Algebra | 1-12
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)
Find the vertex of the parabola. y = -2x² - 8x - 3
(-2, 5)
Solve this linear system by substitution: 2x - y = -2 ; 3x - 6y = 15
(-3, -4)
Solve using the Quadratic Formula. x² = -14x - 40
(-4, -10)
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
Divide the rational expression: x² - 14x + 49 ÷ 3x² - 20x - 7 / 2x² - 3x - 14 x² - 6x - 16
(x - 7) (x - 8) / (2x - 7) (3x + 1)
Factor each polynomial by grouping. Check your answer. x³ + 4x² + 2x + 8
(x² + 2) (x + 4)
Solve using the quadratic formula: 8x² - 4x - 24 = 0
- 3/2, 2
Find the real solution of the equation: ³√5 - 2x = 3
-11
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
Find the real solution of the equation: √5 + x = √3x + 6
-½
Subtract. -¾ - (-¼)
-½
What is the solution set for the equation 18t² + 72t = 0
0, -4
Find the discriminant and determine the nature of the solution. 9x² - 48x + 64 = 0
0; one real solution
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.
Find the median of the numbers 11, 21, 6, 17, 9
11
Find the square root. √121
11
Solve the expression as much as possible: 4 ³√128 - ³√250
11 ³√2
Multiply: (2x² + 3x - 4) (6x - 1)
12x³ + 16x² - 27x + 4
Multiply: (3y^5) (4y^4)
12y^9
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
Find the lowest common denominator of 3x³y² and 18xy³
18x³y³
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)
What is one of the solutions for the quadratic equation x² - 6x - 5 = 0
3 + √14
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
Subtract and simplify the radical expression: x - 5 / x - 3 4x - 12
4x - 5 / 4(x - 3)
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
Divide the Polynomial: 15x² + 9x + 27 / 3
5x² + 3x + 9
Write the expression in simplest radical form: √50x^4y³
5x²y √2y
Fill in the missing term in the geometric sequence. -1 4, -16, ____, -256...
64
What number completes the square? x² - 16x + ______
64
Multiply the rational expression: x² - 9 * 7x / x² x² + x - 12
7 (x + 3) / x (x + 4)
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)
Divide the rational expression: 4x + 20 ÷ x + 5 / x - 3 2x - 6
8
Find the real solution of the equation: √4x - 7 - √2x = 1
8
Simplify: 2^8/2^5
8
Write 0.08 as a percent.
8%
What number completes the square? x² + 6x + _____
9
For the geometric sequence, 8, 12, 18, 27, ... find the 7th term.
91 1/8
Find the discriminant and determine the nature of the solution. -2x² +7x - 5 = 0
9; two real solutions
Multiply the expression using distribution and simplify: (2√x + 1) (5 - √x)
9√x - 2x + 5
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.
This is a way to spot biased survey questions:
All of the ways listed are correct
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
______ 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
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
Name the quadrant in which point B lies.
No quadrant
________ are another way to express the likelihood of an event.
Odds
_______ is the simplest measure of dispersion.
Range
This is an example of a _________ plot.
Stem-and-Leaf
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.
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.
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
True or false. If the data is plotted in a random way, then there is no correlation in the data.
True
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
The ________ of a group of numbers is found by dividing the sum of the numbers by the number of values in the group. In other words, we add all the numbers together and divide by the number of numbers.
arithmetic mean
A(n) _______ is a line that a graph gets closer to as the absolute value of a variable increases.
asymptote
Simplify the expression. Write your answer without negative powers. (ab^-5)² /(b²)
a²/b^14
A(n) _______ plot is formed by placing vertical lines at five positions, corresponding to the smallest value, the first quartile, the median, the third quartile and the greatest value.
box-and-whisker
A _______ graph is made of connected lines or curves.
continuous
Multiplying each numerator in the original rational equation by the denominator from the opposite side of the rational equation is known as ______
cross multiplication
Two events are _______ if the occurrence of one event affects the probability of the other event.
dependent
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
A _______ graph is made of only distinct points.
discrete
The function y = 0.68(2)^x is an example of
exponential growth
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
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
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
In a data set, this is a measure of the most common number , or sometimes the most popular choice.
mode
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
Solve using the quadratic formula: 2x² - 9x + 12 = 0
no solution
Determine whether the trinomial is a perfect square. If so, factor. If not, explain. 25x² + 10x + 4
no; 10x ≠ 2(5)(2)
Tell whether the polynomial is completely factored. If not, factor it. 2x(y³ - 4y² + 5y)
no; 2xy(y² - 4y + 5)
The ________ is the point where the x- axis and the y- axis meet.
origin
A ________ is a grouping of outcomes in which the order does matter.
permutation
A _______ is one that cannot be measured numerically but can be placed in a category.
qualitative variable
A(n) _______ equation is an equation that contains one or more rational expressions.
rational
A(n) _______ expression is an algebraic expression whose numerator and denominator are polynomials.
rational
Often when we work with radicals, we end up with a radical expression in the denominator of a fraction. It's traditional to write our fractions in a form that doesn't have radicals in the denominator, so we use a process called _______ to eliminate them.
rationalizing the denominator
A ______ is a graph showing many data points.
scatter plot
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
There are several ways to choose a population sample from a larger group. The two main types of sampling are random sampling and _______
stratified sampling
Changing the value of b in f(x) = mx + b results in a _____ of the graph.
translation
A(n) _______ is a ratio of the lengths of two sides in a right triangle.
trigonometric ratio
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.
Multiply the rational expression: x² + 6x + 9 * x² - x - 20 / x² - 10x + 25 x² + 7x + 12
x + 3 / x - 5
Simplify and find the excluded value: x² - 7x + 10 / x² - 2x - 15
x - 2 / x + 3 ; x ≠ -3 , 5
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 the quadratic equation: (x - 2)² - 9 = 0
x = -1, 5
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
Use cross multiplication to solve the equation: 2x 5 / x + 4 = x
x = -2.15 or x = 4.65
Solve 17(3x + 4) = 7
x = -61/51
Solve: x(6x - 7) = 0
x = 0, 7/6
For this quadratic function, find the axis of symmetry of its graph. y = ½x² - 5x + 4
x = 5
Solve the quadratic equation: 25x² - 36 = 0
x = ±6/5
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
Tell whether this equation represents a direct variation. If so, identify the constant of variation. 4y = x
yes, ¼
Write the expression as an exponent with a rational value for the exponent. ³√4xy
³√4xy = (4xy)^1/3