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1 QU-Placer Math Sample Test No. 1 Section 1: Elementary Algebra Answer the following questions: 1. The sum of two negative numbers is always a ______________________ . (A) Negative number (B) Positive number (C) Even number (D) Odd number 2. Which subset of real numbers contains 3√2 + 1 ? (A) Irrational Numbers (B) Rational Numbers (C) Integers (D) Whole Numbers 3. Perform the indicated operations and write the answer in the simplest form: (βˆ’ 2 125 Γ· 12 3 25 )Γ—βˆ’ 75 4 2 = β„Ž β‰  0 , β‰  0 (A) 5 16 (B) 3 1125 3 (C) βˆ’ 9 5 125 (D) βˆ’ 5 2 2 16 3 3

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Page 1: QU-Placer Math Sample Test No. 1

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QU-Placer Math Sample Test No. 1 Section 1: Elementary Algebra

Answer the following questions:

1. The sum of two negative numbers is always a ______________________ .

(A) Negative number

(B) Positive number

(C) Even number

(D) Odd number

2. Which subset of real numbers contains 3√2 + 1 ?

(A) Irrational Numbers

(B) Rational Numbers

(C) Integers

(D) Whole Numbers

3. Perform the indicated operations and write the answer in the simplest form:

(βˆ’π‘Ž 𝑏2

125Γ·

12π‘Ž3𝑏

25) Γ— βˆ’

75π‘Ž

4𝑏2= π‘€β„Žπ‘’π‘Ÿπ‘’ π‘Ž β‰  0 , 𝑏 β‰  0

(A) 5

16 π‘Ž 𝑏

(B) 𝑏3

1125 π‘Ž3

(C) βˆ’

9π‘Ž5𝑏

125

(D) βˆ’

5 π‘Ž2𝑏2

16 π‘Ž3 𝑏3

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4. Evaluate 8 + 16 Γ· 4 Γ— 5 βˆ’ 3

(A) 31

(B) 27

(C) 25

(D) 16

5. Evaluate 4 – 5 Β· [5 – (42 – 2)]

(A) 9

(B) 13

(C) 49

(D) 69

6. The statement β€œ81 is the product of a number and three times the same number” is

expressed by which of the following equations?

(A) 81 = π‘₯(π‘₯ + 3)

(B) 81 = π‘₯ βˆ™ 3π‘₯

(C) 81 = 3π‘₯(π‘₯ + 3)

(D) 81 = 3π‘₯ βˆ™ 3π‘₯

7. The solution of the equation 3(π‘₯ + 1) = π‘₯ + 2 is:

(A) 2

(B) 1

2

(C) βˆ’2

(D) βˆ’1

2

8. Which of the following represents the graph of the solution to the inequality

βˆ’12 ≀ 2π‘₯ βˆ’ 4 < 10 ?

(A)

(B)

(C)

(D)

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9. What is the leading coefficient in the polynomial 1

9π‘₯3 βˆ’

3

2π‘₯ + 11 ?

(A) βˆ’ 3

2

(B) 1

9

(C) 3

(D) 11

10. The quotient and the remainder of (π‘₯5 + π‘₯2 + π‘₯ + 1) Γ· (π‘₯2 βˆ’ 1) are: _________________ .

(A) Quotient: π‘₯3 βˆ’ π‘₯ + 1 Remainder: 2

(B) Quotient: π‘₯3 βˆ’ 2 Remainder: 3

(C) Quotient: π‘₯3 + π‘₯ + 1 Remainder: 2π‘₯ + 2

(D) Quotient: π‘₯3 + 2π‘₯ Remainder: 3π‘₯ + 1

11. Expand the binomial (2π‘₯ βˆ’ 3)3

(A) 6π‘₯3 βˆ’ 36π‘₯2 βˆ’ 54π‘₯ + 27

(B) 6π‘₯3 βˆ’ 18π‘₯2 + 27π‘₯ βˆ’ 27

(C) 8π‘₯3 βˆ’ 36π‘₯2 + 54π‘₯ βˆ’ 27

(D) 8π‘₯3 βˆ’ 6π‘₯2 + 6π‘₯ βˆ’ 27

12. π‘₯3 βˆ’ π‘₯2 + π‘₯ βˆ’ 1 is equivalent to: ______________________ .

(A) (1 βˆ’ π‘₯)(π‘₯2 βˆ’ 1)

(B) (π‘₯ βˆ’ 1)(π‘₯2 βˆ’ 1)

(C) (1 βˆ’ π‘₯)(π‘₯2 + 1)

(D) (π‘₯ βˆ’ 1)(π‘₯2 + 1)

13. 2π‘₯2 + π‘₯ βˆ’ 3 = ______________________ .

(A) (2π‘₯ + 1)(π‘₯ βˆ’ 3)

(B) (2π‘₯ βˆ’ 1)(π‘₯ + 3)

(C) (2π‘₯ + 3)(π‘₯ βˆ’ 1)

(D) (2π‘₯ βˆ’ 3)(π‘₯ + 1)

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14. Factor completely (4π‘₯2 βˆ’ 2π‘₯)

(A) π‘₯(4π‘₯2 βˆ’ 2)

(B) 2(2π‘₯2 βˆ’ 2π‘₯)

(C) 2π‘₯(2π‘₯ βˆ’ 1)

(D) 4π‘₯(π‘₯ βˆ’ 1)

15. Given that π‘₯

π‘₯ + 4Γ· 𝐾 =

π‘₯ βˆ’ 4

2 , which expression is equivalent to K ?

(A) 2π‘₯

π‘₯2 βˆ’ 16

(B)

π‘₯2 βˆ’ 16

2π‘₯

(C)

2π‘₯2

π‘₯ βˆ’ 4

(D)

π‘₯ βˆ’ 4

2π‘₯2

16. 8π‘₯+8𝑦

4 Β·

42

48π‘₯+48𝑦=

(A) 7

4(π‘₯ + 𝑦)

(B) 7(π‘₯ + 𝑦)

4

(C)

7

32

(D)

7

4

17. The LCM (Least Common Multiple) of the polynomials 8π‘₯2 βˆ’ 6π‘₯ βˆ’ 9 π‘Žπ‘›π‘‘ 16π‘₯2 βˆ’ 9 is:

(A) (2π‘₯ βˆ’ 3)(4π‘₯ + 3)2(4π‘₯ βˆ’ 3)

(B) (2π‘₯ βˆ’ 3)(4π‘₯ + 3)(4π‘₯ βˆ’ 3)

(C) (2π‘₯ βˆ’ 3)(4π‘₯ βˆ’ 3)2

(D) (2π‘₯ βˆ’ 3)(4π‘₯ + 3)2

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18. Which of the following expressions is equivalent to

2√π‘₯

3√π‘₯βˆ’2 ?

(A) 4π‘₯ + 4

9π‘₯ βˆ’ 4

(B) 4π‘₯

9π‘₯ βˆ’ 4

(C) 6π‘₯ + 4√π‘₯

9π‘₯ βˆ’ 4

(D) 6π‘₯ βˆ’ 4√π‘₯

9π‘₯ βˆ’ 4

19. Simplify

(32π‘₯13𝑦18)13

(π‘₯3𝑦3)13

(A) 2π‘₯𝑦 √2π‘₯𝑦3

(B) 2π‘₯𝑦 √2π‘₯3

(C) 2π‘₯3𝑦5 √4π‘₯𝑦3

(D) 2π‘₯3𝑦5 √4π‘₯3

20. Simplify 5 √27 βˆ’ 6 √3

(A) βˆ’βˆš30

(B) βˆ’βˆš24

(C) 9 √3

(D) 9 √6

21. What is the LCD (Least Common Denominator) of the equation

7

π‘₯ + 2 +

5

π‘₯ βˆ’ 2 =

10π‘₯ βˆ’ 2

π‘₯2 βˆ’ 4 ?

(A) π‘₯2 – 4

(B) π‘₯2 βˆ’ 16

(C) 10π‘₯ βˆ’ 2

(D) 12π‘₯ βˆ’ 2

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22. The solution set of the inequality 2 ≀ 4π‘₯ + 6 < 8 is: ______________________ .

(A) [βˆ’51

2, βˆ’4]

(B) [βˆ’4, 2]

(C) [βˆ’4, 2)

(D) [βˆ’1,1

2)

23. Which of the following equations has 2 and βˆ’10 as solutions?

(A) π‘₯2 βˆ’ 40π‘₯ βˆ’ 20 = 0

(B) π‘₯2 + 40π‘₯ βˆ’ 20 = 0

(C) π‘₯2 + 8π‘₯ βˆ’ 20 = 0

(D) π‘₯2 + 20 = 0

24. For which value(s) of 𝑐 does the equation √√π‘₯ + 4 βˆ’ βˆšπ‘ = 0 has a solution.

(A) 𝑐 = βˆ’4

(B) 𝑐 = 0

(C) 0 < 𝑐 < 4

(D) 𝑐 β‰₯ 4

25. The solution set of the equation 022 234 =+βˆ’βˆ’ xxxx is ______________________.

(A) }3,1,0,1{ βˆ’βˆ’

(B) }2,1,0,1{ βˆ’βˆ’

(C) }3,1,0,1{βˆ’

(D) }2,1,0,1{βˆ’

26. The solution set of the equation 18

π‘₯βˆ’2= 1 +

20

π‘₯+2 is ______________________ .

(A) {βˆ’20, 10}

(B) {8, βˆ’10}

(C) {βˆ’8, 10}

(D) {20, βˆ’10}

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27. The solution set of the equation |π‘₯2 + 3π‘₯ βˆ’ 2| + |βˆ’5| = 7 is ______________________ .

(A) {βˆ’4, βˆ’3, βˆ’1, 0}

(B) {βˆ’4, βˆ’3, 0, 1}

(C) {βˆ’3, βˆ’2, 0, 2}

(D) {βˆ’3, βˆ’1, 0, 4}

28. What is the value of the perimeter of triangle CAR?

(A) 6 + 6√2

(B) 6 + 6√3

(C) 12 + 3√2

(D) 18

29. The midpoint between A(βˆ’1, 3) and B(2, a) is ∢ ______________________ .

(A) (βˆ’3, 3 βˆ’ a)

(B) (1, 3 + a)

(C) (βˆ’

3

2,3 βˆ’ a

2)

(D) (

1

2,3 + a

2)

30. For the line 10π‘₯ + 2𝑦 = 6

(A) The slope = βˆ’10 and y-intercept = 6

(B) The slope = βˆ’5 and y-intercept = 3

(C) The slope = 3 and y-intercept = βˆ’5

(D) The slope = 5 and y-intercept = 3

Page 8: QU-Placer Math Sample Test No. 1

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Section 2: Pre-Calculus

Answer the following questions:

31. Which of the following is the correct graph of 𝑓(π‘₯) = π‘™π‘œπ‘”2(π‘₯ βˆ’ 2) βˆ’ 1 ?

(A)

(B)

(C)

(D)

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32. Using the graph of the function 𝑓 shown below, solve 𝑓(π‘₯) > 0.

(A) [βˆ’2, βˆ’1] βˆͺ [1,5]

(B) [βˆ’2, βˆ’1] βˆͺ (1,5)

(C) (βˆ’2, βˆ’1) βˆͺ (1,5]

(D) (βˆ’2, βˆ’1) βˆͺ (1,5)

33. If 𝑠𝑖𝑛 𝛼 = π‘π‘œπ‘  𝛼 and 𝛼 is in the third quadrant, then 𝛼 is equal to: ______________________ .

(A) πœ‹

4

(B) 7πœ‹

6

(C) 4πœ‹

3

(D) 5πœ‹

4

34. The domain of 𝑓(π‘₯) =√π‘₯+1

π‘₯βˆ’2 is ______________________ .

(A) [βˆ’1, ∞) (B) (βˆ’βˆž, 2) βˆͺ (2, ∞) (C) [βˆ’1,2) βˆͺ (2, ∞) (D) (βˆ’βˆž, ∞)

35. If 8π‘₯ = (

1

2)

2π‘₯βˆ’5 then π‘₯ = ______________________ .

(A) βˆ’5

(B) βˆ’1

(C) 1

(D) 5

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36. If 2π‘₯ βˆ’ 31βˆ’π‘₯ = 0 then π‘₯ = ______________________ .

(A) π‘₯ = βˆ’

ln 3

ln 3+ln 2

(B) π‘₯ =

1

ln 3+ln 2

(C) π‘₯ = βˆ’

1

ln 3+ln 2

(D) π‘₯ =

ln 3

ln 3+ln 2

37. State the domain of the relation {(–10, 9), (6, 0), (–5, 0)}.

(A) Domain = {–10, –5, 0, 6, 9}

(B) Domain = {–10, –5, 0, 6}

(C) Domain = {–10, –5, 6}

(D) Domain = {0, 9}

38. Given the graph of function 𝑓(π‘₯), what is domain of 𝑓(π‘₯)?

(A) [βˆ’5,9)

(B) [βˆ’5,0) βˆͺ (0,9)

(C) [βˆ’5,0) βˆͺ (0,4) βˆͺ (4,9)

(D) [βˆ’5,1) βˆͺ (2,4) βˆͺ (4,9)

[

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39. What is the range of the function 𝑓(π‘₯) = log3(π‘₯2 + 1)?

(A) (0, ∞)

(B) [0 , ∞)

(C) (1, ∞)

(D) [1 , ∞)

40. Find the inverse of the function ( ) – 8f x x=

(A) 1 2( ) + 8f x xβˆ’ = for 8x

(B) 1 2( ) + 8f x xβˆ’ = for 0x

(C) 1 2( ) + 8f x xβˆ’ = for any real number π‘₯

(D) 1 1( )

– 8f x

x

βˆ’ = for 8x

41. If ln 2 = 𝑠 and ln 3 = 𝑑 then ln √243

(A) 𝑠𝑑

(B) 𝑠𝑑

3

(C) 𝑠 +

𝑑

3

(D) None of the above

[

42. Select the possible graph for the function

𝑓(π‘₯) = βˆ’(π‘₯ βˆ’ π‘š)(π‘₯ βˆ’ 𝑛), if π‘š > 0 and 𝑛 > 0

(A)

(B)

(C)

(D)

–6 –5 –4 –3 –2 –1 1 2 3 4–1

1

2

3

4

5

6

7

8

9

10

x

y

–1 1 2 3 4 5 6 7 8 9 10

–4

–3

–2

–1

1

2

3

4

5

6

7

8

9

10

x

y

–5 –4 –3 –2 –1 1 2 3 4 5 6

–5

–4

–3

–2

–1

1

2

3

4

5

6

x

y

–3 –2 –1 1 2 3 4 5

–3

–2

–1

1

2

3

4

5

x

y

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43. If logπ‘₯ 𝑦 = 1

2 then logπ‘₯ π‘₯ 𝑦2 = ______________________ .

(A) 1

(B) 2

(C) 3

(D) 4

44. βˆ’

cot2 π‘₯1βˆ’csc π‘₯

= ______________________ .

(A)

1+cos π‘₯

cos π‘₯

(B)

1+sin π‘₯

sin π‘₯

(C) βˆ’1

(D) 1

45. The graph of the function 𝑔(π‘₯) =π‘₯3βˆ’π‘₯

π‘₯2+4 𝑖𝑠 ______________________ .

(A) Symmetric with respect to the origin

(B) Symmetric with respect to the π‘₯ βˆ’ axis

(C) Symmetric with respect to the 𝑦 βˆ’ axis

(D) Symmetric with respect to the line 𝑦 = π‘₯

46. List all the intervals on which the graph of 𝑓(π‘₯) is decreasing.

(A) (βˆ’1,0), (1,2)

(B) (1,2)

(C) (1,0), (2,1)

(D) (1,0)

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x-axis

y-axis

(-4,-3)

(-2,0)

(-1,1)

(0,0)

(1,2)

(2,1)

(3,4)

f(x)

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47. If π‘₯ & 𝑦 angles are both in the third quadrant and 𝑠𝑖𝑛 π‘₯ = βˆ’3

5 and π‘π‘œπ‘  𝑦 = βˆ’

√3

2 .

Find cos( π‘₯ + 𝑦).

(A)

βˆ’5√3 βˆ’ 10

10

(B)

4√3 βˆ’ 3

10

(C)

βˆ’5√3 + 10

10

(D)

4√3 + 3

10

48. Given 𝑓(π‘₯) = 2(π‘₯ βˆ’ 1) and 𝑔(π‘₯) = π‘₯2 + 1 , find the composite function defined by

(𝑓 ∘ 𝑔)(π‘₯).

(A) 2π‘₯2

(B) 2π‘₯2 βˆ’ 2

(C) 4π‘₯2 βˆ’ 8π‘₯ + 5

(D) 4π‘₯2 + 8π‘₯ + 5

49. To obtain the graph of 𝑔(π‘₯) = (π‘₯ βˆ’ 4)2 + 3 , the graph of 𝑓(π‘₯) = π‘₯2 must be shifted

(A) right 4 units, up 3 units

(B) right 4 units, down 3 units

(C) left 4 units, up 3 units

(D) left 4 units, down 3 units

50. Which angle is co-terminal with 300Β° angle?

(A) 660Β°

(B) 480Β°

(C) 390Β°

(D) 60Β°

51. The solution set to 1 βˆ’ π‘π‘œπ‘ 2 π‘₯ = 0 in interval [ 0, 2πœ‹] is ______________________.

(A) { πœ‹

2 , 2πœ‹ }

(B) { πœ‹

2 , πœ‹ }

(C) { πœ‹

2 , πœ‹ ,

3πœ‹

2 }

(D) { 0 , πœ‹ , 2πœ‹ }

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52. If 𝑓(π‘₯) = π‘₯2 βˆ’ 2π‘₯ + 3 and 𝑔(π‘₯) = |π‘₯ βˆ’ 3|, then 𝑓(0)

𝑔(1)= ______________________ .

(A) βˆ’

3

2

(B) βˆ’1

(C)

2

3

(D)

3

2

23

53. The graph of the function 𝑓(π‘₯) = √π‘₯3

is ______________________ .

(A)

(B)

(C)

(D)

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54. The function representing the following graph is ______________________.

(A) 𝑓(π‘₯) = 2π‘₯ βˆ’ 2

(B) 𝑓(π‘₯) = βˆ’

1

π‘₯+ 1

(C) 𝑓(π‘₯) = ln (π‘₯)

(D) 𝑓(π‘₯) =

1

π‘₯2

55. If 𝑠𝑖𝑛(π‘₯) = βˆ’4

5 and π‘π‘œπ‘ (π‘₯) < 0 then 𝑠𝑖𝑛(2π‘₯) = ______________________ .

(A) βˆ’

24

25

(B) βˆ’

1

25

(C) 1

25

(D) 24

25

56. In which quadrants is π‘‘π‘Žπ‘› π‘₯ = sin π‘₯

√1βˆ’π‘ π‘–π‘›2 π‘₯ ?

(A) I, II

(B) I, III

(C) I, IV

(D) All Quadrants

57. Which of the following functions is one to one?

(A) 𝑓(π‘₯) = π‘₯3

(B) 𝑓(π‘₯) = |π‘₯ + 1| for π‘₯ ≀ 0

(C) 𝑓(π‘₯) = 𝑙𝑛|π‘₯|

(D) 𝑓(π‘₯) = 𝑒π‘₯2+ 1

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58. Using the given graphs, which of the functions has two real zeros?

(A)

(B)

(C)

(D)

59. The graph of the inverse for the function graphed below is ______________________ .

(A)

(B)

(C)

(D)

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60. The graph of function 𝑓 is given below

Which of the following is the graph of (π‘₯) = 1 βˆ’ 𝑓(π‘₯) ?

A)

B)

C)

D)

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Answer Key

Section 1 1. A 2. A 3. A 4. C 5. C 6. B 7. D 8. A 9. B 10. C 11. C 12. D 13. C 14. C 15. A 16. D 17. B 18. C 19. D 20. C 21. A 22. D 23. C 24. D 25. D 26. B 27. B 28. A 29. D 30. B

Section 2 31. C 32. C 33. D 34. C 35. C 36. D 37. C 38. B 39. D 40. B 41. C 42. B 43. B 44. B 45. A 46. A 47. B 48. A 49. A 50. A 51. D 52. D 53. C 54. C 55. D 56. C 57. A 58. C 59. B 60. C