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

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. This is the social stream paper. The other stream sat a different Mathematics paper the same year, listed further down.

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  • Social science stream

    Who sits it

  • 2014 E.C. (2022), social stream

    Exam year

  • 50 questions with answers

    In this set

Try questions from this paper

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 4

A closed right circular cone has a base radius 2 cm and slant height 3√2 cm. What is the total surface area of the cone?

  1. A.2π(1+3√2) cm²
  2. B.2π(2+3√2) cm²
  3. C.6π/√4 cm²
  4. D.2π/√4 cm²
Show the answer and explanation

Answer: B 2π(2+3√2) cm²

Why

The total surface area of a closed cone is given by A = πr(r + l). Substituting r = 2 cm and l = 3√2 cm gives A = 2π(2 + 3√2) cm².

Question 5

The lower and upper bases of the frustum of a regular pyramid are equilateral triangles of side 3 cm long and 2 cm long respectively. If its slant height is 4 cm, then what is the lateral surface area of the frustum?

  1. A.30 cm²
  2. B.48 cm²
  3. C.72 cm²
  4. D.96 cm²
Show the answer and explanation

Answer: A 30 cm²

Why

The lateral surface area of a regular pyramid frustum is LSA = (1/2) * (P1 + P2) * h_s, where P1 and P2 are the perimeters of the bases (9 cm and 6 cm) and h_s is the slant height (4 cm). This gives LSA = 0.5 * 15 * 4 = 30 cm².

Question 6

Which one of the following is true about the signum function, f(x) = sgn x?

  1. A.Its domain is the set of real numbers
  2. B.Its range is the set of real numbers
  3. C.Its domain is {-1, 0, 1}
  4. D.Its range is [0, ∞)
Show the answer and explanation

Answer: A Its domain is the set of real numbers

Why

The signum function f(x) = sgn(x) is defined for all real numbers, so its domain is the set of real numbers, which makes option A correct.

Question 7

Which one of the following is the equation of a circle with center (2, -1) and radius 3 units?

  1. A.x² + y² + 2x + 2y - 4 = 0
  2. B.x² + y² - 4x + 2y - 4 = 0
  3. C.x² + y² + 4x - 2y - 5 = 0
  4. D.x² + y² - 4x + 2y - 5 = 0
Show the answer and explanation

Answer: B x² + y² - 4x + 2y - 4 = 0

Why

The standard equation of a circle is (x - h)² + (y - k)² = r². Substituting h = 2, k = -1, and r = 3 yields (x - 2)² + (y + 1)² = 9, which simplifies to x² + y² - 4x + 2y - 4 = 0.

Question 8

Consider the ellipse given by the equation 4(x + 1)² + (y - 1)² = 16. Which one of the following is the standard form of the equation of the ellipse?

  1. A.(x+1)242+(y−1)212=1\frac{(x + 1)^2}{4^2} + \frac{(y - 1)^2}{1^2} = 1
  2. B.(x+1)242+(y−1)242=1\frac{(x + 1)^2}{4^2} + \frac{(y - 1)^2}{4^2} = 1
  3. C.(x+1)222+(y−1)242=1\frac{(x + 1)^2}{2^2} + \frac{(y - 1)^2}{4^2} = 1
  4. D.(x+1)222+(y−1)212=1\frac{(x + 1)^2}{2^2} + \frac{(y - 1)^2}{1^2} = 1
Show the answer and explanation

Answer: C (x+1)222+(y−1)242=1\frac{(x + 1)^2}{2^2} + \frac{(y - 1)^2}{4^2} = 1

Why

Dividing both sides of the equation 4(x + 1)² + (y - 1)² = 16 by 16 gives ((x + 1)²)/4 + ((y - 1)²)/16 = 1, which in standard form is ((x + 1)²)/(2²) + ((y - 1)²)/(4²) = 1.

Question 9

Which of the following is true? A hyperbola is a locus of points in the plane so that:

  1. A.the sum of the distances from two fixed points is constant
  2. B.the difference between the distances from two fixed points is constant
  3. C.the points have the same distance from a given point and a given line
  4. D.the points have the same distance from any given two points
Show the answer and explanation

Answer: B the difference between the distances from two fixed points is constant

Why

By definition, a hyperbola is the locus of all points in a plane such that the absolute difference of their distances from two fixed points (foci) is constant.

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The other Mathematics papers of 2014 E.C.

2014 E.C. (2022)

Mathematics papers from other years

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 42018 E.C. (2026), version 52018 E.C. (2026), version 62017 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 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 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 50 of its questions, each with its answer and an explanation that points back to the textbook.

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