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Math 1170 – Spring 2015
Test 1 Review
Names________________
For full credit circle answers and show all your work.
1. Simplify the expression:
2 3
3 2
2. Write the number in scientific notation.
Land area of a planet: 61,900,000 square miles
(𝑦) (𝑦) =
3. Factor out the common factor.
4. A soda company had sales of $19,570 million in 2002 and $35,137
(x + 3)2 − 4(x + 3) =
million in 2010. Use the Midpoint Formula to estimate the sales in
2006. Assume that the sales followed a linear pattern.
5. Find the center and radius of the circle.
(x − 1)2 + (y + 5)2 = 16
6. Identify any intercepts and test for symmetry:
y = 4 − |x|
Sketch the graph:
Sketch the graph:
7. Solve the equation and check your
solution.
4x + 8 = 13 − 2x
8. Solve the equation and check your solution:
9. Write the quotient in standard form:
2
3 − 7𝑖
10. Solve the equation:
4𝑥 3𝑥
−
=4
3
8
x4 − 81 = 0
11. Solve the quadratic equation by
completing the square:
12. A winch is used to tow a boat to a dock. The rope is
attached to the boat at a point 15 feet below the level of the
winch (see figure).
x2 + 6x + 4 = 0
Find the distance from the boat to the dock when there is 70 feet of
rope out. (Round to one decimal place.)
13. Write the quotient in standard form:
4
3 + 7𝑖
14. Solve the equation:
15. Solve the quadratic equation by
completing the square:
16. Solve the quadratic equation by
completing the square:
x2 + 6x + 8 = 0
x2 - 8x + 10 = 0
17. Solve the equation:
18. Write an equation that has the given solutions:
0, 7, 9
x4 − 16 = 0
|7x + 3| = 11
19. Solve the quadratic equation by
completing the square:
20. Solve the inequality. Then graph the solution set and give
the answer using set notation.
x2 + 6x + 8 = 0
−7 ≤ −2x − 5 < 3
Inequality solution:
Graph:
Set notation:
21. Find the slope and y-intercept (if
possible) of the equation of the line and
sketch a graph. 15x − 6y = 72
22. Write equation of the line through the point (6, 1) and
perpendicular to the line:
6x − 2y = 9.
Sketch:
23. Solve the quadratic equation by
completing the square:
x2 - 4x - 12 = 0
25. Find the zeros of the function
algebraically.
𝑥 2 − 9𝑥 + 14
𝑓(𝑥) =
2𝑥 − 4
24. A sub shop purchases a used pizza oven for $3265. After
five years, the oven will have to be discarded and replaced.
Write a linear equation giving the value V of the equipment
during the five years it will be in use.
26. Identify the intervals on which the function 𝑓(𝑥) = 𝑥 3 −
3𝑥 2 + 2 is increasing, decreasing, and constant.
Increasing:
Decreasing:
Constant:
27. Solve the quadratic equation by
completing the square:
28. Find the domain and range of the function:
𝑓(𝑥) = √𝑥 − 10
x2 - 4x - 9 = 0
Domain:
Range:
29. Find and simplify a polynomial
function that has the given zeros: 2, −6
30. You plan to construct an open box from a square piece of
material, 11 inches on a side, by cutting equal squares with
sides of length x from the corners and turning up the sides (see
figure).
Write a function V that represents the volume of the box.
V(x) =
31. Write the quadratic function in
standard form and sketch it’s graph:
h(x) = x2 − 4x + 6
32. Write the quadratic function in standard form, then provide
it’s vertex, axis of symmetry, and any x-intercepts.
f(x) = −(x2 + 2x − 3)
Standard form:
Graph:
Vertex:
Axis of symmetry:
X-intercepts:
33. The sales y (in billions of dollars )
for Harley-Davidson from 2000
through 2010 are shown in this table:
Create a scatterplot of the data.
Use regression to find a quadratic
model for the data.
Sketch the data points and the
curve.
In what year were the sales for
Harley-Davidson the greatest and
what are the sales from the
quadratic model. Give both answers
to two decimal places.
Equation:
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Max sales year:
Sales
2.91
3.36
4.09
4.62
5.02
5.34
5.80
5.73
5.59
4.78
4.86
Amount: