standard #1: write an algebraic expression from a word problem. text section: 1.1
TRANSCRIPT
Standard #1:Write an Algebraic Expression
from a word problem.
Text Section: 1.1
Reminders
KEY WORDS•Sum, Increased by, More Than, Plus•Difference, Less Than, Decreased by
•Product, Per, Groups of, Times•Quotient, Divided by, Ratio
ExamplesAddition:
4 plus a number 5 more than a number A number increased by 3 The sum of a number and 2
Subtraction:The difference of a and b *** 3 less than a number ***A number decreased by 8 A number less 6
Multiplication:The product of a and b 5 times a number Twice a number
Division:The quotient of a and b A number divided by 8 The ratio of x and y
AnswersAddition:
4 + xX + 5X + 3X + 2
Subtraction:A - bX - 3X - 8X - 6
Multiplication:ab5x2x
Division:a/bx/8x/y
Standard #2:Combine like terms in an
expression.
Text Section: 1.7
Reminders• Distribute First (if necessary)
• Combine ONLY if they have the SAME variable AND SAME exponent!
Examples1. 12x + 30x 2. 6.8y2 – y2
3. 4n + 11n2 4. 1/2x3 + 3/4x3
5. 2(x + 6) + 3x 6. 9 + (x – 4)6
7. -3(-2 – x) + 8
Answers1. 42x 2. 5.8y2
3.4n + 11n2 4. 1 1/4x3
5. 5x + 12 6. 6x - 15
7. 3x + 14
Standard #3:Evaluate an expression.
Text Section: 1.6
Reminders• Use Parentheses when you substitute in for a Variable.
• PEMDAS!!!
Examples1. 5(1-2) – (3-2)
2. – 9 – (-18) + 6 3. 16 [5- (3 + 2²)]
4. 7x (3 + 2x) for x = -1
Answers1. -6
2. 15 3. -32
4. -7
Standard #4:Solve a 1 step equation.
Text Section: 2.1-2.2
Reminders5 Steps!
X + 3 = 10 - 3 - 3 X = 10 -3 X= 7 7 + 3 = 10
Examples1. n – 3.2 = 5.6
2. x + 7 = 9
3. m = 1.5 3
4. 16 = 4c
Answers1. n = 8.8
2. x = 2
3. m = 4.5 4. 4 = c
Standard #5:Solve a 2 step equation.
Text Section: 2.3
RemindersD C (no M) S then 8 STEPS!
2x – 3 = 13 + 3 + 3 2x = 13 + 3 2x = 16 2 2 x = 16/2 x = 82(8)- 3 = 13
Examples1. 6x + 3 – 8x = 13
2. 9 = 6 – (x + 2) 3. 2a + 3 – 8a = 84. 4(x – 2) + 2x = 40
Answers1. x= -5
2. x = -5 3. a= -5/6
4. x= 8
Standard #6:Solve a Multi-step equation.
Text Section: 2.4
Reminders
DCMS(YES, in that order!)
Examples1. 7k = 4k + 15
2. 4b + 2 = 3b
3. 2(y + 6) = 3y
4. 3 – 5b + 2b = -2 – 2(1 – b)
Answers1. K = 5
2. B = -2
3. Y = 12
4. B = 7/5
Standard #7:Write and solve an equation
from a word problem.
Text Section: 2.1-2.4
Reminders• Use Key words, write the equation and solve.• You may need to use DCMS, 5 steps or 8 steps
ExamplesA person’s maximum heart rate is the highest rate, in beats per minute that the person’s heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15-year-old.
Answers15 + x = 220
X = 205
Standard #8:Solve an Absolute Value
Equation.
Text Section: Ch 2 Extension
RemindersIS IT ALONE????IS IT NEGATIVE?
•If an absolute value equation equals a positive number there are two solutions.•If an absolute value equation equals 0 there is one solution.•If an absolute vale equation equals a negative number there are no solutions.
Examples1. 4|x + 2| = 20
2. |x| - 3 = 4
3. |x + 3| + 4 = 4
4. 5 = |x + 2| + 8
Answers1. x = 3, x = -7
2. x = 7, x = -7
2. x = -3
3. no solution
Standard #9:Isolate a Variable.
Text Section: 2.5
Reminders•Use Opposite Operations
to get the Letter all by itself.
Examples1. Given d = rt, solve for t
2. Given A = ½ bh, solve for b
3. Solve m – n = 5 for m
1. Solve m = x for k
k
Answers1. t = d/r
2. B = 2a/h
3. M = 5 + n
4. K = m x
Standard #10:Write an inequality from a
word problem.
Text Section: 3.1
Reminders< > ≤ ≥ ≠
A < B A > B A ≤ B A ≥ B A ≠ B
A is less than B
A is greater than B
A is less than or
equal to B
A is greater than or
equal to B
A is not equal to B
ExamplesWrite in Words
1.b < - 1.5
2.r ≥ 2
3.5 ≥ w
4. -1/2 < a
Answers1. All real numbers less than - 1.5
2. All real numbers greater than or equal to 23. All real numbers less than or equal to 5
4. All real numbers less than - 1/2
Standard #11:Solve an inequality by
adding and subtracting.
Text Section: 3.2-3.3
RemindersSame 5 Steps as solving an
Equation.
X + 3 < 10 - 3 -3 X < 10 -3 X< 7
Examples1. x + 9 < 15
2. d – 3 > - 6
3. 0.7 ≥ n – 0.4
4. 2 ½ ≥ - 3 + t
Answers1. x < 6
2. d > - 3
3. n< 1.1
4. T < 5 ½
Standard #12:Solve an inequality by
multiplying and dividing.
Text Section: 3.4-3.5
RemindersSAME 5 or 8 Steps with 1 TRICK
If you Multiply or Divide BY (not into) a Negative-
you MUST flip the inequality SIGN!
Examples1. -50 ≥ 5q
2. -42 ≤ 7x
3. 10 ≥ -x
Answers1. q≥ -10
2. x ≥ -6
3. x ≥ -10
Standard #13:Solve an Absolute Value
Inequality.
Text Section: Ch 3 Extension
RemindersIS IT ALONE????
Set up TWO inequalities: Flip the sign AND Negative!
**Tip: Remember “less thAND”**
**Tip: Remember “greatOR”**
Examples1. |x|-3<12
2. |x-4|+7≤-2
3. |x|-20>-13
4. |x-8|+5≥11
Answers1. X < 15 AND x > -15
2. No solution
3. X > 7 OR x < -7
4. X > 14 OR x < 2
Standard #14:Graph an inequality on a
number line.
Text Section: Chapter 3
RemindersGraph on a Number LineOpen Circle when it is < or >Closed Circle when it is < or >Shade Left or Right???
Make sure your solution has the Variable on the left side BEFORE you Graph.
Examples
Graph1.b < - 1.5
2.r ≥ 2
3.5 ≥ w
4. -1/2 < a
Answers1.
2.
3.
4.
Standard #15:Interpret/Describe
solutions of an inequality.
Text Section: Chapter 3
RemindersAT LEAST >
AT MOST <
MORE THAN >
LESS THAN <
Examples1. Give three possible solutions. 5s > 10
2. Which inequality has the solution shown? d < -3 a. 4 > d + 7 c. d – 8 < - 5b. 9 + d > 6 d. 2 < - 1 + d
3. Which inequality has -2 as a solution?a. 2x > 4 b. -2x < 4 c. -2x > 4 d. -2x > -4 4. Which statement justifies the given inequality? x ≥ $300 a. You spent more than $300b. You spent at least $300c. You spent less than $300d. You spent at most $300
Answers1. 3,4,5 etc..
2. A
3. D
4. B
Standard #16:Recognize a function in a
variety of ways.
Text Section: 4.2
RemindersThe x values, MAY NOT REPEAT!!!!Determine if it is a function from:GraphTableChartOrdered PairsMapping DiagramEquation
VERTICAL LINE TEST!
ExamplesIs it a FUNCTION?
1.{(-4,2),(2,3),(0,7),(-4,-1)}
2.
3.
4.
x y−2 5−1 50 51 5
Answers1. No
2. No
3. Yes
4. yes
Standard #17:Identify inputs and outputs.
Text Section: 4.2
RemindersINPUT- X Values
OUTPUT- Y Values
Examples1. List the Inputs
2. List the Outputs {(4,0),(2,-3),(0,-6),(-2,-9)}
x y5 -124 -103 -82 -6
Answers1. (5,4,3,2)
2. (0,-3,-6,-9)
Standard #18:Identify domain and range.
Text Section: 4.2
RemindersDOMAIN- X Values
RANGE- Y VALUES
ExampleWhat is the Domain? Range?
AnswersDomain: (-2,3,4,10)
Range: (-1,0,2,4,6)
Standard #19:Write a rule for a given
function.
Text Section: 4.3
RemindersALL rules Start with:
Y = Ask yourself:
“what do I have to do to x to get y???”
Examples1. Write an equation (rule) for the following function.
2. A caricature artist charges his clients a $10 setup fee plus $15 for every person in a picture. a. Write a rule for the artist’s fee. b. Write ordered pairs for the artist’s fee when there are 1, 2, 3, and 4 people in the picture.
x 2 4 6 8y −3 −1 1 3
Answers1. Y = x – 5
2. A. y = 15x + 10 B. (1,25)(2,40)(3,55)(4, 70)
Standard #20:Evaluate an equation in
function notation.
Text Section: 4.3
RemindersSubstitute in for the given Variable
Follow PEMDAS
DCMS
Examples
Answers1. 14
2. 7
3. 15
4. -1
Standard #21:Graph a linear function.
Text Section: 4.4
RemindersLINEAR means LINE
Make sure your graph is a LINE!
Examples1. Graph y = -4x + 2 2. Graph y = 2x – 5 3. Graph y = -x + 3 4. Graph y = 7
Answers1. 2.
3. 4.
Standard #22:Determine if a Relation is a
Linear Function.
Text Section: 5.1
RemindersLINEAR Function (linear is the KEY word)
DO NOT just look at x values, you have to see if there is a common difference in the
x AND the y values!
No Absolute ValuesExponentsSq Roots
Variable in the Denominator
ExamplesIs it LINEAR (not just a function)!
1. {(-4,3), (-1, 1), (2, -1), (5, -3)}
2.
3. Tell which equation is linear. a.y = x+ 2 c. -2y + 5x = 8b.y = 2x3 d. y = |x|+ 2
x -3 -1 1 3 5y 3 7 12 18 25
Answers1. yes
2. no
3. A
Standard #23:Write a function in
Standard Form
Text Section: 5.1
RemindersAx + By = C
“A” can NOT be a fraction OR negative.
If A is negative- change ALL signs.
If there is a fraction, multiply all by the DENOMINATOR!
ExamplesWrite in Standard Form
1. 5x + 3y = -2
2. x-y = 1
3. -9x = 2y -7
4. 2y = ½ x – 5
Answers1. 5x + 3y = -2 a = 5, b = 3, c = -2
2. x – y = 1 a = 1, b = -1, c = 1
3. 9x + 2y = 7 a = 9, b = 2, c = 7
4. x – 4y = 10 a= 1, b = -4, c = 10
Standard #24:Identify Values of A,B, and C
Text Section: 5.1
RemindersIt has to be in Ax + By = C
A, B, and C are Real numbers- NOT variables!!
ExamplesGive values of A,B, and C1.5x + 3y = -2
2.x – y = 1
3. 9x + 2y = 7 4. x – 4y = 10
Answers1. a = 5, b = 3, c = -2
2. a = 1, b = -1, c = 1
3. a = 9, b = 2, c = 7
4. a= 1, b = -4, c = 10
Standard #25:Find the x and y-intercept in a given situation. (equation, graph, word prob)
Text Section: 5.2-5.3
RemindersAnswer MUST BE an ordered pair!
Cover the y, solve for xCover the x, solve for y
ExamplesFind the x and y intercepts of the following.1.2x + 5y = 10
2. –x + 6y = 18
3.You can earn $12 an hour babysitting and $15 an hour raking leaves. You want to make $360 in one week
Answers1. (5,0),(0,2)
2. (-18,0)(0,3)
3. (30,0)(0,22)
Standard #26:Interpret Rate of Change
(slope in a word problem).
Text Section: 5.4
RemindersRate of Change
= SLOPE
= y- yx - x
Examples
x 2 3 5 7 8
y 56 56 63 71 72
The table shows the average temperature for five months. Find the rate of change for EACH time
period.
Answers2-3 = 0
3-5 = 7/2
5- 7= 4
7- 8= 1
Standard #27:Identify Slope as being:
(positive, negative, zero, undefined)
Text Section: 5.4
RemindersPositive
Negative
Zero
Undefined
ExamplesTell whether the slope of each line is
positive, negative, zero, or undefined.1. 2.
3. 4.
6
4
2
-2
-4
-6
-10 -5 5 10
6
4
2
-2
-4
-6
-10 -5 5 10
6
4
2
-2
-4
-6
-10 -5 5 10
6
4
2
-2
-4
-10 -5 5 10
Answers1. positive
2. undefined
3. negative
4. zero
Standard #28:Identify Slope in a given
situation (ordered pairs, table, graph)
Text Section: 5.4
RemindersRiseRun
Up and Over
Y-yX-x
M=
M= M=
M=
Examples1. (-2, -2) and (7, -2)
2.
3. x 1 2 3 4y 18.5 22 25.5 29
Answers1. M = 0
2. M = 2/3
3. M = 7/2
Standard #29:Write an Equation in Slope
Intercept Form from a given situation
Text Section:5.6
Reminders
y = mx + b
m = slopeb = y intercept
ExamplesWrite an equation in SLOPE INTERCEPT FORM
1.m = 4; (-3, 5)
2. (3, -2)(12, 1)
3. 8x – 4y = 16
Answers1. y = 4x + 17
2. y = 1/3x – 3
3. y = 2x - 4
Standard #30:Graph from Slope Intercept Form
Text Section: 5.6
Reminders
Change to y = mx + b
Plot your b (your beginning point)
Up and Over for your slope
Y =Horizontal Line
x =
Vert
ical Lin
e
Y = x
Diagonal Line
Y = x
Diagonal Line
Examples1. x = 2
2. y = - x - 4
3. y = 3x
8. y = -3
Answers1. 2.
3. 4.
Standard #31:Graph from Standard Form
Text Section: 5.2
Reminders
Change to y = mx + b
Plot your b (your beginning point)
Up and Over for your slope
Y =Horizontal Line
x =
Vert
ical Lin
e
Y = x
Diagonal Line
Y = x
Diagonal Line
Examples1. 6x + 3y = 9
2. -4x + 12y = -24
Answers1. 2.
Standard #32:Write an Equation to a
Line Parallel
Text Section: 5.8
RemindersParallel Lines= SAME Slope
1.Slope2.Pt Slope3.Slope intercept
ExamplesGive all 3 Answers for Each.
PARALLEL1. y = 3x + 4; (2, -5)
2. 5x -10y = 20; (-4,2)
Answers1. m = 3 y + 5 = 3(x -2) y = 3x -11
2. m = ½ y – 2 = ½ (x + 4) y = ½ x + 4
Standard #33:Write an Equation to a
Line Perpendicular
Text Section: 5.8
RemindersPerpendicular Lines= Opposite Inverse
Slopes
1.Slope2.Pt Slope3.Slope intercept
ExamplesGive all 3 Answers for Each.
PERPENDICULAR1. y = 3x + 4; (9, -5)
2. 5x -y = 12; (-10,2)
Answers1. m = -1/3 y + 5 = -1/3(x -9) y = -1/3x -2
2. m = -1/5 y – 2 = -1/5 (x + 10) y = -1/5 x
Standard #34:Graph a Linear Inequality
on a Coordinate Plane
Text Section: 6.5
RemindersDashed or Solid?
Shade Above or Below?
Positive or Negative?
Examples1-2 Graph each linear inequality.1.x ≤ -22.y ≥ x + 4
Write a linear inequality for the given graph.
Answers1. 2.
3. Y > -x + 4
Standard #35:Gather data from a
Scatter Plot.
Text Section: 4.5
RemindersDo NOT Connect the dots
Correlations: Positive, Negative, No
Correlation
Examples1. Describe the correlation
2. Predict typos in 12 chapters
Answers1. Positive Correlation
2. Approx 14
Standard #36:Model a Scatter Plot
Text Section: 4.5
RemindersDots- don’t connect
Titles- x and y axis
Examples
Hours Studied
3 5 2 6 4 1 2 7 1 7 0 1 3
Test Grade 65 80 70 80 75 50 65 80 45 95 20 40 70
Graph a scatter plot using the table. Remember to include all aspects of
the graph.
AnswersTest
Gra
de
Hours Studied
Standard #37:Estimate a Line of Best Fit
Text Section: 4.5
Remindersy = mx + b
Check your slope
Check your y intercept
*especially on multiple choice!
Examples1. Estimate the line of best fit
2. Which equation represents the line of best fit for the given scatter plot?
Answers1. y = -x + 5
2. y = -2x - 1
Standard #38:Find the nth term of a
Sequence
Text Section: 4.6
Reminders
an= a1+ (n-1)d
The 1st term in
the sequence
Term you need to find
Common Difference in the sequence
ExamplesFind the given term of each arithmetic sequence.
1.5,2,-1,-4,…; 23rd term 2.-1.1,0,1.1,2.2…; 51st term
3.407,402,397,392…; 17th term
4. 11,21,31,41,…; 33rd term
Answers1. A23= -61
2. A51= 53.9
3. A17= 327
4. A33= 331
Look how the
Answers are
Written!!
Standard #39:Find the Common
Difference in a Sequence
Text Section: 4.6
RemindersCommon Difference is the d in
the formula
Look at the sequence, do the numbers go up (+) or down (-),
and by what value?
ExamplesFind the common difference (d) in
each arithmetic sequence.
1.107,105,103,101,… 2. 4.85, 5, 5.15, 5.3, … 3. 3 ½ , 2 ¼ , 1, -3/4 , … 4. 2, 15, 28, 41, …
Answers1. d= -2
2. d = .15
3. d = - 1 ¼
4. d = 13
Standard #40:Simplify Exponential
Expressions
Text Section: 1.4
Reminders
Words Multiplication Power Value
3 to the first power
3 3 3
3 to the second power or 3 squared
3 * 3 32 9
3 to the third power, or 3 cubed
3 * 3 * 3 33 27
3 to the fourth power
3 * 3 * 3 * 3 34 81
3 to the fifth power
3 * 3 * 3 * 3 * 3 35 243
Examples
1-3 Simplify each expression1.(-2)3
2. -52
3.(2/3)2
Careful with the
Parentheses
Answers1. -252. -83. 4/9
Standard #41:Write Numbers as a Power
of the given base
Text Section: 1.4
RemindersUse the given base
Then find the exponent for that base to get the given
answer.
Examples4-6 Write each number as a power of the given base.
4. 8; base 2 5.-125, base -56.64, base 8
Answers4. 23
5. -53 or (-5)3
6. 82
Standard #42:Zero and Negative
Exponents
Text Section: 7.1
RemindersNO NEGATIVE
Exponents EVER!!!
ANYTHING Raised to the Zero Power is = to 1
Examples1. m-3n2. -3f-3
3. x-7y2
r3v-4
4. 4x-5
y-6
5. (g0h0)7
Answers1. n m3
2. -3 f3
3. v4y2
r3x7
4. 4y6
x5
5. 1
Standard #43:Multiplication of Exponents
Text Section: 7.3
RemindersYou can only multiply powers that
have the same base- if they do you ADD exponents
When you raise a power to a power you MULTIPLY the exponents and leave
the base the same
Check for Negative and Zero Exponents
Examples1. (f4)6 • g
2. m • (h3)4 • (m-2)3
3. (6y8)2
4. (k4)2 • (m-1)-4
NO Negative
Exponents!
Answers1. f24g
2. h12
m5
3. 36y16
4. k8m4
Standard #44:Division of Exponents
Text Section: 7.4
RemindersWhen we divide with exponents
we subtract the exponents.
You can only divide powers with the same base
Examples38 a5b9 y m5n4
32 (ab)4 y4 (m5)2n
All other Rules
still Apply.
Answers1. 36 = 729
2. ab5
3. 1 y3
4. n3
m5
Standard #45:Standard Form to Scientific Notation
Text Section: 7.2
RemindersThe Number has to be > 1 but <
10
Be careful where you put your decimal.
Is your exponent – or + ?
Examples1. .000000802
2. 8127
3. .678
4. 60228
Answers1. 8.02 x 10-7
2. 8.127 x 103
3. 6.78 x 10-1
4. 6.0228 x 104
Watch your
Exponent sign.
Standard #46:Scientific Notation to
Standard Form
Text Section: 7.2
RemindersJust move the Decimal
Negative Exponent- Move Left
Positive Exponent- Move Right
Examples 1. 6.09 X 104
2. 53.8 X 10-5
3. 0.07 X 108
4. 8.1 X 10-2
Answers1. 6090
2. .000538
3. 7000000
4. .081