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Grade 12 Mathematics (Natural Science) national exam, 2013 E.C. (2021 G.C.)

64 questions · 180 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.Given two vectors $u = (1, 3)$ and $v = (-3, 5)$ in the plane. Then $6u + 2v$ is equal to
    • A. (0, 18)
    • B. (3, 3)
    • C. (2, 28)
    • D. (0, 28)
  2. 2.Which one of the following is the standard form of the equation of the circle centered at $(2, -3)$ and radius 5?
    • A. $\left(x - 2\right)^2 + \left(y - 3\right)^2 = 25$
    • B. $\left(x - 2\right)^2 + \left(y + 3\right)^2 = 25$
    • C. $\left(x + 2\right)^2 + \left(y + 3\right)^2 = 5$
    • D. $\left(x + 2\right)^2 + \left(y - 3\right)^2 = 25$
    Answer: B. A circle’s equation uses its center $(h,k)$ and radius $r$ in $(x-h)^2+(y-k)^2=r^2$. Substituting $(2,-3)$ and $r=5$ gives $(x-2)^2+(y+3)^2=25$. A uses the wrong sign for the center’s $y$-coordinate. C uses the wrong signs and sets the right side to $5$, not $25$. D uses the wrong signs for the center. Textbook: Grade 10, unit 7 · section 7.5.
  3. 3.If $f$ is a continuous function on $[a, b]$ and $F$ is its anti-derivative, then which of the following is true?
    • A. $\int_a^b F'(x)dx = f(b) - f(a)$
    • B. $\int_a^b F(x)dx = f(b) - f(a)$
    • C. $\int_a^b f(x)dx = F(b) - F(a)$
    • D. $\int_a^b f'(x)dx = F(b) - F(a)$
    Answer: C. The key idea is that integrating a function gives the change in any one of its antiderivatives. Since $F'(x)=f(x)$, the fundamental theorem gives $\int_a^b f(x)\,dx=F(b)-F(a)$. A is wrong because its integral equals $F(b)-F(a)$, not $f(b)-f(a)$. B is wrong because it integrates $F$, not $f$. D is wrong because it integrates $f'$, not $F'$. Textbook: Grade 12, unit 2 · section 2.3.
  4. 4.Which of the following defines the equation of a sphere whose center is at $(0, -1, 2)$ and radius 6 units?
    • A. $x^2 + (y+1)^2 + (z-2)^2 = 36$
    • B. $x^2 + (y-1)^2 + (z-2)^2 = 36$
    • C. $x^2 + (y+1)^2 + (z-2)^2 = 12$
    • D. $x^2 + (y+1)^2 + (z+2)^2 = 36$
  5. 5.Which of the following represents the vector $(3, -5, 7)$ in the space using the standard unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$?
    • A. $3\mathbf{i} - 5\mathbf{j} - 7\mathbf{k}$
    • B. $3\mathbf{i} + 5\mathbf{j} + 7\mathbf{k}$
    • C. $3\mathbf{i} - 5\mathbf{j} + 7\mathbf{k}$
    • D. $-3\mathbf{i} - 5\mathbf{j} - 7\mathbf{k}$
    Answer: C. The coordinates give the amounts in the $\mathbf{i}$, $\mathbf{j}$, and $\mathbf{k}$ directions. Thus $(3,-5,7)=3\mathbf{i}-5\mathbf{j}+7\mathbf{k}$, which is C. A has the wrong sign for the $\mathbf{k}$ part; B has the wrong sign for the $\mathbf{j}$ part; D has the wrong sign for the $\mathbf{i}$ and $\mathbf{k}$ parts. Textbook: Grade 11, unit 5 · section 5.3.
  6. 6.Which one of the following is the scalar (dot) product of the vectors $(2, -4, 6)$ and $(-2, -1, 0)$?
    • A. 0
    • B. -8
    • C. 8
    • D. -4
  7. 7.What are the domain and range of the function $f(x) = 2x^{\frac{3}{4}}$ respectively?
    • A. $\mathbb{R}$ and $[0,\infty)$
    • B. $[0,\infty)$ and $\mathbb{R}$
    • C. $[0,\infty)$ and $\mathbb{R}$
    • D. $[0,\infty)$ and $[0,\infty)$
  8. 8.Which one of the following defines a one-to-one function?
    • A. $f = \{(x, y): x \text{ is a sister of } y\}$
    • B. $f = \{(x, y): y = 3x - 1\}$
    • C. $f = f(x, y): y = x^2 + 1\}$
    • D. $f = \{(x, y): y \text{ is a father of } x\}$
  9. 9.The equation of a circle is given by $(x-3)^2+(y+2)^2=9$. What are the center and the radius of the circle respectively?
    • A. (3, -2) and 3
    • B. (3, 2) and 3
    • C. (3, -2) and 9
    • D. (3, 2) and 9
    Answer: A. A circle in standard form shows its center and radius. Comparing with $(x-h)^2+(y-k)^2=r^2$, the center is $(3,-2)$ and the radius is $3$. A gives both correctly. B has the wrong sign for the center’s second coordinate. C gives the square of the radius as the radius. D has the wrong center and radius. Textbook: Grade 10, unit 7 · section 7.5.
  10. 10.Which one of the following sentences has a truth value?
    • A. Man is selfish.
    • B. We shall win!
    • C. Man is mortal!
    • D. Tomorrow is a beautiful day.
  11. 11.What is the determinant of the matrix $\begin{bmatrix} 1 & -7 \\ 6 & 5\end{bmatrix}$?
    • A. -37
    • B. -47
    • C. 47
    • D. 37
    Answer: C. The key idea is to find a $2\times2$ determinant by multiplying the main diagonal entries and subtracting the other diagonal product. The calculation is $1\times5-((-7)\times6)=5+42=47$. A is wrong because it gives $-37$. B is wrong because it gives $-47$. D is wrong because it gives $37$. Textbook: Grade 11, unit 4 · section 4.2.
  12. 12.The additive inverse of the complex number $3 - 4i$ is
    • A. $-3 + 4i$
    • B. $-3 - 4i$
    • C. $3 - 4i$
    • D. $3 + 4i$
    Answer, explanation and textbook page: open in the app.
  13. 13.What is the modulus of the complex number $-6 + 8i$?
    • A. 5
    • B. 2
    • C. 10
    • D. 8
    Answer, explanation and textbook page: open in the app.
  14. 14.Consider the following frequency distribution graph Value 5 3 7 6 8 Frequency 3 4 5 3 5 What is the sixth decile?
    • A. 6.5
    • B. 5
    • C. 7.5
    • D. 7
    Answer, explanation and textbook page: open in the app.
  15. 15.In a certain health center there are 3 doctors, 8 nurses and 2 physicians. In how many ways one can form a group of 5 members consisting of 1 doctor, 3 nurses and 1 physician?
    • A. 168
    • B. 112
    • C. 336
    • D. 330
    Answer, explanation and textbook page: open in the app.
  16. 16.Which one of the following forms represents an exhaustive set of events if a die is thrown once?
    • A. {1, 2}, {4}, {4, 5, 6}
    • B. {1, 2, 3}, {4, 5}, {6}
    • C. {1, 2}, {2}, {4, 5}, {5, 6}
    • D. {1, 2, 3}, {3, 4}, {6}
    Answer, explanation and textbook page: open in the app.
  17. 17.A bag contains 2 red, 3 yellow and 5 green balls. One ball is drawn at random. What is the probability that the drawn ball is NOT yellow?
    • A. $\frac{3}{10}$
    • B. $\frac{1}{5}$
    • C. $\frac{7}{10}$
    • D. $\frac{7}{10}$
    Answer, explanation and textbook page: open in the app.
  18. 18.Which of the following is the product $AB$ of the two matrices $A=\begin{bmatrix}-2 & 3\\ 1 & 4\end{bmatrix}$ and $B=\begin{bmatrix}-1 & 5\\ 3 & 0\end{bmatrix}$?
    • A. $\begin{bmatrix}-11 & -10\\ 11 & 5\end{bmatrix}$
    • B. $\begin{bmatrix}-11 & 10\\ 11 & 5\end{bmatrix}$
    • C. $\begin{bmatrix}11 & -10\\ 11 & 5\end{bmatrix}$
    • D. $\begin{bmatrix}-11 & 10\\ 11 & -5\end{bmatrix}$
    Answer, explanation and textbook page: open in the app.
  19. 19.Which one of the following is NOT true about the determinant of a given square matrix A?
    • A. If A contains a row of zeros, then its determinant is zero.
    • B. If A has identical rows, then its determinant is zero.
    • C. The determinant of A is equal to the determinant of its transpose.
    • D. Interchanging two rows of A gives the same determinant.
    Answer, explanation and textbook page: open in the app.
  20. 20.Which of the following is the inverse of the matrix $\begin{bmatrix}2 & 3\\ 3 & 4\end{bmatrix}$?
    • A. $\begin{bmatrix}-4 & 3\\ 3 & -2\end{bmatrix}$
    • B. $\begin{bmatrix}-2 & 3\\ 3 & -4\end{bmatrix}$
    • C. $\begin{bmatrix}4 & -3\\ -3 & 2\end{bmatrix}$
    • D. $\begin{bmatrix}-4 & -3\\ -3 & -2\end{bmatrix}$
    Answer, explanation and textbook page: open in the app.
  21. 21.Consider the system of linear equation $ \left\{ \begin{array}{r l} 3x - ay & = 1 \\ 6x + 4y & = 5 \end{array} \right. $ Then which of the following is true?
    • A. If $a>-2$, then the system has a unique solution.
    • B. If $a=-2$, then the system has a unique solution.
    • C. If $a=2$, then the system has no solution.
    • D. If $a>2$, then the system has infinitely many solutions.
    Answer, explanation and textbook page: open in the app.
  22. 22.What is the magnitude of the vector whose initial point is at (1, -3) and terminal point is at (4, 1)?
    • A. 5
    • B. 6
    • C. 1
    • D. 4
    Answer, explanation and textbook page: open in the app.
  23. 23.Let T be a translation that takes the origin into (2, 3). Then which of the following is true about the translation T?
    • A. $(x - 4)^2 + (y - 3)^2 =9$ is the translation of $(x - 2)^2 + (y + 6)^2 = 9$.
    • B. $(x - 5)^2 + (y - 6)^2 = 9$ is the translation of $(x - 3)^2 + (y - 3)^2 = 9$.
    • C. $(x - 4)^2 + (y + 3)^2 = 12$ is the translation of $(x - 2)^2 + (y + 6)^2 = 12$.
    • D. $(x + 4)^2 + (y - 3)^2 = 12$ is the translation of $(x - 2)^2 + (y + 6)^2 = 12$.
    Answer, explanation and textbook page: open in the app.
  24. 24.Which of the following is true?
    • A. The domain of $y = \tan^{-1}x$ is $(-\infty, \infty)$.
    • B. The domain of $y = \cos^{-1}x$ is $(-1, 1)$.
    • C. $\sin^{-1}(0) = \frac{\pi}{2}$.
    • D. $\tan^{-1}(0) = 1$.
    Answer, explanation and textbook page: open in the app.
  25. 25.Which of the following functions represents the graph shown in Figure 2?
    • A. f(x) = tan x
    • B. f(x) = sec x
    • C. f(x) = csc x
    • D. f(x) = cot x
    Answer, explanation and textbook page: open in the app.
  26. 26.Which one of the following is the fourth term of the sequence $\left\{\ \cos(\frac{n\pi}{2}) \right\}$?
    • A. 0
    • B. -1
    • C. 1
    • D. 0.5
    Answer, explanation and textbook page: open in the app.
  27. 27.Which of the following is a geometric sequence?
    • A. 1, 1.5, 2.5, 3.5, ...
    • B. 0.1, 0.01, 0.0011, 0.000111, ...
    • C. 8, 4, 2, -1, ...
    • D. 0.1, 0.11, 0.12, 0.13, ...
    Answer, explanation and textbook page: open in the app.
  28. 28.A factory that produces electric cable had sales Birr 1,000,000 the first day. During each successive days the sales increased by Birr 10,000 every day. What is the total sales of the factory in the first 10 days?
    • A. Birr 10,000,000
    • B. Birr 1,090,000
    • C. Birr 20,900,000
    • D. Birr 10,450,000
    Answer, explanation and textbook page: open in the app.
  29. 29.What is the least upper bound of the sequence $\left\{2 + \frac{n}{n+1}\right\}_{n=1}^\infty$?
    • A. 1
    • B. 0
    • C. 3
    • D. 2
    Answer, explanation and textbook page: open in the app.
  30. 30.Which one of the following sequences is a null sequence?
    • A. $\left\{ n \sin\left(\frac{1}{n}\right) \right\}$
    • B. $\left\{1-\frac{1}{n}\right\}$
    • C. $\left\{\ \frac{n}{n+1}\right\}$
    • D. $\left\{\ \cos\frac{n}{n}\right\}$
    Answer, explanation and textbook page: open in the app.
  31. 31.Suppose ${a_n}$ and ${b_n}$ are sequences with $lim a_n = L and lim b_n = M$. Then which of the following is NOT necessarily true?
    • A. $$\lim_{n \to \infty} (3a_{n} + 2b_{n}) = 3L + 2M$$
    • B. $$\lim_{n \to \infty} (a_{n} - b_{n}) = L - M$$
    • C. $$\lim_{n \to \infty} \left( \frac{a_{n}}{b_{n}} \right) = \frac{L}{M}$$
    • D. $$\lim_{n \to \infty} a_{n} b_{n} = LM$$
    Answer, explanation and textbook page: open in the app.
  32. 32.$\lim_{x \to \infty} \frac{3x^{2} + 2x}{5x - 6}$ is equal to
    • A. -1
    • B. -3
    • C. 1
    • D. 0
    Answer, explanation and textbook page: open in the app.
  33. 33.Which of the following is the same as the derivative of a function f' at a point P, where P is on the graph of f?
    • A. The continuity of the function at P.
    • B. The slope of a secant line through P.
    • C. The slope of the tangent line through P.
    • D. The graph of f has no jump at P.
    Answer, explanation and textbook page: open in the app.
  34. 34.What is the derivative of the function $f(x) = 3x^2 + 2\sqrt{x} - 4x$ at $x = 1$?
    • A. -1
    • B. -3
    • C. 3
    • D. 1
    Answer, explanation and textbook page: open in the app.
  35. 35.What are the 2nd and the nth derivative of $f(x) = e^x$ respectively?
    • A. $4f(x)$ and $2nf(x)$
    • B. $2f(x)$ and $nf(x)$
    • C. $9f(x)$ and $3nf(x)$
    • D. $9f(x)$ and $n^2f(x)$
    Answer, explanation and textbook page: open in the app.
  36. 36.Which of the following is true about the zero of a function?
    • A. It is the y-intercept of the function.
    • B. It is the x-intercept of the function.
    • C. It is the concavity point of the function.
    • D. It is the critical point of the function.
    Answer, explanation and textbook page: open in the app.
  37. 37.Which of the following is true about the function defined by $f(x) = x^3 - 3x^2$ on [-1, 3]?
    • A. Its critical numbers are 0 and 2 and its maximum value is 15.
    • B. Its critical numbers are 0, 2, 3 and its maximum value is 0.
    • C. It has critical numbers at 0 and 2 and its maximum value is 0.
    • D. Its critical numbers are 0 and 2 and its maximum value is -4.
    Answer, explanation and textbook page: open in the app.
  38. 38.What is the number that satisfies Rolle's Theorem for $f(x) = x^3 - 3x + 1$ on $[0, 3]$?
    • A. 1
    • B. $-\frac{3}{2}$
    • C. 2
    • D. $\frac{3}{2}$
    Answer, explanation and textbook page: open in the app.
  39. 39.What are the length L and width W of a rectangle with perimeter 10,000m that maximizes the area?
    • A. L = 2,500 m and W = 2,000 m
    • B. L = 2,500 m and W = 2,500 m
    • C. L = 5,000 m and W = 5,000 m.
    • D. L = 3,000 m and W = 2,500 m.
    Answer, explanation and textbook page: open in the app.
  40. 40.If the radius r of a sphere is increasing at the rate of 2 cm/min, then the rate of change of the volume when r = 1 cm is
    • A. $6\pi$ cm$^3$/min
    • B. $4\pi$ cm$^3$/min
    • C. $12\pi$ cm$^3$/min
    • D. $8\pi$ cm$^3$/min
    Answer, explanation and textbook page: open in the app.
  41. 41.Suppose $\int_{1}^{3} f(x) \, dx = 6$ and $\int_{1}^{2} f(x) \, dx = 10$, what is the value of $\int_{2}^{3} f(x) \, dx$ ?
    • A. 2
    • B. -4
    • C. 16
    • D. 4
    Answer, explanation and textbook page: open in the app.
  42. 42.Which of the following statements has a truth value T?
    • A. $(p \land q) \Rightarrow (p \vee q)$
    • B. $(p \land q) \Rightarrow \neg (p \vee q)$
    • C. $(p \vee q) \Rightarrow (p \land q)$
    • D. $(p \Rightarrow q) \Rightarrow (p \vee q)$
    Answer, explanation and textbook page: open in the app.
  43. 43.Which of the following is equal to $\int(\cos x-2x)dx$ where c is a constant?
    • A. sinx + x^2 + c
    • B. -sinx - x^2 + c
    • C. sinx - x^2 + c
    • D. -sinx + x^2 + c
    Answer, explanation and textbook page: open in the app.
  44. 44.What is the area of the region bounded by y = 0 and the graph of $f(x)=4-x^2$ on the interval $[-1, 1]$?
    • A. $$\frac{22}{3}$$
    • B. $$\frac{2}{3}$$
    • C. $$\frac{26}{3}$$
    • D. 8
    Answer, explanation and textbook page: open in the app.
  45. 45.The inverse of the function $y = 3x - 5$ is equal to
    • A. $y = \frac{x + 5}{3}$
    • B. $y = \frac{x + 3}{5}$
    • C. $y = \frac{x - 5}{3}$
    • D. $y = -5x + 3$
    Answer, explanation and textbook page: open in the app.
  46. 46.Which of the following is the universal set of the expression $\frac{1}{x^2} ÷ \frac{x + 1}{x^2+x}$?
    • A. $\mathbb{R}$ \ {$0, 1$}
    • B. $\mathbb{R}\{0\}$
    • C. $\mathbb{R}$ \ {0, 1, -1}
    • D. $\mathbb{R}$ \ {0, -1}
    Answer, explanation and textbook page: open in the app.
  47. 47.The graph of rational function is give as below Which of the following is NOT true about the graph?
    • A. x = 1 is its vertical asymptote
    • B. y = 0 is its horizontal asymptote
    • C. It is decreasing on (1, ∞)
    • D. It is increasing on (-∞, 1)
    Answer, explanation and textbook page: open in the app.
  48. 48.The equation of a line is given by $3x - 2y + 6 = 0$. Then which of the following is true about the line?
    • A. Its y-intercept is $-3$
    • B. Its slope is $\frac{3}{2}$
    • C. (2, 5) lies on the line
    • D. Its x-intercept is $2$
    Answer, explanation and textbook page: open in the app.
  49. 49.Which one of the following is the standard form of the equation of the parabola with vertex $(4, 6)$ and focus $(-8, 6)$?
    • A. $(x-4)^{2} = -12(y-6)$
    • B. $(x-4)^{2} = 12(y-6)$
    • C. $(y-6)^{2} = 48(x-4)$
    • D. $(y-6)^{2} = -48(x-4)$
    Answer, explanation and textbook page: open in the app.
  50. 50.Which of the following is true about the hyperbola given by $\frac{x^2}{4} - y^2 = 1$?
    • A. Its foci are at $(-5, 0)$ and $(5, 0)$
    • B. Its vertices are at $(-2, 0)$ and $(2, 0)$
    • C. Its center is at $(2, 1)$
    • D. An asymptote to the hyperbola is $y = 2x$
    Answer, explanation and textbook page: open in the app.
  51. 51.Two statements $p$ and $q$ are given by: $p: \frac{22}{7}$ is an irrational number. $q:$ The sum of two odd integers is odd. Then which of the following has a truth value $T$?
    • A. $p\land \neg q$
    • B. $p\vee \neg q$
    • C. $-p\land q$
    • D. $p\land q$
    Answer, explanation and textbook page: open in the app.
  52. 52.Which one of the following is the contrapositive of the statement: If 21 is a prime number, then 4 is an odd number?
    • A. If 4 is an odd number, then 21 is not a prime number
    • B. If 4 is an odd number, then 21 is a prime number
    • C. If 4 is not an odd number, then 21 is not a prime number
    • D. If 21 is not a prime number, then 4 is an even number
    Answer, explanation and textbook page: open in the app.
  53. 53.Which of the following is true where c is a constant?
    • A. $$\int \frac{\sin\sqrt{x}}{\sqrt{x}}dx = -2\cos\sqrt{x}+c$$
    • B. $$\int(3x+5)^6dx = \frac{(3x+5)^7}{7}+c$$
    • C. $$\ln xdx = \frac{1}{x}+c$$
    • D. $$\int xe^xdx = \frac{x^2}{2}e^x+c$$
    Answer, explanation and textbook page: open in the app.
  54. 54.The acceleration of a body at any time t is given by $a(t)=4-2t+3t^2$ with initial velocity v(0) = 5. Then what is the velocity v of the body as a function of time?
    • A. $v(t)=1+4t-t^2+t^3$
    • B. $v(t)=5+4t-t^2+t^3$
    • C. $v(t)=-2+6t$
    • D. $v(t)=9-t^2+t^3$
    Answer, explanation and textbook page: open in the app.
  55. 55.Which of the following argument is valid?
    • A. $p,\neg q \vdash p\implies q$
    • B. $\neg p,q \vdash p\implies q$
    • C. $p,\neg q \vdash p\implies q$
    • D. $p,\neg q \vdash p\land q$
    Answer, explanation and textbook page: open in the app.
  56. 56.Which of the following proof is more suitable to prove the assertion: $1+2^3 + 3^3 + ... + n^3 = (1+2+3+...+n)^2$
    • A. Proof by counter example
    • B. Proof by the principle of mathematical induction
    • C. Proof by contradiction
    • D. Proof by indirect proof
    Answer, explanation and textbook page: open in the app.
  57. 57.What is the coefficient of $x^2$ in the binomial expansion of $\left(2x + \frac{3}{x^3}\right)^8$?
    • A. 6
    • B. 0
    • C. 576
    • D. 500
    Answer, explanation and textbook page: open in the app.
  58. 58.Which of the following is true about the graph of $y = -4\cos\left(\frac{2x}{3}\right)$?
    • A. Its period is $3\pi$
    • B. Its amplitude is $-4$
    • C. The graph completes one cycle on the interval $\left[0, \frac{3\pi}{2}\right]$
    • D. The graph completes one cycle on the interval $\left[0, \frac{2\pi}{3}\right]$
    Answer, explanation and textbook page: open in the app.
  59. 59.Math test scores distribution of 20 students is given as in Table 2 below? Scores 1 - 5 6 - 10 11 - 15 16 - 20 Frequency 4 6 8 2 What is the standard deviation of the scores?
    • A. 5
    • B. 4
    • C. $\sqrt{21}$
    • D. $\sqrt{20}$
    Answer, explanation and textbook page: open in the app.
  60. 60.The angle of elevation of the top of a tree is found to be 60° as measured from a point on a level ground. What is the height of the tree if the angle of elevation of a point on the tree that is 8m below the top is 30° as measured from the same point on the ground?
    • A. 8m
    • B. 4m
    • C. 14m
    • D. 12m
    Answer, explanation and textbook page: open in the app.
  61. 61.Which of the following series is convergent?
    • A. $$\sum_{n=1}^{\infty} 5^{11-2n}$$
    • B. $$\sum_{n=1}^{\infty} \left(\frac{2}{5}\right)^{-n}$$
    • C. $$\sum_{n=1}^{\infty} \left(\frac{3}{2}\right)^n$$
    • D. $$\sum_{n=1}^{\infty} 2^{2n-5}$$
    Answer, explanation and textbook page: open in the app.
  62. 62.Let $f$ be a function defined on a closed bounded interval $[a, b]$. Which of the following describes that $f$ is continuous on $[a, b]$?
    • A. $f$ is continuous on $(a, b)$, $f$ is continuous from the right at $a$ and from the left at $b$
    • B. $f$ is continuous at each point in $(a, b)$ and at both $a$ and $b$
    • C. $f$ is continuous on $(a, b)$, $f$ is continuous from the left at $a$ and from the right at $b$
    • D. $f$ is continuous on $(a, b)$, $f$ is continuous from the left at $a$ and from the left at $b$
    Answer, explanation and textbook page: open in the app.
  63. 63.A position of a particle is given by the equation $S(t) = 4t^3 - 4t + 1$ where $t$ is measured in seconds and $S$ in meters. Which of the following is NOT true about the motion of the particle?
    • A. The velocity at 2 seconds is given by 124 m/sec
    • B. The velocity $v$ at any time $t$ is given by $v(t) = 16t^2 - 4$
    • C. The acceleration of the particle at 1 sec is 48 m/sec²
    • D. The particle is at rest at $t = 0.5$ seconds
    Answer, explanation and textbook page: open in the app.
  64. 64.If $f'(1) = 4$, $f(1) = 3$ and $g(3) = 5$, then $(gof)'(1)$ is equal to
    • A. 5
    • B. 3
    • C. 20
    • D. 15
    Answer, explanation and textbook page: open in the app.
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