act math practice exam 3...lastly, go back through the exam using the hints to brush up on the ones...

!Practice!Math!ACT!Test!3!

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© 2013 Sophia Learning, LLC. !

Notes on the Practice Exam This practice exam has three major sections to it: test, answer key with hints, and scoring guide. You’ll get the most out of this practice if you make the experience as authentic as possible so carefully follow the directions below. Good luck. Directions Find a quiet place to spend the next hour or two. Clear away all distractions and set a timer for 60 minutes. Once you start the timer resist the urge to pause for any reason or to peek ahead at the answers and hints. Once the timer goes off stop all work on test. Use the answer key to correct your test and the scoring guide to estimate your score on this practice exam. Lastly, go back through the exam using the hints to brush up on the ones you missed. Practice Exam 3 1. At the gym on Monday, Joe lifted 215 pounds. On Friday he lifted 315 pounds. What was the percent increase in the amount he lifted? A. 21.5% B. 31.7% C. 46.5% D. 68.3% E. 100%

2.

€

3 38

+ 4 56

+ 5 12

= ?

A.

€

12 916

B.

€

121724

C.

€

12 23

D.

€

13 524

E.

€

131724


!


3. In her first six basketball games, Melissa scored 23 points, 25 points, 21 points, 18 points, 23 points and 22 points. How many points does she need to score in her seventh game if she wants to bring her average up to 23 points per game? A. 22 B. 23 C. 25 D. 29 E. 36 4. Find the value of x in the following equation: 3x + 7 = 8x + 13

A. −65

B. −611

C. 65

D. 2011

E. 4 5. Maria went shopping for a pair of shoes at a discount store where all merchandise is 20% off the original retail price. She found a pair that was on clearance for an additional 30% off. If Maria paid $50.40 for the shoes before sales tax, what was the original retail price? A. $60.48 B. $72 C. $78.62 D. $90 E. $100.80 6. Which of the following is NOT a real number? A. π

B.

C. 1.080080008….

D. E. 20

87

−9


!


7. The student council is choosing a committee to plan the spring dance. If there are 15 members of the student council, and the council members have already elected a committee chair, how many possible 5-person committees could be formed if the elected chair must be included on the committee? A. 256 B. 1001 C. 3003 D. 3125 E. 24,024 8. Which of the following numbers is the smallest?

A.

B. 0.078%

C. 7.8×10−5 D. 7.8(0.0001)

E. 0.00078 9. Kendra is baking cookies, and the recipe calls for 3 ½ cups of flour for 18 cookies. If she wants to make 4 dozen cookies, how many cups of flour does she need?

A.

B. 8

C.

D. 14

E.

10. If 30% of y is 36, what is 150% of y? A. 54 B. 60 C. 64.8 D. 120 E. 180

78010,000

€

1 516

€

9 13

€

15 34


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11. Brandon rolls two 6-sided dice. If the first die he rolls lands on 3, what is the probability that the sum of the dice is less than 7?

A.

B.

C.

D.

E.

12. Two thirds of the students on the track and field team compete in running events. One quarter of these students compete at the regional meet. If 8 students compete in running events at the regional meet, what is the total number of students on the team? A. 16 B. 24 C. 32 D. 48 E. 64 13. What is the product of 4.35 x 105 and 9.87 x 10-9? A. 42.93 B. 4.293 x 10-3 C. 4.293 x 10-4

D. 4.293 x 10-5 E. 42.93 x 10-45

14. The after school kickboxing club has a ratio of girls to boys of 2:5 for its first week. In the second week, 12 more girls join the club. If there are 15 boys in the club, what is the new ratio of girls to boys for the second week? A. 6:5 B. 4:5 C. 14:15 D. 5:6 E. 14:5

14112122356


!


15. Which of the following is NOT a monomial? A. 4z

B. 3xy2

C. 54

D. 5x

E. 1

16. If

€

m =6p2taz3

, which of the following expressions is equivalent to t?

A.

€

amz3

6p2

B.

€

6p2maz3

C.

€

6p2

amz3

D.

€

az3

6mp2

E.

€

m6ap2z3

17. Simplify the following expression: (6x - 5)(3x + 4) A. 9x2 - 1 B. 18x2 – 9x - 20 C. 18x2 – 20 D. 9x2 + 2x - 9 E. 18x2 + 9x - 20 18. A rectangular garden has a length that is 3 feet more than the square of two times its width. What is an expression for the area of the garden in terms of the width, w? A. w + 3 B. 8w2 + 6 C. 4w2 + 3 D. 4w2 + 3w E. 4w3 + 3w


!


19. If x and y are both even integers, which of the following could be odd? A. x + y B. x − y C. xy

D. x2+ y

E. x + 4y 20. What is the value of |a –b|3 + 2a if a = -5 and b = -3? A. -18 B. -2 C. 2 D. 18 E. 502

21. Simplify the following expression:

€

(6a2b−3)−2

b2c −4

A.

€

6b4c 4

a4

B.

€

36b4c 4

a4

C.

€

b4c 4

36a4

D.

€

b4c 4

6a4

E.

€

c 4

36a4b8

22. What is the product of the roots of the equation 2x2 + 5x - 3 = 0? A. −3

B. 12

C. −32

D. 32

E. −12


!


23. Solve the following equation for x:

€

6(x − 3)5

=32(x + 7)

A. −1417

B. −47 C. −6 D. −13

E. 697

24. Bonnie is making baskets to sell at the neighborhood festival. She starts the day already having made 5 baskets. If it takes her 2 hours to make one basket, which of the following represents a function that can be used to determine how many baskets she has ready to sell after x hours?

A. f (x) = 12x + 5

B. f (x) = 5x

C. f (x) = 2x + 5

D. f (x) = 2x

E. f (x) = 12x

25. Which of the following is not in the domain of f (x) = 3+ 15− 4x ?

A. −5 B. 0 C. 1

D. 3 E. 4

26. For all x > 4, what is the fully simplified form of the expression

€

(x 2 − x −12)(x − 4)(x − 4)2(2x + 6)

?

A.

€

x 2 − x −12(x − 4)(2x + 6)

B.

€

x + 32x + 6

C.

€

x 2 − x −122x 2 − 2x − 24

D. 12

E. The expression is already fully simplified


!


27. If f (x) = 6x2 + x and g(x) = x2− 5 , what is f (g(6))?

A. -26 B. -2 C. 22 D. 106 E. 222 28. Simplify: (5− i)(6+ i) A. 31− i B. 29− i C. 31 D. 29+ i E. 31+ i 29. At the state fair, a stand sells funnel cakes for $3.75 and footlong hot dogs for $3. On a particularly busy day, the stand sold a total of 1975 items and made a profit of $6,712.50. How much of that day’s profit came from funnel cakes? A. $925 B. $1050 C. $2775 D. $3150 E. $3937.50 30. Which of the following is an arithmetic sequence? A. 3, 6, 10, 15, 21, … B. 2, 4, 8, 16, 32, … C. 5, 2, -1, -4, -7, … D. 1, 1/10, 1/100, 1/1000, …. E. 1, 1, 2, 3, 5, 8, 13, … 31. A rectangle’s length is 4 inches less than 3 times its width. If the area of the rectangle is 27 in2, what is its length?

A. 2 85

B.

€

85 − 2

C.

€

2 + 853

D.

€

85 + 2

E.

€

2 − 853


!


32. Which inequality represents the solution to -2|x - 5| + 7 < 4?

A. 72< x < 13

2

B. x > 132

C. x < 72

or x > 132

D. x < 132

E. x < −10 or x >10

33. Which of the following is NOT a function?

A. y = x2

B. x = y2

C. y = x −1

D. y = 2

E. 2y = 4x 34. The equation 3x – 4y = 6 represents a line in the x-y coordinate plane. If the y-coordinate of a point on this line is -4, what is its x-coordinate?

A. −92

B. −103

C. −32

D. 32

E. 223

35. A triangle in the coordinate plane has the vertices (2, 9), (-6, 1), and (-2, -4). What is the perimeter of the triangle, to the nearest unit? A. 22 B. 23 C. 29 D. 31 E. 33


!


36. Which of these lines is parallel to 2x – 5y = 3?

A. y = 25x + 7

B. y = − 52x + 7

C. y = 52x + 7

D. y = − 25x + 7

E. y = 2x + 7 37. Which of the following inequalities describes the given number line graph?

A. x ≤ -5 and x > 3 B. x > 3 C. x < -5 or x ≥ 3 D. x ≥ -5 or x < 3 E. x ≤ -5 or x > 3 38. What is the slope of the line that goes through the points (-3, 1) and (-6, -8)? A. −3

B. −13

C. 1

D. 13

E. 3 39. A rectangle in the coordinate plane has vertices at (3, 7), (3, 4), (-2, 4), and (-2, 7). What are the coordinates of the intersection point of its diagonals? A. (3, 5.5) B. (0.5, 5.5) C. (-2, 5.5) D. (0.5, 7) E. (0.5, 4)


!


40. A triangle has vertices at (6, 5) and (-4, 3). Which of the following possible third vertices will make this triangle a right triangle? A. (6, 3) B. (6, -4) C. (5, -4) D. (5, 3) E. (-4, 6) 41. Which of the following is the equation of a circle with a radius of 6 and a center at (-2, 1)? A. x2 + y2 = 36 B. (x - 2)2 + (y + 1)2 = 36 C. (x + 2)2 + (y - 1)2 = 6 D. (x + 2)2 + (y - 1)2 = 36 E. x2 + y2 = 6 42. Which of the following equations represents the line in the given graph?

A. y = 2x + 2

B. y = 12x +1

C. y = 2x +1

D. y = 2x − 12

E. y = 12x − 12


!


43. In the diagram below, lines and m are parallel. Which of the following pairs of angles is supplementary?

A. 2 and 3 B. 3 and 7 C. 1 and 8 D. 4 and 6 E. 3 and 6 44. Which of the following statements about rectangles is NOT true? A. All rectangles are parallelograms. B. Opposite sides of a rectangle are congruent. C. Diagonals of a rectangle are perpendicular. D. Diagonals of a rectangle bisect each other. E. Adjacent sides of a rectangle are perpendicular. 45. In the given circle, θ measures 105°. If the radius of the circle is 6 in, what is the area of the shaded region?

A. 36π

B.

€

17π4

C.

€

17π24

D.

€

51π2

E.

€

21π2


!


46. In quadrilateral FGKH,

€

∠FHK = 70° . If FGKH is a parallelogram, what is the sum of

€

∠HFG and

€

∠HKG?

A. 110° B. 140° C. 180° D. 220° E. 240° 47. A function f(x) is graphed on the coordinate plane. A series of transformations are performed, creating the new function -f(x - 4). Which of these best describes the transformations performed on f(x)? A. Reflection over the y-axis and horizontal translation of 4 units to the right B. Reflection over the x-axis and horizontal translation of 4 units to the left C. Reflection over the x-axis and horizontal translation of 4 units to the right D. Reflection over the y-axis and horizontal translation of 4 units to the left E. None of these 48. In the given figure, A, B, and C are collinear,

€

AD ≅DB , and

€

∠DBC =112° . What is the measure of

€

∠ADB?

A. 44° B. 56° C. 68° D. 112° E. 136° 49. A rectangle has an area of 108 in2. If its length is 3 times as long as its width, what is the perimeter of the rectangle? A. 6 in B. 18 in C. 36 in D. 48 in E. 54 in


!


50. The given figure shows a regular pentagon in a circle with the same center. If one of the sides of the pentagon is 5 inches and the radius of the circle is 6 inches, what is the area of the shaded region, to the nearest square inch?

A. 59 in2 B. 70 in2 C. 103 in2

D. 93 in2 E. 113 in2

51. In the given diagram, , m , and n are all parallel to each other. What is the value of x?

A. 5 B. 6 C. 7 D. 12 E. 13.5


!


52. A right circular cone with a radius of 9 cm and a height of 14 cm is placed on top of a cylinder with the

same radius. If the height of the entire figure is 27 cm, what is the volume of the figure? Vcone =13πr2h

A. 378π B. 1053π C. 1431π D. 2187π E. 2565π

53. In the given diagram, C, K and G are collinear, FK ⊥CG and DH ⊥ JE . If

€

∠EKG = 40°, what is the measure of

€

∠DKC?

A. 30° B. 40° C. 50° D. 60° E. Cannot be determined from the information given


!


54. WZ and XY , the diagonals of isosceles trapezoid WXYZ, intersect at point J. If JZ = 8, JW = 6, and YZ

= 12, what is the length of the other base, WX ?

A. 4 B. 6 C. 8 D. 9 E. 10 55. A pirate ship hangs a triangular sail from a mast. The corner of the sail is anchored to the deck of the ship 10 feet away from the base of the mast. If the length of the sail from the anchor point to the top of the mast is 14 feet, how tall is the mast? A. 4 ft

B. 2 74 ft C. 96 ft D. 296 ft

E. 4 6 ft 56. In the given circle, the measure of arc ABC is 290°. What is the measure of

€

∠ABC?

A. 35° B. 70° C. 140° D. 145° E. 290°


!


57. In the given triangle, which of the following is an expression that represents the length x?

A.

B.

C.

D.

E.

58. Which of the following expressions is equivalent to ?

A. -1

B.

C.

D.

E.

59. What is the amplitude of the function f(x) = 3cos(4x) – 2?

A.

B.

C. -2 D. 3 E. 4

6sin(400 )6sin(400 )cos(400 )

6sin(400 )6

6cos(400 )

€

csc(−θ)cot(θ)cos(θ)

€

−1sin2(θ )

€

−1cos2(θ )

€

−cos2(θ )sin2(θ)

€

1sin2(θ )

π213


!


60. If cos(θ ) = − 32

and 90° < θ < 180°, what is the value of csc(θ)?

A. −12

B. 12

C. 2 D. −2

E. 23

ANSWER KEY IS ON THE NEXT PAGE

Answer Key

Question #: Correct Answer Hint

1

C Start by finding the difference in weight lifted from one day to the next. Percent increase is the percent this number is of the original amount.

2

E

If you add the whole numbers and fractions separately, be careful! If you end up with an improper fraction you’re going to need to add one to the whole number part of your simplified answer.

3 D Let x be the number of points scored in the seventh game. Then you can write an equation for the average points scored over seven games, using 23 as the average you want to get.

4 A To solve an equation with variables on both sides, start by getting all the variable terms on one side and all the constants on the other.

5 D Be careful! You can’t just add the percents here! You need to deal with each percent separately.

6 D Remember, a real number is any number that can be found on the number line. So rational and irrational numbers are real numbers, but imaginary numbers are not.

7 B Since the committee chair has already been chosen and must be on the committee, you’re really just choosing 4 more people from the remaining 14 council

act math practice exam 3...lastly, go back through the exam using the hints to brush up on the ones...

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