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Grade 12 Mathematics (Natural Science) national exam, 2016 E.C. (2024 G.C.)

51 questions · 120 minutes. The first 5 answers are shown with explanations; sit the whole paper timed in the app to get your score and the textbook page behind every question.

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  1. 1.Which one of the following is true about the Range and Interquartile Range of a given data?
    • A. Both are measures of the variability of each item in the data.
    • B. Both are measures of variation of the data.
    • C. Both are affected by extreme values in the data.
    • D. Both are considering only the middle 50% of the data.
    Answer: B. The range and interquartile range both describe how spread out data values are. The range measures the distance from the smallest to the largest value, while the interquartile range measures the spread of the middle half, so both are measures of variation. A wrongly says both measure each item's variability; C is wrong because the interquartile range is not affected by extreme values. D applies to the interquartile range, not the range. Textbook: Grade 12, unit 3 · section 3.1.
  2. 2.Which one of the following numbers is the coefficient of $x^6y^4$ in the expansion of $(x+y)^{10}$?
    • A. 240
    • B. 1260
    • C. 210
    • D. 4860
    Answer: C. The key idea is that the coefficient of $x^6y^4$ in $(x+y)^{10}$ is the number of ways to choose which $6$ of the $10$ factors supply $x$. This coefficient is $\binom{10}{6}=\frac{10!}{6!4!}=210$, so C is correct. A, B, and D are not equal to this binomial coefficient. Textbook: Grade 11, unit 8 · section 8.4.
  3. 3.The altitude of a frustum of a regular square pyramid is 9 cm. What is the volume of the frustum if the side length of the upper base is 6 cm and the side length of the lower base is 10 cm? 3 3
    • A. 196 cm
    • B. 324 cm 3 3
    • C. 588 cm
    • D. 108 cm
    Answer: C. The volume of a frustum of a pyramid depends on its height and the areas of its two bases. The square base areas are $6^2=36\,\mathrm{cm^2}$ and $10^2=100\,\mathrm{cm^2}$, so $V=\frac{9}{3}(36+100+\sqrt{36\cdot100})=588\,\mathrm{cm^3}$. A, B, and D are not the volume given by this calculation. Textbook: Grade 10, unit 6 · section 6.3.
  4. 4.Which one of the following intervals is the solution set of the inequality ?
    • A. (-2,8)
    • B. (-4,16)
    • C. (-8,2)
    • D. (-16,4)
  5. 5.A sector of a circle of diameter 8cm is formed by a central angle of 45°. What is the area of the sector?
    • A. cm²
    • B. cm² (2π + 8) 2π π 8π
    • C. cm²
    • D. cm²
    Answer: B. Textbook: Grade 10, unit 5 · section 5.2.
  6. 6.If $a = 2-\sqrt{5}$ and $b = 3 + 2\sqrt{5}$, then which one of the following is true?
    • A. $a - b = -1 - \sqrt{5}$
    • B. $11a ÷ b = -36 + 13\sqrt{5}$
    • C. $a + b = 5$
    • D. $ab = 36$
    Answer: C. Textbook: Grade 11, unit 3 · section 3.2.
  7. 7.The shaded region in the following figure is the graph of a relation R. Which one of the following is the domain and range of R respectively?
    • A. ${(-\infty, -\frac{1}{2}) \text{ and } R}$
    • B. $R \text{ and } {(-\infty, -\frac{1}{2})}$
    • C. $R \text{ and } {(-\infty, -\frac{1}{2}]}$
    • D. ${(-\infty, -\frac{1}{2}] \text{ and } R}$
    Answer, explanation and textbook page: open in the app.
  8. 8.Which one of the following is equal to the sum ?
    • A. 2+8+18+32+50
    • B. 2+4+8+16+32
    • C. 2+4+6+8+10
    • D. 2+8+16+32+64
    Answer, explanation and textbook page: open in the app.
  9. 9.Which one of the following is equal to $\cot(175^{\circ})$?
    • A. -1
    • B. -$\sqrt{3}$
    • C. 1
    • D. $\sqrt{3}$
    Answer, explanation and textbook page: open in the app.
  10. 10.If the fifth and the tenth terms of a geometric sequence are 640 and 20 respectively, then which of the following numbers are the first term and the common ratio of the given geometric sequence respectively?
    • A. 10240 and $\frac{1}{2}$
    • B. 1024 and $\frac{1}{2}$
    • C. 10240 and 2
    • D. 1024 and 2
    Answer, explanation and textbook page: open in the app.
  11. 11.Which one of the following conic section is defined by "the set of points in a plane such that the sum of the distances from two given points is constant"?
    • A. Circle
    • B. Hyperbola
    • C. Parabola
    • D. Ellipse
    Answer, explanation and textbook page: open in the app.
  12. 12.Let $\theta$ be an angle in standard position and $P(-3, 4)$ be a point on the terminal side of $\theta$. Which one of the following is true about the corresponding trigonometric functions?
    • A. $\cos\theta=\frac{4}{5}$
    • B. $\sin\theta=-\frac{4}{5}$
    • C. $\sin\theta=\frac{3}{5}$
    • D. $\cos\theta=-\frac{3}{5}$
    Answer, explanation and textbook page: open in the app.
  13. 13.Given that a graph of a system of linear inequalities is shown below, which one of the following system of linear inequalities is represented by the shaded region in the graph?
    • A. $$ \begin{cases} 2x + y \leq 4 \\ 3x - y \geq 6 \end{cases} $$
    • B. $$ \begin{cases} 2x + y \geq 4 \\ 3x - y \leq 6 \end{cases} $$
    • C. $$ \begin{cases} 2x + y \geq 4 \\ 3x - y \geq 6 \end{cases} $$
    • D. $$ \begin{cases} 2x + y \leq 4 \\ 3x - y \leq 6 \end{cases} $$
    Answer, explanation and textbook page: open in the app.
  14. 14.Let A and B be two sets that contain 15 and 17 elements respectively. If A ∩ B contains 10 elements, what is the number of elements in A ∪ B?
    • A. 32
    • B. 12
    • C. 42
    • D. 22
    Answer, explanation and textbook page: open in the app.
  15. 15.Which one of the following is a simple random sampling?
    • A. Selecting a population into groups formed by dividing the population into groups.
    • B. First divide a city into ten groups and choose the secondary school principals from the randomly selected 3 groups.
    • C. Selecting five students from grade 12 students of the same school randomly.
    • D. First the population is divided into homogenous groups and a sample is selected from each homogenous group.
    Answer, explanation and textbook page: open in the app.
  16. 16.Which one of the following numbers is the determinant of the matrix $M = \begin{pmatrix}1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 10\end{pmatrix}$?
    • A. 3
    • B. 6
    • C. -6
    • D. -3
    Answer, explanation and textbook page: open in the app.
  17. 17.Which one of the following pairs of functions is an inverse of each other in their respective domains?
    • A. $f(x)=\frac{x+1}{x-1}$ and $g(x)=\frac{x-1}{x+1}$
    • B. $f(x)=x^5$ and $g(x)=\frac{1}{x^5}$
    • C. $f(x)=x^3-1$ and $g(x)=\sqrt[3]{x+1}$
    • D. $f(x)=\sqrt{x+3}$ and $g(x)=x^2-9$
    Answer, explanation and textbook page: open in the app.
  18. 18.Which one of the following ordered pairs of numbers gives the coordinates of the point that divides a line segment with end points A(1, 1) and B(-6, 8) in the ratio of 3:4?
    • A. (-2, 4)
    • B. (-2, -4)
    • C. (2, 4)
    • D. (2, -4)
    Answer, explanation and textbook page: open in the app.
  19. 19.Which one of the following is a primary data?
    • A. The data obtained from a document prepared by the MOE regarding the achievements of students in a National Examination.
    • B. The data obtained by reading a journal regarding the opinion of the society about holidays.
    • C. The data obtained by measuring the heights of students in a certain school.
    • D. The data obtained from a chart prepared by Ministry of Health regarding the spread of HIV/AIDS.
    Answer, explanation and textbook page: open in the app.
  20. 20.Which one of the following is the solution set of the equation $(\sqrt{16})^{2x-1}=(\sqrt[3]{4096})^{3x-5}$?
    • A. $\left\{\frac{11}{4}\right\}$
    • B. $\left\{\frac{9}{2}\right\}$
    • C. $\left\{\frac{11}{2}\right\}$
    • D. $\left\{\frac{9}{4}\right\}$
    Answer, explanation and textbook page: open in the app.
  21. 21.If the measure of each interior angle of a regular polygon is 135°, then which one of the following is the number of lines of symmetry of the polygon?
    • A. 8
    • B. 6
    • C. 9
    • D. 7
    Answer, explanation and textbook page: open in the app.
  22. 22.What is the perimeter of a regular hexagon of radius 6 cm?
    • A. 36.3 cm
    • B. 18 cm
    • C. 36 cm
    • D. 18.3 cm
    Answer, explanation and textbook page: open in the app.
  23. 23.Which one of the following is a quantitative data?
    • A. Checking the quality of a new product.
    • B. Determining the tastes of foods in a restaurant.
    • C. Identifying the social status of individuals.
    • D. Measuring the heights of each students in the given class.
    Answer, explanation and textbook page: open in the app.
  24. 24.Which one of the following is the solution set of the equation $(\sqrt{16})^{2x-1} = \left(^3\sqrt{4096}\right)^{3x-5}$?
    • A. {$\frac{11}{4}$}
    • B. {$\frac{9}{2}$}
    • C. {$\frac{11}{2}$}
    • D. {$\frac{9}{4}$}
    Answer, explanation and textbook page: open in the app.
  25. 25.Which one of the following is NOT a valid reason for saving?
    • A. For the time of retirement
    • B. For vacation
    • C. To maximize interest
    • D. For betting in football
    Answer, explanation and textbook page: open in the app.
  26. 26.Consider the following graph of a given exponential function f(x). Which one of the following functions represents the graph shown above?
    • A. $f(x) = \left(\frac{1}{2}\right)^x - 2$
    • B. $f(x) = \left(\frac{1}{2}\right)^{x-2}$
    • C. $f(x) = (2)^x - 2$
    • D. $f(x) = (2)^{x-2}$
    Answer, explanation and textbook page: open in the app.
  27. 27.Which one of the following is equal to the sum $ \sum_{k=1}^{7} 729(3^{1-k}) $?
    • A. 1092
    • B. 1079
    • C. 1093
    • D. 1088
    Answer, explanation and textbook page: open in the app.
  28. 28.Which one of the following is an equation of the parabola with vertex $V(0, 0)$ and focus $F(2, 0)$?
    • A. $y^2=\frac{1}{8}x$
    • B. $x^2=\frac{1}{8}y$
    • C. $y^2=8x$
    • D. $x^2=8y$
    Answer, explanation and textbook page: open in the app.
  29. 29.Which one of the following is true about the function f(x) = tan x?
    • A. The range of f is the set of real numbers, R. π )
    • B. The graph of f intersects y-axis at . , 0 ( 2
    • C. The domain of f is $ \mathbb{R} \setminus \left(-\frac{\pi}{2},\frac{\pi}{2}\right) $. 2 π
    • D. f is a periodic function with period .
    Answer, explanation and textbook page: open in the app.
  30. 30.Which one of the following is equal to the polynomial function $f(x)=x^2+4x+4$?
    • A. $h(x)=(x^2+6x+8)-(2x-4)$
    • B. $l(x)=(x^2+10x+3)+(-6x+1)$
    • C. $g(x)=\frac{x^4+4x^2+4}{x^2+2}$
    • D. $k(x)=(x-2)(x+2)$
    Answer, explanation and textbook page: open in the app.
  31. 31.Let S, R and T be any three sets. Which one of the following is NOT true about the union of the sets?
    • A. $S\cup T=T$
    • B. $S\cup S=S$
    • C. $S\cup R=R\cup S$
    • D. $(S\cup R)\cup T=T\cup(R\cup S)$
    Answer, explanation and textbook page: open in the app.
  32. 32.Let $r_1$ and $r_2$ be the roots of a quadratic equation $ax^2+bx+c=0$, such that $r_1+r_2=-2.5$ and $r_1r_2=1.5$. Which one of the following can be the values of $a$, $b$ and $c$ respectively?
    • A. 2, 5, and 3
    • B. 2, 3, and 5
    • C. 1, 5, and 6
    • D. 1, 6, and 5
    Answer, explanation and textbook page: open in the app.
  33. 33.The following data gives the scores of 10 students in a Mathematics examination: 6, 10, 8, 5, 9, 8, 5, 10, 10, 9. Which one of the following is the standard deviation of the given data?
    • A. $\sqrt{5.8}$
    • B. $\sqrt{3.6}$
    • C. 5.8
    • D. 3.6
    Answer, explanation and textbook page: open in the app.
  34. 34.Which of the following pairs of lines with the given equations are parallel?
    • A. $\ell_1:x-2y+1=0$ and $\ell_2:x+2y-1=0$
    • B. $\ell_1:4x-y=2$ and $\ell_2:-x+4y-3=0$
    • C. $\ell_1:2x+3y=5$ and $\ell_2:3x+2y=4$
    • D. $\ell_1:x-y+3=0$ and $\ell_2:-x+y-9=0$
    Answer, explanation and textbook page: open in the app.
  35. 35.Which one of the following is equal to the polynomial function $f(x) = x^2 + 4x + 4$?
    • A. $h(x) = (x^2 + 6x + 8) - (2x - 4)$
    • B. $l(x) = (x^2 + 10x + 3) + (-6x + 1)$
    • C. $g(x) = \frac{x^4 + 4x^2 + 4}{x^2 + 2}$
    • D. $k(x) = (x - 2)(x + 2)$
    Answer, explanation and textbook page: open in the app.
  36. 36.The following table presents the number of traffic accidents in a certain city per year for five consecutive years from 2019 to 2023. Year | 2019 | 2020 | 2021 | 2022 | 2023 Number of Accidents | 3500 | 2750 | 2850 | 3500 | 3750 What is the average number of accidents per year for the given five years?
    • A. 3210
    • B. 3270
    • C. 3200
    • D. 3250
    Answer, explanation and textbook page: open in the app.
  37. 37.Consider that a data set given below: 10, 8, 10, 2, 12, 6, 12, 18, 3, 7, 10, 8, 8 Which one of the following is the coefficient of range of the data?
    • A. 4/5
    • B. 20
    • C. 16
    • D. 5/4
    Answer, explanation and textbook page: open in the app.
  38. 38.M 3 2 Let be a matrix such that . Which one of the following matrices is equal to ? 0 3 6 −8 8 6 9 4 10 6 −8 16 12 18 4 10
    • B. 0 2 0 2 3 −4 8 6 9 2 5 1 6 −8 16 12 18 2 10
    • D. 0 0 2
    Answer, explanation and textbook page: open in the app.
  39. 39.Which of the following pairs of lines with the given equations are parallel?
    • A. $\ell_1: x - 2y + 1 = 0$ and $\ell_2: x + 2y - 1 = 0$
    • B. $\ell_1: 4x - y = 2$ and $\ell_2: -x + 4y - 3 = 0$
    • C. $\ell_1: 2x + 3y = 5$ and $\ell_2: 3x + 2y = 4$
    • D. $\ell_1: x - y + 3 = 0$ and $\ell_2: -x + y - 9 = 0$
    Answer, explanation and textbook page: open in the app.
  40. 40.Which one of the following is the range of the function $f(x) = \frac{2x - 1}{x + 3}$?
    • A. $\mathbb{R} \setminus \left(\frac{1}{2}\right)$
    • B. $\mathbb{R} \setminus \left(\frac{1}{2}\right)$
    • C. $\mathbb{R} \setminus \left(-\frac{1}{3}\right)$
    • D. $\mathbb{R} \setminus \left(-\frac{1}{3}\right)$
    Answer, explanation and textbook page: open in the app.
  41. 41.Which one of the following is equal to the expression $\frac{(125)^{\frac{2}{3}}(81)^{-\frac{3}{4}}}{(27)^{-\frac{2}{3}}(625)^{\frac{3}{4}}}$?
    • A. $\frac{5}{3}$
    • B. $15$
    • C. $\frac{3}{5}$
    • D. $\frac{1}{15}$
    Answer, explanation and textbook page: open in the app.
  42. 42.Which one of the following numbers is a common multiple of 324 and 1152?
    • A. 7776
    • B. 20736
    • C. 5184
    • D. 13824
    Answer, explanation and textbook page: open in the app.
  43. 43.Which one of the following is the solution of the equation $(243)^{2x-3}= rac{(81)^{-3x+2}}{3}$ in the set of real numbers?
    • A. 1
    • B. −2
    • C. −1
    • D. 2
    Answer, explanation and textbook page: open in the app.
  44. 44.What is the total surface area of a regular square pyramid with slant height $8\text{cm}$ and base area $25\,\text{cm}^2$?
    • A. 90 $\text{cm}^2$
    • B. 65 $\text{cm}^2$
    • C. 105 $\text{cm}^2$
    • D. 80 $\text{cm}^2$
    Answer, explanation and textbook page: open in the app.
  45. 45.The following table presents the scores of Grade 11 students of a certain school in a Mathematics Examination. Score | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 | 81-90 | 91-100 Number of Students | 10 | 9 | 15 | 12 | 10 | 4 | 2 What is the median of the data given in the above table?
    • A. 55.5
    • B. 60.5
    • C. 50.5
    • D. 58.5
    Answer, explanation and textbook page: open in the app.
  46. 46.What is the area of the region bounded by the graph of $f(x)=x^3$ and the x-axis on the interval $[-4, 2]$?
    • A. 68 Square units
    • B. 136 Square units
    • C. 60 Square units
    • D. 120 Square units
    Answer, explanation and textbook page: open in the app.
  47. 47.Let $f(x)=\frac{x+1}{x-1}$ and $g(x)=\sqrt{x+2}$ be two functions. Which one of the following is true about the combination values of $f$ and $g$ at $x=2$?
    • A. $(f-g)(2)=-1$
    • B. $\left(\frac{f}{g}\right)(2)=\frac{2}{3}$
    • C. $(f+g)(2)=3$
    • D. $(f.g)(2)=6$
    Answer, explanation and textbook page: open in the app.
  48. 48.Which one of the following defines an exponential function?
    • A. $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=x^b$, where $b>0$ and $b\ne 1$.
    • B. $f:\mathbb{R}\to(0,\infty)$ defined by $f(x)=x^b$, where $b>0$ and $b\ne 1$.
    • C. $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=b^x$, where $b>0$ and $b\ne 1$.
    • D. $f:\mathbb{R}\to(0,\infty)$ defined by $f(x)=b^x$, where $b>0$ and $b\ne 1$.
    Answer, explanation and textbook page: open in the app.
  49. 49.In the following figure, O is the center of the circle and the line segments and are intersecting the AB AC m(∠ACD) = 30∘ m(∠BEC) = 50∘ circle at D and E respectively. If and , then which one of the following is m(∠BAC) equal to ? 30∘ 80∘
    • B. 20∘ 70∘
    Answer, explanation and textbook page: open in the app.
  50. 50.Let $f$ be a differentiable function at a number 'a' for $a \in \mathrm{Domain}\ f$. In the expression $\frac{f(a+h)-f(a)}{h}$ for $h \ne 0$, as $h$ gets closer and closer to zero from both directions, the expression becomes closer to $f'(a)$, which is equal to
    • A. The gradient of the tangent line to the graph of $f$ at a point $(a, f(a))$.
    • B. The gradient of the vertical line to the graph of $f$ at a point $(a, f(a))$.
    • C. The gradient of the secant line to the graph of $f$ at a point $(a, f(a))$.
    • D. The gradient of the normal line to the graph of $f$ at a point $(a, f(a))$.
    Answer, explanation and textbook page: open in the app.
  51. 51.If 180 individuals can complete a job in 15 days by working 10 hours a day, how many individuals are needed to complete the job in 10 days if they work 12 hours a day?
    • A. 220
    • B. 144
    • C. 225
    • D. 200
    Answer, explanation and textbook page: open in the app.
Other Mathematics (Natural Science) years: 2018 2017 2015 2014 2013