Name: 
 

Math 11 Foundations LG 18 Unit 4 Practice Test #1


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Which set of data is correct for this graph?
mc001-1.jpg

 
Axis of Symmetry
Vertex
Domain
Range
A.
x = 3
(3, 2)
x Î R
2 £ y
B.
x = 3
(2, 3)
x Î R
y Î R
C.
x = 2
(2, 3)
–1 £ x £ 7
2 £ y
D.
x = 3
(3, 2)
–2 £ x £ 8
0 £ y
a.
Set A.
b.
Set C.
c.
Set D.
d.
Set B.
 

 2. 
What are the x- and y-intercepts for the function f(x) = x2 + 5x + 6?
a.
x = –4, x = –2, y = 6
b.
no x-intercepts, y = 6
c.
x = –2.5, y = 6
d.
x = –3, x = –2, y = 6
 

 3. 
What are the x- and y-intercepts for the function f(x) = x2 + 7x + 10?
a.
x = –5, x = 5, no y-intercept
b.
x = 10, y = –2
c.
x = –5, x = –2, y = 10
d.
no x-intercepts, y = –2
 

 4. 
Solve –2x2 – 24x + 75 = 0 by graphing the corresponding function and determining the zeros.
a.
x = 5, x = –3
b.
There are no zeros.
c.
x = 0, x = –8.333
d.
x = –3, x = –5
 

 5. 
What is the correct quadratic function for this parabola?
mc005-1.jpg
a.
f(x) = (x – 2)(x – 3)
b.
f(x) = (x + 2)(x – 3)
c.
f(x) = (x – 2)(x + 3)
d.
f(x) = (x + 2)(x + 3)
 

 6. 
What is the correct quadratic function for this parabola?
mc006-1.jpg
a.
 f(x) = (x – 1)(x + 3)
b.
 f(x) = (x + 1)(x + 3)
c.
 f(x) = –(x + 1)(x – 3)
d.
 f(x) = (1 – x)(3 – x)
 

 7. 
Which relation is the factored form of f(x) = –2x2 – 5x – 2?
a.
f(x) = 2(x – 2)(x – 0.5)
b.
f(x) = –2(x – 1)(x – 5)
c.
f(x) = –2(x + 2)(x + 0.5)
d.
f(x) = 2(x – 2)(x + 0.5)
 

 8. 
Which function has a maximum value?
a.
f(x) = 4(x + 7)2 + 9
b.
f(x) = –14(x + 4)2 – 7
c.
f(x) = 7(x + 14)2 – 4
d.
f(x) = (x – 9)2 –14
 

 9. 
Solve 2y2 + 3y = 5y2 – 1 using the quadratic formula.
a.
y = mc009-1.jpg + mc009-2.jpg, y = mc009-3.jpg – mc009-4.jpg
b.
y = mc009-5.jpg + mc009-6.jpg, y = mc009-7.jpg – mc009-8.jpg
c.
y = –mc009-9.jpg + mc009-10.jpg, y = –mc009-11.jpg – mc009-12.jpg
d.
y = –mc009-13.jpg + mc009-14.jpg, y = –mc009-15.jpg – mc009-16.jpg
 

 10. 
Solve 2w2 + 9w = 3 – 3w2 – 5w using the quadratic formula.
a.
w = –mc010-1.jpg, w = –3
b.
w = mc010-2.jpg, w = –3
c.
w = –mc010-3.jpg, w = 3
d.
w = mc010-4.jpg, w = 3
 

 11. 
A company manufactures cylindrical planters. A town council wants planters with a wide rim for people to sit on. The company suggests that the area of the soil in the planter be about equal to the area of the rim. If the outer radius of the planter is 8.0 m, what is the radius of the soil?
a.
4.9 m
b.
5.7 m
c.
6.1 m
d.
2.3 m
 

 12. 
A rug company sells circular rugs that have a uniform circular border. The area of the border and the area of the circular rug it surrounds are equal. If the radius of the entire rug is 8.5 m, what is the width of the border?
a.
3.6 m
b.
2.5 m
c.
3.0 m
d.
2.8 m
 

 13. 
The original pushpin for these scale diagrams was 24 mm long.
Which diagram was drawn using a scale factor of 3.5?
a.
mc013-1.jpg
b.
mc013-2.jpg
c.
mc013-3.jpg
d.
mc013-4.jpg
 

 14. 
The original eraser for these scale diagrams was 7.0 cm long.
Which diagram was drawn using a scale factor of 0.9?
a.
mc014-1.jpg
b.
mc014-2.jpg
c.
mc014-3.jpg
d.
mc014-4.jpg
 

 15. 
A picture is 46 cm by 32 cm. A scale diagram of the picture must fit in a space that is 3 m by 2 m. Which scale would be the most reasonable one to use for the scale diagram?
a.
60%
b.
1 cm:60 cm
c.
6 cm:1 m
d.
1 cm:6 cm
 

 16. 
Data for triangle ABC is shown on the first line of the table.
Triangle ABC is enlarged by a scale factor of 3.5.
Which triangle is the enlargement of triangle ABC?

Triangle Name
Length of Base (cm)
Height of Triangle (cm)
Scale Factor
Area (cm2)
mc016-1.jpg
ABC
  5.00
  3.00
1.0
7.5
1  
DEF
17.50
10.50
3.5
  91.875
12.25
GHI
17.50
12.25
3.5
80.75
10.5 
JKL
12.25
10.50
3.5
  91.875
17.5 
MNO
13.50
    9.875
3.5
80.75
12.25
a.
DEF
b.
GHI
c.
JKL
d.
MNO
 

 17. 
Data for rectangle ABCD is shown on the first line of the table.
Rectangle ABCD is enlarged so the width is 19.5 cm.
Which rectangle is the enlargement of rectangle ABCD?

Rectangle Name
Length (cm)
Width (cm)
Scale Factor
Area (cm2)
mc017-1.jpg
ABCD
  9.0
13.0
1.00
117.00
1    
EFGH
13.5
19.5
1.35
265.25
2.25
JKLM
12.5
19.5
1.25
253.25
  2.125
NOPQ
13.5
19.5
1.50
263.25
2.25
RSTU
15.5
19.5
1.50
302.25
2.5 
a.
EFGH
b.
JKLM
c.
NOPQ
d.
RSTU
 

 18. 
A 1:7 scale model of a shopping cart is 15 cm tall, 8.4 cm wide, and 13.4 cm long. What are the dimensions of the actual shopping cart?
a.
95 cm by 40 cm by 45 cm
b.
105 cm by 58.8 cm by 93.8 cm
c.
150 cm by 160 cm by 195 cm
d.
1 m by 0.6 m by 1 m
 

 19. 
A wardrobe is 202.8 cm tall, 96.0 cm wide, and 73.2 cm deep. What are the dimensions of a scale model built using a scale of 1:6?
a.
101.4 cm tall, 48.0 cm wide, 36.6 cm deep
b.
50.7 cm tall, 24.0 cm wide, 18.3 cm deep
c.
33.8 cm tall, 12.2 cm wide, 16.0 cm deep
d.
33.8 cm tall, 16.0 cm wide, 12.2 cm deep
 

 20. 
A cylindrical oil tank has a surface area of 1800 m2.
A similar oil tank has dimensions that are reduced by a scale factor of mc020-1.jpg.
What is the surface area of the smaller tank?
a.
800 m2
b.
630 m2
c.
1200 m2
d.
533 m2
 

Short Answer
 

 21. 
Fill in the table for the relation y = x2 – 1.5x + 2.
Maximum or minimum 
Axis of symmetry 
Vertex 
 

 22. 
Fill in the table for the relation y = –2x2 + 2x – 1.
Maximum or minimum 
Axis of symmetry 
Vertex 
 

 23. 
Use the graph to determine the equation of the parabola.
sa023-1.jpg
 

 24. 
Use the graph to determine the equation of the parabola.
sa024-1.jpg
 

 25. 
Solve x2 + 6x + 4 = 0 using the quadratic formula. Verify by graphing.
 

Problem
 

 26. 
Determine the equation for this quadratic function. Write the equation in standard form. Show all your steps.
pr026-1.jpg
 

 27. 
A parabola has the vertex (4.5, –10).
a) Write an equation to describe all parabolas with this vertex.
b) A parabola with the given vertex passes through the point (–1, 0). Determine the equation for this parabola.
c) State the domain and range of the function.
 

 28. 
A parabolic arch has zeros located at (2, 0) and (32, 0). The parabola has a maximum height of 112.5 ft.
a) Define the equation of the parabola in vertex form. Explain your reasoning.
b) State the domain and range of the function describing the arch.
 

 29. 
A landscaper is designing a rectangular garden, which will be 5.5 m wide by 6.5 m long. She has enough crushed rock to cover an area of 6.0 m2 and she wants to make a uniform border around the garden. How wide should the border be if she wants to use all the crushed rock?
 

 30. 
A cook has a set of four mixing bowls with lids. Each bowl is a half sphere.
The bowls stack inside each other and are similar to each other.
The diameters of the two largest bowls are 30 cm and 26 cm.
The scale factor is the same from each bowl to the next smaller bowl.
The cook estimates that the largest bowl has a capacity of about 7400 cm3.
Estimate the capacity of the smallest of the four bowls.
 



 
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