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UNIT 12
GROUP TEST QUESTIONS
A ball is thrown upward. Its height H (in feet) after T seconds is given by the
equation
H = 96T - 16T2.
a) Draw a graph relating the height of the ball to time.
b) How high is the ball after two seconds?
c) What is the maximum height of the ball?
d) Approximately when is the ball 100 feet above the ground?
e) Write and solve an equation to get the exact answer to part (d).
Here is some information about how long it takes to roast a turkey:
pounds (p)
10
18
time (t) in hours
5
7
a) The formula for how long to cook a turkey is a linear equation (that is, its graph is
a line). Use the given information to find an equation relating the weight of a
turkey to its roasting time.
b) How long should a 22-pound turkey be cooked?
To solve the following problem, draw a diagram, then write an equation and solve it.
A photograph is twice as long as it is wide. There is a three-inch border around the
photograph. If the area of the border is 180 square inches, find the dimensions of the
photograph.
Solve each of the following equations by any method you choose.
a)
x2 - 4x - 7 = 0
b) 5x2 - 8x + 3 = 0
c)
d) (x + 6)2 = 25
e)
2x - 3 + 5 = 7
x
5
2 = x+1
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 12 GROUP TEST QUESTIONS
2
Find where the graphs of these equations intersect each other:
2x - y = 1
y = x2 - 2
To solve the following problem, draw a diagram, then write an equation and solve it.
The hypotenuse of a certain right triangle is 23 units long, and one leg is three units
longer than the other. Find the lengths of the sides of the triangle.
Saundra, Lee and Kim each evaluated the following expression:
–3+
32 - 4(2)(-5)
2(2)
Saundra said the answer is -1.25, Lee said the problem was impossible because you
can't take the square root of a negative number, and Kim said the answer is one. Help
this group figure out who is correct. If you can, explain what errors the people with
incorrect answers made.
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 12
ELECTION POSTER
TEST QUESTIONS
Recall that quadratic equations can be solved by factoring or by using the quadratic formula if the
equation is equal to zero. For your convenience the quadratic equation is given here:
–b + b2 - 4ac
For 0 = ax2 + bx + c ,
x=
2a
Either give exact answers or approximate answers to the nearest 0.01.
a) Graph the equation y = x2 - 2x - 2.
b) Solve the equation x2 - 2x - 2 = 0.
c) How do parts (a) and (b) relate to what you know about graphs and solutions to
equations?
Solve each of the following equations for r.
a)
C = 2πr
b) A = πr2
The area of a certain rectangle is 24 square units. On a set of coordinate axes, draw
a graph showing all possible lengths and widths for the rectangle.
For the graph at the right,
a) draw a line of best fit for the graph of the data
shown on the right.
b) write an equation for the line you drew in part (a).
8
6
4
2
•
• • •
• • •
•• •
•
2 4 6 8 10
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 12 TEST QUESTIONS
2
Use the quadratic formula to solve each of the following equations.
a) x2 - 2x - 2 = 0
b) 2x2 - 5x + 3 = 0
Solve each of the following equations by any method you choose.
a)
x2 - 4x - 7 = 0
b) 3x2 = 18
c)
x2 = 6x + 16
d) 3x2 + 5x - 6 = x2 - 3x + 2
Graph the equation y = 2(x + 1)2 - 3.
Solve each of the following equations by factoring.
a) x2 + 2x - 15 = 0
b) 3n2 + 6n = 0
Solve each of the following equations by factoring.
a) x2 + 5x - 24 = 0
b) 3x2 + 7x = -2
a) Find an equation of the line passing through the points (2, 2) and (6, 4).
b) Is the point (50, 26) on the same line as the points (2, 2) and (6, 4) ? Explain
your answer.
To solve each of the following problems, draw a diagram, then write an equation and
solve it.
a) Maria and Hector rode their bikes toward each other starting from two towns 24
miles apart. Maria rode three miles per hour faster than Hector and they met in
two hours. How fast did each person ride?
b) The length of a certain rectangle is two units more than its width. If the area of
the rectangle is 20 square units, find the length and width.
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2
UNIT 12 TEST QUESTIONS
3
For the points (-2, 1) and (-4, 4), find:
a) the distance between the two points
b) the slope of the line containing the two points.
c) an equation of the line containing the two points.
Solve each of the following systems for x and y.
a) 2x + 3y = 2
4x + y = -1
b) y = 3
x2 + y = 9
Solve each of the following equations.
a)
x+3
x-2
= 2
3
x x
b) x + 2 + 3 = 22
Write an equation for each of these lines:
a)
b)
c)
y
y
y
3
(0,3)
x
-3
-2
-1
2
2
1
1
1
2
3
x
1
3
x
(-5,0)
Sarah has a 3' x 5' pen for her chickens. She know they will grow to about four times
the size that they are now and will need four times as much room to run around. She
decides to build a pen that is four times as large. Help Sarah out…
a) What should the dimensions of the new pen be?
b) What is the area of the original pen?
c) What is the area of the new pen? Is there four times as much room for the
chickens?
d) Compare the perimeters of the two pens. How much more fencing will she need
to buy?
© 1993 College Preparatory Mathematics: Change from Within Project; Funded by CPEC Eisenhower Grant
v.3.2