Let $f(x)$ be a polynomial of degree at least 1, $g(x)$ be a non-zero polynomial and $c \in \mathbb{R}$. Which of the following states the Factor Theorem?

$f(c) = 0$ if and only if $x - c$ is a factor of $f(x)$.

For distinct real numbers $a$ and $b$, if $f(a)f(b) < 0$, then $f(x)$ has at least one zero between $a$ and $b$.

There exist polynomials $q(x)$ and $r(x)$ such that $f(x) = g(x)q(x) + r(x)$.

If $f(x)$ is divided by $x - c$, then the remainder is $f(c)$.

Let $A = \{1,2\}$ and $B = \{1,3\}$ be sets. Then which one of the following Cartesian products is correct?

$A\times A = \{(1,1),(2,2),(2,1),(1,2)\}$.

$B\times A = \{(1,1),(3,1),(1,2),(3,2),(2,3)\}$.

$B\times B = \{(1,1),(1,3),(3,3),(2,3)\}$.

$A\times B = \{(1,1),(1,3),(2,1),(2,3),(3,2)\}$.

When converting the recurring decimal into a fraction using convergent geometric series, then what are the first term and the common ratio respectively?

and 0.25 0.01 25 0.01 0.25 0.1 2.5 0.1

Gobezoch › Past exams › Mathematics (Social Science)

Grade 12 Mathematics (Social Science) national exam, 2017 E.C. (2025 G.C.)

62 questions · 95 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.

Sit this paper (timed)Practice mode

1.Consider the figure shown below. If $m(\angle BAE) = 50^\circ$ and $m(\angle CBD) = 80^\circ$, then $m(\widehat{BXE})$ is equal to:
- A. $65^\circ$
- B. $20^\circ$
- C. $60^\circ$
- D. $30^\circ$
2.Let $f(x)$ be a polynomial of degree at least 1, $g(x)$ be a non-zero polynomial and $c \in \mathbb{R}$. Which of the following states the Factor Theorem?
- A. $f(c) = 0$ if and only if $x - c$ is a factor of $f(x)$.
- B. For distinct real numbers $a$ and $b$, if $f(a)f(b) < 0$, then $f(x)$ has at least one zero between $a$ and $b$.
- C. There exist polynomials $q(x)$ and $r(x)$ such that $f(x) = g(x)q(x) + r(x)$.
- D. If $f(x)$ is divided by $x - c$, then the remainder is $f(c)$.
Answer: A. The Factor Theorem links a zero of a polynomial to a factor. It says $f(c)=0$ exactly when $x-c$ is a factor, so A states the theorem. B is the sign-change result; C is the polynomial division rule; D is the Remainder Theorem. Textbook: Grade 10, unit 2 · section 2.3.
3.Let $A = \{1,2\}$ and $B = \{1,3\}$ be sets. Then which one of the following Cartesian products is correct?
- A. $B\times A = \{(1,1),(3,1),(1,2),(3,2),(2,3)\}$.
- B. $B\times B = \{(1,1),(1,3),(3,3),(2,3)\}$.
- C. $A\times B = \{(1,1),(1,3),(2,1),(2,3),(3,2)\}$.
- D. $A\times A = \{(1,1),(2,2),(2,1),(1,2)\}$.
Answer: D. The key idea is that in a Cartesian product, the first entry comes from the first set and the second entry comes from the second set. Since $A=\{1,2\}$, $A\times A=\{(1,1),(1,2),(2,1),(2,2)\}$, which is option D. Option A includes $(2,3)$, which is not in $B\times A$. Option B includes $(2,3)$, which is not in $B\times B$. Option C includes $(3,2)$, which is not in $A\times B$. Textbook: Grade 9, unit 1 · section 1.4.
4.Consider the matrix $\begin{pmatrix} 2 & -3 & 1 \\ 0 & -1 & \pi \\ 3 & 1 & 4 \end{pmatrix}$. What is the cofactor of entry $\pi$?
- A. $7$
- B. $-11$
- C. $-11\pi$
- D. $-7\pi$
Answer: B. A cofactor is the determinant of the minor, with a sign set by the entry's row and column. For $\pi$ in row $2$, column $3$, the minor determinant is $\begin{vmatrix}2&-3\\3&1\end{vmatrix}=2+9=11$, and the sign is $(-1)^{2+3}=-1$, giving $-11$. A has the wrong sign. C incorrectly includes $\pi$. D has the wrong value and includes $\pi$. Textbook: Grade 11, unit 4 · section 4.2.
5.When converting the recurring decimal into a fraction using convergent geometric series, then what are the first term and the common ratio respectively?
- A. and
- B. and 0.25 0.01 25 0.01 0.25 0.1 2.5 0.1
- C. and
- D. and
Answer: A. The question tests the first term and common ratio of a geometric series for a recurring decimal. For $0.\overline{25}=0.25+0.0025+\cdots$, the first term is $0.25$ and each term is multiplied by $0.01$. B has the wrong first term. C has the wrong common ratio. D has both the wrong first term and the wrong common ratio. Textbook: Grade 12, unit 1 · section 1.4.
6.What are the maximum and minimum values respectively of $z = 3x + y$ subject to constraints $\begin{cases} 3x + 2y \leq 20 \\ 2x - y \geq 4 \\ x \geq 0, y \geq 0 \end{cases}$?
- A. $20$ and $6$
- B. $40$ and $6$
- C. $16$ and $6$
- D. $18$ and $8$
Answer: A. The key idea is to find the largest and smallest values at the corner points of the feasible region. The corner points are $(2,0)$, $(4,4)$, and $(20/3,0)$, giving $z=6$, $16$, and $20$ respectively. B is wrong because the maximum is not $40$. C is wrong because $16$ is not the maximum. D is wrong because neither $18$ nor $8$ is an extreme value. Textbook: Grade 12, unit 4 · section 4.3.
7.What is the domain of the function $f(x) = \sqrt{3 - x^2}$?
- A. $[\sqrt{3}, \infty)$
- B. $[-\sqrt{3}, \sqrt{3}]$
- C. $[-3, 3]$
- D. $(-\infty, \sqrt{3}] \cup [\sqrt{3}, \infty)$
Answer, explanation and textbook page: open in the app.
8.If $x = 0.00471$, then which of the following gives the mantissa of $\log x$?
- A. $-3$
- B. $3$
- C. $\log 4.71$
- D. $\log 0.471$
Answer, explanation and textbook page: open in the app.
9.Dibabe was hired in an elementary school with a monthly salary of Birr 30,000. The agreement was to raise her salary every year by Birr 3,000. What is the total amount of money that Dibabe will earn at the end of the 8th year in Birr?
- A. 2,964,000
- B. 3,888,000
- C. 2,976,000
- D. 324,000
Answer, explanation and textbook page: open in the app.
10.For what value of $x$ is the matrix $\begin{pmatrix} 1 & 0 & 1 \\ 2x+1 & 3 & 0 \\ 1 & -1 & x \end{pmatrix}$ invertible?
- A. $\{x \in \mathbb{R}: x \neq -1\}$
- B. $\{x \in \mathbb{R}: x \neq 4\}$
- C. $\{x \in \mathbb{R}: x \neq 0\}$
- D. $\{x \in \mathbb{R}: x \neq 3\}$
Answer, explanation and textbook page: open in the app.
11.What is the surface area (in cm$^2$) of leather material required to make a spherical shape ball of radius 25cm?
- A. $625\pi$
- B. $2500\pi$
- C. $100\pi$
- D. $1250\ sphere$
Answer, explanation and textbook page: open in the app.
12.Mr. Bekele finances two investments, $I_1$ and $I_2$. The profits of $I_1$ and $I_2$ are 8% and 10%, respectively. The total investment is Birr one million with at least Birr 50,000 in $I_1$ and at most Birr 300,000 in $I_2$. Which of the following is the Mathematical representation of the problem if Mr. Bekele wishes to maximize his profit? (Let $x$ and $y$ be the amount of money invested on $I_1$ and $I_2$ in Birr, respectively)
- A. $\begin{cases} \text{Maximize } z = 0.08x + 0.1y \\ \text{s.t. } x + y \geq 1,000,000 \\ x \leq 50,000 \\ y \geq 300,000 \\ x, y \geq 0 \end{cases}$
- B. $\begin{cases} \text{Maximize } z = 0.08x + 0.1y \\ \text{s.t. } x + y \geq 1,000,000 \\ x \geq 50,000 \\ y \leq 300,000 \\ x, y \geq 0 \end{cases}$
- C. $\begin{cases} \text{Maximize } z = 0.08x + 0.1y \\ \text{s.t. } x + y \leq 1,000,000 \\ x \leq 50,000 \\ y \geq 300,000 \\ x, y \geq 0 \end{cases}$
- D. $\begin{cases} \text{Maximize } z = 0.08x + 0.1y \\ \text{s.t. } x + y \leq 1,000,000 \\ x \geq 50,000 \\ y \leq 300,000 \\ x, y \geq 0 \end{cases}$
Answer, explanation and textbook page: open in the app.
13.What is the result when $3\sqrt{2} - 7\sqrt{6}$ is subtracted from $2\sqrt{2} + 4\sqrt{3}$?
- A. $\sqrt{2} + (4 - 7\sqrt{2})\sqrt{3}$
- B. $-\sqrt{2} + 11\sqrt{2}\sqrt{3}$
- C. $-\sqrt{2} + (4 + 7\sqrt{2})\sqrt{3}$
- D. $\sqrt{2} - \sqrt{3}(7\sqrt{2} + 4)$
Answer, explanation and textbook page: open in the app.
14.Which one of the following is qualitative data?
- A. The time Derartu took to win Atlanta Olympic.
- B. Age of President Trump.
- C. The volume of oil in a container.
- D. The type of Coffee produced in Keffa.
Answer, explanation and textbook page: open in the app.
15.Consider the functions $f(x)=5^x$ and $g(x)=\log_5 x$. Which of the following is correct about the relations of domains and ranges of $f$ and $g$?
- A. $\text{Domain}(f) = \text{Range}(g)$
- B. $\text{Domain}(f) \subseteq \text{Domain}(g)$
- C. $\text{Domain}(f) = \text{Domain}(g)$
- D. $\text{Range}(f) = \text{Range}(g)$
Answer, explanation and textbook page: open in the app.
16.In the figure shown below, $\overline{AC} = \overline{DE}$, $\angle BAC = \angle DEF$, $\angle ACB = \angle FDE$ and $\overline{AC}\equiv \overline{DE}$ Then which one of the following is true?
- A. $\triangle ABC \equiv \triangle FED$
- B. $\triangle ABC \equiv \triangle EFD$
- C. $\triangle ABC \equiv \triangle DEF$
- D. $\triangle ABC \equiv \triangle DFE$
Answer, explanation and textbook page: open in the app.
17.Let $f$ be a function and let $c$ be an element of domain of $f$ at which the gradient of $f$ is zero. Which one of the following statements is true about $f'(c)$?
- A. $f'(c)=0$
- B. $f'(c)\neq 0$
- C. $f'(c)>0$
- D. $f'(c)<0$
Answer, explanation and textbook page: open in the app.
18.What is the solution set of the equation $|2x - 3| - 1 = 0$?
- A. $\left[\frac{3}{2}, \infty\right)$
- B. $\{2\}$
- C. $\{1, 2\}$
- D. $\{\}$
Answer, explanation and textbook page: open in the app.
19.An equilateral triangle is inscribed in a circle with radius $\sqrt{3}$ cm. Then what is the perimeter (in cm) of the triangle?
- A. $\frac{9}{2}$
- B. $\frac{9\sqrt{3}}{8}$
- C. $9$
- D. $3\sqrt{3}$
Answer, explanation and textbook page: open in the app.
20.Which of the following statements defines frustum of a pyramid?
- A. It is part of a pyramid excluded the base of the pyramid and horizontal cross-section made by the plane slant to the base.
- B. It is part of a pyramid included between the base of the pyramid and a horizontal cross-section made by the plane parallel to the base.
- C. It is part of a cone included between the base of the cone and a plane parallel to the base.
- D. It is a surface in space all points of which are equidistant from a point.
Answer, explanation and textbook page: open in the app.
21.If $\mathbf{u} = (1, -1)$ and $\mathbf{v} = (2, -4)$ are vectors, then $\mathbf{u} - \mathbf{v}$ is equal to:
- A. $(-1,3)$
- B. $(-3,5)$
- C. $(3,-5)$
- D. $(1,-3)$
Answer, explanation and textbook page: open in the app.
22.The gradient of a function $f(x) = \frac{1}{x^2}$ at $x = a$, $a \neq 0$ is equal to:
- A. $-\frac{2}{a^4}$
- B. $-\frac{2}{a^3}$
- C. $\frac{2}{a^2}$
- D. $\frac{2}{a^3}$
Answer, explanation and textbook page: open in the app.
23.Which of the following is NOT a valid reason for a person to save money?
- A. To buy shares from private banks
- B. To give loan to other people and collect profit
- C. For down payment of a house
- D. To support life after retirement
Answer, explanation and textbook page: open in the app.
24.Consider the following data. 12, 21, 16, 15, 10, 11, 12, 18, 9, 10, 13, 14, 15, 13, 19 Which one of the following is true?
- A. $Q_3 = 16$
- B. $Q_2 = 13.5$
- C. $Q_1 = 4$
- D. $Q_1 = 12$
Answer, explanation and textbook page: open in the app.
25.A line $\ell_1$ in the $x, y$-plane has equation $x - y + 3 = 0$. A second line $\ell_2$ which is perpendicular to $\ell_1$ contains the point $(2, 3)$. Which one of the following gives equation of $\ell_2$?
- A. $3y + 2x + 3 = 0$
- B. $y - x + 5 = 0$
- C. $y + x - 5 = 0$
- D. $y - x - 3 = 0$
Answer, explanation and textbook page: open in the app.
26.When the Division Algorithm is applied to the fraction $\frac{283}{20}$, then which one of the following is the corresponding representation?
- A. $283 = 10 \times 20 + 83$
- B. $283 = 1 \times 283 + 0$
- C. $283 = 7 \times 20 + 143$
- D. $283 = 14 \times 20 + 3$
Answer, explanation and textbook page: open in the app.
27.Consider the data 7, 12, 21, x, 14. What is the value of if its range is 23? x
- A. 30
- B. 33.5
- C. 2
- D. 23
Answer, explanation and textbook page: open in the app.
28.The following is raw data of 15 students in a test: 9, 6, 6, 10, 6, 10, 9, 7, 7, 5, 9, 7, 10, 7, 7 Which one of the following is frequency distribution of the given data?
- A. $\begin{array}{c|c|c|c|c|c} v & 5 & 6 & 7 & 9 & 10 \\ \hline f & 5 & 4 & 3 & 2 & 1 \end{array}$
- B. $\begin{array}{c|c|c|c|c|c} v & 5 & 6 & 7 & 9 & 10 \\ \hline f & 1 & 3 & 5 & 3 & 3 \end{array}$
- C. $\begin{array}{c|c|c|c|c|c} v & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline f & 1 & 3 & 5 & 1 & 3 & 2 \end{array}$
- D. $\begin{array}{c|c|c|c|c|c} v & 1 & 3 & 5 & 3 & 3 \\ \hline f & 5 & 6 & 7 & 9 & 10 \end{array}$
Answer, explanation and textbook page: open in the app.
29.Let $R_1(x) = \frac{x^3 - 9x}{x^2 - 2}, x \neq \pm \sqrt{2}$, and $R_2(x) = \frac{x^2 + 3x}{x - \sqrt{2}}, x \neq \sqrt{2}$ be rational functions. Then what is the simplified form of $\frac{R_1(x)}{R_2(x)}$?
- A. $1$
- B. $x - 3$
- C. $\frac{x - \sqrt{2}}{x + 3}, x \neq -3, 0$
- D. $\frac{x - 3}{x + \sqrt{2}}, x \neq \pm \sqrt{2}, 0$
Answer, explanation and textbook page: open in the app.
30.Which one of the following is a scalar quantity?
- A. Displacement of an object to change its position.
- B. The average velocity of airplane to travel.
- C. Force applied on an object to change its place.
- D. The total time taken to complete surgery.
Answer, explanation and textbook page: open in the app.
32.A spherical fuel container with radius 3m is filled with fuel. What is the amount (in m$^3$) of fuel in the container?
- A. $\frac{12}{3}\pi$
- B. $9\pi$
- C. $36\pi$
- D. $18\pi$
Answer, explanation and textbook page: open in the app.
33.A circle with radius 3 cm increases its radius at a rate of 0.2 cm/sec. What is the area of the circle at the 5 second? 9.64π 2 4π 2
- A. cm
- B. cm 16π 2 9π 2
- C. cm
- D. cm
Answer, explanation and textbook page: open in the app.
34.A school has 6,000 students. The ratio of female students to the total number of students is 2:3. Which one of the following is true about the students in the school?
- A. The number of female students is twice the number of male students.
- B. The ratio of male students to female students is 1:3.
- C. The number of male students is greater than that of female students.
- D. About 33% of the students in the school are female.
Answer, explanation and textbook page: open in the app.
35.Let $S$ be a set given by $\{x \in \mathbb{N}: 1 < x \leq 100\}$. Then which one of the following statement is true?
- A. $S$ is equal to $\{2,3,4, \dots, 99,100\}$.
- B. $S$ is equivalent to $\{1,2,3, \dots, 100\}$.
- C. $S$ is equal to $\{2,3,4,\dots,99\}$.
- D. $S$ is equivalent to $\{101,102, \dots, 198\}$.
Answer, explanation and textbook page: open in the app.
36.What is the inverse of the matrix $\begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix}$?
- A. $\begin{pmatrix} 2 & -1 \\ 0 & 3 \end{pmatrix}$
- B. $\frac{-1}{6} \begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix}$
- C. $\begin{pmatrix} -\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3} \end{pmatrix}$
- D. $\begin{pmatrix} -2 & 0 \\ 1 & 3 \end{pmatrix}$
Answer, explanation and textbook page: open in the app.
37.Which one of the following is equal to ?
- A. 20
- B. 30
- C. 16
- D. 32
Answer, explanation and textbook page: open in the app.
38.Given the polynomial function $p(x) = 5x^2 - x^3 - \sqrt{2}$. Then what are the degree, leading coefficient and constant term of the polynomial function $p(x)$ respectively?
- A. $3, 5, -\sqrt{2}$
- B. $3, -1, -\sqrt{2}$
- C. $2, 5, -\sqrt{2}$
- D. $3, 1, \sqrt{2}$
Answer, explanation and textbook page: open in the app.
39.Let $S$ be a set given by $\{x \in \mathbb{N}: 1 < x \leq 100\}$. Then which one of the following statement is true?
- A. $S$ is equal to $\{2,3,4, \dots, 99,100\}$.
- B. $S$ is equivalent to $\{1,2,3, \dots, 100\}$.
- C. $S$ is equal to $\{2,3,4,\dots,99\}$.
- D. $S$ is equivalent to $\{101,102, \dots, 198\}$.
Answer, explanation and textbook page: open in the app.
40.What is the inverse of the matrix $\begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix}$?
- A. $\begin{pmatrix} 2 & -1 \\ 0 & 3 \end{pmatrix}$
- B. $\frac{-1}{6} \begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix}$
- C. $\begin{pmatrix} -\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3} \end{pmatrix}$
- D. $\begin{pmatrix} -2 & 0 \\ 1 & 3 \end{pmatrix}$
Answer, explanation and textbook page: open in the app.
41.Which one of the following is equal to ?
- A. 20
- B. 30
- C. 16
- D. 32
Answer, explanation and textbook page: open in the app.
42.Given the polynomial function $p(x) = 5x^2 - x^3 - \sqrt{2}$. Then what are the degree, leading coefficient and constant term of the polynomial function $p(x)$ respectively?
- A. $3, 5, -\sqrt{2}$
- B. $3, -1, -\sqrt{2}$
- C. $2, 5, -\sqrt{2}$
- D. $3, 1, \sqrt{2}$
Answer, explanation and textbook page: open in the app.
43.A person, whose height is 2 m, is standing away from a 16 m tall building. The angle of depression from the top of the building to the head of the person is $30^\circ$. How far is the person from the building in meters?
- A. $14\sqrt{3}$
- B. $\frac{16}{\sqrt{3}}$
- C. $16\sqrt{3}$
- D. $\frac{14}{\sqrt{3}}$
Answer, explanation and textbook page: open in the app.
44.If a sampling interval is calculated by dividing the size of the population by the size of the sample, then which probability sampling technique is used?
- A. Stratified Sampling
- B. Systematic Sampling
- C. Simple Random Sampling
- D. Cluster Sampling
Answer, explanation and textbook page: open in the app.
45.Which one of the following systems of equations possesses no solution?
- A. $\begin{cases} -x + 3y = -2 \\ -2x + 6y = -4 \end{cases}$
- B. $\begin{cases} -2x + y = 2 \\ 4x - 2y = 4 \end{cases}$
- C. $\begin{cases} x - 3y = 0 \\ 2x + y = -7 \end{cases}$
- D. $\begin{cases} x + y = \sqrt{2} \\ -x + y = \pi \end{cases}$
Answer, explanation and textbook page: open in the app.
46.Let $A(-1, 2)$ and $B(0, 5)$ be initial and terminal points of vector $\overrightarrow{AB}$. What is the position vector of $\overrightarrow{AB}$?
- A. $-i + 7j$
- B. $5j$
- C. $-i - 3j$
- D. $i + 3j$
Answer, explanation and textbook page: open in the app.
47.The system of linear equations $\begin{cases} x + z = 0 \\ 2x + y = 1 \\ x + 2y + z = 0 \end{cases}$ in matrix form is equal to:
- A. $\begin{pmatrix} 1 & 1 & 0 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$
- B. $\begin{pmatrix} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$
- C. $\begin{pmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$
- D. $\begin{pmatrix} 1 & 1 & 1 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$
Answer, explanation and textbook page: open in the app.
48.Which one of the following is NOT true about the coefficient of variation?
- A. It is used to evaluate the variation of a data.
- B. It is the ratio of standard deviation to the mean.
- C. It is a measure of relative dispersion that is based on standard deviation.
- D. It is a relative measure used to measure the degree of consistency.
Answer, explanation and textbook page: open in the app.
49.Which of the following describe combination of objects?
- A. The number of ways of arrangement of n objects in a specific order using r objects at a time.
- B. The number of ways of arranging the seat of n people in a circle.
- C. The number of ways of choosing r objects from n objects disregarding the order of selection.
- D. The number of ways of arranging n objects taking n at a time considering the order of the objects.
Answer, explanation and textbook page: open in the app.
50.Which one of the following is true about measures of dispersion?
- A. It gives representative of the whole data.
- B. It locates the central value of the data.
- C. It measures the scatter of the data.
- D. It gives the middle value of the data.
Answer, explanation and textbook page: open in the app.
51.The solution set of $\sqrt[3]{64^{x-1}} = \left(\frac{1}{16}\right)^{2x+3}$ is equal to:
- A. $\left\{-\frac{1}{2}\right\}$
- B. $\left\{\frac{1}{3}\right\}$
- C. $\{-1\}$
- D. $\{1\}$
Answer, explanation and textbook page: open in the app.
52.In how many ways can the name for vertices of a triangle be given in different order by using letters A, B, C, D, E?
- A. 20
- B. 120
- C. 10
- D. 60
Answer, explanation and textbook page: open in the app.
53.If $\sin(-53^\circ) = \beta$, then which one of the following is correct?
- A. $\sin(37^\circ) = \beta$
- B. $\sin(127^\circ) = \beta$
- C. $\sin(-37^\circ) = \beta$
- D. $\sin(307^\circ) = \beta$
Answer, explanation and textbook page: open in the app.
54.What is the solution set of the inequality $1 - \frac{3}{x} \le \frac{4}{x^2}$?
- A. $[-1, 0) \cup (0, 4]$
- B. $[-1, 4]$
- C. $(-\infty, -1) \cup (4, \infty)$
- D. $(-\infty, -1] \cup [4, \infty)$
Answer, explanation and textbook page: open in the app.
55.The slope of a line passing through and is equal to:
- A. 2
- B. -1
- C. 3
- D. -2
Answer, explanation and textbook page: open in the app.
56.Given the function $f(x) = 2\operatorname{sgn} x + 1$. Then what are the domain and the range of $f(x)$ respectively?
- A. $\mathbb{R}$ and $\{-3, 1, 3\}$
- B. $\mathbb{R}$ and $\{-3, -1, 3\}$
- C. $\mathbb{R}$ and $\{-2, 0, 2\}$
- D. $\mathbb{R}$ and $\{-1, 1, 3\}$
Answer, explanation and textbook page: open in the app.
57.What is the rationalizing factor of the number $\frac{5\sqrt{3}}{\sqrt{3} - \sqrt{2}}$?
- A. $\frac{1}{\sqrt{3} + \sqrt{2}}$
- B. $\frac{\sqrt{3}}{\sqrt{3} + \sqrt{2}}$
- C. $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$
- D. $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$
Answer, explanation and textbook page: open in the app.
58.An entrance examination for a certain job was given to 35 applicants and their results are summarized in the table below. Results Number of applicants 41-50 3 51-60 14 61-70 10 71-80 5 81-90 2 91-100 1 Then which one of the following is NOT true?
- A. The upper class limit of the second class is 60.
- B. The class midpoint of the second class is 55.
- C. 61-70 is the class interval of the third class.
- D. The lower class limit of the fifth class is 81.
Answer, explanation and textbook page: open in the app.
59.What is the equation of the tangent line to the graph of $f(x) = 2x^3 - 3x^2 + 1$ at $x = 2$?
- A. $y = 120x - 235$
- B. $y = 6x - 7$
- C. $y = 2x + 5$
- D. $y = 12x - 19$
Answer, explanation and textbook page: open in the app.
60.An entrance examination for a certain job was given to 35 applicants and their results are summarized in the table below. Results Number of applicants 41-50 3 51-60 14 61-70 10 71-80 5 81-90 2 91-100 1 Then which one of the following is NOT true?
- A. The upper class limit of the second class is 60.
- B. The class midpoint of the second class is 55.
- C. 61-70 is the class interval of the third class.
- D. The lower class limit of the fifth class is 81.
Answer, explanation and textbook page: open in the app.
61.Which one of the following graphs represents $f(x) = \log_4 x$?
Answer, explanation and textbook page: open in the app.
63.Which of the following graphs represent the graph of $f(x) = \cos x$ on the interval $[-\pi, \pi]$?
Answer, explanation and textbook page: open in the app.
64.Consider the diagram below: ABCD is a parallelogram with length of base 7 cm and $\triangle APB$ is an isosceles right angled triangle with right angle at P and hypotenuse 4 cm. What is the area of ABCD in cm$^2$?
- A. $14\sqrt{2}$
- B. 8
- C. 28
- D. $7\sqrt{2}$
Answer, explanation and textbook page: open in the app.

Other Mathematics (Social Science) years: 2018 2016 2015 2014 2013