Algebra Practice Test
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1. A television is on sale for $400. If the sale price is 20 % less than the regular price, what was the regular price in dollars? Give your answer to the nearest one hundredth.
a. / 501b. / 502
c. / 497
d. / 503
e. / 500
2. The total surface area S of a triangular box
is given by the following formula
S = 2(a + b)h + 2ab
Find h , if S = 332 , a = 4 , and b = 9 .
a. / 5b. / 12
c. / 8
d. / 5
e. / 10
3. The total surface area A of a right circular cone
is given by the following formula
A = π r a + π r2
Find a , if A =44 π and r = 4 .
a. / 8b. / 9
c. / 7
d. / 4
e. / 10
4. Solve for x:
5(x - 3) + 19 = 3(x - 6) + 44
.
a. / 10b. / 9
c. / 14
d. / 8
e. / 11
5. The equation of a line in general form is given by:
6 x - 4 y + 6 =0 .
Find the slope of that line. Give your answer as a common fraction in lowest terms in the form a/b.
b. / 1
c. / 3/2
d. / 5/2
e. / 1/2
6. The equation of a line in general form is given by:
2 x - 6 y + 2 =0 .
Find the y -intercept of line that contains the point (-12, -2) and is parallel to the line above.
b. / 0
c. / 2
d. / 5
e. / -1
7. Which line a, b, c, d or e is the graph of the equation
y = -3 x + 4 ?
b.
c.
d.
e.
8. The sum of two numbers is 23 and their product is 120. Find the biggest number.
a. / 16b. / 17
c. / 12
d. / 15
e. / 18
9. When you factor completely the following polynomial:
y2 - 8 y + 15 .
One of the factors is:
a. / (y+3)b. / (y+5)
c. / (y-4)
d. / (y-2)
e. / (y-5)
10. One of the graphs below ( a, b, c, d or e ) is the graph of the rational function
1y / =
(x + 1)x(x - 2)
Which one?
b.
c.
d.
e.
11. One of the graphs below ( a, b, c, d or e ) is the graph of a one to one function defined on the interval [-3,3] . Which one?
a.b.
c.
d.
e.
12. Let f(x) = exand g(x) =ln(x) . Compute f(g(2)) .
a. / e2b. / 1/2
c. / 2
d. / ln(2)
e. / -2
13. Solve 22 x -3 = 8 . Give your answer as a common fraction in lowest terms.
a. / 3b. / 2
c. / 4
d. / 1
e. / 5
14. Solve the logarithmic equation
3 log9 x = log9 27 .
b. / 9
c. / 3
d. / -9
e. / 12
15. Let f(x) = ln(x-2) + 4 . One and only one of the statements below is true:
a. / The inverse of the function f is the function g(x)= e(x+4) + 2b. / The inverse of the function f is the function g(x)= e(x-2) + 2
c. / The inverse of the function f is the function g(x)= e(x-4) + 2
d. / The inverse of the function f is the function g(x)= e(x-4) + 4
e. / The inverse of the function f is the function g(x)= e(x-2) + 4
16. Let f(x) = ex-3 - 6 . One and only one of the statements below is true:
a. / The inverse of the function f is the function g(x)= ln(x-6) + 3b. / The inverse of the function f is the function g(x)= ln(x+6) - 3
c. / The inverse of the function f is the function g(x)= ln(x-6) - 3
d. / The inverse of the function f is the function g(x)= ln(x+6) + 3
e. / The inverse of the function f is the function g(x)= ln(x-3) + 6
17. The following is the equation of an ellipse
9 x2 + 25 y2 = 225
Find its positive x -intercept.
a. / 6b. / 7
c. / 5
d. / 2
e. / 8
18. The graph below is the graph of the hyperbola
(x - m)2 / (y - n)2- / = 1
9 / 16
Find the sum m+n of the coordinates of its center (m,n) .
a. / 3b. / 2
c. / 4
d. / 7
e. / 1
19. The graph below is the graph of a parabola and its directrix ( both in red ). Find the x- coordinate of its focus?
a. / -9b. / 9
c. / 6
d. / -6
e. / 10
20. Solve the inequality (9 x + 10)/(x + 7) < 8 . The solution set is one of the following
Which one?
b. / The interval (-7,46)
c. / The intervals (- ∞,-7) or (46, ∞)
d. / The interval (-∞,7]
e. / The interval [-7,46]
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