ACT Math Practice and Test 2 Exam 103 Questions with Verified Answers
Distance Formula - CORRECT ANSWER d=√(x₁-x₂)² + (y₁-y₂)²
Slope -
... [Show More] CORRECT ANSWER M=y₂-y₁/x₁-x₂
Slope Intercept - CORRECT ANSWER y=mx+b
Midpoint Formula - CORRECT ANSWER (x₁+x₂)/2, (y₁+y₂)/2
PEDMAS - CORRECT ANSWER order of operations
Parenthesis, Exponents, Multiplication, Division, Add, Subtract.
Quadratic Equation - CORRECT ANSWER ax²+bx+c= 0
Quadratic Formula - CORRECT ANSWER x = −b ± √b²-4ac/2a
Percent Formula - CORRECT ANSWER Part=Percent x Whole
Multiply Power Exponents - CORRECT ANSWER add exponents and keep the same base
Dividing Power Exponents - CORRECT ANSWER subtract exponents and keep same base
Raising Power to Powers - CORRECT ANSWER multiply the exponents
Negative Exponent - CORRECT ANSWER X⁻ⁿ = 1/Xⁿ
Absolute Value - CORRECT ANSWER |-3| = 3
FOIL - CORRECT ANSWER First, Outside, Inside and Last.
Factoring Difference of squares - CORRECT ANSWER a²-b² = (a-b) (a+b)
Area of a Triangle - CORRECT ANSWER area= ½ (base)(height)
Pythagorean Theorem - CORRECT ANSWER a²+b²=c²
Area of rectangle - CORRECT ANSWER area= length x width
Area of parallelogram - CORRECT ANSWER area= base x height
Area of square - CORRECT ANSWER area = (side)²
Circumference of a circle - CORRECT ANSWER area = 2πr
Area of a circle - CORRECT ANSWER πr²
Sal - CORRECT ANSWER 52 cards are dealt clockwise to the players shown above, beginning with Al. Who gets the last card?
returning: 45 minutes - CORRECT ANSWER Mr. Bailey drove 300 miles from Carville to Dayton at an average speed of 50 miles per hour. He returned 300 miles to Carville in 5 l/4 hours. Which trip took less time? How many minutes less did it take?
$1861.60 - CORRECT ANSWER Vance made a down payment of $250 on the purchase of a trombone. He paid off the balance in 24 equal payments of $67.15. What is the total amount he paid?
20,202 - CORRECT ANSWER 200/10 + 20/100 + 2/1000 = ?
0.668 - CORRECT ANSWER 0.0668/0.1 = ?
$13.30 - CORRECT ANSWER A taxi ride costs $2.50 for the first mile and $0.60 for each additional half-mile. How much does a 9-mile ride cost?
-2 or 3 - CORRECT ANSWER (x + 2)(x - 3) = 0. Then x = ?
-6 - CORRECT ANSWER Find the value of 3 - (2 - p) when p = 5.
3k = n - 4 - CORRECT ANSWER Which of the following equations represents this statement: 3 times k is 4 less than n?
2x + y/2 - CORRECT ANSWER Find z if x/3 + y/3 + z/3 = x + y/2.
24 - CORRECT ANSWER The area of rectangle ACDF is 54. what is the area of parallelogram BCEF?
10 π - CORRECT ANSWER Find the circumference of a circle with an area of 25 π.
10 - CORRECT ANSWER The slope of the line through (2,1) and (5,n) is 3.
n = ?
66 - CORRECT ANSWER What is the value of x in triangle RST?
2 - CORRECT ANSWER
90º - CORRECT ANSWER
I and II only - CORRECT ANSWER
A - CORRECT ANSWER
complementary angles - CORRECT ANSWER two angles that add to 90 degress
supplementary angles - CORRECT ANSWER two angles that add to 180 degrees
acute angle - CORRECT ANSWER less than 90 degrees
obtuse angle - CORRECT ANSWER greater than 90 degrees
trapezoid formula - CORRECT ANSWER (B1+b2)h/2
common right triangles - CORRECT ANSWER 3-4-5
6-8-10
5-12-13
similar triangles - CORRECT ANSWER the sides are proportionate to each other
parallel lines - CORRECT ANSWER have the same slope
perpendicular lines - CORRECT ANSWER slope is flipped and changed to a negative
2/3 would be -3/2
mean - CORRECT ANSWER add up and divide by the amount of numbers added
mode - CORRECT ANSWER number that occurs the most
median - CORRECT ANSWER number in the middle
range - CORRECT ANSWER biggest number - smallest number
inequalities - CORRECT ANSWER > = open circle on graph
≥ = closed circle on graph
-2y < 3x = flip the sign in your answer
if f(x) = 3x^2 and g(x) = 4, what is f(g(x)) - CORRECT ANSWER f(g(x)) = f(4) = 3(4)^2 = 48
logrithms - CORRECT ANSWER LOGbX=Y converts to b^Y=X
ex: LOG3(9) = Y would be 3^Y = 9
Probability - CORRECT ANSWER number/total number
Odds - CORRECT ANSWER number/remaining
Quadratic Formula - CORRECT ANSWER [-b ± √(b² - 4ac)] / (2a)
Distance Formula - CORRECT ANSWER d = √[( x₂ - x₁)² + (y₂ - y₁)²]
midpoint formula - CORRECT ANSWER (x₁+x₂)/2, (y₁+y₂)/2
30-60-90 triangle - CORRECT ANSWER leg=x, base=x√3, hypotenuse=2x
45-45-90 triangle - CORRECT ANSWER leg=x, base=x, hypotenuse=x√2
sin - CORRECT ANSWER opposite/hypotenuse
cosin - CORRECT ANSWER adjacent/hypotenuse
tangent - CORRECT ANSWER opposite/adjacent
supplementary angles - CORRECT ANSWER Two angles whose sum is 180 degrees
Adjacent angles - CORRECT ANSWER Angles that have a common side and a common vertex
complementary angles - CORRECT ANSWER Two angles whose sum is 90 degrees
Opposite angles... - CORRECT ANSWER are congruent
finding the slope of 2 points - CORRECT ANSWER (y2−y1)/(x2−x1)
average speed formula - CORRECT ANSWER total distance/total time
Pythagorean Theorem - CORRECT ANSWER a²+b²=c²
area of a circle - CORRECT ANSWER πr²
Circumference of a circle - CORRECT ANSWER 2πr
degree of an arc from an angle at the center of a circle - CORRECT ANSWER = to the angle
degree of an arc from an inscribed angle (other side of the circle) - CORRECT ANSWER 2x the angle
Barbie answered 2 out of 20 questions on her math test incorrectly. What percent of the questions did Barbie answer correctly? - CORRECT ANSWER Options: 2/20 x 100%, 2/ (20 x 100%), 18/20 x 100%, 18/ (20 x 100%), 2/100% x 20.
Answer: 18/20 x 100%. Number of correct questions over number of total questions multiplied by 100.
Set S = {0, x + 2, x + 4, x + 6}. What is the average of Set S? - CORRECT ANSWER Options: 3/4x +3, x+2, x+3, x+4, 3x+12.
Answer: ¾ x + 3. Add all the terms in Set S together and divide by 4 to get the average.
A bag contains only red, blue, and green marbles. There are a total of 20 marbles in the bag, and the probability of NOT selecting a blue marble is ¼. How many blue marbles are in the bag? - CORRECT ANSWER Options: 4, 5, 8, 10, 15.
Answer: 15. The probability of actually selecting a blue marble is now ¾. ¾ = the amount of blue marbles / 20.
Solve for x to equal 15 marbles.
Joanie's scores for 3 tests are 100, x, and 80. If the median of her scores is higher than the mean of her scores, then which of the following numbers could be x? - CORRECT ANSWER Options: 60, 70, 80, 90, 100
Answer: 100.
Go through the answers to solve for median and mean of the test scores until the median is greater than the mean.
What is the smallest positive value of x for which cos3x = 0? - CORRECT ANSWER Options: 0, pi/6, pi/3, pi/2, 2pi/3.
Answer: pi/6. Find when cosine equals 0. Multiply that answer by 3.
A fish tank has a length of 24 inches, a width of 8 inches, and a height of 10 inches. If the tank contains 1,728 cubic inches of water, what is the depth, in inches, of water in the tank? - CORRECT ANSWER Options: 6, 7, 8, 9, 10.
Answer: 9. The length and width of the water is the same as those of the tank. The water's volume now equals the area of the tank's base times the water's depth. 1,728 = (24)(8)(d). d=9.
A car rental company charges $20 per day for a rental car, plus $0.50 for each mile driven. If Kecia kept a car for 3 days and was charged $156.00 dollars, how many miles did she drive? - CORRECT ANSWER Options: 312, 272, 192, 156, 96.
Answer: 192. She had the car for 3 days: 3($20)= $60. $156 - $60= $96 is the mileage charges. 96/0.50= 192 miles.
Rain is falling at a rate of 0.25 cm each hour. At this rate, how many hours would it take for c centimeters of rain to fall? - CORRECT ANSWER Options: c/0.25, 0.25/c, 0.25c, 2.5c, c-0.25.
Answer: c/0.25. Set up a proportion with the ratio of rainfall in one hour to the ratio of rainfall © per x hours. Solve for x.
If x > y and z > y, which of the following MUST be true? - CORRECT ANSWER Options: x > z, z > x, x^2 > y, z^2 > y^2, x + z > 2y.
Answer: x + z > y. X and Z are greater than Y but we do not know how they relate to each other so eliminate the first two choices. Eliminate the next two because if y is a "large" negative number, it will out-do x and z. The last option is left.
In the figure below, a circle is inscribed within a square. If the perimeter of the square is 36 feet, what is the area of the shaded region, in square feet? (Area around the circle.) - CORRECT ANSWER Options: 9-4.5pi, 36-6pi, 36-9pi, 81-20,25pi, 81-36pi.
Answer: 81-20.25pi. If the square's perimeter is 36, then each side is 9 feet. This means the square's diameter is 9 feet. The area of the square is 9x9= 81 feet^2. The area of the circle is pi(4.5)^2= 20.25pi. Subtract the area of the circle from the area of the square.
The length of the radius of circle A is 3 times as long as the radius of circle B. If the area of circle A is x, what is the area of circle B? - CORRECT ANSWER Options: x/9, x/6, x/3, 3x, 9x.
Answer: x/9. Substitute values in for the radii of A and B and make a proportion of A to B.
If the area of triangle ABC is 24 square feet, what is the perimeter of parallelogram BCED, in feet? - CORRECT ANSWER Options: 72 feet, 70 feet, 68 feet, 64 feet, 50+ 2root73 feet.
Answer: 64 feet. Using side AC, solve for the base (6) in the area formula, then the hypotenuse using the pythagorean theorem. Since BD is 28, solve for the perimeter.
A ball thrown upward from the ground level is s feet high after t seconds, where s=80t - 16t^2. At which of the following times will the ball be 96 feet above the ground? - CORRECT ANSWER Options: ¼ second, 1 second, 2 seconds, 2.5 seconds, 4 seconds.
Answer: 2 seconds. Plus is 96 for s and use the quadratic equation to solve for t.
Working together, a standard printer and a high-speed printer can complete a certain print job in 3 ⅓ hours. If it takes the high-speed printer 5 hours to do the job alone, how many hours would it take the standard printer to do the job alone? - CORRECT ANSWER Options: 1 ⅔, 4 1/6, 6 ⅔, 8 ⅓, 10.
Answer: 10. The printers do 1/x of the job every hour. The high-speed printer does 1/5 of the job for 5 hours,, but together they finish the job in 10/3 hours. Each hour they do 3/10 of the job. 1/x + 1/5 = 3/10, solve for x.
The average of a set of 6 integers is 22. When one of these numbers is removed, the average of the set increases to 25. What is this number? - CORRECT ANSWER Options 3, 7, 15, 16, 18.
Answer: 7. Re-arrange the mean formula to solve for sum. (Sum = average x number of terms). Find the sum of the 6 integers to be 132. Find the sum of 5 integers to be 125. Subtract 15 from 132 to find 7.
If a fair coin is tossed 4 times, what is the probability of NOT obtaining exactly 3 heads? - CORRECT ANSWER Options: ¼, ½, ⅝, ¾, 15/16.
Answer: ¾. Find the total number of possible outcomes to be 16. Which of those contain three heads? (4). If 4 contain 3 heads, then 12 do not. 12/16 = ¾.
If x+y=1, and x-y=1, then y=?
A. -1
B. 0
C. 1/2
D. 1
E. 2 - CORRECT ANSWER Answer: B
What is the slope of the line containing the points (-2,7) and (3,-3)?
F. 4
G. 1/4
H. 0
J. -1/2
K. -2 - CORRECT ANSWER Answer: K
What is the total cost of 2.5 pounds of bananas at $0.34 per pound and 2.5 pounds of tomatoes at $0.66 per pound?
A. $1.00
B. $2.40
C. $2.50
D. $3.50
E. $5.00 - CORRECT ANSWER Answer: C
The relationship between temperature expressed in degrees Fahrenheit (F) and degrees Celsius (C) is given by the formula
F=9/5C + 32
If the temperature is 14 degrees Fahrenheit, what is it in degrees Celsius?
F. -10 degrees Celsius
G. -12 degrees Celsius
H. -14 degrees Celsius
J. -16 degrees Celsius
K. -18 degrees Celsius - CORRECT ANSWER Answer: F
A person 2 meters tall cast a shadow 3 meters long. At the same time, a telephone pole casts a shadow 12 meters long. How many meters tall is the pole?
A. 4
B. 6
C. 8
D. 11
E. 18 - CORRECT ANSWER Answer: C
If 537^102 were calculated, it would have 279 digits. What would the digit farthest to the right be (the ones digit)?
A. 1
B. 3
C. 4
D. 7
E. 9 - CORRECT ANSWER Answer: E
In the standard (x,y) coordinate plane, the triangle with vertices at (0,0), (0,k), and (2,m), where m is constant, changes shape as k changes. What happens to the triangle's area, expressed in square coordinate units, as k increase starting from 2?
F. The area increases as k increases.
G. The area decreases as k increases.
H. The area always equals 2.
J. The area always equals m.
K. The area always equals 2m. - CORRECT ANSWER Answer: F
A bag of pennies could be divided among 6 children, or 7 children, or 8 children, with each getting the same number, and with 1 penny left over in each case. What is the smallest number of pennies that could be in the bag?
F. 22
G. 43
H. 57
J. 169
K. 337 - CORRECT ANSWER Answer: J
An object detected on radar is 5 miles to the east, 4 miles to the north, and 1 mile above the tracking station. Among the following, which is the closest approximation to the distance, in miles, that the object is from the tracking station?
A. 6.5
B. 7.2
C. 8.3
D. 9.0
E. 10.0 - CORRECT ANSWER Answer: A
If you rent a full-size car from Quick Car Rental for 1 day, how much more would the total rental cost be if you drove the car 78 miles than if you drove it 77 miles?
A. $0.10
B. $0.15
C. $0.20
D. $0.40
E. $0.55 - CORRECT ANSWER Answer: D [Show Less]