Algebra 1 Final Review Set

Algebra 1 Final Review Set

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Section 1

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Solving a System of Equations by Elimination Method - Adding Equations

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Cards (36)

Section 1

(36 cards)

Solving a System of Equations by Elimination Method - Adding Equations

Front

Notice in this example one equation has 6y and the other has -6y. So, by simply adding the equations, they y-values cancel out leaving you with x = 2. Then you plug the x-value in ANY one of the original two equation to find the y-value

Back

Same (overlapping) Lines Equations - 2 Cases

Front

Case 1. They have the same equation ex: y = 2x + 5 y = 2x + 5 Case 2. The equation of one is a multiple of the equation of the other y = 2x + 5 -2y = -4x - 10 Note that if you multiply the first equation by -2, you obtain the second equation.

Back

Final Review Q.7 - Simplifying Expressions

Front

3 * [ (9-1)^2 / 4 ] = 3 * [ (8)^2 /4] = 3 * [64/4] = 3 * 16 = 48 Note: ^ refers to exponent and / refers to the division sign.

Back

Box and Whisker Plot

Front

Recall: Lower Quartile or First Quartile (Q1) Upper Quartile or Third Quartile (Q3) Median (Q2) Min Max Range = Max - Min Interquartile Range (IQR) = Q3 - Q1

Back

Point Slope Form of the Equation of a Line

Front

y - y1 = m (x - x1)

Back

Histogram

Front

The y-axis always represents the frequency axis (how many students, how many cars, how many patients, etc.) and the x-axis represents the intervals.

Back

Find the equation of a line given two points and write it in Standard Form

Front

Find the equation of the line that passes through (-2, 5) and (-3, 4). Step 1. You find the slope using the (attached) slope formula (4 - 5)/(-3 - (-2)) = -1/ -1 = 1 Step 2. Use the slope and one of the points to write the equation in point slope form: y - 5 = 1 (x - (-2) ) Step 3. Distribute and rearrange the terms so they are in the Ax + By = C form: y - 5 = x + 2 y = x + 7 (by adding 5 to both sides) -x + y = 7 (by subtracting x from both sides) A = -1, B = 1, C = 7 (if you ended up with x - y = -7, that is also correct)

Back

Standard Form of the Equation of a Line

Front

Ax + By = C

Back

Is this relation a function? From table of values

Front

Each value in the domain can have at most one value in the range and no two values in the range can have the same value in the domain. See image for more info.

Back

Slopes of a line: Positive, Negative, Zero, and Undefined.

Front

Looking at the slope guy. Positive slope: as we move from left to right, the line goes up Negative slope: as we move from left to right, the line goes down Vertical line: undefined slope (the nose is the u) Horizontal line: slope is zero

Back

X-intercept

Front

The point at which a line intersects the x-axis. This point is in the form (x, 0) In 2x + 4y = 8, to find the x-intercept, set y = 0 This gives: 2x + 0 = 8 2x = 8 x = 4 The x-intercept is (4, 0)

Back

Vertical and Horizontal Lines

Front

Vertical line: x = number. The slope of this line is undefined. Horizontal line: y = number. The slope of this line is 0

Back

Scatterplot and Correlation

Front

Recall positive, negative, and no correlation. Make sure you know how to explain an ordered pair in the context of a given problem.

Back

Solutions to equation versus inequality

Front

Notice for equation, you have one answer (one value = one point) but for inequalities you have a range of values.

Back

Slope-intercept Form of the Equation of a Line

Front

y = mx + b

Back

Multi-step Inequality

Front

9 + 4t > 21 Step 1. subtract 9 from both sides: 4t > 12 Step 2. Divide both sides by 4: t > 3 Graph your solution (open circle and to the right of 3)

Back

Order Pair

Front

A pair that identifies the location of a point. An ordered pair is always in the form (x, y)

Back

Algebraic Expression

Front

A mathematical phrase that can include numbers, variables, and operation symbols

Back

Solving a System of Equations by Elimination Method - Multiplying Both Equations

Front

See textbook page 290 Example 5

Back

Quadrants of the xy Coordinate Axes

Front

In Quadrant 1, x and y are both + In Quadrant 2, x is - and y is + In Quadrant 3, x and y are both - In Quadrant 4, x is + and y is -

Back

Slope of a Line

Front

The slope, m, of a line is defined a the RISE over the RUN and given by the equation: m = (y2- y1)/(x2- x1) - See image

Back

Equation

Front

A mathematical sentence that uses the equal sign. The example shows an algebraic equation NOT an algebraic expression

Back

Rational Number

Front

Any number that can be written in the form a/b, where a and b are integers and b is not equal to 0

Back

Inequality

Front

A mathematical sentence that compares the values of two expressions using one of five symbols

Back

Parallel v. Perpendicular Lines

Front

Example y = 2x + 2 and y = 2x + 7 are parallel because they have the same slope. y = 2x + 3 and y = -1/2 x + 8 are perpendicular because the slope of one is the opposite of the reciprocal of the slope of the other. You can also see that for two lines to be perpendicular, the product of their slopes is equal to -1. In this example, 2 * (-1/2) = -1.

Back

Writing a Rule for a Sequence & Finding the nth term

Front

Ex: Write an expression to describe a rule for the sequence: -1, 4, 9, 14, 19,... Then find the 90th term. Answer: Rule: 5n - 6 (Since the difference from -1 to 4, and from 4 to 9, and from 9 to 14 etc. is 5, I start by writing 5n. Then, I plug in n = 1 to see if my first value is off or not. For n = 1, 5n becomes 5*1 = 5. Since the first term of the sequence is - 1 not 5, we need to subtract 6. Our formula is now 5n - 6. Check to make sure the formula works for n =2, n = 3, etc. To find the 90th terms, plug in n = 90 in the expression. We now have: 5 * (90) - 6 = 450 - 6 = 444. The 90th terms is equal to 444.

Back

Solving an Inequality Example

Front

Only when you multiply or divide an inequality by a negative or swap the position of the elements (example from x > 5 to 5 < x), you are allowed to switch the sign of the inequality)

Back

P.E.M.D.A.S

Front

Acronym used to remember the order of operations. For PEMDAS remember to also use the LEFT to RIGHT rule

Back

Solving an Equation Example

Front

Sometimes we use the term evaluate, meaning find the value of the variable. This is the same as solving for the variable.

Back

System of Linear Equations - 3 Possible Scenarios

Front

Scenario 1. One solution = one point of intersection Scenario 2. No solution = no points of intersection (the lines are parallel) Scenario 3. Infinitely many solutions = infinitely many points of intersection (the two lines overlap)

Back

Is this relation a function? Vertical Line Test

Front

A visual test that determines if a relation is a function. If a vertical line drawn anywhere on the graph meets the graph at 2 or more points, then the graph is not that of a function.

Back

Solving a System of Equations by Elimination Method - Multiplying One Equation

Front

See textbook pages 288-289 Example 3

Back

Solving a System of Equation by Substitution Method

Front

Step 1. Solve for one of the variables. Step 2. Substitute the right-hand side of the variable you just solved for into the second given equation. This allows you to solve for the value of the second variable. In the given example, step 1 was already done as we have y = 2x + 1 In step 2, (2x + 1) was substituted for y in to the second equation. This gave us x = 4 Step 3. plug the value found in step 2 (here, x = 4) in to the equation in step one to solve for the other variable (here, y)

Back

Mean Median Mode

Front

Mean = average of numbers Median: Step 1. Arrange values in order from least to greatest Step 2. Eliminate the values left and right. The value at the center is the median. If there are two values left in the middle, average them. The average is the median. Mode: the most repeated value in a set. A set can have more than one mode.

Back

Y-intercept

Front

The point at which a line intersect the y-axis. This point is in the form (0, y) In 2x + 4y = 8, to find the y-intercept, set x = 0 This gives: 2(0) + 4y = 8 4y = 8 y = 2 The y-intercept is (0, 2)

Back

Solving for x in a perimeter question (Question #18 -Final Review)

Front

Perimeter of a rectangle = 2 l + 2 w This gives us: 62 = 2 (3x) + 2 (13) 62 = 6x + 26 36 = 6x x = 6 cm (Make sure you include the units in your answers. Here the units are cm)

Back