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Algebra 1 FSA Study Set
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Gravity
Terms in this set (86)
Box and Whisker Plots
Use the five number summary (the minimum value, lower quartile, median, upper quartile and the maximum value) to show spread in a data set.
Interquartile Range (IQR)
The difference of Q3 (upper quartile, or - median of upper half of data) and Q1 (lower quartile, or - median of lower half of data).
Histogram
Like a bar graph, but no space between bars on the graph AND - data have been organized into intervals.
Formula for Area of a Circle
A=πr^2 (pi times the radius squared.) Be sure to square the radius first, according to PEMDAS, before multiplying by pi (3.14).
Circumference of a Circle
The "perimeter" of a circle. The formula is pi times diameter.
You just solved an equation and got 5 = 0. 5 doesn't equal zero. What does this tell you about the solutions to the equation?
There are no solutions.
You just solved an equation and got 5 = 5 (this is called an identity). What does this tell you about the solutions to the equation?
All real numbers are solutions.
Commutative Property (addition and multiplication only).
Change the order of the addends or factors & you'll still get the same sum or product.
Associative Property (addition and multiplication only).
Group the addends or factors in any way and you'll still get the same sum or product.
Polynomials are CLOSED under addition, subtraction and multiplication. This means...?
You can add, subtract or multiply polynomials and the result will always be a polynomial.
Polynomials are NOT closed under...?
Division.
The coefficient of a term is the...?
Numerical factor. So in the term 7ab, 7 is the coefficient.
Define "set".
A collection of objects or numbers that's often shown using braces. {3, 5, 7, 9} is a set. Each number within the set is called an "element" of the set.
Domain
x-values
Range
y-values
Independent variable
x
Dependent variable
y
A "mapping" shows how each element of the domain relates to the elements of the range. You can tell if the relation is NOT a function if...?
It's not a function if one of the x-values (elements of the domain) is paired with more than one y-value (elements of range). Remember the analogy - the domain represents kids in our algebra class. The range represents their averages in class. One student (domain) can't possibly have two different averages at the same time, but two different students (elements of the domain) can have the same grade in class (elements of the range).
How can you tell if a graph is a function or not?
Use the vertical line test. If a vertical line intersects the graph more than once, the graph isn't a function.
In function notation, y is most typically expressed as:
f(x)
How do you solve consecutive integer problems?
Consecutive integers are numbers that go in sequence/counting order. Consecutive integers can be represented like this: x, x+1, x+2, etc. Example: Find three consecutive integers with a sum of 21. You'd write: x + (x+1) + (x+2) = 21. Then combine like terms and solve. When you've solved for x, you can extrapolate the other two integers.
How do you solve consecutive EVEN or ODD integer problems?
Consecutive even or odd numbers can be represented like this: x, x+2, x+4, etc. Example: Find three consecutive odd integers with a sum of 75. You'd write: x + (x+2) + (x+4) = 75. Combine like terms to solve. When you've solved for x, use that value to extrapolate the other two integers.
When solving absolute value equations, there are two cases to consider...what are they?
(1) That the expression inside the absolute value bars is positive or zero, and (2) That the expression inside the absolute value bars is negative.
What is cool about proportions?
Their cross products are always equal.
How do you solve a proportion? For example: (4v + 7)/15 = (6v + 2)/10 *Note - this is hard to type into Quizlet...imagine these two division problems written as fractions and set equal to one another.
Remember that cross products of proportions are always equal. Multiply the numerator of one fraction by the denominator of the other, and set that product equal to the product of the denominator of the first fraction and the numerator of the second. Then solve the equation. In the sample problem, x = .8!
How do you write "3% of x" algebraically?
.03x
How would you write "3% more than x" algebraically?
1.03x
A linear function, when graphed, makes a ... (don't miss this one.)
Line.
In a linear function, the x-intercept can be found by substituting WHAT for y? (Hint, when a graph crosses the x-axis, what is the value of y?)
0
In a linear function, the y-intercept can be found by substituting WHAT value for x?
0
What is the parent function of a linear equation?
f(x) = x
What does the parent function of a linear equation look like when graphed?
It's a line with the slope (rate of change/constant of variation, "k", or "m", coefficient of the x term, etc - they all kind of mean the same thing) of ONE, passing through the origin (0,0).
Zeros, roots, solutions of equations are also known as the ... ?
x-intercepts
"Change in y over the change in x" is otherwise known as...?
Slope, or rate of change.
The slope of a line, using two points on the line, can be found by...?
m = (y - y) OVER (x-x)
What's the slope of a vertical line?
Undefined
What's the slope of a horizontal line?
0
What would this graph look like? y = 3
A horizontal line passing through (0, 3).
How many x-intercepts would this line have? x = 6
One, at (6,0). It's a vertical line passing through the x-axis at positive 6.
Arithmetic sequences have a common...
difference. An example would be 3, 5, 7, 9... the common difference, or "d" of the arithmetic sequence would be 2.
What is the common difference (d) of this arithmetic sequence? 33, 29, 25, 21, 17...
-4
How do you find the "nth term" of an arithmetic sequence? For example, find the ninth term of this sequence: -12, -8, -4, 0...
an = a1 + d(n-1). This means that the "nth term" (an) is equal to the initial term in the sequence (a1, which in this case is -12) plus the common difference (d, which in this case is 4), times the difference of n and 1 (in this case, n is 9 because we are being asked to find the "nth term". The ninth term in the sequence would be 20.
The equation used for a line written in slope-intercept form is:
y = mx +b
y = mx + b; What does b represent?
The y-intercept
Write the equation for a line passing through (4, 2) and (-2, -4).
First find the slope (difference in y-values over difference in x-values). Then - using y = mx +b, plug in the slope for m, and use one of the points given for x and y. Then solve for b. Rewrite the equation in slope-intercept form. For this one - y = x - 2.
Parallel lines have the same...
Slope.
A line perpendicular to this line y = 5x + 2 has what slope?
negative one-fifth. Perpendicular lines have "opposite reciprocal" slopes. So - take the slope of your original line (5), and flip it (reciprocal) and change its sign. - 1/5.
A scatterplot shows positive correlation if....
The bivariate data (data in two variables, x and y) graphed tend to show a positive slope when the line of best fit is sketched. In English - if the dots seem to trend upward as x increases, there's a positive correlation.
A scatterplot shows negative correlation if....
The bivariate data graphed shows a negative slope when the line of best fit is sketched.
A scatterplot shows no correlation when the bivariate data graphed looks like what?
snow. Everywhere on the coordinate plane with no correlation at all.
Correlation coefficient
This number tells you if the correlation is positive or negative. Also - the closer the correlation coefficient is to -1 or 1, the more closely the graph models the data.
An inverse relation is...?
Changing the x and y coordinates. So the inverse of (3,5) is (5,3).
When graphing an inequality in one variable, what type of dot would you use on the number line for these two symbols? < , >
Use an open dot.
When graphing an inequality in one variable, you'd use a CLOSED DOT for which two symbols?
Greater than or equal to and less than or equal to.
When solving an inequality, you have to flip the inequality symbol as you solve each time you....?
Multiply or divide each side of the inequality by a negative number.
When graphing boundary lines for systems of inequalities, you use a DASHED line for what type of inequalities?
< or >
A solid line is drawn when graphing systems of inequalities when the symbols are...
Greater than or equal to and less than or equal to.
How would you solve this compound inequality?
-2 < x - 3 < 4
Write two separate inequalities and solve both. (1) -2 , x - 3 and (2) x - 3 < 4. Solve both and then graph the intersection.
How can you be absolutely sure you have graphed and shaded a system of inequalities correctly?
Choose a test point within the shaded areas of your graph. Substitute the x and y values of your test point into the original inequalities. If the statements are true, the graphs are correct. If they're not - try again.
Systems of equations can result in three relationships. They can have exactly ONE solution, an infinite number of solutions, or no solutions. Think (before clicking the answer) about what the graphs of these systems would look like in each scenario.
One solution - the graphs of the two lines intersect in only one point. Infinite solutions - the graphs of the two lines are exactly the same, meaning all (x,y) values would satisfy either equation. No solutions - the lines would be parallel and would never intersect.
There are several ways to solve a system of equations. How would you solve this one?
y = 4x - 6
5x + 3y = -1
Right. Substitution. The first equation is already solved for y, so you can just substitute (4x - 6) in place of y in the second equation and solve.
There are several ways to solve a system of equations. How would you solve this one?
4x + 6y = 32
3x - 6y = 3
Right again! Elimination!! If you add the equations vertically, the x terms cancel each other out, therefore ELIMINATING a variable. Ahh. Nice, now you can solve.
You just solved this system of equations:
y = 2x
y = 6 - x
You got (2,4). How can you be ABSOLUTELY sure your answer is correct?
Yes, you could graph it and see if the two lines really intersect in the point 2,4. But even better - substitute 2 for x and 4 for y in BOTH equations and make sure they work.
How would you simplify b^3 times b^6?
When you multiply powers with the same base like these, you just add the exponents. So the answer is b^9.
How would you simplify (4b^7)^2? This means "Four times b to the seventh, all raised to the second power".
16b^14. When you raise powers to powers, multiply the exponents.
When you divide powers that have the same base, like x^7/x^5, what is the rule for the exponents?
Subtract the exponents. The example would equal x^2.
When there is a negative exponent in an expression, is the expression simplified? If not - what can you do to get rid of the negative exponent?
x^-2 = 1/x^2 (flip the negative power to the opposite - either the numerator or the denominator - and make it positive).
How do you raise a fraction to a power? Like (x^5/y^3)^2.
Raise both dividend and divisor to the power. Answer: x^10/y^6.
Rational Exponents - I'm not going to attempt to type these into Quizlet because they will look confusing. Please refer to pages 406 - 413 in your textbook to review these thoroughly before the FSA.
Thank you.
This is a number written in scientific notation.
6.32 x 10^9
Rewrite it in standard form.
6,320,000,000 (the exponent was 9, so the decimal moved nine times to the right).
This is small number written in scientific notation.
4 x 10^ -7
Rewrite it in standard form.
0.0000004 (the exponent was -7, so the decimal moved left 7 spaces.)
Write this number in scientific notation:
201,000,000
2.01 x 10^8
What is the equation for exponential growth?
y = a(1+r)^t
y = the ending amount
a = the initial (beginning) amount
r = the rate of change (percent usually) expressed as a decimal
t = time
What is the equation for exponential decay?
y = a(1-r)^t
y = the ending or final amount
a = the initial (or beginning) amount
r = the rate of change (usually a percent) expressed as a decimal
t = time
Geometric Sequences are sequences of numbers that have a common factor or ratio. Like this: 6, 24, 96, 384. Notice the terms don't increase by a common DIFFERENCE (that's an arithmetic sequence), but they're increasing by a common factor of 4.
That's the difference between arithmetic and geometric sequences.
To find the "nth term" of a geometric sequence, use this formula:
an = a1r^(n-1)
an = the value of the nth term
a1 = the value of the first term in the series
r = the common ratio (or common factor)
n = the number of the term in the sequence you are trying to find)
What's the degree of this polynomial?
5y - 9 - 2y^4 - 6y^3
4. When you rewrite the polynomial in standard form (decreasing degrees of monomials), the leading term is 2y^4, and so 4 is the degree of the polynomial.
What's the leading coefficient of this polynomial?
8 - 2x +4x^5 - 3x^2
4. 4 is the coefficient of the term with the highest degree (4 x^5).
-4^2 = ?
-16
(-4)^2 = ?
16
What is 5x^2, when x = 2?
20
What does foil mean, and when can it be used?
"first, outside, inside, last" - used to multiply binomials.
Multiply.
(6x +5) (2x^2 - 3x - 5)
12x^3 - 8x^2 - 45x -25
Use the zero product property to solve:
(x - 8) (x +7) = 0
x = 8, x = -7
Factor our the GCF:
*By the way, this is always the first step in factoring quadratics...
-4a^2b - 8ab^2 + 2ab
2ab(-2a - 4b +1)
Solve x^2 + 6x = 27
The roots are 3 and -9.
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