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Ethiopia
3. If \( f \) and \( g \) are any two polynomials, then which of the following will always be a polynomial function? \( \begin{array}{ll}\text { a. } f+g & \text { b. } f-g \\ \text { c. } f . g & \text { d. } \frac{f}{g} \\ \text { e. } f^{2}-g & \text { f. } \frac{f+g}{g-f} \\ \text { g. } 3 f-\frac{4}{5} g & \text { 4. In each of the following, find the quotient and the remainder when the first } \\ \text { polynomial is divided by the second: } \\ \text { a. } f(x)=3 x^{3}+5 x^{2}-7 x-6 ; x+1 \\ \text { b. } f(x)=4 x^{3}-5 x^{2}+4 x-17 ; x^{2}-1 \\ \text { c. } f(x)=2 x^{4}+5 x^{2}-6 ; x^{2}-x+1 \\ \text { d. } f(x)=x^{5}+3 x^{4}+2 x^{3}-x^{2}+2 x-7: x+2 \\ \text { 4 } f \\ \text { e. } f(x)=x^{5}+2 x^{4}-x^{3}+5 x^{2}-x-2 ; x^{3}+1 \\ \text { f. } f(x)=2 x^{3}-x^{2}+2 x-1: 2 x+1\end{array} \) Summary and Review Exercise
Algebra Jan 19, 2025
4. In each of the following, find the quotient and the remainder when the firs polynomial is divided by the second: \( f(x)=3 x^{3}+5 x^{2}-7 x-6 ; x+1 \) b. \( f(x)=4 x^{3}-5 x^{2}+4 x-17 ; x^{2}-1 \) c. \( f(x)=2 x^{4}+5 x^{2}-6 ; x^{2}-x+1 \) d. \( f(x)=x^{5}+3 x^{4}+2 x^{3}-x^{2}+2 x-7: x+2 \)
Algebra Jan 19, 2025
\( (5 ;-1) \) B. \( (-1,5) \) C. \( (1,2) \) D. \( (-1,-2) \) is the equation of the circle whose end points of a diameter are \( p(-1,-1) \) and \( q(4, \) \[ \begin{array}{ll}\nx^{2}+y^{2}-3 x-10 y+15-0 & C\left(x^{2}+y^{2}-3 x-10 y-15=0\right. \\ x^{2}+y^{2}-3 x+10 y+15-0 & \text { D. } x^{2}+y^{2}+3 x-10 y+15=0 \end{array} \] is the equation of the tangent line to the circle \( x^{2}+y^{2}+10 x+2 y+13=0 \) point \( (-3,2) \) ? \[ x+3 y=0 \] B. \( 2 x-3 y=0 \) C. \( 2 x+3 y=4 \) D. \( -2 x+3 y=0 \)
Geometry Jan 19, 2025
II. Work out (show all necessary steps)( 6 points) :onsider the line passing through the point \( (2,-9) \) and \( (8,4) \), then find: a. Find the vector equation of the line b. the parametric equations of the line c. the standard equation of the line nd \( |u \times v| \) where \( u=3 i+4 j+5 k \) and \( v=7 i+8 j+9 k \)
Geometry Jan 19, 2025
Writy 'frue' it the statepsent is correct or 'False' if it is not correct for each of the following statements 3nfayphon of the circle centre at \( [2.3] \) and radius 4 units is \( x^{2}+y^{2}+4 x-5 y-3=0 \). Redi molianlis a motion that preserves distance. If thy boint p is translated to point \( P \), then the vector \( P P \) is called the transbution unctor If the point \( (x, y) \) is reflected in the line \( y=\alpha \), then its limage is the point \( \mid-x, y) \). Choose the correct answer among the alternatives for the following questio The image of the point \( (1,2) \) under translation \( T \) is \( (2,4) \) then. What is the image of the point \( (-2,3) \) under the same translation? A. \( (5,-1) \) B. \( (-1,5) \) C. (1,2) D. \( (-1,-2) \) What is the equation of the circle whose end points of a diameter are \( p(-1,-1) \) and a(4, 1 . A. \( x^{2}+y^{2}-3 x-10 y+15=0 \quad 4 x^{2}+y^{2}-3 x-10 y-15=0 \) a. \( x^{2}+y^{2}-3 x+10 y+15=0 \quad 0 \cdot x^{2}+y^{2}+3 x-10 y+15=0 \) What is the equation of the targent line to the clicle \( x^{2}+y^{2}+10 x+2 y+13 \quad 0 \) at pointw-3, 2y? A \( 2 x+3 y=0 \) ह. \( 2 x-3 y-0 \) (2 \( 2 x+3 y=1 \) \( 0^{2}-2 x+3 y-6 \) et translate \( y \) circle \( x^{2}+y^{2}-4 x=21 \) by the translation vectar \( 1(3,-5) \), then the innag circlertquation is A. \( x^{2}+y^{2}-6 x+10 y=7 \) C. \( x^{2}+y^{2}-3 x+10 y=0 \) B. \( x^{2}+y^{2}-3 x-10 y+15=0 \) D. \( x^{2}+y^{2}-6 x+6 y-7=0 \) Vhich of the following statement is false? The dot product of two vectors is scalar C. Dot product is commutative Dot pjoduct is distributive over vector addition D. All Whjeh one of the following is NOT true about transformation? R. Translations move angles to congruent angles C. Reflection is NOT a rigid mo Rotation move triangles in to congruent triangles D. Rotation is a rigid motion
Geometry Jan 19, 2025
\( \qquad \) 1. The fire has destroyed the house. The house \( \qquad \) by the fire. has been destroyed C) is destroyed was being destroyed D) was destroyed \( \qquad \) 2 I have seen the girl \( \qquad \) . where she was crossing the road C) which she was crossing the road if she was crossing the road D) while she was crossing the road \( \qquad \) 3. He kept looking at her wondering where he \( \qquad \) her before. will see B) saw C) has seen D) had seen \( \qquad \) 4. \( \qquad \) the door, he put the key into his pocket. Being locked C) Having locked By locking D) To lock \( \qquad \) 5. We have no reason \( \qquad \) that he will come back. having believed C) of believing believing D) to believe \( \qquad \) 6.1 \( \qquad \) smoke when I was 20 . use to B) used to C) wouldn't D) couldn't \( \qquad \) 7. Let us go see them off. They \( \qquad \) for London. leave B) leaves C) has left D) have left \( \qquad \) 8. She \( \qquad \) about her experience in order to get that job. lay B) lied C) laid D) lies
English Jan 19, 2025
(1) The domain of the function \( f(x)=\frac{1}{\sqrt{x-|x|}} \) is \( \qquad \) (A) \( \mathbb{R} \) (C) \( (-\infty, 0) \) (B) \( (0, \infty) \) (D) \( f \) is not defined for any \( x \in \mathbb{R} \) (2) What is the fourth term of a geometric sequence whose third term is 1 and whose eighth term is \( \frac{1}{32} \) ? (A) 4 (C) \( \frac{1}{8} \) (B) \( \frac{1}{2} \) (D) \( \frac{1}{16} \) (3) In a random arrangement of the word "SOCIETY" what is the total number of words in which all the three vowels come together? (A) 120 (C) 420 (B) 720 (D) 840 (4) Consider the experiment of rolling a die whose sample space is \( \{1,2,3,4,5,6\} \). If two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other? (A) \( \frac{1}{3} \) (B) \( \frac{2}{3} \) (C) \( \frac{1}{6} \) (D) \( \frac{5}{6} \) (5) A three digited library identification card is to be printed from the numbers \( 0,1,2,3,4 \) and 5 in such a way that the first is non-zero and no number is to be repeated, how many such cards can be printed? (A) 100 (B) 120 (C) 180 (D) 150
Pre Algebra Jan 19, 2025
(1) The domain of the function \( f(x)=\frac{1}{\sqrt{x-|x|}} \) is \( \qquad \) (A) \( \mathbb{R} \) (C) \( (-\infty, 0) \) (B) \( (0, \infty) \) (D) \( f \) is not defined for any \( x \in \mathbb{R} \) (2) What is the fourth term of a geometric sequence whose third term is 1 and whose eighth term is \( \frac{1}{32} \) ? (A) 4 (C) \( \frac{1}{8} \) (B) \( \frac{1}{2} \) (D) \( \frac{1}{16} \) (3) In a random arrangement of the word "SOCIETY" what is the total number of words in which all the three vowels come together? (A) 120 (C) 420 (B) 720 (D) 840 (4) Consider the experiment of rolling a die whose sample space is \( \{1,2,3,4,5,6\} \). If two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other? (A) \( \frac{1}{3} \) (B) \( \frac{2}{3} \) (C) \( \frac{1}{6} \) (D) \( \frac{5}{6} \) (5) A three digited library identification card is to be printed from the numbers \( 0,1,2,3,4 \) and 5 in such a way that the first is non-zero and no number is to be repeated, how many such cards can be printed? (A) 100 (B) 120 (C) 180 (D) 150
Pre Algebra Jan 19, 2025
(1) The domain of the function \( f(x)=\frac{1}{\sqrt{x-|x|}} \) is \( \qquad \) (A) \( \mathbb{R} \) (C) \( (-\infty, 0) \) (B) \( (0, \infty) \) (D) \( f \) is not defined for any \( x \in \mathbb{R} \) (2) What is the fourth term of a geometric sequence whose third term is 1 and whose eighth term is \( \frac{1}{32} \) ? (A) 4 (C) \( \frac{1}{8} \) (B) \( \frac{1}{2} \) (D) \( \frac{1}{16} \) (3) In a random arrangement of the word "SOCIETY" what is the total number of words in which all the three vowels come together? (A) 120 (C) 420 (B) 720 (D) 840 (4) Consider the experiment of rolling a die whose sample space is \( \{1,2,3,4,5,6\} \). If two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other? (A) \( \frac{1}{3} \) (B) \( \frac{2}{3} \) (C) \( \frac{1}{6} \) (D) \( \frac{5}{6} \) (5) A three digited library identification card is to be printed from the numbers \( 0,1,2,3,4 \) and 5 in such a way that the first is non-zero and no number is to be repeated, how many such cards can be printed? (A) 100 (B) 120 (C) 180 (D) 150
Pre Algebra Jan 19, 2025
Which of the following is a rational expression? hoose the best answer for the following questions \( \begin{array}{llll}\left\lvert\, \frac{x+1}{x^{2}+1}\right. & \text { B. } \sqrt{x}+x+1 & \text { C. } \frac{x}{x}\end{array} \)
Algebra Jan 18, 2025
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