A second chance for Pre

Algebra State Standards with Examples

The following are questions that address the California State Standards. I use these for test questions.

1.0

What is the best classification for –2

whole number, integer, real number
integer, rational number, real number
irrational number, real number
rational number, real number

What is the best classification for –0.4?

whole number, integer, real number
integer, rational number, real number
rational number, real number
irrational number, real number

Which of the following square roots is an irrational number?

Which of the following statements is false?

The product of two integers is an integer.

The sum of two integers is an integer.

The difference of two integers is an integer.

The quotient of two integers is an integer.

Which of the following mathematical statements illustrates the commutative property of multiplication?

2.0

Simplify

3.0

Simplify

Evaluate the expression for a = -5 and b = -3.

Solve

Graph the solution to the inequality:

4.0

Simplify:

2y + 1 + (-5x) + 7y - 4x

-6+3x-y-4x+4y+5

Multiply: -7(x-2)

Simplify:

8(3x-2) - 5(2x-3)

2(x+5) + 3(4x-5) - 7

5.0

Solve:

The daily cost of renting a car is $40 plus $0.35 per mile traveled. If Juan paid $121.20n for a day’s rental, how many miles did he travel?

Graph the solution to the inequality: 5x + 3 < 3(x + 2)

The width of a rectangle is 18 centimeters. Find all possible values for the length of the rectangle if the perimeter is at least 360 centimeters.

6.0

What is the x-intercept of the line 5x – y = -5?

What is the y-intercept of the line 4x - y = -4?

Graph

7.0

Write the standard form of the equation of the line with slope 0 passing through the point (-1,3).

Write an equation of the line that passes through the point (-2,4) with slope –4.

Write equation is correct for a line through (5,-3) with slope 0.75?

Which of the following points lies on the line 3x + 2y = 5?

(10,-5) (5,-10) (7,-3) (-3,7)

Which of the following lines lies on the point (5,-9)?

X/3 + y = 2

3x + y = 6

7x + 4y =1

5x + 9y = 0

8.0

Write the standard form of the equation of the line passing through the point

(-2,4) and perpendicular to the line –3x – y = -2.

Write the standard form of the equation of the line passing through the point

(-4,-1) and parallel to the line 2x + 5y = -2.

Which of the following equations has a graph that is parallel to the graph of 4x – 2y = 7?

2y = 4x + 7

-2y = 4x + 2

4x + 2y = 2

–4x – 2y = –7

Which of the following lines is perpendicular to y = 2x + 3?

2x – y = -5

x + 2y = 8

x – 2y = –4

y + 2x = 2

Which of the following lines is not parallel to y = 5x + 1?

5x – y = –4

5x + y = 1

10x – 2y = –4

y – 5x = 4

9.0

What is the solution to the system of equations graphed below?

ADD GRAPH

Solve the system of equations:

3x + 2y = –10

y = – x – 4

Which system has no solution has no solution?

Y = 2x y = 2x + 2 y = –x + 1 4x – 2y = 1

2x + y = 1 x – 2y = 1 x – 1 =1 y = 2x – 7

Solve the system of equations:

4x – 4y = –8

x + 4y = –7

Solve the system of graphically:

ADD GRAPHS

10.0

Add

Subtract

Multiply

The area of a rectangle is and its width is x – 2. What is its length?

11.0

Factor

12.0

Simplify

13.0

Multiply:

Divide:

Add:

Solve: &

14.0

Solve:

Solve by completing the square:

15.0

At noon Juan bikes toward Beth’s home at 12 mph and Beth bikes toward Juan’s home at 8 mph. When will they meet, if their homes are 30 miles apart?

If it takes 3 hours to travel 15 miles downstream and 5 hours to travel upstream, how fast is the current if the speed of the boat remains constant?

When working alone, George can clean the house in 3 hours and Connie can clean it in 2 hours. If they work together, how long should it take them?

Susan has a container with a 30% solution of juice and a container with a 5% solution of juice. How much of the 30% solution does she need to mix with the 5% solution to get 3 liters of a 15% solution of juice?

Raul wants to make 10 lb of a dried fruit and nut mixture to sell for $2.75/lb, using dried fruit that sells for $2.25/lb and nuts that sell for $3.50/lb. How many pounds of the nuts should he put in the mixture?

16.0

Which point could not be part of the graph of a function containing (7,5)?

(-7,-5) (7,2) (2,5) (5,7)

Consider the equation . Which of the following statements is true?

y is a function of x but x is not a function of y.

y is a function of x but x is a function of y.

y is not a function of x but x is not a function of y.

y is not a function of x but x is a function of y.

Consider the day numbers (1-365) of a non-leap year and the month numbers (1-12) of the year. Which of the following statements is true?

Month number is a function of day number.

Day number is a function of month number.

Month number is a function of day number and day number is a function of month number.

Neither one is a function of the other.

Which of the following statements is true of functions?

The number of elements in the domain is less than or equal to the number of elements in the range.

The number of elements in the domain equals the number of elements in the range.

The number of elements in the domain is greater than or equal to the number of elements in the range.

The number of elements in the domain has no relation to the number of elements in the range.

Suppose that your grade in math is a function of the amount of time you spent studying. Which of the following statements is true?

The longer you study, the higher your grade.

If your grade is known, your study time can be determined.

If your study time is known, your grade can be determined.

If your grade is high, then you studied for a long time.

17.0

What is the domain of the function graphed below?

ADD GRAPH

What is the range of the function when the domain is {1,3,5}?

What is the domain of the set {(-3,2),(-2,6),(5,-1)}?

What is the range of the function ?

What is the domain of ?

18.0

Determine which relation is a function?

X	1	1	1	1
Y	4	3	2	1

X	3	3	1	1
Y	4	3	2	5

X	1	2	3	4
Y	3	6	9	12

X	3	2	5	3
Y	4	43	1	5

Which of the following statements justifies why a circle centered at the origin with radius 5 is not the graph of a function?

The circle is not defined for x > 5.

The circle is not defined for y > 5.

The circle contains (-5,0) and (5,0).

The circle contains (0,5) and (0,-5).

Which equation represents a function?

Which of the following sets is a function?

{(-8,-6), (-6,-8), (0,0)}

{(-8,-6), (-6,-2), (-8,0)}

{-8, -6, -2, 0}

{(-8,-6), (-2,0), (-2,-8), (0,-2)}

Determine which graph represents a function.

ADD GRAPHS

17.0

What is the domain of the function graphed below?

ADD GRAPH

What is the range of the function when the domain is {1, 3, 5}?

What is the domain of the set {(-3,2), (-2,6), (5,-1)}?

What is the range of the function ?

What is the domain of ?

19.0

Which of the following equations is the quadratic formula?

Which of the following cannot be found using the quadratic formula?

The slope of a linear equation.

The number of x-intercepts of a 2^nd degree polynomial function.

The x-intercepts of a 2^nd degree polynomial function.

The solution of a quadratic equation.

What technique can be used to derive the quadratic formula?

Factoring

Completing the square

Graphing

Square root property

When using the quadratic formula to solve , what is the value of b?

Which of the following statements is true?

There are exactly two unique solutions to every quadratic equation.

The quadratic formula can be used to solve equations that cannot be solved by completing the square.

Linear equations can be solved using the quadratic formula.

The quadratic formula can be used to solve all quadratic equations in one variable.

20.0

Find the roots of the equation:

Solve:

21.0

Graph:

If the solutions of an equation are -2 and 3, what is true about the graph of ?

Its x-intercepts are (2,0) and (-3,0)

Its x-intercepts are (-2,0) and (3,0)

Its x-intercept is (-2,0) and y-intercept is (0,3)

Its y-intercepts are (0,2) and (0,-3)

If the equation has no real solution, what is true about the graph of the equation ?

The graph has no x-intercepts

The graph has exactly 1 x-intercept

The graph has 2 x-intercepts

The equation cannot be graphed

Graph

Which quadratic function is graphed below?

ADD GRAGH AND EQUATIONS

22.0

Determine the number of x-intercepts found in the graph of each quadratic function

23.0

A firecracker is launched from a launch pad which is 6 feet above the ground. The height h, in feet, of the firecracker shell t seconds after it is launched is given by When is the shell 160 feet from the ground?

The motion of a ball scooped by a field hockey player can be modeled by , where t is the time in seconds and h is the height of the ball. When will the ball reach 25 feet?

The stopping distance of some cars can be modeled by where v is the speed of the car in miles per hour and d is the stopping distance in feet. According to this model, what is the speed a car whose stopping distance is 75 feet?

The height h of a ball on the moon t seconds after it is thrown upward with an initial velocity of 5 meters per second is modeled by . When will the ball land on the moon?

A rock is thrown from the top of a tall building. The distance d, in feet, between the rock and the ground t seconds after it is thrown is given by . How high will the rock be after 5.5 seconds?

24.0

If it is raining, the sidewalk will be wet.

What is the hypothesis of the statement?

Rain causes the sidewalk to be wet.

It is raining.

The weather influences the environment.

The sidewalk will be wet.

What conclusion can be drawn from the statement if it is not raining?

The sidewalk is dry.

It may be raining.

The sidewalk is wet.

No conclusion can be drawn.

If the sidewalk is wet, which of the following statements is true?

It is raining.

No conclusion can be drawn.

It is not raining.

The grass is wet.

If is a real number, then is positive.

Which of the following is true?

The statement is true because

The statement is false because

The statement is true because

The statement is false because

All cats have whiskers.

Using only the statements above, which of the following statements is false?

If an animal has whiskers, it is a cat.

If an animal is a cat, it has whiskers.

Some cats have whiskers.

If an animal does not have whiskers it is not a cat.

What conclusion can be drawn from the statements?

My friend will come to dinner.

I will invite my friend to dinner.

I will cook on Friday.

I will have enough money to take my friend to dinner.

What kind of reasoning is required to draw a conclusion?

Deductive reasoning

Inductive reasoning

Recursive reasoning

All the above.

Sara gets hives each time she eats strawberries. From this information alone, her doctor concludes that she is allergic to strawberries. What kind of reasoning does the doctor use?

Deductive reasoning

Inductive reasoning

Recursive reasoning

All the above.

If x - y = 0, then x = y

Why is the statement true?

The statement is true because 3 – 3 = 0.

The statement is true because it is true for an infinite number of values.

The statement is true because 4 – 3 0

The statement is true by the addition property of equality.

If x and y have different signs then xy 0.

Using only the statements above, what conclusion can be reached about p and q if p and have different signs?

Which of the following statements can be concluded from x + 2 < y and y < 2x + 7?

X + 2 < 2x + 7

X + 2 > 2x + 7

2 < 7

No conclusion can be made

Which of the following statements can be concluded from the equation (x + 5)(x- 6) = 0?

X = 0

X = 5 or x = -6

X + 5 = 0 and x – 6 = 0

X + 5 = 0 or x – 6 = 0

Consider the “proof” of the assertion: If x – 6 < 3, then <81.

Step 1: x – 6 < 3 1. Given

Step 2: x<9 2. Addition Property of Equality

Step 3: 3. Square both sides.

Step 4: 4. Simplify

Which of the following statement is true about the proof?

The proof is valid.

The proof has an error in step 2.

The proof has an error in step 3.

The proof has an error in step 4.

If x < y, which of the following statements is false?

X + 5 < y + 5

X - 5 < y – 5

-2x < -2y

2x < 2y

Which expression is not defined for x = 3?