Mathematics TAKS Exit Level Review
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Transcript of Mathematics TAKS Exit Level Review
TAKS Mathematics Exit Level
Formulas, Rules & Things to Remember
Arc Length _____ =_____
360 2 r
Degree measure
of arc angle x
Degree measure
of arc angle
Arc Length represented
by xFormula for
CIRCUMFERENCE of the whole circle
Number of degrees in a circle
Set a proportion
Questions that ask about degrees, arc length, arc area or involve circles, remember to use proportions!
r
x
Arc AreaArea of Arc, represented
by x
_____ =_____
360 r²
xFormula for AREA of the whole circle
Number of degrees in a circle
Degree measure
of arc angle
Set a proportion
r
x
Degree measure
of arc angle
Sample Data & DegreesSandwiches Sold in One day
Sandwich Sold in a Day
Turkey 40
Meat Balls 25
Ham & Cheese 60
Roast Beef 25_____ =_____
Set a proportion
360
x40
150
Based on how many sandwiches were sold per day, if the data was so be shown in a circle graph what would be the degree measure of the angle for Turkey sandwiches?
Total Number of Sandwiches sold
X represents unknown degrees
Cross-Multiply, solve for x
Answer:
150x=40(360)
x=40(360)/150
x=96
The degree measure of the angle would be 96 degrees
Sample Data
Activity Number of People
Running 30
Biking 70
Rollerblading 45
Ice Skating 55
Sample Data
Based on the sample data about how many students out of a group of 2,300 are more likely to choose ice skating?
_____ =_____
Set a proportion Sample Data proportioned to Needed Data
x55
Total Number in Sample
200 2,300
Cross-Multiply, solve for x
Set a proportion
Answer:
200x=55(2,300)
x=55(2300)/200
x=632.5
There would be approximately 633 students out of 2,300 that would prefer
ice skating.
Similar ShapesSet a proportion
15
8
10
_____ =_____
Find the height of smaller triangle
hH
B b
_____ =_____h8
15 10
Cross-Multiply, solve for h
Answer:
15h=80
h=80/15
h=5.3
Big SmallBig Small
h
Area
Area of Square= x²
Area of rectangle=bxh
Perimeter
Perimeter is the total of all the sides of a polygon
12
12
12
12
P=21P=48
x
x
x
x√2
x√3
2x
45, 45, 90
x, x, x √2
30, 60, 90
x, x √3,2 x
Special Right Triangles
Solving with a 30,60,90 triangle
30
2400
A
B
C
Rule: x, x √3,2 x30, 60, 90
x
2x
x√3
What is the distance from AC= (2400 √3)=4156.9
What is the distance from BC= (2(2400))=4,800
60
30
Finding the x-intercept
Given y=x²+x-12
In your calculator go to y= insert the equation
2nd GRAPH and check when y=0, those are the x-intercepts
For this particular equation the x-intercept is x= -4, x= 3
Use calculator
Finding an Equation Number of Square feet (x) Total Cost (y)
1800 630
2300 805
2900 1015
For questions that have a table with the x and y values and it is asking you to find an equation that represents the data, you need to use your
graphing calculator.
•STAT, 1) Edit
•Put all the x’s under L1, and all the y’s under L2,
•STATCALC, 4)LingReg(ax+b), ENTER
It will give you y=ax+b, the a=is your slope and the b= is your y-intercept.
The answer for this particular questions would be y=0.35x
Use calculator
Setting up Equations As a waiter in a restaurant, Steven works 6-hour shifts. He earns $5 per hour and keeps 80% of his tip money. How much tip money does he need to receive per shift to earn a total of exactly $50 before taxes are deducted?
The equation will be set up as y=mx+b
6(5) + .8(t)=50
30 + .8t=50
.8t=50-30
.8t=20
t=25
Where:y=the total amount earned
mx=80% of tips
b=hourly earnings (wage)
Volume
For volume on the formula sheet the volume of a prism or a
cylinder is V=Bh
For the cylinder the B, is r²
For the prism the B, is lw
Faces, Edges & Vertices
This prism has 5 faces, 8 edges, 5 vertices
The face are the flat sides.
The edges are the intersection of the flat sides.
The vertices are the corners or points.
FOIL- Simplified
Rules for SimplifyingExample
(5n-2)3n-(5n-2)(n-1)
1st step: 15n²-6n-(5n²-5n-2n+2)
2nd step: 15n²-6n-5n²-7n+2
3rd step: 10n²-13n+2
FOIL
combine like terms
Finding the percent (%)The original price of a car is 20,000. Joe bought the car for 15,000. What percent of the original cost did Joe save?
(20,000-15,000)
_____________X 100= %
(20,000)
5,000/20,000 x100= 25%
Joe saved 25% from the original price of the car.
Mean, Median, ModeMEAN is the average
MODE is the one that repeats the most
MEDIAN is the number in the middle when you put the numbers from least to greatest
RANGE is the difference between the biggest number and the smallest number. (big# - small#)
Rules Negative & Positive Numbers The bigger sign indicates that the positive number is bigger than the negative number.
The bigger sign indicates that the negative number is bigger than the positive number.
Things to RememberANGLES & DEGREES• A Circle has 360 degrees• A line is 180 degrees• A triangle has180 degrees • A right angle has 90 degrees
• Complementary angles total 90 degrees
• Supplementary angles total 180 degrees
LINES• When the slope of two lines is the same
regardless of the y-intercept the lines are parallel (they don’t intersect).
• Solution is where two lines intersect
More things to RememberFUNCTIONS• A function is when all the x values DON’T repeatEX: (0,1) (1,5) (-1,3) (10,0) Function (-10,1) (1,0) (1,1) (5,3) NOT a Function, 1’s repeat
DEPENDENT & INDEPENDENT VARIABLES• Y= is the output, dependent variable• X= is the input, independent variable
DOMAIN & RANGE• Domain is all the x-values• Range is all the y-values
Notes
Notes