Algebra 1

Solve the system by elimination: 4x + y = -1, 2x - y = -5

(-1, 3 )

Solve this linear system by substitution: y = 5 - x ; 4x + 3y = 1

(-14, 19)

Solve the system of linear equations y= 3x + 2; y= 2x

(-2, -4)

Solve by completing the square. x² - 10x = 24

(-2, 12)

Solve this linear system by substitution: 2x - y = -2 ; 3x - 6y = 15

(-3, -4)

Find the intercepts of the following equation: 7x - 3y = 21

(0, -7) is the y-intercept and (3, 0) is the x-intercept.

Factor the trinomial, if possible. 4x² - 12x + 9

(2x - 3) (2x - 3)

Factor out the common binomial: x(4x + 5) + (4x + 5)

(4x + 5) (x + 1)

Factor the trinomial by grouping. Check your answer. 12y² + 17y - 5

(4y - 1) (3y + 5)

Factor the quadratic trinomial by grouping: 5x² - 6x + 1

(5x - 1) (x - 1)

Factor each polynomial by grouping. Check your answer. 7r³ - 35r² + 6r - 30

(7r² + 6) (r - 5)

Factor the polynomial completely. Check your answer. 2k³ + 3k² + 6k + 9

(k² + 3) (2k + 3)

Factor the difference of the square: x² - 100

(x + 10) (x - 10)

Factor the perfect square trinomial: x² + 14x + 49

(x + 7)²

Simplify this expression. (-4²)

-16

The value of y varies directly with x, and y = 8 when x = -32. Find y when x = 64

-16

Simplify the polynomial 3x - 4x² + 7 + 2x² - 3 + 5x

-2x² + 8x + 4

Divide. 3/20 ÷ (-¼)

-3/5

Add -18 + (-12)

-30

Simplify this expression -7(x + 2) + 4x

-3x - 14

Subtract x³ - 2x² + 7x + 13 from 6x² + 4x - 5

-x³ + 8x² - 3x - 18

Subtract. -¾ - (-¼)

-½

What is the solution set for the equation 18t² + 72t = 0

0, -4

Multiply 17(1/17)

1

Evaluate the expression and write your answer in scientific notation. (2.1 x 10^4) (7.3 x 10^8)

1.533 x 10^13

Dwayne was told by his chemistry teacher to measure the weight of an empty beaker using a balance. Dwayne found only one-pound weights, and so devised the following way of balancing the scales. Knowing that each weight is one lb, calculate the weight of one beaker.

1/3lb = x The weight of the beaker is one-third of a pound.

Convert 32.5% to a fraction.

13/40

Simplify this expression 7y - 3 + 6y - 7

13y - 10

Simplify: (5³)²

15,625

Simplify: (2x²y³) (3x²y²)²²

18x^6 y^7

Evaluate this expression for r= 6, s= 5, and t= 3. r ÷ t

2

Find the value of this expression 9.75 + (-7 ¾)

2

Evaluate the expression and write your answer in scientific notation. (4.8 x 10^-5) (4.4 x 10^-4)

2.112 x 10^-8

Evaluate the expression for x = 3, y = -1, and z = 2. (5xy³)² /( 4z²)

225/256

Convert 2/7 to a percent rounded to the nearest tenth.

28.6%

Factor the polynomial completely. Check your answer. 98x³ - 50xy²

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

Solve the compound inequality: 1 ≤ 2n - 5 ≤ 7

3 ≤ n ≤ 6

Multiply and simplify: (6x + 8y) (6x - 8y)

36x² - 64y²

Solve for n when 2(n + 9) = 6n

4.5 = n

Find the missing term in this perfect-square trinomial. x² + 14x + . . .

49

Find the missing term in this perfect-square trinomial. ____ -36y + 81

4y²

Define the variable and translate the following expression into an inequality: "The sum of 5 and a number is less than or equal to 2"

5 + n ≤ 2

Find the indicated term of the arithmetic sequence: 31st term: 1.40, 1.55, 1.70 ...

5.9

Add 3/8 + ¼. Write the answer in simplest form.

5/8

Write the number in scientific notation. 789, 521, 000

7.89521 x 10^8

The chart for converting temperature from Fahrenheit to Celsius is shown. Use the graph to convert the following: 70˚Fahrenheit to Celsius

70˚Fahrenheit is approximately equivalent to 21˚Celsius.

Write this division expression as a multiplication expression. 75 ÷ 15

75(1/15)

Simplify: 2^8/2^5

8

Triangle ABC is shown in the diagram shown. Find the coordinates of the vertices A,B and C

A (-2, 5) B( 3, -3) C (-4, -1)

The _______ of a number is its distance from zero on a number line.

Absolute value

Which is a common strategy in problem solving?

All of the above.

Give the domain and range of this relation: {( -5, 7), (0, 0), (2, -8), (5, -20)}

D: {-5, 0, 2, 5} R: {-20, -8, 0, 7}

Identify the following system as consistent, inconsistent or dependent. 4x + y = 3; 12x + 3y = 9

Dependent

Name the property that is illustrated in the equation. 3(2r - 7) = 3(2r) - 3(7)

Distributive Property

A trend line always passes through every point on a scatter plot.

False

Determine if the ordered pair is a solution of the system of equations. (4, 7); x + y = 3; 5x - y = -27

False

Determine if the ordered pair is a solution of the system of equations. (-5, 1); x + 5y = 0; 2x - y = -9

False

Name the quadrant in which point B lies.

No quadrant

A stretched spring has a length of 12 inches when a weight of 2 lbs is attached to the spring. The same spring has a length of 18 inches when a weight of 5 lbs is attached to the spring. What is the length of the spring when no weights are attached?

The length of the spring with no weights is 8 inches.

Graph each point and connect them in the order they are listed. Connect the last point to the first. Describe the figure drawn. (-6, 3), (2, -2), (-7, -3)

Triangle

The solution of inequality can be expressed in which way?

WRONG: Interval notation

______ is a way of writing the relationship between the two quantities being graphed.

WRONG: ratio

Solve the inequality: 2a - ( -3)² ≥ 13

a ≥ 11

Simplify the expression. Write your answer without negative powers. (ab^-5)² /(b²)

a²/b^14

A _______ graph is made of connected lines or curves.

continuous

A _______ graph is made of only distinct points.

discrete

Evaluate this function for the given input values: For f(x) = 7x + 2, find f(x) when x = 0 & when x = 1

f(0) = 2; f(1) = 9

Identify the independent and dependent variables. Write a rule in function notation for each situation: "A car can travel 28 miles per gallon of gas."

independent variable: gallons of gas; dependent variable: miles; f(x) = 28x

Identify the correlation you would expect to see between each pair of data sets: The volume of water poured into a container and the amount of empty space left in the container.

negative correlation

Tell whether the polynomial is completely factored. If not, factor it. 2x(y³ - 4y² + 5y)

no; 2xy(y² - 4y + 5)

Identify the slope and y- intercept of the following equation: y = 3x + 2

slope of 3 and a y- intercept of (0, 2)

The ________ consists of all the ordered pairs that satisfy all the inequalities in the system.

solution of a system of linear inequalities

Changing the value of b in f(x) = mx + b results in a _____ of the graph.

translation

The kind of solution displayed in this example is called ______, because it continues forever in at least one direction (in this case, forever upward and to the left)

unbounded

A ratio with a denominator of one is called a ________.

unit rate.

Solve the inequality: -2 > 7x - 2(x - 4)

x < -2

Solve the compound inequality: 2x + 1 < 1 OR x +5 > 8

x < 0 OR x > 3

Solve 7x + 2 = 5x - 3 /6

x = -15/37

Solve for x: 0.1(3.2 + 2x) + ½ (3 - x/5) = 0

x = -18.2

Solve 6(x + 4) = 12

x = -2

Solve 17(3x + 4) = 7

x = -61/51

Solve: x(6x - 7) = 0

x = 0, 7/6

Solve the quadratic equation: 25x² - 36 = 0

x = ±6/5

Tell whether this equation represents a direct variation. If so, identify the constant of variation. 4y = x

yes, ¼

Factor each polynomial by grouping. Check your answer. x³ + 4x² + 2x + 8

(x² + 2) (x + 4)

______ are a way that we can relate one quantity to another and they can also be plotted on the coordinate plane.

Functions

Choose the graph that best represents given situation: "A person alternates between running and walking"

Graph B

Name the quadrant in which point F lies.

I

Determine whether the trinomial is a perfect square. If so, factor. If not, explain. 25x² + 10x + 4

no; 10x ≠ 2(5)(2)

Find the square root. √121

11

Multiply: (2x² + 3x - 4) (6x - 1)

12x³ + 16x² - 27x + 4

Multiply: (3y^5) (4y^4)

12y^9

Write 0.08 as a percent.

8%

Identify the independent and dependent variables in this situation. "A small-size bottle of water costs $1.99 and a large-size bottle of water costs $3.49."

Independent variable: size of bottle; dependent variable: cost of water

You arrange tennis balls in triangular shapes as shown. How many balls will there be in a triangle that has 8 rows?

There are 36 balls in a triangle arrangement with 8 rows.

If a linear system has an infinite number of solutions, and the two equations are really just different forms of the same equation, it is called a ________

dependent system

The shaded region in the graph is called the ______. All possible solutions to the system occur in that region.

feasibility region

When Asia was young her Daddy marked her height on the door frame every month. Asia's Daddy noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches and multiplying the result by one-third. Determine her predicted height on her second birthday.

h = 33

Simplify: (x^9 / x^4)²

x^10

Write the equation that describes this line in slope-intercept form. Slope = 8, y - intercept = 2

y = 8x + 2