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1 Santa Monica College Practicing College Algebra MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the standard equation for the circle. 1) Center at -, - 3, radius 3 1) A) x = 3 B) x = 9 C) x = 3 D) x = 9 Solve the problem. ) The graph shows an idealized linear relationship for the average monthl paments to retirees ) from 199 through Find the midpoint of the line segment to estimate the pament for Average Monthl Paments to Retiree Pament 0 a 1 3 Year a = $; b = $8 b A) 8 dollars B) 8 dollars C) 00 dollars D) 1 dollars 3) The cost, T, in hundreds of dollars, of tuition at one communit college is given b T = c, 3) where c is the number of credits for which a student registers. Estimate the cost of tuition if a student registers for 13 credits. A) About $3000 B) About $100 C) About $00 D) About $1800 ) Jim had grades of 78 and 100 on two chemistr tests. What is the lowest score he can get on the ) third test to maintain an average of 8? A) 77 B) 88 C) 8 D) 89 1

2 ) Decide whether or not the points are the vertices of a right triangle. ) (1, 1), (7, 3), (11, -9) A) No B) Yes ) Your compan uses the quadratic model =.x + 10x to represent the average number of ) new customers who will be signed on (x) weeks after the release of our new service. How man new customers can ou expect to gain in week 8? A) 91 customers B) customers C) 31 customers D) 11 customers Solve the equation. 7) a a = ) A) {-13} B) {33} C) {-33} D) {13} Find the center and radius of the circle. 8) (x - 8) + ( + ) = 1 8) A) Center: (, 8); radius: 1 B) Center: (8, ); radius: 1 C) Center: (, 8); radius: D) Center: (8, ); radius: Use the method of our choice to find all real solutions of the equation. 9) x - x = -1 9) 9 3 A) 3 ± B) 3 C) - 3 D) 3 Solve the equation. Identif the equation as an identit, an inconsistent equation, or a conditional equation. 10) 3(f + 8) = f + 1 A) Inconsistent, B) Conditional, {all real numbers} 10) C) Identit, {all real numbers} D) Conditional, {1} Find the equation of the line through the given pair of points in standard form using onl integers. 11) (, -3) and (, ) A) = B) x = -3 C) x = D) = -3 11) Write the standard equation for the circle. 1) Center (19, 1), passing through (0, 1) A) (x - 19) + ( - 1) = 31 B) (x - 1) + ( - 19) = 31 C) (x - 1) + ( - 19) = 19 D) (x - 19) + ( - 1) = 19 1) Determine whether or not the function is one -to-one. 3 13) f(x) = - x ) A) Yes B) No

3 Solve the problem. 1) A balloon (in the shape of a sphere) is being inflated. The radius is increasing at a rate of 10 cm per second. Find a function, r(t), for the radius in terms of t. Find a function, V(r), for the volume of the balloon in terms of r. Find (V r)(t). A) (V r)(t) = 000πt 3 C) (V r)(t) = 000πt 3 3 B) (V r)(t) = 0000π t 3 D) (V r)(t) = 700πt 3 3 1) Write the equation of the graph after the indicated transformation(s). 3 1) The graph of = x is shifted. units to the left. This graph is then verticall stretched b a 1) factor of.. Finall, the graph is reflected across the x -axis. 3 3 A) f(x) =. x +. B) f(x) =. x C) f(x) =. x +. D) f(x) =. x +. Solve the problem. 1) Assume it costs cents to mail a letter weighing one ounce or less, and then 0 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph = L(x). 1) A) B) x 1 3 x Evaluate. 17) If f(x) = (x + 8), find f(7). A) 30 B) 1 C) D) 17) 3

4 Graph the equation b plotting ordered pairs of numbers. 18) = 1 (x + ) + 18) x x 10 x A) B) x 10 x C) D) Solve the problem. 19) Emploees of a publishing compan received an increase in salar of 3% plus a bonus of $1100. Let S(x) represent the new salar in terms of the previous salar x. Find the value of S(1,000). 19) A) $0,00 B) $1,100 C) $1,0 D) $13,9

5 Solve the inequalit b reading the given graph. State the solution set using interval notation. 0) -x 3 + x + x - 0 < 0 A related function is graphed below ) 0 10 x 0 0 x-intercepts: (, 0), (, 0), (, 0) A) (, ) (, ) B) (-, ) (, ) C) [, ] [, ) D) (, ) Use the vertical line test to determine whether is a function of x. 1) 10 1) 10 x A) Yes B) No Graph the function. ) f(x) = for x 1 - x for x < 1 ) x

6 A) B) x x C) D) x x Solve the problem. 3) The weight of a liquid varies directl as its volume V. If the weight of the liquid in a cubical container cm on a side is 37 g, find the weight of the liquid in a cubical container 3 cm on a side. 3) A) 81 g B) 1 g C) 7 g D) 9 g Use the rational zero theorem to find all possible rational zeros for the polnomial function. ) P(x) = x 3 + x + 1x - 8 ) A) ±1, ±, ±, ±8 B) ±1, ±, ± C) ±1, ± 1, ±, ±, ±8 D) ±1, ± 1, ± 1, ± 1, ± 8 Determine whether the given number is a zero of the polnomial function. ) P(x) = -8x 3 + x + x - 7; A) No B) Yes ) Use the theorem on bounds to establish the best integral bounds for the roots of the equation. ) 3x - 8x 3-8x - 9 = 0 A) < x < B) -1 < x < 1 C) -1 < x < D) < x < 1 )

7 For the given function, find all asmptotes of the tpe indicated (if there are an). 7) f(x) = x + 8x + 9, oblique x + 7) A) = x - 10 B) x = + C) None D) = x + Use ordinar division of polnomials to find the quotient and remainder when the first polnomial is divided b the second. 8) x + x 3-3x + x +, x + 1 A) x + x - B) x - x - ; x - C) x + x - ; x - D) x - x - 8) Solve the problem. 9) The polnomial G(x) = -0.00x x 3-0.3x x measures the concentration of a de in the bloodstream x seconds after it is injected. Does the concentration increase between 9 and 10 seconds? 9) A) No B) Yes Sketch the graph of the rational function. Note that the function is not in lowest terms. x ) f(x) = x - x + 30) x A) x -3, x -8 7

8 B) x, x -8 C) x, x D) x -3, x -8 Find a polnomial equation with real coefficients that has the given roots. 31) 1, -8 A) x - 8x + 7 = 0 B) x - 8x - 7 = 0 C) x - 7x - 8 = 0 D) x + 7x - 8 = 0 31) 8

9 Explain the behavior of the graph of f(x) as it approaches its vertical asmptote. (-1) 3) f(x) = (x - ) 3) A) Approaches from the left and the right B) Approaches - from the left, approaches from the right C) Approaches from the left, approaches - from the right D) Approaches - from the left and the right Solve the equation. If necessar, round to thousandths. 33) 1 x = ) A).79 B).7 C) D).79 Solve the equation. 3) 79 x = 9 3) A) -3 B) C) 1 3 D) 3 Graph the function. 3) = x + 3) x A) B) x x 9

10 C) D) x x Solve the equation. Round to four decimal places. 3) 100(1.08) x = 0(1.0) x A) B).38 C).97 D) ) Graph the function. 37) f(x) = 3 (3x - ) 37) x A) B) x x 10

11 C) D) x x Solve the problem. 38) At what interest rate would a deposit of $,000 grow to $110,8 in 30 ears with continuous compounding? 38) A) % B) 1% C) 3% D) % Solve the equation. 39) log 3 3 = x 39) A) B) 1 C) D) Solve the equation. Round our answer to three decimal places. 0) 1 x = 18 3 A).000 B) C).31 D).31 0) 11

12 Graph the solution set of the sstem. 1) x + x ) x A) B) x x C) D) x x Classif the sstem as independent, inconsistent, or dependent. ) x - 3 = = x ) A) Dependent B) Inconsistent C) Independent Solve the sstem. 3) x - = 39 x - = 3 3) A) {(-8, )} B) {(-8, )} C) {(8, )} D) {(8, )} 1

13 Solve the sstem b substitution. ) x + 8 = 0 x - 8 = 3 ) A) {(8, -1)} B) {(1, )} C) {(, 1)} D) {(1, )} ) 0.9x + 0. = 3 x =. ) A) {(, -3)} B) {(0., -0.3)} C) D) {(-3, )} Classif the sstem as independent, inconsistent, or dependent. ) x + = x + = ) A) Inconsistent B) Independent C) Dependent Graph the sstem of inequalities. Indicate the solution set b shading. 7) (x + 3) 3 (x + 3) - + x 7) x -8 A) B) x x -8 13

14 C) D) x -8 8 x -8-8 Use a graphing calculator to solve the sstem b finding A-1 and A -1 B. (Round to the nearest integer if necessar.) x z = 10. 8) z = 1.8 8) -0.0x - 1.z = A) {(3, -9, )} B) {(3, 9, )} C) {(, 7, )} D) {(9,, 9)} Find the product. 9) ) A) B) C) D) Solve the problem. 0) A compan makes 3 tpes of cable. Cable A requires 3 black, 3 white, and red wires. B requires 1 black, white, and 1 red. C requires black, 1 white, and red. The used 9 black, 100 white and 80 red wires. How man of each cable were made? 0) A) 1 cable A 1 cable B 1 cable C B) 8 cable A 0 cable B 1 cable C C) 1 cable A 0 cable B 1 cable C D) 0 cable A 1 cable B 1 cable C Perform the indicated operation, if possible. -9x - x + k - 9z 1) - k + 3z -1w + 7v w - 3v m + n 8m + 8n 1) A) -1x + 3 1k - z -17w + v m + 10n B) C) x - 7 k - 1z -7w + 10v m - n -1x - 7 1k - 1z -17w + 10v m - n D) x + 3 k - z -7w + v m + 10n 1

15 Determine the size of the matrix. 0 ) ) A) 3 3 B) C) 9 D) 3 Solve the problem. 3) Sara works at a fast food restaurant. On one da she sold 79 double hamburgers, 88 fish sandwiches, 1 orders of French fries, 8 small drinks, medium drinks, and 9 large drinks. On the next da she sold 30 double hamburgers, 8 fish sandwiches, 9 orders of French fries, 8 small drinks, 7 medium drinks, and 1 large drinks. Write this information in a x matrix. 3) A) B) C) D) Graph the hperbola. ) x - = ) 10 x 1

16 A) B) x 10 x C) D) x 10 x Solve. ) The roof of a building is in the shape of the hperbola - x =, where x and are in meters. Refer to the figure and determine the height h of the outside walls. ) A = m A) 8. m B) 7 m C) 37 m D) -17 m Identif the equation as a parabola, ellipse, or circle. ) = 3 - x ) A) Circle B) Ellipse C) Parabola D) None of the above 1

17 Find the foci of the ellipse. 7) 9x - x = 0 A) (-1, ), (7, ) B) (, 0), (, ) C) (, -1), (, 7) D) (0, ), (, ) 7) Identif the equation as a parabola, ellipse, or circle. 8) x = 3 - A) Ellipse B) Circle C) Parabola D) None of the above 8) Write a recursion formula for the sequence. 9), -8, -3, -18,... A) an = an-1 + 8, a1 = B) an = 8an-1, a1 = 9) C) an = an-1 +, a1 = D) an = an-1, a1 = Find all the terms of the finite sequence. 0) an = n - n, 1 n 0) A) 0,,, 1, 0 B) 1,, 9, 1, C),, 1, 0, 30 D) 0, 3, 8, 1, Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula. 1) 9, 13, 17, 1,... A) 9 B) C) 3 D) Not arithmetic 1) Determine whether the statement is true for n = 1,, 3,, and. Use the number of true statements as our answer. ) n < n ) A) B) 3 C) D) Solve the problem. 3) How man -card poker hands consisting of aces and 3 kings are possible with an ordinar -card deck? 3) A) 1 B) C) 88 D) Find the slope of the line containing the pair of points. ) (7, ), (, 1) ) A) - B) 13 C) - 13 D) Solve the problem. ) A triangular lake-front lot has a perimeter of 1900 feet. One side is 00 feet longer than the shortest side, while the third side is 00 feet longer than the shortest side. Find the lengths of all three sides. ) A) 100 ft, 00 ft, 300 ft B) 00 ft, 700 ft, 1000 ft C) 00 ft, 00 ft, 00 ft D) 00 ft, 00 ft, 900 ft 17

18 Graph the equation in the rectangular coordinate sstem. ) x = ) 10 x A) B) x 10 x C) D) x 10 x 18

19 7) = ) 10 x A) B) x 10 x C) D) x 10 x Write the equation of the graph after the indicated transformation(s). 8) The graph of = x is verticall stretched b a factor of.8. This graph is then reflected across the x-axis. Finall, the graph is shifted 0.3 units downward. 8) A) f(x) =.8 -x B) f(x) =.8 x C) f(x) =.8 x D) f(x) =.8 x

20 Write the formula expressed b the variation. 9) varies inversel as x: = 8, when x = 9) A) = 33 x B) = 10 x C) =. x D) =.x Solve the problem. 70) If f varies jointl as q and h, and f = when q = 3 and h = 3, find f when q = and h =. A) f = 0 B) f = C) f = 0 D) f = -8 70) List the smmetries of the given function, if there are an. Otherwise, state ʺNo smmetrʺ. 71) f(x) = x + 8 A) x = 8 B) x = -8, origin C) -axis D) x = -8 71) Solve the problem. 7) In the following formula, is the minimum number of hours of studing required to attain a test 7) 0.x score of x: =. How man hours of stud are needed to score 8? x A) hr B).3 hr C). hr D).0 hr Use the factor theorem to decide whether or not the second polnomial is a factor of the first. 73) x + x + 70; x - A) No B) Yes 73) For the given function, find all asmptotes of the tpe indicated (if there are an). 7) f(x) = x + 7x - 9, oblique x - 9 7) A) = x - B) = x + 1 C) None D) x = + 1 Solve the problem. 7) If $000 is invested in an account that pas interest compounded continuousl, how long will it take to grow to $10,000 at.%? 7) A) 1.1 ears B).9 ears C) 1.3 ears D) 1.8 ears 7) In the formula A = Iekt, A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is a negative constant determined b the nature of the material. An artifact is discovered at a certain site. If it has % of the carbon-1 it originall contained, what is the approximate age of the artifact? (carbon -1 decas at the rate of 0.01% annuall.) (Round to the nearest ear.) 7) A) 800 r B) 00 r C) 3 r D) 197 r 77) A certain noise measures 30 decibels. If the intensit is multiplied b 10, how man decibels will the new noise measure? D = 10 log 10 (S/So). 77) A) 0 decibels B) 30 decibels C) 300 decibels D) 31 decibels 0

21 78) The perimeter of a rectangle is 8 m. If the width were doubled and the length were increased b 19 m, the perimeter would be 100 m. What are the length and width of the rectangle? 78) A) width 7, length 17 B) width 7, length 1 C) width 1, length 1 D) width 17, length 7 Solve the sstem b addition. 79) x + 9 = -3 x - = 79) A) {(, 1)} B) {(, 1)} C) D) {(, 0)} Use the determinant feature of a graphing calculator to solve the sstem b Cramerʹs rule. (Round to one decimal place.) 80) 1.x z = 3.7.8x z = -3.3.x -. -.z =. 80) A) {(0., 0., 0.3)} B) {(0., 0.8, 0.)} C) {(0., 0., 0.)} D) {(0.1, 0., 0.)} Find the indicated matrix. 81) Let C =. Find 1 C. 1 81) A) B) C) D) Graph the parabola. 8) = (x + 3) + 8) x 1

22 A) B) x 10 x C) D) x 10 x Identif the equation as a parabola, circle, ellipse, or hperbola. 83) = x A) Hperbola B) Ellipse C) Circle D) Parabola 83) Rewrite the series using the new index j as indicated. 3 8) i = i=1 j=0 3 3 A) j-1 B) j+1 C) j-1 D) j+1 j=0 j=0 j=0 j=0 8) Find the sum of the geometric series. 8) A) 33 B) -33 C) 183 D) ) Find the slope of the line containing the pair of points. 8) (3, -8), (3, ) A) 1 B) No slope C) 0 D) -1 8)

23 Solve the inequalit b reading the given graph. State the solution set using interval notation. 87) x + x < 3x + 1 A related function is graphed below ) 10 x x-intercepts: (, 0), (3, 0) A) (, 3) B) [, 3] C) (3, ) D) (-, ) (3, ) Explain the behavior of the graph of f(x) as it approaches its vertical asmptote. 88) f(x) = (x - 8) 88) A) Approaches - from the left and the right B) Approaches from the left, approaches - from the right C) Approaches - from the left, approaches from the right D) Approaches from the left and the right Graph the function. 89) f(x) =.3 x 89) x 3

24 A) B) x x C) D) x x Solve the sstem b graphing. 90) x + 3 = 3 x - = -1 90) x A) {(, 1)} B) {(1, )} C) {(, )} D) Determine whether the matrix is invertible b finding the determinant of the matrix. 91) -1 1 A) Not invertible B) Invertible 91) Graph the hperbola.

25 9) - x = 1 9) x A) B) x 10 x C) D) x 10 x Solve the problem. 93) What is the coefficient of x 7 3 in the expansion of (x + ) 10? 93) A) 0,800 B) 7 C) 8,00 D) 10

26 Solve the problem using our calculator. 9) Two separate tests are designed to measure a studentʹs abilit to solve problems. Several students are randoml selected to take both tests and the results are shown below. Use linear regression to find a linear function that predicts a studentʹs score on Test B as a function of his or her score on Test A. Test A Test B ) A) = x B) = x C) = x D) = x Determine whether the relation is a function. 9) {(, 8), (, -8), (-1, ), (-1, )} A) Yes B) No 9) Use the rational zero theorem, Descartesʹs rule of signs, and the theorem on bounds as aids in finding all real and imaginar roots to the equation. 9) x 3 + 8x - x - 0 = 0 A) - 8, multiplicit ; B) -8, -, C) - 8, multiplicit ; -, multiplicit D) -8,, 9) Solve the problem. 97) The number of bacteria growing in an incubation culture increases with time according to B = 800(3)x, where x is time in das. Find the number of bacteria when x = 0 and x =. A),00;,01,00 B) 800; 1,000 C) 800;,800 D) 800;,01,00 97) Graph the sstem of inequalities. Indicate the solution set b shading. 98) x + 3 x - 3 x 1 98) x

27 A) B) x x C) D) x x Find the values that make the equation true. 99) x+3 + = k A) x = ; = -3; k = B) x = ; = 3; k = C) x = ; = ; k = D) x = ; = 1; k = 99) 7

28 Graph the circle. 100) (x - ) + ( - 3) = ) 10 x A) B) x 10 x C) D) x 10 x 8

29 Answer Ke Testname: COLLEGE ALGEBRA 1) B ) A 3) B ) A ) B ) A 7) A 8) D 9) D 10) C 11) C 1) A 13) A 1) C 1) A 1) A 17) D 18) D 19) C 0) A 1) A ) B 3) A ) C ) A ) C 7) D 8) A 9) B 30) C 31) D 3) A 33) D 3) C 3) B 3) B 37) B 38) C 39) B 0) C 1) A ) B 3) D ) D ) A ) A 7) D 8) B 9) C 0) C 9 1) C ) A 3) A ) D ) A ) A 7) A 8) B 9) D 0) A 1) B ) B 3) B ) A ) D ) B 7) A 8) B 9) B 70) A 71) D 7) C 73) A 7) B 7) C 7) C 77) A 78) A 79) D 80) B 81) C 8) A 83) C 8) D 8) C 8) B 87) A 88) A 89) C 90) A 91) B 9) A 93) D 9) C 9) B 9) B 97) D 98) C 99) A 100) D

30 Santa Monica College Practicing College Algebra 1) 1) ) ) 3) 3) ) ) ) ) ) ) 7) 7) 8) 8) 9) 9) 10) 0) 11) 1) 1) ) 13) 3) 1) ) 1) ) 1) ) 17) 7) 18) 8) 19) 9) 0) 70) 1) 71) ) 7) 3) 73) ) 7) ) 7) ) 7) 7) 77) 8) 78) 9) 79) 30) 80) 31) 81) 3) 8) 33) 83) 3) 8) 3) 8) 3) 8) 37) 87) 38) 88) 39) 89) 0) 90) 1) 91) ) 9) 3) 93) ) 9) ) 9) ) 9) 7) 97) 8) 98) 9) 99) 0) 100) 1

Exam practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help you understand the material.

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