2)+2(5)3=4y = \frac{1(2) + 2(5)}{3} = 4, which is the point (1,4)(1,4).

Question 8

Given sets A = {x: x²-12x+20=0} and B = {x: x²+5x-14=0}, then relative complement of A with respect to B (B\A) is:

  1. A.{-7}
  2. B.{10}
  3. C.{-7,10}
  4. D.{-10,7}
Show the answer and explanation

Answer: A {-7}

Why

Solving the quadratic equations gives A={2,10}A = \{2, 10\} and B={−7,2}B = \{-7, 2\}. The relative complement B∖AB \setminus A consists of elements in BB that are not in AA, which is {−7}\{-7\}.

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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 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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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 50 of its questions, each with its answer and an explanation that points back to the textbook.

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