a. Complete the chart of equivalent numbers.
b. Graph the points corresponding to the numbers. Place a dot on the number line and write the
A) -7/8 ..............D) 75%B) 0.125 ............E) -(0.7)2
C) 0.25² .............F) (1/4)2
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a. Simplify and evaluate the variable expression for a = -2.
b. What is the value of the expression if n = 3 ?-3a2 (-3a)2(2a - 7)2
3(n + 2) - (n - 5)2
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Simplify each expression mentally using the properties of real numbers. Write your simplified expression below the original expression. Write your result and the properties used in the spaces provided.
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a. A company packages its
special marking pens according to color. Yellow pens are packaged
with six in
a box. Blue pens are packaged with eight in a box. Red pens are packaged
with ten
in a box. The
pens are sold only by the box. How many boxes of each color would have
to be
purchased to
have the same number of each color of pen?
b. A human red blood cell
has a diameter of 9.0 x 10-3 mm. A molecule of amino acid has
a
diameter of
9.0 x 10-7 mm. What is the ratio of the diameter of the red
blood cell to the diameter
of the molecule
of amino acid?
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a. A waiter receives a tip
of $21.60 from a group of 12 people. This tip represents 15% of the
cost of dinner.
How much did each person pay if each paid an equal share of the cost of
dinner
and the tip?
b. The regular price of a
stereo is $360. It is put on sale at a 20% discount. If the stereo does
not
sell after
one month, it is put on the clearance shelf with an additional reduction
of 25% off the
sale price.
What is the difference between the final clearance price and a discount
of 45% off
the original
price?
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A student had earned $1,000 by the end of the summer and invested it in an account that pays 8% per year compounded annually from the date of deposit. How much money will the student have in the account four years after making the deposit?
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Write the equation represented by
the illustration. Use Lab Gear to obtain a solution.
Verify the solution by solving
the equation on paper, showing the algebraic steps.
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a. Solve the equation algebraically. Show the steps of your work.
b. Write an algebraic check of your solution.5(x + 3) = 4(x - 1)
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Write and solve the equation represented by the word sentence.
Four times a number equals twice the sum of the number and six.
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For triangle ABC, what is the measure of angle BCA?
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In a seventh grade class, 5/8 of
the students are girls. If the number of boys were doubled and three were
added to the number of girls, then there would be an equal number of girls
and boys in the class. How many students are in the class?
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a. Circle the inequalities that are represented by the graph.
b. Justify your choices.
x + 3 > 12x + 5 > 2
3x + 2 > -1
x + 1 > 0
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Make a graph of the pairs of numbers in the table. Draw a line that connects the points on the graph. Write an equation that represents the relationship between x and y. The domain and range are the set of real numbers.
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a. Graph the triangle whose
coordinates are A(3, -4), B(5, -1), and C(2, 4).
Reflect
the triangle across the y-axis.
b. What are the coordinates of the vertices of the image?
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Triangle ABC is similar to triangle ADE. What is the measure of segment BD?
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Complete the diagram to illustrate the relationships among various types of quadrilaterals.
Quadrilaterals Rectangles Squares
Trapezoids Rhombuses Parallelograms
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A circle with a diameter of 12 cm and center A is inscribed in a square. What is the total area of the shaded parts of the figure? Use 3.14 as an approximation for pi.
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Parallelogram ABCD has sides with lengths AB = 8 units, BC = 6 units, and DE = 4 units.
What is the measure of segment DF?
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A rectangle has a perimeter of 42
cm and an area of 108 cm2.
What is the length of a diagonal
of the rectangle?
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Construct the three-dimensional
figure whose views are illustrated.
What are the total surface area
and the volume of the three-dimensional figure?
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a. What is the difference between the surface areas of the containers?
b. What is the difference in the volume of the containers?
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Students in eleven homerooms sold magazine subscriptions for a school fund raiser.
Make a box-and-whisker plot that shows the number of subscription orders sold by each homeroom.
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The box-and-whisker plot shows the number of hits for each member of a summer baseball team.
Estimate the following:
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A class of twenty-four students completed a mathematics assessment task.
Suppose that two of the students who received a score of 4 had instead received a score of 3. Which of the measures of central tendency would change and which would remain the same? Explain your reasoning.
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The bag contains 4 red marbles,
3 green marbles, 2 black marbles, and 1 white marble.
Marbles are selected from the bag
at random.
a. What is the probability that the first marble selected will not be black or white?
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Boxes of caramel corn are packaged in 54-box cartons. In each carton, one out of every six boxes contains a baseball card and one out every nine boxes contains a free-offer coupon.
a. In any given carton, how many
boxes are likely to contain a baseball card?
b. In any given carton, how many
boxes are likely to contain a free-offer coupon?
c. In any given
carton, how many boxes are likely to contain both?
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How many more license plates could
be made using four letters followed by three digits than could be made
using three letters followed by four digits.
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Describe, in writing and with diagrams,
how measurement concepts of distance and area are used in the design of
a basketball court.
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Illustrate and explain three different strategies for solving the equation below:
2(3x + 1) = 4(x + 2)
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Restate and explain in your own words the meaning of the statement below.
For all real numbers a, b, and c:
a(b + c) = ab + ac
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Use algebraic symbols to show how to change the fraction from one form to another.
2 3/4 = 11/4
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Use color tiles to illustrate the
rectangle closest in shape to 1 less than a number squared.
Write the same relationship algebraically.
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a. Simplify the expression,
showing the steps of your work.
2x + 15 - x2
+ (4x)x - 7
b. The starting salary for
a salesperson at Shop-Smart is $1500 a month plus a 6% sales commission
on total
sales over $500. How much would a salesperson earn in one month if his
sales for the
month
were $5,480?
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Construct a Venn diagram of the
real number system that shows the relationships between natural numbers,
whole numbers, integers, rational numbers and irrational numbers. Place
numbers in each region of the diagram to illustrate numbers that are unique
to that classification, if possible.
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a. A large drink at the video
arcade costs $2.50 and each video game costs $0.75 to play. Bart has
$7.50 to spend
at the arcade. What is the maximum number of games that Bart can play if
he buys
a large soda?
b. The space shuttle solid rocket
boosters (SRBs) provide thrust to lift the shuttle from the launch
pad to an altitude
of about 1.5 x 105
feet. Each of the two SRBs carries about 1.1 x 106
pounds
of solid fuel.
1). On the average,
how many pounds of fuel are burned by the SRBs for each foot of travel
during the launch?
2). The boosters are
shutdown after about 2 minutes and 15 seconds. On the average, how much
fuel is burned by the SRBs each second?
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Kim received $50 for her birthday. She decided to spend it on music CDs and tapes. Each music CD costs $12 and each tape costs $5. What combinations of CDs and tapes can she buy for the total $50?
a. Write an equation that
expresses the possible solutions.
b. Complete a table of values
for the number of CDs and tapes.
c. Make a graph of the relationship
of the tapes to CDs that she can buy.
| # Tapes | ||||
| # CDs |
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Triangle ABC has coordinates
A(–5,
-3), B(1, –3), and C(–1, 2).
What are the coordinates of the
triangle after a clockwise rotation of 90º about vertex B?
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In the figure below, lines 1 and
2 are parallel and 3 and 4 are parallel.
What is the measure of angle x?
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An ice cream cone manufacturer,
in order to sell more ice cream, increased the radius of his original cone
(on the left) from ½ inch to 1 inch. He did not change the height
of the cone. By how much did the volume increase?
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The table shown below contains the
grams of fat and number of calories for some common foods. Make a scatter
plot of the data.
|
|
of Fat |
Calories |
| Milk |
|
|
| Eggs |
|
|
| Chicken |
|
|
| Ham |
|
|
| Ice Cream |
|
|
| Corn |
|
|
| Beef |
|
|
| Broccoli |
|
|
| Cheese |
|
|
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Commuting from school to home combines walking and taking the Metro. The graph describes the trip home by relating time and the distance from school. Describe in detail what each part of the graph represents.
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a. From a track team of twelve
students, the coach must select four students for the relay race.
How many different
groups can be selected?
b. Andy played a game ten
times and decided it was an unfair game. Sam simulated playing the game
by using random
digits and after 100 games decided that it was fair. With whom do you agree
and why?
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Describe, in writing, and with a
diagram, why the result of two reflections of a figure over parallel lines
is the same as a translation of the figure twice the distance between the
parallel lines.
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Illustrate and explain two different
strategies for finding the factors of 6x + 8.
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Restate and explain in your own words the meaning of the equation below.
For all
real numbers a, b, and c:
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Point P, with coordinates (a,b),
is translated c units to the right. Diagram the translation using
a coordinate grid and state the coordinates of the translated point P'.
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Use a geometric model to represent
the greatest common factors of 4x2
and 6x.
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