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MATH MAJOR 112- COLLEGE AND ADVANCE ALGEBRA

Total questions: 50

Worksheet time: 29mins

Name
Class
Date
1.

1. When finding the inverse of a relation, First; you replace f(x) with y, Second, switch the x's and y's. What do you do next?

a)
solve for y
b)
replace y with f-1(x)
c)
solve for x
d)
find the greatest common factor
2.

2. If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?

a)
(1, 4) and (4, 6)
b)
(-4, -1) and (-6, -4)
c)
(-1, -4) and (-4, -6)
d)
(4, 1) and (6, 4)
3.

3. Which is greater,  26540 or 50?

a)
26540
b)
50
c)
They are the same
d)
Zero is greater
4.

4. Solve for x and y.

y = 2x + 1

y = 4x - 1

a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
5.

5. What is the inverse of the points (1,3)(2,4)(6,2)

a)
(2,6)(3,1)(4,2)
b)
(-3,-1)(-4,-2)(-2,-6)
c)
(1,3)(2,4)(6,2)
d)
(-1,-3)(-2,-4)(-6,-2)
6.

6. What is the solution?

a)

one solution

b)

no solution

c)

infinitely many solution

d)

two solutions

7.

7. If a system of equations has no solution, what does the graph look like? 

a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
8.

8. A mathematical phrase that uses variables, numerals, and operation symbols.

a)

algebra

b)

equation

c)

algebraic expression

d)

quadratic equation

9.

9. Which of the following expresses 1+3+5+...+39

a)

∑k=1202k−1\sum_{k=1}^{20}2k-1

b)

∑k=240k−1\sum_{k=2}^{40}k-1

c)

∑k=−137k+2\sum_{k=-1}^{37}k+2

d)

∑k=1392k−1\sum_{k=1}^{39}2k-1

10.

10. A ______ is a letter which represents an unknown number (quantity). 

a)
expression
b)
variable
c)
term
d)
like term
11.

11. What does it mean to find the inverse of a function?

a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
12.

12. The algebraic expression that best describes the sequence 12, 24, 36, 48... is

a)
x + 12
b)
12x
c)
2x + 12
d)
3x + 2
13.

13. What is the value of the expression 2x2 - 5y + 3 when x=3 and y=3

a)

0

b)

30

c)

6

d)

-3

14.

14. Jovelyn has c cookies for lunch and Elizabeth has 3 times as many. Which expression shows how many cookies Elizabeth has for lunch?

a)

3 + c

b)

3c + c

c)

3/c

d)

3c

15.

15. Which property is displayed?

(8 + 7) + 9 = 8 +(7 + 9)\left(8\ +\ 7\right)\ +\ 9\ =\ 8\ +\left(7\ +\ 9\right)  

a)

Commutative Property of Addition

b)

Associative Property of Addition

c)

Additive Identity Property

d)

Distributive Property

16.

16. Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)).  Are the two functions inverses of each other?

a)
x + 20 ; Yes they are inverses
b)
x + 20 ; No, they are not inverses
c)
x ; Yes they are inverses
d)
x ; No, they are not inverses
17.

17. The process of finding the value of a numerical or algebraic EXPRESSION is called what?

a)

identifying

b)

graphing

c)

evaluating

d)

solving

18.

18. Simplify the exponential expression:

a)
10x-2
b)
2x2
c)
2x12
d)
10x12
19.

19. What is the degree of the polynomial function P(x)=3x4-7x2-2x7-x+4?

a)
4
b)
7
c)
2
d)
11
20.

20. A website charges $5.99 to download a game, and there is a $6.99 membership fee. Write an expression to represent the total cost to download "g" games

a)

5.99g

b)

6.99g

c)

5.99g + 6.99

d)

6.99g + 5.99

21.

21. True or False. A polynomial function with rational coefficients of degree 4 must have at least 1 rational zero.

a)
True
b)
False
22.

22. Solve for x and y.

y = 2x + 1

y = 4x - 1

a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
23.

23. Exponential functions have _________.

a)

Vertical asymptote at x=0

b)

Vertical asymptote at x=1

c)

Horizontal asymptote at y=1

d)

Horizontal asymptote at y=0

24.

24. True or False: In order to multiply powers with the same base, add the exponents.

a)

True

b)

False

25.

25. Find all zeros for the polynomial function P(x)=x3−3x2−5x+15P(x)=x^3-3x^2-5x+15  .

a)
3, √5 
b)
3, √5, -√5
c)
-3, √5, -√5
d)
-3, 5i, -5i
26.

26. Solve the system of equations.

y = 4x+1

3x + 2y = 13

a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
27.

27. Rewrite log28 = 3 in exponential form.

a)
28 = 3
b)
23 = 8
c)
32 = 8
d)
83 = 2
28.

28. According to exponent rules, when we raise a power to another exponent we _____ the exponents.

a)

multiply

b)

divide

c)

subtract

d)

add

29.

29. What property of equality is shown below?

If 2x - 5 = 10, then 2x = 15.

a)
Subtraction Property of Equality
b)
Addition Property of Equality
c)
Division Property of Equality
d)
Substitution
30.

30. Logarithmic functions are the inverse of ______.

a)
Linear Functions
b)
Exponential Functions 
c)
Quadratic Functions 
d)
Polynomial Functions 
31.

31. Is this set state as a relation: D={(16,-4), (9,3), (9, -3), (16, 4), (1, -1)}?

a)

Yes

b)

No

c)

Maybe

32.

32. The y-coordinate of a point is also called?

a)

abscissa

b)

ordinate

c)

ordered pair

d)

quadrant

33.

33. True or False. If there is only one point of intersection between the graph and the vertical line, then, the graph is a graph of a function.

a)

True

b)

False

34.

34. Identify if this ordered pair a function or relation, then what should be the reason for your answer: I={(4, 3), (-1, 2), (3, 5), (4, -7), (8, 10), (-3, 2)}.

a)

Relation. It has no repetition of x values.

b)

Relation. There are common elements in the given set.

c)

Function. No common x-coordinates exist in the given set.

d)

Function. It has positive values in some coordinates.

35.

35. Which quadrant contains the point named by (2, 5)?

a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
36.

36. What is the distance between the points (-5 ,2) and (2 ,-2)?

a)

3

b)

9

c)

13\sqrt{13}  

d)

65\sqrt{65}  

37.

37. Who introduced the rectangular coordinate system?

a)

Rene Requiestas

b)

Reneé Descartes

c)

René Descartes

d)

René Descarts

38.

38. What refers to the checkmark symbol that tells us to square root something?

a)
the index
b)
the radical sign
c)
the radicand
d)
none
39.

39. True or False. The Cartesian coordinate plane is composed of infinite number of points

a)

True

b)

False

40.

40. Find the distance between (1/2,1) and (-3/2, 3)

a)

2√5

b)

2√10

c)

4√10

d)

none of the choices

41.

41. True or False: The rectangular coordinate system is named after Albert Einstein?

a)

True

b)

False

42.

42. True or False. The ordinate of any point on the y-axis has non-zero value except at the origin.

a)

True

b)

False

43.

43. True or False. All functions are relation, but not all relations are function.

a)

True

b)

False

44.

44. Simplify the following radical: √32

a)
3√2
b)
4√8
c)
16√2
d)
4√2
45.

45. Consider the function y<2x+3. Which is true?

a)
The line would be solid with shading above.
b)
The line would be dashed with shading above.
c)
The line would be solid with shading below.
d)
None of these.
46.

46. If f(x) = 5x and g(x) = 2x-1, What is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x2-1

d)

5x2-5

47.

47. The number inside the radical is called ______.

a)
the index
b)
the radical sign
c)
the radicand
d)
none
48.

48. True or False. The inverse of f(x) = x2 is f-1(x) = √(x).

a)

True

b)

False

49.

49. Solve the inequality: x + 5 ≤ 13

a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8 
d)
x ≤ 18 
50.

50. Given g(x) = -2x+2 and f(x) = 3x2+4, find (g+f)(-3).

a)
39
b)
-27
c)
-23
d)
-19

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