Relations & Functions

(x, y)D RI D

1

Relations & FunctionsTest administrator: Before administration begins, show students the front of this

card and say:

• Remember that relations and functions are sets of ordered pairs, usually named with x and y coordinates.

• There are other words that are used to describe the x- and y-values in a relationship.

• For example, what do “D” and “R” stand for? Domain and Range• Which goes with the x-values? Domain.• So which goes with the y-values? Range.• What could “I” and “D” stand for? Independent and Dependent• Is the “independent variable” usually x or y? x• So which is dependent? y• Here’s an easy way to remember this chart: Say, “Every DOCTOR (DR) must

have an ID.” It means that x and y (x,y) come in the same order as Domain and Range (D,R) and Independent, Dependent (I,D).

1 Grades 9-11

Slope2

2

3 run

rise

12

12

xx

yy

SlopeTest administrator: Before administration begins, show students the front of this

card and say:

• You probably also know a lot about slope. Slope is a rate of change that tells how quickly a line moves up or down. Sometimes teachers use the phrase “rise over run” to describe slope.

• In this picture, would the slope of this line be 2 over 3, or 3 over 2? The slope is 2 over 3, or two-thirds.

• Yes, the slope of this line is 2 over 3. The “rise” is 2, and it goes on the top of the slope fraction.

• A formula to find slope says that you can subtract y-coordinates and x-coordinates and write them in a fraction. This formula is printed for you on your TAKS formula chart, but look at it—Which values go on top of the fraction: X-values or Y-values? The y-values.

• Please remember that the y-values go on TOP of the slope fraction. • Here’s something to help you remember: RISE rhymes with Y’s. Both RISE

and Y’s go on the top of the slope fraction.

2 Grades 9-11

Slope-Intercept Form

3

(0,1)

bmxy 1,3

2 bm

132 xy

y

x

SlopeTest administrator: Before administration begins, show

students the front of this card and say:

• A lot of the time, equations for lines require you to use the slope.

• For example, the slope-intercept form of a line is “y equals mx plus b.” Here, the m stands for the slope, and the b represents the value of the line’s y-intercept.

• In this picture, the line has a slope of two-thirds. Also, since it crosses the y-axis at the point (0, 1), we say that the y-intercept is 1.

• So, the equation for the line is “y equals two-thirds x plus one.”

3 Grades 9-11

Graphing Calculator

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Graphing CalculatorTest administrator: Before administration begins, show students the front of this

card and say:

• Remember that you can use a graphing calculator on any part of the test.• As long as an x-and-y equation is in “Y Equals” form, you can enter it into a

graphing calculator.• To do this, you simply find the “Y Equals” button, which is just below the

screen on the left-hand side.• In this example, the student types in the expression “Two-thirds x plus one”

next to the “Y Equals” that appears on the screen. Notice that if you have a fraction (like two-thirds) in the problem, many teachers recommend that you write it in a set of parentheses.

• To see the graph of this equation, you simply have to hit the “GRAPH” button, which is also under the screen, but on the RIGHT side.

• What if you need to see a TABLE for the equation? The “TABLE” command is written in small letters above the GRAPH button. To use this command, you must hit the “SECOND” button, then press “GRAPH.”

4 Grades 9-11

Formula Chart• Perimeter • Circumference• Area • Surface Area• Volume• Algebra

5

Formula ChartTest administrator: Before administration begins, show students the front of this card and

say:

• Many problems will require you to use the formula chart.• It is separated into about three sections: Perimeter and Circumference are at the top; then

comes Area, and then Volume.• What’s the difference between perimeter, area and volume? Answers may vary.• Repeat these phrases after me:

– Area covers [Students repeat: “Area covers.”] – Volume fills [Students repeat: “Volume fills.”]– Perimeter goes around. [Students repeat: “Perimeter goes around.”]

• Repeat these phrases after me:– Area is in square units [Students repeat: “Area is in square units.”] – Volume is in cubic units [Students repeat: “Volume is in cubic units.”]– Perimeter is in plain units. [Students repeat: “Perimeter is in plain units.”]

• In a measurement problem, ask yourself whether you must cover, fill, or go around an object to know which formula or units to use.

4 Grades 9-11

5*BhV Capital “B” in

“B” is the Area of the Base

Base Area = lw

Volume = (lw)h

Base Area = r2

Volume = (r2)h

Test administrator: Before administration begins, show students the front of this card and say:

• On the formula chart, Volume for a prism or cylinder is listed as “V equals capital B times h.” Remember that the CAPITAL B does not represent one number from the picture that you can plug into this formula. Instead, CAPITAL B represents the AREA of the BASE of the prism or cylinder.

• For example, for the prism that looks like a box, what shape is on its Base? A rectangle

• How do you find the area of a rectangle? Length times width• This means that you could re-write the formula for the volume of a box as,

“length times width times height.”• Now look at the cylinder. What shape is on the Base of a cylinder? A circle• How do you find the area of a circle? Pi times the radius squared• This means that you could re-write the formula for the volume of a cylinder as,

“pi, times the radius squared, times the height.”• Again, remember—CAPITAL B represents the AREA of the BASE of the prism,

pyramid, cylinder or cone.

5 Capital “B” in V=Bh*Grades 9-11

6

Probability

36

1

6

1

6

1

Test administrator: Before administration begins, show students the front of this card and say:

• Look at this picture. It shows two dice, and both are showing the value “1.”

• If you were asked to find the probability that you would roll two die and get BOTH of them to land on “1,” you would have to complete these two steps:

• First, write the probability that the first die land on “1,” which is 1 out of 6.

• Then, write the probability that the second die also lands on “1,” which is also 1 out of 6.

• Finally, you must MULTIPLY these two ratios to get 1 out of 36.• Remember: ANY TIME you must find the probability that TWO

things happen at the same time, you must MULTIPLY their individual probabilities together.

6 ProbabilityGrades 9-11

8

Other TipsRead

Re-Read

Underline the question

Circle important information

Draw a picture

Label pictures

Test administrator: Before administration begins, show students the front of this card and say:

• You are about ready to start the Math TAKS test. Here are a few more test-taking strategies that could make a big difference in your performance:

• First, remember that this is NOT a timed test. You have as much time as you need. So, read every question carefully, then re-read it.

• Underline the question to make sure you understand what is being asked.

• Circle any important information in the problem, such as numbers, labels, units, and other mathematical terms.

• If you are given information about a graph or geometric figure, sketch it on your test paper. Then label on it the information provided in the question.

• Or, if a figure is already provided for you, label it with the given information from the problem.

8 Other TipsGrades 9-11