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Grade 12 Mathematics entrance exam, 2016 E.C. (2024), social stream

Real questions from the Grade 12 university entrance exam in Mathematics, as students sat it in 2016 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

  • 2016 E.C. (2024), social stream

    Exam year

  • 38 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

In the set of natural numbers, which one of the following defines a composite number?

  1. A.A number that has only two distinct factors.
  2. B.A number that is divisible by numbers from 2 to 9.
  3. C.A number that has two or more different factors.
  4. D.A number that has three or more different divisors.
Show the answer and explanation

Answer: D A number that has three or more different divisors.

Why

A composite number is defined as a natural number greater than 1 that has more than two distinct positive divisors, meaning it must have three or more different divisors.

Question 2

Which of the following is true about rationalizing the denominator?

  1. A.Only denominators can be multiplied by an irrational number.
  2. B.Only numerators can be rationalized when there is a radical.
  3. C.It is a method of changing the denominator into a rational number.
  4. D.It is a technique of multiplying a given number by an irrational expression.
Show the answer and explanation

Answer: C It is a method of changing the denominator into a rational number.

Why

Rationalizing the denominator refers to the algebraic process of multiplying the numerator and denominator by an appropriate radical expression to eliminate any radicals from the denominator, converting it to a rational number.

Question 6

Which one of the following refers to the definition of similar plane figures?

  1. A.Figures whose corresponding angles have the same ratio.
  2. B.Figures where one is an enlargement of the other.
  3. C.Figures whose ratios of length of corresponding sides are different.
  4. D.Figures that have different shapes but might have same size.
Show the answer and explanation

Answer: B Figures where one is an enlargement of the other.

Why

By definition, two plane figures are similar if they have the exact same shape but not necessarily the same size, meaning one is a scaled enlargement (or reduction) of the other.

Question 7

In △ABC\triangle ABC m(< B) = 90°, with m(< A) = 30° and BC = 11cm, then what is the length of AC‾\overline{AC}?

  1. A.22 cm
  2. B.2233cm\frac{22\sqrt{3}}{3} cm
  3. C.11311\sqrt{3} cm
  4. D.1133cm\frac{11\sqrt{3}}{3} cm
Show the answer and explanation

Answer: A 22 cm

Why

Since m(∠B)=90∘m(\angle B) = 90^\circ, the triangle is right-angled with hypotenuse ACAC. Using the sine ratio for ∠A\angle A, we have sin⁡(30∘)=BCAC\sin(30^\circ) = \frac{BC}{AC}, which simplifies to 12=11AC\frac{1}{2} = \frac{11}{AC} and gives AC=22 cmAC = 22\text{ cm}.

Question 8

Given a circle of diameter 16 cm, a chord of the circle is 6 cm far from the center of the circle. Which of the following is the length of the chord?

  1. A.272\sqrt{7} cm
  2. B.8 cm
  3. C.474\sqrt{7} cm
  4. D.16 cm
Show the answer and explanation

Answer: C 474\sqrt{7} cm

Why

Since the diameter is 16 cm16\text{ cm}, the radius is 8 cm8\text{ cm}. Using the Pythagorean theorem, the half-chord length is 82−62=28=27 cm\sqrt{8^2 - 6^2} = \sqrt{28} = 2\sqrt{7}\text{ cm}, making the full chord length 47 cm4\sqrt{7}\text{ cm}.

Question 10

Let x‾\overline{x} denote the arithmetic mean of a numerical data. If each observation is multiplied by 0.5, which of the following is the new mean?

  1. A.x‾\overline{x}
  2. B.12x‾\frac{1}{2}\overline{x}
  3. C.2x‾2\overline{x}
  4. D.x‾−0.5\overline{x}- 0.5
Show the answer and explanation

Answer: B 12x‾\frac{1}{2}\overline{x}

Why

A property of the arithmetic mean is that if every data point in a set is multiplied by a constant factor, the new mean is the original mean multiplied by that same factor. Thus, multiplying by 0.5 results in (1/2)¯x.

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The other Mathematics papers of 2016 E.C.

2016 E.C. (2024)2016 E.C. (2024), natural stream2016 E.C. model exam

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 42015 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 2016 E.C. Mathematics entrance exam questions?

Yes. They come from the national university entrance exam in Mathematics that students sat in 2016 E.C. (2024). Our set holds 38 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 2016 E.C. paper as a PDF?

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