Download E. x = − 2 5 4 17 - Vinemont High School

 Practice Math ACT® Test 2 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 2
1. Which of the following numbers is the smallest?
A. 8.5%
B. 85/100
C. 8.5
D. 85(0.001)
-3
E. 8.5 x 10
2. Find the value of x in the following equation: 4x – 7 = 6x + 3
A. x = -10
B. x = -5
C. x = -2
D. x = -1
E.
x=−
2
5
3. Which of the following is NOT a rational number?
A.
16
B. 12
C. 12%
4
D. 17
E. 0.3
€
© 2013 Sophia Learning, LLC.
Practice Math ACT® Test 2 4. Amanda scored 87%, 97%, 88%, and 94% on the first four out of six tests in her math class. If she needs
an average of 93% on all of the tests to get an A in the class, what must her average score be for the last two
tests in order to get an A?
A. 91.8%
B. 93%
C. 94.5%
D. 96%
E. 99%
5. A car’s tank holds 11 gallons of gasoline when full. After driving 76 miles, the tank is 79% full. How many
miles can the car go on a full tank of gas, to the nearest tenth of a mile?
A. 96.2
B. 361.9
C. 376.2
D. 660.4
E. 1058.2
6. A bag contains 16 blue candies, 8 yellow candies, and 12 red candies. What is the probability that a candy
randomly drawn from the bag is NOT blue?
2
A. 9
1
B. 3
4
C. 9
5
D. 9
4
E. 5
7. Jennifer found a jacket at the store that originally cost $119.95 on sale for 30% off. If there was a 7.5%
sales tax applied after the discount, how much did Jennifer pay for the jacket to the nearest cent?
A. $35.99
B. $38.68
C. $83.97
D. $90.26
E. $92.96
8. In the senior class, the ratio of female to male students is 5:3. If there are 195 male students, what is the
total number of students in the senior class?
A. 117
B. 312
C. 325
D. 520
E. 975
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Practice Math ACT® Test 2 9. If 60% of z is 90, what is 140% of z?
A. 54
B. 75.6
C. 126
D. 150
E. 210
10. At the school cafeteria, students can get a lunch combo with an entrée, side, drink, and dessert. The
options are listed in the table below. How many different lunch combos are possible?
Entrée
Side
Drink
Dessert
Hamburger
Salad
Milk
Cookie
Pizza
Soup
Juice
Brownie
Turkey Sandwich
Fruit
Lemonade
Grilled Cheese
Chips
A. 13
B. 48
C. 96
D. 1001
E. 24,024
11. What is the greatest common factor of 32, 48, and 120?
A. 4
B. 8
C. 16
D. 24
E. 32
th
12. Ryan is driving to his grandparents’ house for his grandmother’s 80 birthday and is running late. Their
house is 210 miles away, and the party starts at 3:00 pm. If he leaves at 1:00 pm and drives at a rate of 65
miles per hour, how many minutes late will he be to the party (choose the closest answer)?
A. 3
B. 14
C. 74
D. 134
E. 194
7
-5
13. What is the product of (8.5 x 10 )(6.3 x 10 )?
-35
A. 53.55 x 10
B. 5.355
2
C. 5.355 x 10
3
D. 5.355 x 10
12
E. 53.55 x 10
© 2013 Sophia Learning, LLC.
Practice Math ACT® Test 2 14. Which of the following is a prime number?
A. 1
B. 2
C. 21
D. 57
E. None of these
2
2
15. What is the simplest expanded form of (4x - 3y) ?
4
2
A. 16x + 9y
4
2
B. 16x - 9y
4
2
2
C. 16x -12x y + 9y
4
2
2
D. 16x - 24x y + 3y
4
2
2
E. 16x - 24x y + 9y
2
16. What is the product of the roots of the equation 2x + 9x – 18 = 0?
A. -9
B. 9
C. -18
D. 18
E. -9/2
17. What is the simplified form of the expression
€
€
€
€
€
y 2z 2
A.
2x 2
y2
B.
2x 2 z 4
1
C.
2 2 4
2x y z
3x −2 y 4 z −3
, written without negative exponents?
6y 2 z
€
y 2z 4
2x 2
y2
E.
2x 2 z 2
D.
18. Graham and John both have summer jobs mowing lawns for a yard service. Graham gets paid a base
rate of $10 per week, plus $8 for each lawn that he mows. John gets paid a base rate of $18 per week, plus
$6 for each lawn that he mows. If in one week, Graham and John mow the same number of lawns and make
the same amount of money, how many lawns do they each mow?
A. 1/4
B. 2
C. 4
D. 6
E. 8
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Practice Math ACT® Test 2 19. The length of a fenced-in garden is 4 feet more than the square of its width. Which equation gives the
length, l, of the garden in terms of its width, w?
2
A. l = w + 4
2
B. l = w - 4
C. l = 2w + 4
D. l = 2w - 4
2
E. l = (1/2)w + 4
20. To convert a temperature from degrees Fahrenheit to degrees Celsius, you can use the formula C =
(5/9)(F-32), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
How can this formula be written in terms of degrees Celsius?
A. F = (5/9)C + 32
B. F = (9/5)C - 32
C. F = (9/5)(C + 32)
D. F = (9/5)C + 32
E. F = (5/9)(C + 32)
21. What is the value of |a – 3| + 2 if a = -4?
A. -5
B. 1
C. 3
D. 7
E. 9
22. In a set of numbers, the second number is 3 more than twice the first, and the third number is 7 less than
5 times the second. Which of the following is an expression that represents the sum of the three numbers in
terms of the first number, x?
A. 2x + 3
B. 10x + 3
C. 13x + 11
D. 8x - 4
E. 5x - 7
A.
a is an even integer and b is an odd integer, which of the following must be an even integer?
a+b
B.
(a + b)2
C.
4(a + b)
23. If
(a − b)
2
D.
E. a − b
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Practice Math ACT® Test 2 24. Solve for x: 3(x+6) = 7(2x-1)
1
A. 6
7
B. 11
16
C. 11
25
D. 11
17
E. 6
25. What is the simplified form of the expression
y 2z 2
2x 2
y2
B.
2x 2 z 4
1
C.
2 2 4
2x y z
3x −2 y 4 z −3
, written without negative exponents?
6y 2 z
A.
€
€
€
€
€
€
y 2z 4
2x 2
y2
E.
2x 2 z 2
D.
26. If 2x + 3y = 3 and 2x - 4y = -11, then what is the value of x + y?
21
A. 2
5
−
B. 2
−
3
C. 2
1
D. 2
−
E.
2
2
27. What is the value of i • i?
A. i
B. -i
C. 1
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Practice Math ACT® Test 2 D. -1
E. 0
2
28. If f(x) = 4x + 2, what is f(x - 1)?
2
A. 4x + 3
2
B. 4x – 2x + 6
2
C. 4x – 8x + 4
2
D. 4x – 8x + 6
2
E. 4x + 1
29. Which of the following represents the solution to -3|x - 4| + 4 ≥ 1?
A. 3 ≤ x ≤ 5
B. x ≤ -3
C. x ≥ 5
D. x ≤ -3 or x ≥ 5
E. -1 ≤ x ≤ 1
x2 + x − 6
2
30. Which of the following is not in the domain of the function f(x) = x − 9x + 20 ?
A. 2
B. -3
C. 4
D. -4
E. All of these are in the domain of f(x)
31. What is the simplest form of
A.
B.
C.
D.
E.
€
(xy 3 z) • (3xy) • (6x 3 z 2 ) ?
(18x 5 y 4 z 3 )
3x 2 y 2 z (2xz)
9x 4 y 4 z (2xz)
3x 2 y 2 z (xz)
3x 2 y 2 z (2x 3 y 2 z 2 )
2
3 2
32. Find the next term in the following geometric sequence: 3x, 6x y, 12x y , ____
3 2
A. 24x y z
4 3 2
B. 24x y z
4 3 2
C. 18x y z
4 3
D. 18x y
4 3
E. 24x y
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Practice Math ACT® Test 2 33. What is the solution set for the equation
(4 − x) = −5?
A. {-21}
B. {-3}
C. {7}
D. {29}
E. Ø
34. What is the slope of the line represented by the equation 3x – 4y = 7?
3
B. −4
4
C. 3
3
D. 4
7
−
E. 4
A.
35. Find the equation of a line perpendicular to 6x – 4y = 3 that goes through the point (-3,4)
A.
y=
3
3
x−
2
4
2
x+6
3
B.
2
y =− x+2
3
C.
y=
2
1
y=− x−
3
3
D.
E.
y=
3
17
x+
2
2
36. A map of a state park can be represented by placing it on a standard x-y coordinate plane. On this map,
there is a ranger station located at the point (7, -12) and a trailhead located at the point (-3, 14). If each unit
on the coordinate plane represents a quarter of a mile, about how many miles is the ranger station from the
trailhead?
A. 6
B. 6.96
C. 27.86
D. 111.43
E. 194
37. A circle on the standard x-y coordinate plane has a diameter with endpoints at (-4, 3) and (6, -5). What is
the length of the radius of the circle?
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Practice Math ACT® Test 2 A. 2
41
41
B.
C. 2
D.
2
2
2
E. 2
38. Which of the following equations represents the line in the given graph?
4
y=− x+4
3
A.
4
x+4
3
B.
4
y = − x+3
3
C.
y=
3
y=− x+4
4
D.
3
y = − x+3
4
E.
39. Which of the following number line graphs shows the solution to the inequality 3(x + 2) + 1 < 4?
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Practice Math ACT® Test 2 40. Megan’s house is located at the point (5, 6) on the x-y coordinate plane. If Diana’s house is located at (-3,
-8), what are the coordinates of the point halfway between their two houses if a straight line is drawn between
them?
A. (4, 7)
B. (-8, -14)
C. (2, -2)
D. (-4, -7)
E. (1, -1)
2
2
41. A circle in the coordinate plane has the equation (x – 2) + (y + 3) = 16. What is the circumference of the
circle?
A. 2π
B. 4π
C. 8π
D. 9π
E. 16π
42. What is the slope of the line between the points (3, 9) and (-2, 5) in the x-y coordinate plane?
5
A. 4
B. 4
4
−
C. 5
1
D. 4
4
E. 5
43. Two similar triangles have a ratio of side lengths of 5:3. If the sides of the smaller triangle are 4 in, 7 in,
and 10 in, what is the perimeter of the larger triangle?
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Practice Math ACT® Test 2 A. 12.6
B. 21
C. 35
D. 63
E. 105
44. What is the area of the given figure?
A. 48 ft
2
B. 56 ft
2
C. 112 ft
2
D. 120 ft
3
E. 168 ft
2
45. Line l is tangent to circle C at A. If the radius of circle C is 5 and BC = 15, what is the length of segment
AB ?
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Practice Math ACT® Test 2 A. 5
3
B. 5
2
C. 2
10
D. 10
2
E. 20
46. A circle has an area of 64π. What is the diameter of the circle?
A. 4
B. 8
C. 16
D. 32
E. 64
47. The given pie chart shows students’ participation in after school sports. What is the measure of the
central angle for the section representing the number of students that play golf?
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Practice Math ACT® Test 2 A. 18°
B. 32.4°
C. 64.8°
D. 97.2°
E. 108°
2
48. A sphere is inscribed in a cube whose faces each have an area of 36 ft . What is the volume of the
sphere?
4
Vsphere = π r 3
3
A. 27π
B. 36π
C. 216π
D. 288π
E. 972π
49. In quadrilateral CDEF,
€
A. 40°
B. 50°
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CD ≅ FE .
€
If
∠CFE measures 50°, what is the measure of ∠CDE ?
€
Practice Math ACT® Test 2 C. 100°
D. 130°
E. 260°
50. In rhombus FGKH, diagonal
diagonal
FK measures 6 cm and GK measures 5 cm. What is the length of
HG , in cm?
A. 4
B. 6
C. 8
D. 10
E. 16
51. A cylindrical well is no longer in use and is being filled with concrete. The well is 250 ft deep and has a
radius of 4 ft. If the concrete is poured into the well at a rate of 175 cubic yards per hour, about how many
hours will it take to fill the well?
A. 5.98
B. 17.95
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Vcylinder = π r 2 h
Practice Math ACT® Test 2 C. 23.94
D. 71.81
E. 4188.79
52. A circular swimming pool is being built in a fenced in yard. If the dimensions of the yard are 10 yd by 15
yd and there must be at least one yard between the edge of the swimming pool and the fence, what is the
radius of the largest swimming pool that can be built, in yards?
A. 4
B. 4.5
C. 7.5
D. 8
E. 9
53. In the given figure,
A.
25 2
2
B.
25 2
JM , the diameter of the circle, is 5 2 , and JL ≅ LM . What is the area of ∆JLM?
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Practice Math ACT® Test 2 C.
25
D.
25
2
E.
5
54. In the given diagram,
QR measures 11 ft, the radius of circle D is 3 ft, and QR and ST are both tangent
to circle D. What is the area of the shaded region?
A. 66 – 3π
B. 33 – 6π
C. 66 – 9π
D. 66 - 6π
E. 33 – 9π
55. In order for
l and m to be parallel, which of the following must be true?
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Practice Math ACT® Test 2 A.
∠2 and ∠ 3 are congruent
B.
∠4 and ∠ 6 are supplementary
€
C.
€
∠ 6 and ∠ 8 are supplementary
€
D.
€
∠ 1 and ∠ 7 are congruent
€
E.
€ ∠3 and
€
€
€
€
∠ 6 are supplementary
56. The measure of
∠ZWX is 80°. What is the measure of ∠ZYX?
€
€
A. 40°
B. 80°
C. 90°
D. 100°
E. 120°
8
57. The sine of an angle θ between 90° and 180° is 17 . What is tan(θ)?
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Practice Math ACT® Test 2 8
A. 15
−
8
B. 15
15
C. 17
−
15
D. 17
15
E. 8
−
2
58. If 180° < θ < 270° and 4sin θ = 3, what is the value of θ?
A. 120°
B. 150°
C. 210°
D. 225°
E. 240°
59. Which of the following is equivalent to
A. 1
1
2
B. cos (θ )
1
2
C. cos (θ )
−
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(csc(θ )tan(θ ))
?
cos(−θ )
Practice Math ACT® Test 2 1
3
D. cos (θ )
1
2
E. sin (θ )
60. Jamie is sitting on a cliff looking down at a campsite. As she looks down, her line of vision makes an 8.5°
angle with the horizon. If the campsite is 100 feet away from the base of the cliff, how tall is the cliff?
A. 14.78 ft
B. 14.95 ft
C. 98.90 ft
D. 101.11 ft
E. 669.12 ft
ANSWER KEY IS ON THE NEXT PAGE
Answer Key
Question #:
Correct
Answer
1
E
These numbers will be easier to compare if they’re all in the same form. Try
converting all of them to decimals.
2
B
Start by moving all the variable terms to one side and all the constants to
the other.
3
B
Remember, a rational number is any number that can be written in the form
a/b, where A and B are both integers.
4
D
Be careful! There are SIX tests total. Make sure to take that into account
when computing the average!
5
B
Think about what percent of gas the car USED to go the first 76 miles.
6
D
To find the probability that the candy is NOT blue, you need to find the
© 2013 Sophia Learning, LLC.
Hint
Practice Math ACT® Test 2 probability that the candy is yellow or red.
7
D
Find the price of the jacket after the discount FIRST, then determine the
sales tax on the new price.
8
D
Try setting up a proportion to find the number of female students. Then
you’ll be able to find the total number of students in the senior class.
9
E
Set up an equation to find z first using the information you know. Then use
that value for z to determine 140% of z.
10
C
Remember the Fundamental Counting Principle? See if you can apply that
here.
11
B
Start by factoring each number completely and seeing what factors they
have in common.
12
C
Start by figuring out how long it takes Ryan to travel the distance to his
grandparents’ house.
13
D
You can use the Associative Property of Multiplication and multiply the
decimals and the powers of 10 separately.
14
B
Remember, a prime number is a number whose only factors are 1 and
itself.
15
E
There is a formula to help you simplify the square of a difference quickly,
but if you don’t remember it you can always just multiply it out using FOIL.
If it helps you, write out the two binomials and set up the multiplication so
you don’t miss any terms!
16
A
Remember, the roots of a quadratic equation are just its solutions. Start by
factoring the equation to find the roots.
17
B
Remember, to simplify a negative exponent in the numerator of a fraction
you can move it to the denominator and make it positive.
18
C
A good way to start a word problem like this is to identify known and
unknown information, and then define a variable to represent what’s
unknown.
19
A
Remember, squaring a number means taking it to the power of 2.
20
D
If you want to skip some unnecessary fraction multiplication by applying the
distributive property, a shortcut to get rid of the parentheses is to multiply
both sides by the reciprocal of 5/9.
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Practice Math ACT® Test 2 21
E
Remember, absolute value will always give you a POSITIVE number.
22
C
Don’t get overwhelmed by all the words! Break up the problem into smaller
chunks and find expressions for each number first.
23
C
If you get stuck, try picking some numbers for a and b and seeing what you
get for each answer choice.
24
D
Apply the distributive property first to get rid of the parentheses.
25
B
Remember, to simplify a negative exponent in the numerator of a fraction,
you can move it to the denominator and make it positive.
26
D
Look closely! You can subtract these two equations to quickly find the value
of y.
27
B
28
D
You can plug expressions into functions just like you can plug in numbers.
So wherever you see an x in the function, replace it with x-1.
29
A
Be careful here! Remember, when you divide both sides of an inequality by
a negative number, the inequality sign flips!
30
C
Remember, if the denominator of a fraction is equal to 0, the expression will
be undefined.
31
B
When you’re multiplying radicals that have the same index, you can just
multiply everything under the radical together and put that product
underneath one big radical.
32
E
Remember, in a geometric sequence the next terms are found by
multiplying by the same factor each time (the common ratio).
33
E
Before you jump right into solving, take a close look at this equation.
Thinking about what you know about square roots, do you see anything
here that might cause an issue?
34
D
Try putting the equation into slope-intercept form first by solving for y.
35
C
Remember, perpendicular lines have slopes that are opposite reciprocals.
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Remember that i =
−1 . What happens when you square i?
Practice Math ACT® Test 2 36
B
Start by finding the distance between the two points on the coordinate
plane using the distance formula.
37
B
You can find the length of the diameter using the distance formula. Then
you’re just a step away from finding the radius.
38
A
You can determine the slope of the line by taking the change in y over the
change in x, or the rise over the run.
39
A
Start by solving the inequality for x. Be careful with the order of operations
when simplifying!
40
E
You can find the midpoint between two (x,y) coordinates by just averaging
the x coordinates and the y coordinates.
41
C
You can identify the radius of this circle from its equation: the standard
2
2
2
equation for a circle is (x-h) + (y-k) = r , where r is the radius.
42
E
Remember, you can find the slope of a line from two points by taking the
difference in the y coordinate over the difference in the x coordinates.
43
C
Similar figures have side lengths that are proportional, but their perimeters
are proportional as well.
44
E
You can break this irregular figure into two smaller rectangles. Then just
find the area of each rectangle and add to get the total area.
45
D
Remember, a tangent line to a circle is perpendicular to its radius at the
point of tangency.
46
C
Remember, the formula for the area of a circle is πr , where r is the radius.
47
C
In a circle, the measures of all the central angles will always add up to 360°.
48
B
The faces of a cube are all congruent squares, so you can use the given
area to figure out the length of one edge, which will be the same as the
diameter of the sphere.
49
D
In an isosceles trapezoid, remember that the opposite angles are
supplementary.
50
C
The diagonals of a rhombus are perpendicular at their point of intersection.
51
C
Start by finding the volume of the cylinder to figure out how much total
concrete is needed to fill the well. Be careful with units!
52
A
Be careful here! There needs to be one yard of space on EACH SIDE of
© 2013 Sophia Learning, LLC.
2
Practice Math ACT® Test 2 the circular pool.
53
D
An angle that intercepts the diameter of a circle must be a right angle. So
∆JLM is a right triangle.
54
C
You can find the width of the rectangle from the radius of the circle – since
the circle is tangent to both sides of the rectangle, the width is twice the
radius of the circle.
55
B
When a transversal intersects two parallel lines, consecutive interior angles
are supplementary.
56
D
When a quadrilateral is inscribed in a circle, opposite angles are
supplementary.
57
A
Try drawing a right triangle on the coordinate plane.
58
E
Start by rearranging the equation so you have sinθ by itself on one side.
59
B
Try rewriting each trig function in terms of sin(θ) and cos(θ). Then see if you
can cancel anything.
60
B
Try drawing a picture and seeing if you can find any right triangles that can
help you.
© 2013 Sophia Learning, LLC.
Practice Math ACT® Test 2 Scoring Guide*
Estimated Score
Number Correct
36
60
35
58 – 59
34
57
33
55 – 56
32
54
31
52 – 53
30
50 – 51
29
48 – 49
28
47
27
43 – 46
26
41 – 42
25
40
24
37 – 39
23
35 – 36
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Practice Math ACT® Test 2 22
33 – 34
21
31 – 32
20
30
19
27 – 29
18
25 – 26
17
22 – 24
16
18 – 21
15
14 – 17
14
10 - 13
13
8–9
12
6–7
11
5
10
—
9
4
8
—
7
3
6
—
5
2
4
—
3
1
2
—
1
0
*The scoring guide is an estimate based on Sophia.org’s
calculations and the ACT® was not involved in the production of
this product and does not endorse it.
© 2013 Sophia Learning, LLC.