Algebra Warm-Up Questions
CST Preparation
Standard 1.0
1. State the name of the property illustrated. (3 + 9) + 4 = (9 + 3) + 4
A. Associative Property
B. Distributive Property
C. Closure Property
D. Commutative Property
2. All of the following are rational numbers EXCEPT
A. B. C. D.
3. What justifies the following statement?
=
A. Commutative Property
B. Reflexive Property
C. Distributive Property
D. Associative Property
4. Under what subset of integers is the
A. Integers
B. Irrational
C. Natural Numbers
D. Rational Numbers
5. State the name of the property illustrated. (3 ∙ 9) ∙ 7 = 3 ∙(9 ∙ 7)
A. Associative Property
B. Commutative Property
C. Distributive Property
D. 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
- Which is a solution to the following inequality?
3
a. x b. x c. - d. -
- Solve the following equation:
x =
a. -3.7 b. 3.7 c. -3 d. 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
- What is the solution set of the inequality
5 - -3
a. -2 b. x or x 6 c. -12 d. x or x
- 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 = 14x
c. -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 = 56
c. 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 -12
c. -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 = 14x
C. -9x + 2 = 14x D. 12 – 1 = 14x
3. Solve 3(x + 5) = 2x + 35
Step 1: 3x + 15 = 2x + 35
Step 2: 5x + 15 = 35
Step 3: 5x = 20
Step 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. 4
6. 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 Multiplication
B. Addition Property of Equality
C. Distributive Prop of Multiplication with Respect to Addition
D. 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 = + 4A. / 4
B. /
C. / y
D. /
2. Determine the slope of the line derived from the equation: 3x - y = 4
A. / 3
B. / 4
C. / -1
D. / 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 = 25
D. / 3x + 4y =
5. What is the equation of a line that passes through the points (5 , 6) and (6 , 9)?
A. / y = -2x + 16
B. / 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 = 2x
B y = -x + 6
C y = -2x
D y = x + 1
4. If the equation of a line is 4x + 4y = 1 and the equation of a second line is
x + 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 = 2
B 6x + 10y = -6
C -5x + 3y = 2
D -3x + 5y = -3
Standard 9
1. What is the solution to this system of equations?
y = -3x – 2
6x + 2y = -4
A (6,2)
B (1, -5)
C no solution
D infinitely many solutions
2. Solve the linear system:
3x + 2y = 8
5x + 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 2
B 10
C 2x – 40
D -2
4. Solve the linear system:
y = x -1
2x + 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 – 4
C. 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 14
1) 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
- 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)}
- 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)}
- Which of the following is not a function?
A. X = 3Y2 + 5 B. {(X, Y) | Y = 3X2 + 5}
C. {(X, Y) | Y = 3 , X0} D. {(3, -1), (-3, -4), (-2, -1)}
- 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)}
- Which of the following is not a function?
A. {(X, Y) | Y = 4, X0} B. {(2, 1), (-2, 5), (0, 1)}
C. {(X, Y) | Y = 4X2 – 5} D. {(1, -2), (1, 5), (2, 0)}
Standard 17.0
1. 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 = 1