Algebra Warm-Up QuestionsCST Preparation

Standard 1.0

1. State the name of the property illustrated. (3 + 9) + 4 = (9 + 3) + 4

A. Associative PropertyB. Distributive PropertyC. Closure PropertyD. Commutative Property

2. All of the following are rational numbers EXCEPT

A. B. C. D.

3. What justifies the following statement? =

A. Commutative PropertyB. Reflexive PropertyC. Distributive PropertyD. Associative Property

4. Under what subset of integers is the

A. IntegersB. IrrationalC. Natural NumbersD. Rational Numbers

5. State the name of the property illustrated. (3 ∙ 9) ∙ 7 = 3 ∙(9 ∙ 7)

A. Associative PropertyB. Commutative PropertyC. Distributive PropertyD. Transitive Property

Standard 2.0

1. Identify the opposite of -

A. B. C. - D. - .75

2. Evaluate 4

A. -12 B. -64 C. - D.

3. Simplify

A. 2 B. 3 C. 9 D. 9

4. Simplify -

A. - B. - C. - D. -

5. Evaluate the expression

A. 6 B. 6 C. 6 D.

Standard 3

1. Which is a solution to the following inequality?

3

a. x b. x c. - d. -

2. Solve the following equation:

x =

a. -3.7 b. 3.7 c. -3 d. 3

3. What is the solution for this equation?

= 5

a. x = -4 or x = 4 b. x = -4 or x = 3 c. x = -1 or x = 4 d x= -1 or x=3

4. What is the solution set of the inequality

5 - -3

a. -2 b. x or x 6 c. -12 d. x or x

5. What is the solution for the following inequality?

a. b. y or y c. y or y d. -5

Standard 4

1. Which equation is equivalent to

5x – 2(7x + 1) = 14x

a. -9x – 2 = 14x b. -9x + 1 = 14xc. -9x + 2 = 14x d. 12x – 1 = 14x

2. Which equation is equivalent to

4(2 – 5x) = 6 – 3(1 – 3x)

a. 8x = 5 b. 8x = 17 c. 29x = 5 d. 29x = 17

3. Which is the simplified version of 7x – 4(x – 8) = 56?

a. 11x + 32 = 56 b. 3x – 8 = 56c. 3x – 32 = 56 d. 3x + 32 = 56

4. Which of the following is the simplified form of 6x – 5 – 7x -12

a. -13x – 5 -12 b. –x – 5 -12c. -6x -12 d. 13x – 5 -12

5. Simplify: 8x + 3(x + 5) – 5(x – 4)

a. 6x + 35 b. 6x + 1 c. 6x – 5 d. 43x

Standard 5

1. Solve for x: 4(1 – x) + 2x = –3(x + 1)

A. -7 B. C. -1.4 D. 1.4

2. Which equation is equivalent to 5x – 2(7x + 1) = 14x

A. -9x – 2 = 14x B. -9x + 1 = 14xC. -9x + 2 = 14x D. 12 – 1 = 14x

3. Solve 3(x + 5) = 2x + 35

Step 1: 3x + 15 = 2x + 35Step 2: 5x + 15 = 35Step 3: 5x = 20Step 4: x = 4

Which is the first incorrect step in the solution shown above?

A. Step 1 B. Step 2 C. Step 3 D. Step 4

4. Solve the compound inequality: 2x – 4 < -8 or x + 2 > 5

A. x < -2 B. x > -2 or x < 3 C. x < -2 or x > 3 D. x > 3

5. Which value could x be if -2 < x + 2 4

A. -4 B. 3 C. -3 D. 46. Pick the correct justification in the problem below:

6(3x – 4) – 26 = 40

18x – 24 – 26 = 40 Associative property of Multiplication 18x – 50 = 40 Addition Property of Equality 18x = 90 Distributive Prop of Multiplication w/ Respect to Addition x = 5 Multiplication Property of Equality

A. Associative Property of MultiplicationB. Addition Property of EqualityC. Distributive Prop of Multiplication with Respect to AdditionD. Multiplication Property of Equality

Standard 6

1. What is the y-intercept of the graph of 4x + 2y = 12?

A. -4 B. -2 C. 6 D. 12

2. Which inequality is shown on the graph below?

A. y < B. y C. y > x – 1 D. y x - 1

3. Determine the y-intercept of 4x – y = -6

A. (0, 4) B. (0, 6) C. (0, -6) D. (0, -4)

4. Find the x-intercept for 3x – 5y = 30

A. (0, -6) B. (0, -10) C. (10, 0) D. (0, 6)

5. Which line is graphed below?

A. y = -2x - 4 B. y = 2x + 4 C. x + 2y = 4 D. y = -2x + 4

Standard 7

1. Determine the slope of the line derived from the equation: y = + 4

A. 4B.

C. yD.

2. Determine the slope of the line derived from the equation: 3x - y = 4A. 3B. 4C. -1D. 3x

3. Which point lies on the line 2x - y = 7? A. (-1 , -9)B. (-1 , 9)C. (5 , -3)D. (4 , -1)

4. Which is an equation of a line that has a slope of and passes through the point (3 , 4)?

A. y =

B. y =

C. 3x + 4y = 25D.

3x + 4y =

5. What is the equation of a line that passes through the points (5 , 6) and (6 , 9)? A. y = -2x + 16B.

y =

C. y = 3x - 9

D. y =

Standard 8

1. The equation of line l is 6x + 5y = 3, and the equation of line q is 5x – 6y = 0. Which statement about the two lines is true?

A Lines l and q have the same y-intercept.B Lines l and q are parallel.C Lines l and q have the same x-intercept.D Lines l and q are perpendicular.

2. Which equation represents a line that is parallel to y = - x + 2?

A y = - x + 1

B y = - x + 2

C y = x + 3

D y = x + 4

3. Which line is perpendicular to the line y = x?

A y = 2xB y = -x + 6C y = -2xD y = x + 1

4. If the equation of a line is 4x + 4y = 1 and the equation of a second line isx + y = -8. Which of the following is true?

A The lines share the same x-intercept.B Both lines intersect at point (0,-8).C The lines are perpendicular.D The lines are parallel.

5. Which of the following equations represents a line that is parallel to the line represented by 3x + 5y = -3?

A 3x + 5y = 2B 6x + 10y = -6C -5x + 3y = 2D -3x + 5y = -3

Standard 9

1. What is the solution to this system of equations?y = -3x – 26x + 2y = -4

A (6,2)B (1, -5)C no solutionD infinitely many solutions

2. Solve the linear system:3x + 2y = 85x + 2y = 12

A (-2, 7)B (2, 1)C (1, 2)D (2, 4)

3. Solve the following system for y:2x – 15y = -10-4x + 5y = -30

A 2B 10C 2x – 40D -2

4. Solve the linear system:y = x -12x + 3y = 12

A (3, 2)B (6, 2)C (2, 2)D (4, 4)

Standard 10

1. Find the difference: (x2 + xz + 2y2) – (y2 – 4xz + z2)

A. 3y2 – 3xz + z2 B. y2 + 5xz – z2 + x2

C. –y2 – 5xz + z2 – x2 D. 2y2 + 4xz + y2

2. Find the product: (3t – 2)(4t + 2)

A. 7t B. 12t2 +2t + 4 C. 12t2 – 4 D. 12t2 – 2t – 4

3. Solve: 3x + 2 = x + 8

A. 1.5 B. 2.5 C. 3 D. 5

4. Simplify:

A. 2x4 B. C D.

5. Simplify: (4x3 + 2x2 – 5x – 7) + (6x3 – x2 – 5x + 3)

A. 10x6 + x4 – 10x2 – 4 B. 10x3 + 10x2 – 10x – 4C. 10x6 + 10x4 – 4 D. 10x3 + x2 – 4

Standard 11

1. Factor: 3a2 – 24ab + 48b2

A. (3a – 8b)(a – 6b) B. (3a – 16b)(a – b) C. 3(a – 4b)(a – 4b) D. 3(a – 8b)(a – 8b)

2. Which is a factor of x2 – 11x + 24

A. x + 3 B. x – 3 C. x + 4 D. x – 4

3. Factor: x2 + 4x + 3

A.(x + 2)(x + 2) B.(x +4)(x + 1) C.(x2 + 3)(x + 1) D.(x + 3)(x + 1)

4. Factor: x2 – 16

A.(x – 1)(x + 16) B. (x + 2)(x – 8) C. (x + 4)(x – 4) D. (x – 4)(x – 4)

5. Factor: x2 + 8x + 16

A.(x + 8)(x + 2) B. (x – 4)(x – 4) C. (x + 4)(x + 4) D. (x + 12)(x – 4)

Standard 12

1. What is reduced to lowest terms?

A. B. C. D.

2. Simplify:

A. B. C. D.

3. Simplify the expression:

A. x + 1 B. x – 2 C. D. already in

Simplest form

4. Simplify the expression:

A. x3 – 2 B. C. x + 1 D.

5. Simplify the expression:

A. B. C. D.

Standard 13

1. Simplify:

A. B. C. D.

2. Simplify:

A. B. C. D.

3. Simplify:

A. B. C. D. can’t be simplified

4. Simplify:

A. B. C. D.

5. Simplify:

A. B. C. D.

Standard 141) Which is a factor of ? A. C. B. D.

2) Which of the following shows factored completely? A. C. B. D.

3) If is added to x, the sum is 42. Which of the following could be a value of x? A. C. 14 B. D. 42

4) What quantity should be added to both sides of this equation to complete the square?

A. 4 C. 16 B. D.

5) What are the solutions for the quadratic equation ? A. C. B. D.

6) Al is solving this equation by completing the square.

A.

B.

C.

D.

7) Solve by factoring. A. C. B. D.

8) Solve for x.

A. C.

B. D. All of the above

9) Solve for x. . A. C. B. D.

10) Solve for x. . A. C.

B. D.

Standard 15

1. A pharmacist mixed some 10%- saline solution with some 15%- saline solution to obtain 100 ml of a 12%- saline solution. How much of the 10%- saline solution did the pharmacist use in the mixture?

A. 60 ml B. 45 ml C. 40 ml D. 25 ml

2. Andy’s average driving speed for a 4-hour trip was 45 miles per hour. During the first three hours he drove 40 miles per hour. What was his average speed for the last hour of his trip.

A. 50 mph B. 60 mph C. 65 mph D. 70 mph

3. Leanne and Jenn are on a road trip. If they are traveling 80 miles per hour on the freeway, how long will it take them to go 240 miles?

A. 3 hours B. 4 hours C. 30 hours D. 80 hours

4. A car uses 9.8 gallons of gas to travel 245 miles. How many miles can the car travel if it has 20 gallons of gas?

A. 500 miles B. 12.25 miles C. 25 miles D. 196 miles

5. A person travels 120 miles in one direction. The return trip was accomplished at twice the speed and took three hours less time. What was the person’s original speed?

A. 6 mph B. 60 mph C. 10 mph D. 20 mph

6. Jason can paint the room in 4 hours. John can paint the room in 6 hours. How long would it take if they were working together?

A. hours B. 5 hours C. hours D. 2 hours

7. Ten pounds of peanuts that cost $2.00 per pound are mixed with six pounds of cashews that cost $5.00 per pound. How much will the mixture cost per pound?

A. $ 3.13 B. $ 7.00 C. $ 3.50 D. $ 50.00

8. A 50% acidic solution is created by combining 100 liters of Solution A with 50 liters of Solution B. If the acidity of Solution B is 70%, what is the acidity of Solution A?

A 60% B 30% C 40% D 20%

Standard 16

1. Which of the following is a function?

A. {(-4, -7), (-7, 0), (-4, 8)} B. {(-4,-7), (0, 8), (0, -4), (-8, 0)}

C. {(-4, -7), (-7, -4), (-8, -8)} D. {(-4, -7, 0, -8)}

2. Which of the following is a one-to-one function?

A. {(-6, -8), (-1, 0), (0, -1), (-6, -6)} B. {(-7, -8), (-1, 3), (0, -2), (-6, -8)}

C. {(-7, -8), (-1, 3), (-7, -2), (3, -1)} D. {(-7, -8), (-1, 3), (0, 0), (-1, 2)}

3. Which of the following is not a function?

A. X = 3Y2 + 5 B. {(X, Y) | Y = 3X2 + 5}

C. {(X, Y) | Y = 3 , X 0} D. {(3, -1), (-3, -4), (-2, -1)}

4. Which of the following is a one-to-one function?

A. {(7, 1), (6, -6), (-4, -5), (-9, 1)} B. {(7, 1), (6, -6), (7, -5), (-6, 6)}

C. {(7, 1), (6, -4), (-4, 6), (-4, -9)} D. {(7,1), (6, -6), (-4, -4), (6, 8)}

5. Which of the following is not a function?

A. {(X, Y) | Y = 4 , X 0} B. {(2, 1), (-2, 5), (0, 1)}

C. {(X, Y) | Y = 4X2 – 5} D. {(1, -2), (1, 5), (2, 0)}

Standard 17.01. Find the domain and range: { (X, Y) | Y = 1 + X}

A. D = {-1 X 1}; R = {all real numbers}

B. D = {all real numbers}; R = {all real numbers}

C. D = {all real numbers}; R = {X | X -1}

D. D = {X | X -1}; R = {all real numbers}

2. Find the range of the relation {(-5 ,-6), (-3, -1), (0, -5)}

A. {4, 3, 2} B. {1, -4, 2} C. {1, -4, -2} D. {4, 3, -2}

3. Find the domain of the relation {(-5, -6), (-3, -1), (0, 5)}.

A. {-6, -1, 0} B. {-5, -3, 0} C. {-5 ,-3, 5} D.{-6, -1, 5}

4. Find the domain and range:

A. D = {x is a real number} R = {y 3}B. D = { x } R = {y is a real number}C. D = {x is a real number} R = { y is a real number}D. D = { x > 5} R = { y > 5}

Standard 18

1) Which set or ordered pairs below is a function?

I. (3,3), (6,1), (2,3)II. (4,7), (2,8), (4,2)

III. (9,6), (3,1), (7,3)

A) I only B) II only C) III only D) I and III

2) Evaluate f(x) = 3x – 4, when x = -2

A) f(-2) = -2 B) f(-2) = 2 C) f(-2) = 1 D) f(-2) = -10

3) Evaluate f(x) = x2 +2x + 1 When x = -3

A) f(-3) = -14 B) f(-3) = 4 C) f(-3) = -2 D) f(-3) = 16

4) f(x) = -2x – 4, Find f(4).

A) f(4) = -12 B) f(4) = 4 C) f(4) = 12 D) f(4) = -4

5) Which of the following graphs are functions?

1) 2) 3) 4)

A. 4 only B. 1 and 2 C. 1, 2 and 3 D. all of them

Standard 19

1. Solve x2 + 8x = 20 by completing the square.

A) x = 2 B) x = 2 or x = -10 C) x = -10 D) x = 10 or x = -2

2. Solve x2 - 4x – 12 = 0 by completing the square.

A) x = -2 B) x = -6 or x = 2 C) x = -2 or x = 6 D) x = -6

3. Solve x2 - 12x - 13 = 0 by completing the square.

A) x = -1 or x = 13 B) x = -13 or x = 1 C) x = 13 D) x = 14. Solve x2 + 16x = 17 by completing the square.

A) x = 1 or x = 17 B) x = -17 pr x = 1 C) x = 17 D) x = 1

5. Solve x2 - 24x = -44 by completing the square.

A) x = 2 B) x = -22 C) x = 2 or x = 22 D) x = -22 or x = 2

Standard 20

1. What are the roots of the following equation:

A) B)

C) D)

2. What are the solutions for the quadratic equation:

A) B)

C) D)

3. Use the quadratic formula to solve the following equation:

A) B)

C) D)

4. Solve the following equation:

A) B)

C) D) No Real Solution

5. What is the solution set of the quadratic equation ?

A) B)

C) D) No real solution

Standard 21

1. What are the roots of the function shown:

A)

B)

C)

D) ; no second root

2. What is the equation of the function shown:

A)

B)

C)

D) 3. What are the roots of the equation: ?

A) B)

C) D)

4. The graph of the equation is shown below.

For what value or values of x is ?

A) only B) only

C) D)

5. What are the roots of the function shown?

A)

B)

C)

D) No roots existStandard 22.0

1. How many times does the graph of y = x² + 4x - 5 intersect the x-axis?

a. noneb. onec. twod. three

2. How many times does the graph of y = x² - 11x + 24 intersect the x-axis?

a. noneb. onec. twod. three

3. How many times does the graph of y = 2x² - 2x + 3 intersect the x-axis?

a. noneb. onec. twod. three

4. How many times does the graph of y = 3x² - 5x - 2 intersect the x-axis?

a. noneb. onec. twod. three

5. How many times does the graph of y = 6x² - 13x + 6 intersect the x-axis?

a. noneb. onec. twod. three

Standard 23.0

1. An object that is projected straight downward with initial velocity v feet per second travels a distance s = vt + 16t², where t = time in seconds. If Ramon is standing on a balcony 84 feet above the ground and throws a penny straight down with an initial velocity of 10 feet per second, in how many seconds will it reach the ground?

a. 2 secondsb. 3 secondsc. 6 secondsd. 8 seconds

2. The height of a triangle is 4 inches greater than twice its base. The area of the triangle is 168 square inches. What is the base of the triangle?

a. 7 in.b. 8 in.c. 12 in.d. 14 in.

3. Use the falling object model, h = -16t² + s.If h is ground level and s is the initial height of 140 feet above the ground, determine the time (t) is seconds it will take an object to fall to the ground.

a. 1.71 secondsb. 2.96 secondsc. 3.06 secondsd. 8.75 seconds

4. Use the falling object model, h = -16t² + s.If an object is dropped from 190 ft, how long will it take for the object to reach the ground?

a. 4 secondsb. 3.45 secondsc. 11.87 secondsd. 13.19 seconds

5. A sandbag is released from a hot air balloon that is 400 ft above the ground. Using the falling object model, h = -16t² + s, where h = height in feet, t = time in seconds, and s = initial height in feet, how long will it take for the sandbag to hit the ground?

a. 4 secondsb. 5 secondsc. 20 secondsd. 25 seconds

Standard 24

1. Which number serves as a counterexample to the statement below: All positive integers are divisible by 2 or 3.

A. 100 B. 57 C. 30 D. 25

2. Ms. Lopez has given her students homework every Tuesday so far this year. One student concludes that she will give the class homework next Tuesday. What type of reasoning did the student use o make this conclusion?

A. abstract B. deductive C. factual D. inductive

3. Read the following logical argument:

All cats have whiskers. All animals with whiskers do not like water.

Jelly is a cat.Therefore, Jelly does not like water.

Identify the conclusion of the argument:

A. All cats have whiskers. B. All animals with whiskers do not like water.C. Jelly is a cat. D. Therefore, Jelly does not like water.

4. Read the following statement:If I pass the driving test, then I will get my driver’s license.

Identify the hypothesis of the statement.

A. I will get my driver’s license. B. I want my driver’s license.C. I pass the driving test. D. I should get a car.

Standard 25

1. Consider the following: 3(2x – 4) = 18 6x – 12 = 18 Distributive property 6x = 30 ______________________ x = 5 multiplication property of equality

What is the missing justification? A. Addition property of equality B. Associative property C. Commutative property D. Additive Identity

2. The statement that is ________________ true.

A. always B. sometimes C. never D. cannot tell

3. In solving the equation, which step contains an error?

4 – 8(x + 3) = -28 step 1: -4(x + 3) = -28 step 2: x + 3 = 7 step 3: x = 4

A. step 1 B. step 2 C. step 3 D. no errors

4. Complete the sentence with the word that makes the sentence true. An equation ______________ represents a function.

A. always B. sometimes C. never D. cannot tell