Download Unit 08_Lunch Bunch_Test

UNIT 8
GROUP TEST QUESTIONS
Solve each of the following equations. For (b) and (c) you will need to factor the
quadratic first.
a) (x + 3)(x - 2) = 0
c) y2 - 3y - 10 = 0
b) x2 + 5x + 6 = 0
d) 3x + 4(x - 2) = 7
Solve each of the following equations. You will need to factor (b), (c), and (d) before
you can solve them.
a) (x + 1)(x - 2) = 0
c) y2 - 2y - 35 = 0
b) x2 + 6x + 8 = 0
d) 3x2 + 6x = 0
For the equation x2 + 3x + 2 = y
a) Graph the equation using a table of values.
b) Estimate the coordinates of the points where the graph crosses the x-axis.
c) Let y = 0 and use the zero product property to solve for the exact coordinates of
the points where the graph crosses the x-axis.
1
a) Graph the equations y = -x - 2 and y = 2 x + 2 on the same set of axes.
b) Estimate the coordinates of the point of intersection of the two lines.
c) Solve the system algebraically using substitution.
d) How can you tell if the answers you got in parts (b) and (c) are correct?
Khalilah has a bag of fruit containing apricots, plums, and peaches. Forty percent of
the pieces of fruit in the bag are plums. There are 2 peaches for every 3 apricots.
There are 50 pieces of fruit altogether. How many pieces of each type of fruit are
there? Show clearly how you arrived at your answers.
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 8 GROUP TEST QUESTIONS
2
Tomas says that x8 . x3 = x11. Nhung says that x8 . x3 = x24. Who is correct? Write
an explanation that will convince the person who is wrong why they are wrong.
A Quick Photo shop charges $2.25 plus $0.05 per picture for developing and
printing a roll of film. The cost at a Fast Photo shop is $1.25 plus $0.09 for each
picture.
a) For each shop, define a variable and then write an equation to show the
relationship between cost for developing and printing a roll of film and number of
pictures.
b) For what number of pictures is the cost at both shops the same? What is that
cost?
Find each sum or difference.
a) (x2 + 5x + 6) + (2x2 + x + 7)
b) (3x2 + 6x + 5) - (x2 + 8x + 5)
c) (x2 + 8x + 17) + (x2 + x + 3) - (2x2 - 3x + 10)
a)
x
+
1
2x - 3
b)
x
2
2x
Write an algebraic equation for each figure below to express the relationship
"area as a product equals area as a sum."
3x 6
Rewrite each of the following expressions in a simpler form. Show how you got each
answer.
a) 3x2 . 5xy3
b) (x2)3
8x2y
d) 4xy
e) (2x2)3
c) 53 + 35
f)
3x3y
9xy4
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 8
THE LUNCH BUNCH
TEST QUESTIONS
Solve each of the following pairs of equations for x and y.
a)
y = -3x
y = -4x + 2
b) y = 2x - 1
3x + y = 11
c)
x = 2y - 3
2x + 3y = -6
Solve each of the following pairs of equations for x and y.
a)
y = 2x + 6
y = 3x - 4
b) y = 5x - 13
2x + y = 8
c)
x-y=7
y = 2x - 1
a) Graph the equation y = x2 - 3x.
b) Where does the graph cross the x-axis?
c) Solve the equation 0 = x2 - 3x by factoring.
d) Why does it make sense that the solutions in parts (b) and (c) identify the same
points?
a) Graph the equation y = x2 - 3x + 2.
b) Where does the graph cross the x-axis?
c) Solve the equation 0 = x2 - 3x + 2 by factoring.
d) Why does it make sense that the solutions in parts (b) and (c) identify the same
points?
Estimate the solution(s) of the following system of equations.
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 8 TEST QUESTIONS
2
At the Pico de Gallo Restaurante the dinner specials include combinations of tacos
and enchiladas. The Number One special offers 2 tacos and 3 enchiladas for
$8.00. The Number Two special offers 3 tacos and 1 enchilada for $5.70.
a) For each special, define two variables and then write an equation to show the cost
of the dinner.
b) Use what you know about solving systems of equations to find the cost of one
enchilada and the cost of one taco.
Answer the following question by writing a pair of equations and solving them.
Thea has two kinds of bamboo in her yard. One is now 20 centimeters tall and
growing at a rate of three centimeters per week. The other is 35 centimeters tall and
growing at a rate of two centimeters per week. How long will it be before both kinds
of bamboo are the same height?
Solve each of the following equations for x.
a) x2 = 30
c)
b) x2 + 2 = 27
x+1
x
=
3
7
d) 4x + 3(2x - 1) = x - 3
Graph the following equations on one set of axes. Label each graph.
a) y = 3
b) x = -2
c) y = -2x + 3
In parts (a) and (b), multiply the expressions. Factor the expressions in parts (c) and
(d).
a) (2x + 1)(x - 3)
c) 4m + 8
b) x3(x2 + 5x + 6)
d) 2y2 + 5y + 2
Answer the following question by writing an equation and solving it.
A vinyl floor covering installer can complete three houses in two days. At this rate,
how long should it take the installer to complete a subdivision with 40 houses?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 8 TEST QUESTIONS
3
1
Decide whether or not each of the following points is on the line y = - 2 x + 1. Show
your work.
a) (0, 1)
b) (1, 0)
c) (-40, 21)
d) (20, -11)
Answer the following question by writing an equation and solving it.
Sandy cut a 150-centimeter board into five pieces. The three shortest pieces are the
same length and the two longer pieces are each three centimeters longer than a short
piece. How long is each piece of board?
Graph each of the following equations.
a) y = -2
b) y = x2 - 3x
In parts (a) and (b), multiply the expressions. Factor the expressions in parts (c)
and (d).
a) (x + 3)(2x - 5)
c) y2 + 8y + 7
b) (2x + 1)(2x - 1)
d) 3y2 + 4y + 1
Scott has 22 marbles in a bag, 15 of which are red. He adds more red marbles to the
bag until the probability of picking a red marble is approximately 73%. How many
red marbles did he add?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2