Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Advanced Algebra Review for Midterm

Short Answer

1. The flow rate of IV fluids is calculated using the formula F V d

t, where V is the volume of the solution in

milliliters, d is the drip factor in drips per minute, and t is the time in minutes. Determine the flow rate of 1200 milliliter IV fluid for a patient for 24 hours if the drip factor is 1 milliliter per minute.

2. The formula for the area A of a square with side s is A s2 . Write an expression to represent the area of the square.

3. Name the sets of numbers to which the given number belongs.

4

Simplify the given expression.

4. 8 0.3x 0.3yÊËÁÁ

ˆ¯̃̃ 21 0.2x 0.7yÊ

ËÁÁˆ¯̃̃

Write an algebraic expression to represent the following verbal expression.

5. the sum of 80 and 5 times a number

Write a verbal expression to represent the given equation.

6. 2n 4 20

7. x8 3 x 5( )

8. Evaluate the given expression if k = –32.5 k 10 4k

Solve the given equation. Check your solution.

9. 32 2s 5 64

Name: ________________________ ID: A

2

Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line.

10. 9.9 2p 0

11. 0.4x 2.6 2.8

12. Anne earns $8 an hour working at Vampire Audios. Each week, 10% of her total pay is deducted for taxes. If Anne wants her take-home pay to be at least $250 a week, solve the inequality 8m 0.1 8m( ) 250 to determine how many hours she must work.

Solve the given inequality. Graph the solution set on a number line.

13. p 1 3 or p 1 5

14. m 7

15. Find the slope of the line that passes through the pair of points (–1, –5) and (–3, 10).

16. Graph the line that passes through (–5, –1), parallel to the graph of 3.9x + 6y = –5.

17. Graph the line that is perpendicular to the graph of 5x + 10y = 4.5 and intersects that graph at its x-intercept.

18. Write an equation in slope-intercept form for the line that satisfies the following condition.

slope 415

and passes through (5, –15)

Name: ________________________ ID: A

3

19. The ideal weight (in stones) of people of varying heights is given in the table below. Draw a scatter plot for the data.

Height (meters) 1.52 1.55 1.57 1.60 1.63 1.65

Weight (stones) 9.1 9.5 9.8 10 10.4 10.8

Height (meters)Graph I

Height (meters)Graph III

Height (meters)Graph II

Height (meters)Graph IV

20. The table below indicates the variation in weight of a person with respect to height. Use the first and fourth ordered pairs shown below to write a prediction equation. Use the prediction equation to predict the missing value.

Weight (lbs)

150 165 191 200 220

Height (cm) 165 165 179 190 ?

Name: ________________________ ID: A

4

Identify the type of function represented by the graph.

21.

Identify the type of function represented by the equation.

22. y = | 5x |

23. Graph the given inequality. 7x 18y 1

Solve each system of equations by using substitution.

24. 2r + 4s = 165r 6s =24

Solve each system of equations by using elimination.

25. 6a + 6b = 64a 3b 18

Solve the system of inequalities by graphing.

26. x > 3y > 9

Solve the given system of equations.

27. –3a = 368a + 3c = 95b + 9c = 15

Name: ________________________ ID: A

5

28. Consider the quadratic function f x( ) 2x 2 3x 2. Find the y-intercept and the equation of the axis of symmetry.

29. Graph the quadratic function f(x) 2x 2 5x 2.

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function.

30. f(x) x 2 2x 6

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

31. x2 4x 0

32. x 2 2x 8 0

Solve the equation by factoring.

33. x 2 7x 30 0

34. 2x 2 x 10 0

Simplify.

35. 70449

36. 10 5i( ) 1 19i( )

37. 2 9i( )(10 15i)

38. 6 3i20 i

Solve the equation by using the Square Root Property.

39. 36x 2 48x 16 25

Solve the equation by completing the square.

40. 2x 2 3x 0

Name: ________________________ ID: A

6

Find the exact solution of the following quadratic equation by using the Quadratic Formula.

41. x2 11x 9 0

Write the following quadratic function in vertex form. Then, identify the axis of symmetry.

42. y 3x 2 24x

Graph the quadratic inequality.

43. y x 2 4x 7

44. Evaluate the given expression if x = 25, y = 10, w = 36, and z = 2.

x yÊËÁÁ

ˆ¯̃̃

2 10wz

Factor the polynomial.

45. 45j 3 k 30j 6 k 6 15j 2

Factor the polynomial, if possible. If the polynomial cannot be factored, write prime.

46. 100v2 324

Solve the equation by factoring.

47. w 12( ) 2 36

Factor the trinomial, if possible. If the trinomial cannot be factored using integers, write prime.

48. 5t2 17t 6

Find the product.

49. 3f 12ÊËÁÁ

ˆ¯̃̃ f 4ÊËÁÁ

ˆ¯̃̃

Factor the polynomial.

50. r2 2r 15

51. g 2 10g 25

ID: A

1

Advanced Algebra Review for MidtermAnswer Section

SHORT ANSWER

1. ANS: 1.04Substitute the known values in the formula to find the value of the remaining variable.

PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.2 Use formulas.NAT: NA 1 | NA 4 | NA 9 | NA 2 TOP: Use formulas. KEY: Formulas

2. ANS:

x 3( ) 2

Substitute the value of s in the equation to find the required answer.

PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.2 Use formulas.NAT: NA 1 | NA 4 | NA 9 | NA 2 TOP: Use formulas. KEY: Formulas

3. ANS: N, W, Z, Q, RClassify the given number according to the definition of each type of number.

PTS: 1 DIF: Basic REF: Lesson 1-2 OBJ: 1-2.1 Classify real numbers.NAT: NA 1 | NA 9 STA: A2.2.A TOP: Classify real numbers.KEY: Real Numbers | Classify Numbers

4. ANS: 6.6x 12.3yApply the Distributive Law and simplify the given expression to get the required answer.

PTS: 1 DIF: Advanced REF: Lesson 1-2 OBJ: 1-2.2 Use the properties of real numbers to evaluate expressions. NAT: NA 1 | NA 9 TOP: Use the properties of real numbers to evaluate expressions.KEY: Real Numbers | Evaluate Expressions

5. ANS: 200 7xRepresent the expression by using appropriate numbers and variables.

PTS: 1 DIF: Basic REF: Lesson 1-3 OBJ: 1-3.1 Translate verbal expressions into algebraic expressions. NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate verbal expressions into algebraic expressions.KEY: Translate Expressions | Verbal Expressions | Algebraic Expressions

ID: A

2

6. ANS: Four times a number minus 3 is equal to 21.Read the given expression and represent it verbally.

PTS: 1 DIF: Basic REF: Lesson 1-3 OBJ: 1-3.2 Translate algebraic equations into verbal expressions. NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate algebraic equations into verbal expressions.KEY: Translate Equations | Verbal Expressions

7. ANS: A number divided by 48 is equal to 4 multiplied by the sum of that number and 2.Read the given expression and represent the given expression verbally.

PTS: 1 DIF: Basic REF: Lesson 1-3 OBJ: 1-3.2 Translate algebraic equations into verbal expressions. NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate algebraic equations into verbal expressions.KEY: Translate Equations | Verbal Expressions

8. ANS: –18For any real number a, if a is positive or zero, the absolute value of a is a. If a is negative, the absolute value of a is the opposite of a. Substitute the value of k in the equation and solve it.

PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.1 Evaluate expressions involving absolute values. NAT: NA 1 | NA 9 | NA 10 | NA 2TOP: Evaluate expressions involving absolute values. KEY: Evaluate Expressions | Absolute Value

9. ANS: {-1.5, -3.5}For any real numbers a and b, where b 0, if a b, then a b, or a b.

PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.2 Solve absolute value equations. NAT: NA 1 | NA 9 | NA 10 | NA 2TOP: Solve absolute value equations. KEY: Solve Equations | Absolute Value

10. ANS:

The solution set is p p 4.95ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ .

Solve the inequality and then graph the solution.

PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.1 Solve inequalities with one operation. NAT: NA 1 | NA 6 | NA 9 | NA 2STA: A2.1.C TOP: Solve inequalities with one operation. KEY: Solve Inequalities

ID: A

3

11. ANS:

The solution set is x x 0.5ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ .

Solve the inequality and then graph the solution.

PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.3 Solve inequalities with decimals with one operation. NAT: NA 1 | NA 6 | NA 9 | NA 2 STA: A2.1.C TOP: Solve inequalities with decimals with one operation. KEY: Solve Inequalities | Decimals

12. ANS: at least 34Solve the given inequality to determine the number of hours.

PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.5 Solve real-world multi-step inequalities. NAT: NA 1 | NA 6 | NA 9 | NA 2STA: A2.1.C TOP: Solve real-world multi-step inequalities. KEY: Solve Inequalities | Real-World Problems

13. ANS:

p | p 4ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

Solve the inequalities and then plot the graph.

PTS: 1 DIF: Advanced REF: Lesson 1-6 OBJ: 1-6.1 Solve compound inequalities with or. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2STA: A2.1.C TOP: Solve compound inequalities with or. KEY: Solve Inequalities | Compound Inequalities

14. ANS:

The solution set is m m 7ÏÌÓÔÔÔÔ or m 7}.

Solve the given inequality and plot the solution on a number line.

PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.3 Solve absolute value inequalities. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2STA: A2.1.C TOP: Solve absolute value inequalities. KEY: Solve Inequalities | Absolute Value

ID: A

4

15. ANS:

–152

The slope of a line is the ratio of the change in the y-coordinates to the corresponding change in the x-coordinates.

That is, the slope of a line = y 2 y 1

x 2 x1

.

Substitute the values of x 1 , y 1 , x 2 , and y 2 to find the slope of the line.

PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.1 Find and use the slope of a line with integer points. NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2TOP: Find and use the slope of a line with integer points. KEY: Slope | Integers | Graphs

16. ANS:

Use the equation y y 1 m x x1ÊËÁÁ

ˆ¯̃̃ to find the equation of the line passing through the point.

PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.4 Graph parallel lines.NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2 TOP: Graph parallel lines. KEY: Graphs | Parallel Lines

ID: A

5

17. ANS: x-intercept at (0.9, 0)

Substitute the values of x 1 and y 1 in the equation y y 1 m x x1ÊËÁÁ

ˆ¯̃̃ to get the equation of the line passing

through the x-intercept.

PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.5 Graph perpendicular lines.NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2 TOP: Graph perpendicular lines.KEY: Graphs | Perpendicular Lines

18. ANS:

y = 415

x 16.33

Substitute values of the x- and y-coordinates in the equation y y 1 m x x1ÊËÁÁ

ˆ¯̃̃ . Manipulate the equation to

get it in the slope-intercept form.

PTS: 1 DIF: Advanced REF: Lesson 2-4 OBJ: 2-4.1 Write an equation of a line given the slope and a point on the line.NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 TOP: Write an equation of a line given the slope and a point on the line. KEY: Equations of Lines | Slope | Graphs

19. ANS: Graph IPlot the points on the graph with height on the x-axis and weight on the y-axis.

PTS: 1 DIF: Basic REF: Lesson 2-5 OBJ: 2-5.1 Draw scatter plots.NAT: NA 1 | NA 5 | NA 6 | NA 10 | NA 2 TOP: Draw scatter plots.KEY: Scatter Plots

ID: A

6

20. ANS: y 0.55x 76.9; 192.4

Write the prediction equation using the slope formula m y 2 y1

x2 x 1

.

Then use the point-slope form, y – y1 = m(x – x1).

PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.2 Find and use prediction equations. NAT: NA 1 | NA 5 | NA 6 | NA 10 | NA 2STA: A2.6.E TOP: Find and use prediction equations. KEY: Prediction Equations | Scatter Plots

21. ANS: quadratic functionIdentify the general function represented by the graph.

PTS: 1 DIF: Basic REF: Lesson 2-7 OBJ: 2-7.1 Identify graphs as different types of functions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6TOP: Identify graphs as different types of functions. KEY: Graphs | Types of Functions | Functions

22. ANS: absolute value functionThe general equation of an absolute value function is y = | x |.

PTS: 1 DIF: Basic REF: Lesson 2-7 OBJ: 2-7.2 Identify equations as different types of functions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6TOP: Identify equations as different types of functions. KEY: Equations | Types of Functions | Functions

23. ANS:

Plotting the x-coordinates and the y-coordinates gives a graph of the inequality.

PTS: 1 DIF: Average REF: Lesson 2-8 OBJ: 2-8.1 Graph linear inequalities.NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 STA: A2.1.CTOP: Graph linear inequalities. KEY: Linear Inequalities | Graphs | Graph Inequalities

ID: A

7

24. ANS: (6, 1)By using the method of substitution, solve one equation for one variable in terms of the other variable. Then, substitute this expression for the variable in the other equation.

PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.1 Solve systems of linear equations by using substitution. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 STA: A2.1.B TOP: Solve systems of linear equations by using substitution. KEY: System of Linear Equations | Substitution

25. ANS: (3, –2)Use the method of elimination to obtain the required answer.

PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.2 Solve systems of linear equations by using elimination. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 STA: A2.1.B TOP: Solve systems of linear equations by using elimination. KEY: System of Linear Equations | Elimination

26. ANS:

Both the inequalities should be plotted and the region common to both should be shaded.

PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.1 Solve systems of inequalities by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2STA: A2.1.B TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities | Graphs

27. ANS: a = –12, b = –60, c = 35Solve three equations simultaneously.

PTS: 1 DIF: Average REF: Lesson 3-5 OBJ: 3-5.1 Solve systems of linear equations in three variables. NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 STA: A2.7.ATOP: Solve systems of linear equations in three variables. KEY: System of Equations | Three Variables

ID: A

8

28. ANS: The y-intercept is – 2.

The equation of the axis of symmetry is x = 34

.

For the quadratic equation ax2 bx c, the y-intercept is c and the equation of axis of

symmetry is x b2a

.

PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: A2.3.ATOP: Graph quadratic functions. KEY: Quadratic Functions | Graph Quadratic Functions

29. ANS:

First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate pairs and connect the points with a smooth curve.

PTS: 1 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: A2.3.ATOP: Graph quadratic functions. KEY: Quadratic Functions | Graph Quadratic Functions

30. ANS: The function has a minimum value. The minimum value of the function is 5.The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the function.

PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: A2.3.ATOP: Find and interpret the maximum and minimum values of a quadratic function.KEY: Maximum Values | Minimum Values | Quadratic Functions

ID: A

9

31. ANS: The solution set is 4, 0{ }.

The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because f(x) 0 at those points.

PTS: 1 DIF: Advanced REF: Lesson 5-2 OBJ: 5-2.1 Solve quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2STA: A2.3.C TOP: Solve quadratic equations by graphing. KEY: Quadratic Equations | Solve Quadratic Equations

32. ANS:

The solution set is 4, 2{ }.The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because f(x) 0 at those points.

PTS: 1 DIF: Advanced REF: Lesson 5-2 OBJ: 5-2.1 Solve quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2STA: A2.3.C TOP: Solve quadratic equations by graphing. KEY: Quadratic Equations | Solve Quadratic Equations

ID: A

10

33. ANS: 10, 3{ }

For any real numbers a and b, if ab 0, then either a 0, b 0, or both a and b are equal to zero.

PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2STA: A2.3.C TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

34. ANS:

{52

, 2}

For any real numbers a and b, if ab 0, then either a 0, b 0, or both a and b are equal to zero.

PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2STA: A2.3.C TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

35. ANS:

8 117

ab

a

b

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 TOP: Find square roots.

36. ANS: 11 14iCombine the real and imaginary parts of the complex numbers to add them.

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 TOP: Perform addition and subtraction operations with complex numbers.KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers

37. ANS: 155 60iUse the FOIL method to multiply the complex numbers and use the formula i2 1. Combine the real parts and then the imaginary parts of the two numbers.

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.4 Perform multiplication operations with complex numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 TOP: Perform multiplication operations with complex numbers. KEY: Complex Numbers | Multiply Complex Numbers

ID: A

11

38. ANS: 123401

54401

i

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression.

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.5 Perform division operations with complex numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 TOP: Perform division operations with complex numbers. KEY: Complex Numbers | Divide Complex Numbers

39. ANS:

{16

, 32

}

For any real number n, if x 2 n, then x n .

PTS: 1 DIF: Average REF: Lesson 5-5 OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: A2.3.CTOP: Solve quadratic equations by using the Square Root Property. KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

40. ANS: 1.5, 0{ }

To complete the square for any quadratic expression of the form x 2 bx, find half of b, and square the result.

Then, add the result to x 2 bx.

PTS: 1 DIF: Average REF: Lesson 5-5 OBJ: 5-5.2 Solve quadratic equations by completing the square. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: A2.3.CTOP: Solve quadratic equations by completing the square. KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

41. ANS:

11 157

2,11 157

2

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

¸

˝

˛

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

The solution of a quadratic equation of the form ax2 bx c 0, where a 0, is obtained by using the

formula x b b 2 4ac

2a.

PTS: 1 DIF: Average REF: Lesson 5-6 OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: A2.3.C TOP: Solve quadratic equations by using the Quadratic Formula. KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

ID: A

12

42. ANS:

The vertex form of the function is y 3 x 4( ) 2 48.The equation of the axis of symmetry is x 4.

The vertex form of a quadratic function is y a(x h)2 k .The equation of the axis of symmetry of a parabola is x h.

PTS: 1 DIF: Basic REF: Lesson 5-7 OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k. NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6 STA: A2.3.ATOP: Analyze quadratic functions in the form y = a(x - h)^2 + k. KEY: Quadratic Functions | Axis of Symmetry

43. ANS:

Graph the related quadratic equation. Because the inequality symbol is >, the parabola should be dashed. Test a point (x 1 , y 1 ) inside the parabola. If (x 1 , y 1 ) is the solution of the inequality, shade the region inside the

parabola. If (x 1 , y 1 ) is not a solution, shade the region outside the parabola.

PTS: 1 DIF: Advanced REF: Lesson 5-8 OBJ: 5-8.1 Graph quadratic inequalities in two variables. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3STA: A2.3.C TOP: Graph quadratic inequalities in two variables.KEY: Quadratic Inequalities | Graph Quadratic Inequalities

44. ANS: 945Evaluate the expression by replacing each variable with its corresponding number and then applying the order of operations.

PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.1 Use the order of operations to evaluate expressions. NAT: NA 1 | NA 4 | NA 9 | NA 2 TOP: Use the order of operations to evaluate expressions.KEY: Evaluate Expressions

ID: A

13

45. ANS:

15j 2 3jk 2j 4k 6 1ÊËÁÁÁ

ˆ¯˜̃̃

The factors of 45j 3 k are 3 3 5 j j j k .

The factors of 30j 6k 6 are 1 2 3 5 j j j j j j k k k k k k .

The factors of 15j 2 are 3 5 j j.The GCF of 45j 3 k 30j 6 k 6 15j 2 is 15 j j.Writing each term as the product of the GCF and its remaining factors gives

15j 2 3jkÊËÁÁ

ˆ¯̃̃ 15j 2 2j 4k 6Ê

ËÁÁÁ

ˆ¯˜̃̃ 15j 2 1( ) .

Use the Distributive Property to factor out the GCF: 15j 2 3jk 2j 4k 6 1ÊËÁÁÁ

ˆ¯˜̃̃ .

PTS: 1 DIF: Average REF: Lesson 8-2 OBJ: 8-2.1 Factor polynomials by using the Distributive Property. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 STA: A1.2.ETOP: Factor polynomials by using the Distributive Property KEY: Factor Polynomials | Distributive Property

46. ANS: 4 5v 9( ) 5v 9( )First divide both numbers by 4.

4 25v 2 81ÊËÁÁÁ

ˆ¯˜̃̃

4 a 2 v2 b 2ÊËÁÁÁ

ˆ¯˜̃̃ 4 av b( ) av b( )

4 5v 9( ) 5v 9( )

PTS: 1 DIF: Basic REF: Lesson 8-5 OBJ: 8-5.1 Find binomials that are differences of squares. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6STA: A1.2.E TOP: Factor binomials that are the differences of squaresKEY: Factor Binomials | Difference of Squares

47. ANS: 6, 18{ }

Take the square root of both sides.

w 12( ) 36

w 12( ) 6

w 12 6

w 6, 18{ }

PTS: 1 DIF: Average REF: Lesson 8-6 OBJ: 8-6.2 Solve equations involving perfect squares. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6STA: A1.5.C TOP: Solve equations involving perfect squares KEY: Perfect Squares | Solve Equations

ID: A

14

48. ANS: (5t + 2)( t + 3)

Two variables, m and n, exist such that at2 m n( )t c.m n 17 and m n a c 5(6).Make a table to find the possible solutions.

The solutions, 12 and 3 must be substituted into the equation at2 mt nt c and factored.

5t2 12t 3t 65t t 3( ) 2 t 3( )The correct factors are 5t 2( ) t 3( ) .

PTS: 1 DIF: Basic REF: Lesson 8-4 OBJ: 8-4.1 Factor trinomials of the form ax^2 + bx + c. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6STA: A1.2.E TOP: Factor trinomials of the form ax^2 + bx + c KEY: Factor Trinomials

49. ANS:

4f 2 7f 30

PTS: 1 DIF: Average REF: Lesson 0-2 OBJ: 0-2.2 Solve multi-step problems.STA: A2.2.C TOP: FOIL KEY: FOIL

50. ANS: r 7( ) r 2( )

PTS: 1 DIF: Average REF: Lesson 0-3 OBJ: 0-3.2 Solve multi-step problems.STA: A2.3.C TOP: Factoring polynomials.

51. ANS:

g 3ÊËÁÁ

ˆ¯̃̃

2

PTS: 1 DIF: Average REF: Lesson 0-3 OBJ: 0-3.2 Solve multi-step problems.STA: A2.3.C TOP: Factoring polynomials.