Intermediate Algebra Math 097. Evaluates/Practice Tests. For solutions, refer to the back of the PAN.

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1 Intermediate Algebra Math 097 Evaluates/Practice Tests For solutions, refer to the back of the PAN. Page of 8

2 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Solve for x: (x + ) 3x = 0. Solve for : 5 0 = 9 3. Circle the value of z that is the solution of the equation z + = 0. z = 3 z = 0 z =. Solve for x: (x + 3) = 5 5. Solve for x: x + = x + 7. Solve for x: z = 3x 5 7. Circle the values of that are solutions of the inequalit <. = = = 3 = 5 8. Solve the following inequalit, then graph the solution on the number line. 0 5(x + ) < TOPIC EII ESSENTIALS OF ALGEBRA Page of 8

3 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Look at Figure EII.E.0. Determine in which quadrant the points P, Q, and R lie. P x 5. Circle the equation of the line through the point (0, 7) that has slope 9. 7 = 9(x 0) 0 = 9(x + 7) x + 7 = 9( 0) + 7 = 9(x 0) R Figure EII.E.0 Q. Find the -intercept of the line that has slope m = and passes through the point 3,. 7. Find the equation of the vertical line and the equation of the horizontal line that pass through the point (, 7).. Find the distance, d, between the point (, ) and the point ( 3, ). 3. Find both the rise (change in ) and the run (change in x) in moving from the point (, 3) to the point (5, ). 8. Find the standard form of the equation of the line that passes through the point (0, 5) and is perpendicular to 8 = x A line passes through the points (0, ) and ( 3, 3). Find its slope. Page 3 of 8 LESSON EII.E GRAPHING LINES 87

4 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Find the solutions of the following equations. a. x 5 = 9 b. 8x =. Solve for x: x = 9 3. Solve for x: x + 5 = x + 7. Circle the solution of this equation: 5 x 7 + = 7 x = or x = 3 x = or x = 3 x = or x = 3 x = or x = 3 the equation has no solution. Solve for x: x > 8 7. Circle the inequalit whose solution is graphed below x x x > x 8. Solve for x: x < 5. Circle the graph that represents the solution of this inequalit: x Page of 8 LESSON EII.F ABSOLUTE VALUE 05

5 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Graph the inequalit > x.. The graph of the line x + = is shown in Figure.3.5. Circle the point(s) below that satisf the inequalit x +. x + = (0, 0) (5, ) ( 3, ) x (8, ) Figure Graph the inequalit x.. Circle the point(s) below that satisf the linear inequalit. (3, 5) (0, 0) (8, ) (, 7) 5. Circle the inequalit below that has a solution represented on the graph shown in Figure.3.. 5x + > 0 x 5 < 0 x + 5 > 0 x 5x < 0. Graph the inequalit x The graph of the equation = x is shown in Figure.3.7. Circle the point(s) below that satisf the inequalit > x. (, ) ( 3, 3) ( 5, ) (, 5) Figure Circle the inequalit below that has a solution represented on the graph shown in Figure.3.8. > x + Figure.3.8 = x x < x + x + x + x Figure.3. 7 TOPIC GRAPHING LINEAR EQUATIONS AND INEQUALITIES Page 5 of 8

6 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. The sum of two numbers is 5. When twice the larger number is subtracted from four times the smaller number, the result is. What are the two numbers?. Sunil has 9 five dollar and ten dollar bills worth a total of $50. How man of each does she have? 3. Last ear a small college accepted 33 students out of the 30 people that applied. If the college accepted 30% of the female applicants and 5% of the male applicants, how man women applied?. The local coffee shop combines two kinds of beans to make a blended mixture of beans. If Ethiopian Harrar beans cost $7.5 per pound, and Arabian Mocha beans cost $3.70 per pound, how man pounds of each should be used to make 3 pounds of a blend that costs $0. per pound? 5. In 7 ears Deac will be twice as old as Irina. Four ears ago he was three times as old as Irina was then. How old are each of them now?. Admission to a skating rink is $.5 for children and $7.50 for adults. If one evening the skating rink collected $930 and 50 people were admitted, how man children went skating? 7. Nobutaka needs 00 ml of % HCl. If he has solutions of 5% HCl and 9% HCl, how man milliliters of each should he mix together? 8. Alexis had $375 to invest last ear. She put some of her mone in a savings account that paid % interest and the rest of her mone in a mutual fund that paid % interest. If she earned $8.50 in interest, how did she divide her mone between the two accounts? 0 TOPIC 5 SOLVING LINEAR SYSTEMS Page of 8

7 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Graph the sstem of inequalities below. Use the grid in Figure Then write the coordinates of the plotted points that are solutions of this sstem. < x + x + x Figure Graph the sstem of inequalities below to find its solution. x + > 3 3. Graph the sstem of inequalities below. Use the grid in Figure Then write the coordinates of the plotted points that are not solutions of either inequalit in this sstem. x 5 < 5 3x + 5. Graph the sstem of inequalities below to find its solution. x + 3 x 5. Graph the sstem of inequalities below to find its solution. x 3 3x +. Graph the sstem of inequalities below. Use the grid in Figure Then write the coordinates of the plotted points that are solutions of this sstem. 0 x x + x Figure 5.3. x Figure Page 7 of 8 LESSON 5.3 SYSTEMS OF INEQUALITIES

8 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. A positive number, a, has principal square root.. a. What is another square root of a? b. What is the value of a?. The number 30 lies between what two consecutive integers? 3. Simplif the quotient of these square roots: 7 3. Use prime factorization to simplif this radical: 8 u Here, u is a nonnegative number. 5. Find: Multipl 3 5 b its conjugate. Enter the result. 7. For each given radical expression, rationalize the denominator. a. b Solve this equation for x: 3 5 x = 38 TOPIC 9 RATIONAL EXPONENTS AND RADICALS Page 8 of 8

9 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate. Assume that x,, and z are positive numbers.. Simplif: 5 x x. Rewrite the expression using rational exponents Circle the real number(s) in the list below: Simplif: 7 3 x 9 5. Simplif: 5 7. Which of the radical expressions below is simplified? 3 x x 8. Simplif: z 9. Simplif: 5x + 3 5x 3 0. Find: (3 5 8)( ). Find: (3 + 3)( ). Find: 3. Calculate: ( 9 ) Page 9 of 8 LESSON 9. RATIONAL EXPONENTS 05

10 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Write this quadratic equation in standard form and identif a, b, and c. + x(x 8) = x + 3. Solve the equation x x = 0 b factoring. 3. Circle the quadratic equations. x = + = (x 3) x = x + 3 x x(x + 9) = x 9 = 7x + + 8x. Solve x x 5 = Circle the expressions below that are equal to 8. ( 8 ) Solve x = 33 using the square root propert. 7. Solve this equation for x: x = Solve (x 5) = using the square root propert. Page 0 of 8 LESSON 0. QUADRATIC EQUATIONS I 9

11 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Complete the square for this expression. x + 9x +? What is the perfect square?. Solve x + 8x = 5 b completing the square. 3. After completing the square b adding to both sides, the result is (x + ) =. What was the original equation?. Solve x 5x + = 0 b completing the square. 5. Circle the equation below that has the solution x =. x + x 7 = 0 x + x 7 = 0 ± 3 8. Find the two values for b for which the quadratic equation 9x + bx +3 = 0 has two equal real solutions. 9. The quadratic equation x 7x + c = 0 has a discriminant of 5. What is the value of c? What are the solutions of the equation? 0. The sum of the solutions of a quadratic equation is. The product of its solutions is 3. What is the equation?. Find a quadratic equation whose two solutions are 3 5 and.. Find the greatest possible value of c in the quadratic equation x 7x + c = 0 for which there are two real solutions. 3 x + x + 7 = 0 x x 7 = 0. Use the quadratic formula to solve this quadratic equation: x = 5x 7. Circle the quadratic equations below that have no real solutions. x + 5x 9 = 0 x + x + = 0 x x + = 0 x + 5x + = 0 x 0x 3 = 0 x + x + 5 = 0 38 TOPIC 0 QUADRATIC EQUATIONS Page of 8

12 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Find: a. (7 + i) + ( + i) b. (7 + i) ( + i). Circle the expressions below that are equal to 8 + i. (i)(i + ) 3i + i i 8i i 3 3. Find: (3 + ) + ( + 9 ). Find: ( + i)(3 + 5i) 5. Find: (5 + 3i)(5 3i). Find: ( + 7i) 7. Circle the expressions below that are equal to i. i i 37 (i 5 ) 0 i 3 8. Use the quadratic formula to find the solutions of each equation below. a. x + 3x + 7 = 0 b. x 5x + 9 = 0 c. 3x + x + = 0 Page of 8 LESSON 0.3 COMPLEX NUMBERS 5

13 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Which of the points below satisf the function = 3x +? (0, ) (, 3) (3, 8) (, ) (, ). Given the function f(x) = x + 3x, find: a. f(0) b. f(3) c. f( ) d. f( 5) 3. Use the graph of the function = x, shown on the grid in Figure.., to find its domain and range. Write the domain and the range in interval notation. x Figure... Given the functions f(x) = x 5 and g(x) = 3x, find: a. f(7) b. g(7) 5. The graph of the function = x is shown on the grid in Figure... a. Find the equation of line A. b. Find the equation of line B. A B x = x Figure... The graph of the function = x 5 is shown on the grid in Figure..3. Use this graph to find the domain and range of = x 5. Write the domain and the range in interval notation. x Figure..3 c. f( ) d. g( ) Page 3 of 8 LESSON. FUNCTIONS 89

14 7. The graphs of the functions = x + 3 and = x + 3 are shown on the grid in Figure... Use these graphs to decide which of the statements below are true. Both functions have the same domain. Both functions have the same range. The point (0, 3) satisfies both equations. The point (3, 0) satisfies both equations. = x + 3 x = x + 3 Figure.. 8. The graph of the function = x is shown on the grid in Figure..5. Circle the points below that lie on the graph of = x. (5, ) (, ) (, 3) 9. The graph of the parabola = x x 5 is shown on the grid in Figure... Use this graph to help ou find the x-intercepts of the function. 8 8 x Figure.. 0. The graphs of the parabolas = x and = x 8 are shown on the grid in Figure..7. Use these graphs to decide which of the statements below are true. Both functions have the same domain. Both functions have the same range. Both graphs have the same vertex. Both graphs have the same x-intercepts. = x = x (0, ) 8 8 x 8 Figure..7 x Figure..5. Circle the functions below that are not quadratic functions. = x = x + f(x) = 3x + 7 = x 5x + 8 f(x) = + x 90 TOPIC FUNCTIONS AND GRAPHING Page of 8

15 . The graph of the parabola = x + x + 3 is shown on the grid in Figure..8. If the graph is moved up 3 units, what is the vertex of the new parabola? x Figure The graph of the function f(x) = x 3 is shown on the grid in Figure..9. Use this graph to find the values of: a. f() b. f(0) c. f( ) x Figure..9. The graph of = x + is shown on the grid in Figure..30. Use the graph to decide which of the statements below are true. The domain of = x + is all real numbers. The range of = x + is the interval [, ). For each input value, x, there is onl one output value. For each output value,, there is onl one input value x. x Figure Determine which of the graphs below are functions b using the vertical line test. a. b. x c. d. x x x. The graph of the function = x x + 5 is shown on the grid in Figure..3. Use this graph to: a. Find the domain of the function = x x + 5. b. Find the range of the function = x x + 5. c. Find the vertex of the function = x x x 8 Figure..3 Page 5 of 8 LESSON. FUNCTIONS 9

16 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate. x. Solve for x: =. What value of u can ou substitute into the equation 5x 8 + 3x = 0 to get an equation in standard quadratic form? 3. Solve for : 3 8 = 7 w w. Solve for w: = 5 5. Solve for x: x + x = 3. Solve for : = 7. Solve for x: x + 5 = x w w 8. Solve for w: (w + 5) 5 = 9. Graph the parabola = x x. Use our graph to find the solutions of the quadratic equation x x = Graph the parabola = x x and the line = 3. Use our graphs to find the solutions of the equation x x = 3.. The graphs of four parabolas are shown on the grid in Figure 3... Use these graphs to decide which of the equations below have one positive solution and one negative solution = x + x + 5 (use graph a) 0 = x x 3 (use graph b) 0 = x x + (use graph c) 8 0 = x x (use graph d) a d c x b Figure 3... Graph the parabolas below. Use our graphs to determine for what values of c the equation x + x + c = 0 has no solution. = x + x 3 = x + x + = x + x + 59 TOPIC 3 MORE NONLINEAR EQUATIONS AND INEQUALITIES Page of 8

17 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. The graph of the function = x + x 3 is shown on the grid in Figure Use this graph to solve the 5 inequalit x + x 3 < 0. x Figure Solve the inequalit x 0 3x using the test point method. 3. Solve the inequalit x 8x using the test point method.. The graph of = x + 5x + 8 is shown on the grid in Figure Use this graph to decide whether each statement below is true or false. a. The solution of the inequalit x + 5x + 8 > 0 is all real numbers. b. The solution of the inequalit x + 5x + 8 < 0 is all real numbers. c. The solution of the equation x + 5x + 8 = 0 is all real numbers. d. The inequalit x + 5x + 8 > 0 has no solutions. e. The inequalit x + 5x + 8 < 0 has no solutions. 5 f. The equation x + 5x + 8 = 0 has no real solutions x 8 Figure Solve the rational inequalit > 0 using the test point method.. Solve the rational inequalit 0 using the test point method. 7. Solve the rational inequalit < The graph of the function = is shown on the grid in Figure x x x x 9 x x 5 x x x x Find the solution of the inequalit 0. x Figure 3.3. Page 7 of 8 LESSON 3.3 INEQUALITIES

18 9. The graphs of = x x 8 and = x x are shown on the grid in Figure Find the values of x that satisf both x x 8 0 and x x 0. Figure The graph of = x x + is shown on the grid in Figure Find where x x + < x 8 5 = x x 8 = x x 5 x x x x 0. The graph of = is shown on the grid in Figure Use the graph of the function to find the x x x 0 solution of the inequalit 0. x Figure x 9 x 5. Given the function =, for each value of x below, determine whether is positive, negative, 0, or undefined. a. 0 b. 3 c. 0 d. 5 e. Figure 3.3. TOPIC 3 MORE NONLINEAR EQUATIONS AND INEQUALITIES Page 8 of 8