Download Unit 06_Tiling Rectangle

UNIT 6
GROUP TEST QUESTIONS
Is it true that (x + 3)2 = x2 + 9 ? Use a diagram to explain your answer.
The sum of two numbers is negative. The product of the two numbers is also
negative. Explain the relationship between the two numbers as specifically as
possible.
Factor each of the following expressions. Use generic rectangles or diamonds to help
you.
a) x2 + 6x + 9
d) y2 + 6y - 16
b) y2 + 7y + 6
e) x2 - 16
c) 10x + 15
f) 3y2 + 7y + 2
For each of the following figures, write an equation to express the statement:
"the area written as a product equals the area written as a sum."
a)
7x
-3
4
2x
b)
3
3x
2
c)
x2
-3x
-2x
6
In a recent survey, seven out of ten basketball players recommended Itch-gone
athlete's foot powder.
a) If 150 players were surveyed, how many recommended Itch-gone foot powder?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 GROUP TEST QUESTIONS
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b) What is the probability that a player did not recommend the product?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 GROUP TEST QUESTIONS
3
The triangles shown below are similar. Use this fact to solve for x.
5
10
12
13
x
Simplify each of the following expressions.
a) (4x2 + 2x + 1) + (x - 8)
b) (3x2 - x + 7) - (2x2 - x + 1)
Solve each of the following equations. Show your work. Check your solution.
a) 2(x + 5) - 7 = 15
b) 3 - 2x = -7
c)
x-2 x
3 =5
x 9
d) 4 = x
e)
x+2
-3 + 7 = -4
Solve the problem and write an equation. You may do this in either order. If you do
not need a guess and check chart to solve the problem, use it to define your variables.
Be sure to state your answer as a sentence.
When Alex banged on the Coke machine, all the coins came out, but no Coke. There
were nickels, dimes, and quarters. There were three times as many dimes as nickels,
and 40 more quarters than nickels. If the total amount of money was $17.20, how
many coins fell out of the machine?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6
TILING RECTANGLES
TEST QUESTIONS
For each of the following figures, write an equation to express the statement
"the area written as a product equals the area written as a sum."
a)
3x
x
-2
b)
3x
7
x2
-2x
-3x
6
x
4
c)
Elaine has one big square tile, seven rectangular tiles, and ten small square tiles. She
claims that she can form one big rectangle using all the tiles, but Judy isn't so sure that
it can be done. Which claim is right? Use a diagram to help explain your answer.
Find each of the following products.
a) 4x(7x - 3)
b) (x + 4)(x + 6)
c) (x - 3)(x + 2)
d) (2x + 1)(2x - 1)
A certain floor tile has dimensions x by x + 2. How many such tiles are needed to
tile a kitchen floor that has dimensions 6x by 6x + 12? Explain your answer. You
may include a drawing as part of your explanation.
6x+12
x+2
x
6x
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 TEST QUESTIONS
2
Simplify each of the following expressions.
a) (4x2 + 2x + 1) + (x - 8)
b) (3x2 + 2x + 7) - (2x2 + x + 1)
How many of each kind of algebra tile (big squares, rectangles, and little squares) are
needed to make a big rectangle with dimensions (3x + 1) by (x + 2) ? Show how
you made your decision.
Solve these Diamond Problems:
a)
b)
c)
-77
-1
-4
d)
-12
20
-16
9
-11
e) Write the multiplication/factorization problem associated with part (a).
x2 + ___x + ___ = (
)(
)
Simplify each of the following expressions.
a) 5x2y . 6x2
b)
(2x)3
x
c) (3x2 + 2x + 1) + (x - 8)
d) (3x2 - 2x - 3) - (x + 1)
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 TEST QUESTIONS
3
Find each of the following products. Use the generic rectangles provided.
a)
3x(2x + 5)
b) (x + 3)(x + 5)
c)
(x - 4)(x + 6)
d) (2x + 1)(3x - 5)
Factor each of the following expressions. Use the generic rectangles provided.
a) x2 + 4x + 4
b) y2 + 8y + 7
c) 3x + 6
x2
4
y2
7
3x
6
Factor each of the following expressions. Use the generic rectangle provided.
a) x2 - 6x - 16
b) y2 - 9
c) 2y2 + 7y + 3
x2
-16
y2
-9
2y 2
3
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 TEST QUESTIONS
4
a) Use the graph below to solve for the length x.
y
(10,4)
(x,3)
x
x
b) Write equivalent ratios to compare the lengths of the sides of the large triangle to
the lengths of corresponding sides of the small triangle.
Solve the problem and write an equation. You may do this in either order. If you do
not need a guess and check chart to solve the problem, use it to define your variables.
Be sure to state your answer as a sentence.
The perimeter of a certain quadrilateral is 89 inches. The second side is twice the
length of the first. The third side is five inches longer than the first side, and the
fourth side is six inches shorter than the first. Find the length of each side.
An advertisement for Brite toothpaste claimed that four out of five dentists
recommended the product in a recently conducted survey.
a) If 240 dentists were surveyed, how many recommended Brite toothpaste?
b) What is the probability that a dentist didn't recommend the product?
Solve each of the following equations. Show your work. Check your answer.
a) 3(2x - 3) = 24
b) 4x + 7 = -x - 9
c)
x+1 7
x =5
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 TEST QUESTIONS
5
Match each of the following equations with its graph. Use your calculator to check
some points if you are unsure.
d) y = 3x
3
e) y = x
a) y = 3x
b) y = x + 3
c) y = x3
Solve the problem and write an equation. You may do this in either order. If you do
not need a guess and check chart to solve the problem, use it to define your variables.
Be sure to state your answer as a sentence.
A set of children's blocks contain three shapes: longs, flats, and cubes. There are
three times as many longs as cubes, and 30 fewer flats than longs. If there are 600
blocks in all, how many longs are there?
The triangles shown below are similar. Use this fact to solve for x.
5
10
12
13
x
Complete the table below for the equation y = 2x and then carefully graph the equation.
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 6 TEST QUESTIONS
x
y
-3
-2
6
-1
0
1
2
3
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2