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Grade 12 Mathematics entrance exam, 2013 E.C. (2021)

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2013 E.C. Every question comes with the correct answer and a worked explanation.

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  • Social science stream

    Who sits it

  • 2013 E.C. (2021)

    Exam year

  • 65 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 one of the following is a discrete variable?

  1. A.The temperature of an object.
  2. B.The speed of a moving object.
  3. C.Profit earned by a company.
  4. D.Number of road accidents in Ethiopia.
Show the answer and explanation

Answer: D Number of road accidents in Ethiopia.

Why

A discrete variable is one that can take on a countable number of values. The number of road accidents in Ethiopia is a countable quantity, unlike temperature, speed, or profit which are continuous variables.

Question 2

The frequency distribution table of a grouped data X is given as shown below. | X | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | | --- | --- | --- | --- | --- | | Frequency | 2 | 3 | 5 | 4 | Which one of the following is true about this data?

  1. A.The upper class boundary of the 3ʳᵈ class is 24
  2. B.The class mark of the 2ⁿᵈ class is 17
  3. C.The class mid-point of the 3ʳᵈ class is 22.5
  4. D.The lower class limit of the 4ᵗʰ class is 24.5
Show the answer and explanation

Answer: B The class mark of the 2ⁿᵈ class is 17

Why

The class mark is the midpoint of a class interval. For the second class (15 – 19), the class mark is calculated as (15 + 19) / 2 = 17.

Question 3

What is the range of the function ff given by f(x)=∣x−12∣+3f(x) = \left|x - \frac{1}{2}\right| + 3?

  1. A.[3,∞)[3, \infty)
  2. B.[12,∞)\left[\frac{1}{2}, \infty\right)
  3. C.[−12,∞)\left[-\frac{1}{2}, \infty\right)
  4. D.[−3,∞)[-3, \infty)
Show the answer and explanation

Answer: A [3,∞)[3, \infty)

Why

The absolute value term |x - 1/2| is always non-negative (greater than or equal to 0). Adding 3 means that the range of the function is [3, infinity).

Question 4

Let A and B be two sets and ff be a function from A in to B (f:A→Bf: A \rightarrow B). In order to say ff is an on-to function which one of the following conditions should be fulfilled?

  1. A.If each element x in A is the pre-image of at least one element y in B under ff, then ff is onto function.
  2. B.If any two elements in B are the images of exactly one element of A, then ff is onto function.
  3. C.If you can find two distinct elements in A that are the pre-image of exactly one elements of B, then ff cannot be onto function.
  4. D.If you can find an element y in B that is not an image of any one of the elements of A, then ff is not onto function.
Show the answer and explanation

Answer: D If you can find an element y in B that is not an image of any one of the elements of A, then ff is not onto function.

Why

A function f from A to B is onto (surjective) if every element in B has at least one pre-image in A. Therefore, if there is even one element in B with no pre-image, f cannot be onto.

Question 5

For a given ellipse, what do you call the ratio of the distance between the two foci to the length of the major axis?

  1. A.Eccentricity
  2. B.Latus rectum
  3. C.Directrix
  4. D.Length of minor axis
Show the answer and explanation

Answer: A Eccentricity

Why

By definition, the eccentricity (e) of an ellipse is the ratio of the distance between the two foci (2c) to the length of the major axis (2a), which simplifies to c/a.

Question 6

Which one is the standard form of the equation of the parabola with vertex (−2,3)(-2, 3) and focus (2,3)(2, 3)?

  1. A.(x+2)2=16(y−3)(x + 2)^2 = 16(y - 3)
  2. B.(x+2)2=−16(y−3)(x + 2)^2 = -16(y - 3)
  3. C.(y−3)2=16(x+2)(y - 3)^2 = 16(x + 2)
  4. D.(y−3)2=−16(x+2)(y - 3)^2 = -16(x + 2)
Show the answer and explanation

Answer: C (y−3)2=16(x+2)(y - 3)^2 = 16(x + 2)

Why

The vertex is (h, k) = (-2, 3) and the focus is (h + p, k) = (2, 3), which yields p = 4. Since the axis is horizontal, the standard equation is (y - k)^2 = 4p(x - h), which gives (y - 3)^2 = 16(x + 2).

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Mathematics papers from other years

2018 E.C. (2026)2017 E.C. (2025)2016 E.C. (2024)2015 E.C. (2023)2014 E.C. (2022)2011 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 2013 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2013 E.C. (2021). Our set holds 65 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 2013 E.C. paper as a PDF?

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