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Grade 12 Mathematics entrance exam, 2014 E.C. (2022)

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2014 E.C. Every question comes with the correct answer and a worked explanation.

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  • Natural science stream

    Who sits it

  • 2014 E.C. (2022)

    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

What is the locus all points in the plane in which the sum of the distances from two fixed points is constant?

  1. A.Hyperbola
  2. B.Parabola
  3. C.Ellipse
  4. D.Circle
Show the answer and explanation

Answer: C Ellipse

Why

The ellipse is defined as the set of all points in a plane for which the sum of the distances from two fixed points (the foci) is constant.

Question 2

The radian measure of an angle of 120° is equal to:

  1. A.2π3\frac{2\pi}{3}
  2. B.4π3\frac{4\pi}{3}
  3. C.π2\frac{\pi}{2}
  4. D.π4\frac{\pi}{4}
Show the answer and explanation

Answer: A 2π3\frac{2\pi}{3}

Why

To convert degrees to radians, multiply by π/180∘\pi/180^\circ, giving 120∘×π/180∘=2π/3120^\circ \times \pi/180^\circ = 2\pi/3 radians.

Question 3

What is the surface area of a sphere with radius 6 cm?

  1. A.24π cm²
  2. B.36π cm²
  3. C.48π cm²
  4. D.144π cm²
Show the answer and explanation

Answer: D 144π cm²

Why

The surface area of a sphere is given by 4πr24\pi r^2. For r=6 cmr = 6\text{ cm}, the surface area is 4π(6)2=144π cm24\pi (6)^2 = 144\pi\text{ cm}^2.

Question 4

Which of the following is the measure of an exterior angle of a 10 sided regular polygon?

  1. A.72°
  2. B.144°
  3. C.180°
  4. D.36°
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Answer: D 36°

Why

The sum of the exterior angles of any regular polygon is 360∘360^\circ, so for a 10-sided regular polygon, each exterior angle is 360∘/10=36∘360^\circ / 10 = 36^\circ.

Question 5

If the volume of a right circular cone is 64π cm 3 and the diameter of its base is 8 cm, what is the height of the cone?

  1. A.4cm
  2. B.12cm
  3. C.8cm
  4. D.3cm
Show the answer and explanation

Answer: B 12cm

Why

The volume of a cone is V=13πr2hV = \frac{1}{3}\pi r^2 h. Since the base diameter is 8 cm8\text{ cm}, the radius is r=4 cmr=4\text{ cm}. Solving 64π=13π(4)2h64\pi = \frac{1}{3}\pi (4)^2 h yields h=12 cmh = 12\text{ cm}.

Question 6

What are the quotient and remainder respectively, when 75 is divided by 20?

  1. A.3 and 15
  2. B.4 and 5
  3. C.15 and 3
  4. D.2 and 19
Show the answer and explanation

Answer: A 3 and 15

Why

When 7575 is divided by 2020, the division algorithm gives 75=3×20+1575 = 3 \times 20 + 15, so the quotient is 33 and the remainder is 1515.

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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)2013 E.C. (2021)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 2014 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2014 E.C. (2022). 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 2014 E.C. paper as a PDF?

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