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Grade 12 Mathematics entrance exam, 2017 E.C. (2025), version 4

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2017 E.C. Every question comes with the correct answer and a worked explanation. The 2017 E.C. exam went out in several versions. This page holds version 4; the others are listed further down.

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  • Both streams

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  • 2017 E.C. (2025), version 4

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  • 59 questions with answers

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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

After rationalizing the denominator of 5/(3√3 - 2√2), the denominator is equal to ______.

  1. A.35
  2. B.5(3√3-2√2)/19
  3. C.19
  4. D.5(3√3+2√2)/19
Show the answer and explanation

Answer: C 19

Why

Multiplying both the numerator and the denominator of the fraction by the conjugate of the denominator, 33+223\sqrt{3} + 2\sqrt{2}, yields (33)2−(22)2=27−8=19(3\sqrt{3})^2 - (2\sqrt{2})^2 = 27 - 8 = 19 in the denominator.

Question 2

The solution set of the equation 5|2x-1| - 3|4x+5| = 2 is equal to:

  1. A.{6/11}
  2. B.{-11, -9, -6/11}
  3. C.{}
  4. D.{-9, -6/11}
Show the answer and explanation

Answer: D {-9, -6/11}

Why

By analyzing the critical points of the absolute values, x=1/2x = 1/2 and x=−5/4x = -5/4, we solve the equation in three intervals. Only x=−9x = -9 (for x<−5/4x < -5/4) and x=−6/11x = -6/11 (for −5/4≤x<1/2-5/4 \le x < 1/2) are valid solutions, giving the solution set {−9,−6/11}\{-9, -6/11\}.

Question 3

In a survey of 600 students, 250 drink tea, 225 drink coffee, 75 drink both. How many drink neither?

  1. A.400
  2. B.550
  3. C.200
  4. D.125
Show the answer and explanation

Answer: C 200

Why

Using the principle of inclusion-exclusion, the number of students who drink tea or coffee is 250+225−75=400250 + 225 - 75 = 400. The number of students who drink neither is the total number of surveyed students minus this union, which is 600−400=200600 - 400 = 200.

Question 4

Given relation R = {(x,y): y > x-2, y > -x-2, y ≤ 4}. Which is the domain and range of R respectively?

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

Answer: A (-6,6) and (-2,4]

Why

The region is bounded below by y=x−2y = x-2 and y=−x−2y = -x-2 (intersecting at (0,−2)(0,-2)), and above by y=4y = 4. Thus, the range of yy is (−2,4](-2, 4], and the maximum horizontal span (domain of xx) occurs at y=4y = 4, which gives −6<x<6-6 < x < 6.

Question 5

ΔABC and ΔDEF are similar. Area of ΔABC = 12 m². DE is twice AB. Area of ΔDEF?

  1. A.6 m²
  2. B.48 m²
  3. C.36 m²
  4. D.24 m²
Show the answer and explanation

Answer: B 48 m²

Why

Since ΔABC\Delta ABC and ΔDEF\Delta DEF are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Since DE=2ABDE = 2AB, the area of ΔDEF\Delta DEF is 22×12 m2=48 m22^2 \times 12\text{ m}^2 = 48\text{ m}^2.

Question 6

Vector AB has initial A(2,-1) and terminal B(-4,7). Which is a unit vector in same direction?

  1. A.-(3/5)i + (4/5)j
  2. B.(3/5)i - (4/5)j
  3. C.-(3/50)i - (4/50)j
  4. D.(3/50)i + (4/50)j
Show the answer and explanation

Answer: A -(3/5)i + (4/5)j

Why

The vector AB⃗\vec{AB} is given by B−A=(−4−2)i⃗+(7−(−1))j⃗=−6i⃗+8j⃗B - A = (-4-2)\vec{i} + (7-(-1))\vec{j} = -6\vec{i} + 8\vec{j}, which has magnitude (−6)2+82=10\sqrt{(-6)^2 + 8^2} = 10. The unit vector in the same direction is u⃗=−6i⃗+8j⃗10=−35i⃗+45j⃗\vec{u} = \frac{-6\vec{i} + 8\vec{j}}{10} = -\frac{3}{5}\vec{i} + \frac{4}{5}\vec{j}.

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The other Mathematics papers of 2017 E.C.

2017 E.C. (2025)2017 E.C. (2025), natural stream2017 E.C. (2025), version 12017 E.C. (2025), version 2

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 62016 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 2017 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2017 E.C. (2025). Our set holds 59 of its questions, each with its answer and an explanation that points back to the textbook.

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