ACT Math Review

If m, n, and p are positive integers such that m + n is even and the value of (m + n)2 + n + p is odd, which of the following must be true? A. m is odd B. n is even C. p is odd D. If n is even, p is odd E. If p is odd, n is odd

D.

If the circumference of a circle is larger than x, then the circle's radius must be larger than? A. 2π B. 2πx C. x − 2π D. x/2π E. 1/2π

D.

In the complex numbers, where i^2 = −1, 1/(1+i) × (1−i)/(1−i)=? A. i − 1 B. 1 + i C. 1 − i D. (1−i)/2 E. (1+i)/2

D.

A horse eats 12 bales of hay in 5 days. At this rate, how many bales of hay does the horse eat in 5 + x days? A. 12+12/5x B. 12+x/5 C. 12/5+12/5x D. 12/5+x/5 E. 12/5+x

A.

For the complex number i such that i^2 = −1, what is the value of i^5/(i−1) × i^8/(i+1)? A. −i/2 B. i/2i−2 C. i D. 2i E. 2i/i−1

A.

If xy^2 < 0, then which of the following statements MUST be true? A. The value of x is negative, while the value of y is positive or negative. B. The value of y is negative, while the value of x is positive or negative. C. The sign of x must be the same as the sign of y. D. The sign of x must be different from the sign of y. E. The values of x and y must be the same.

A.

The length of a rectangle is 40% larger than its width. If the area of the rectangle is 140 square feet, what is the width of the rectangle in feet? A. 10 B. 22 C. 35 D. 56 E. 64

A.

The value of x+y/y is an integer when y = 4. Which of the following is a possible value of x? A. −16 B. 2 C. 9 D. 15 E. 26

A.

Using the complex number i, where i/2 = −1, 2/(1−i) × (1+i)/(1+i) = ? A. 1 + i B. i − 1 C. 1 − i D. 2(1 + i) E. 2(1 − i)

A.

Which of the following is equivalent to i2, where i is the imaginary number? A. −1 B. 0 C. 1 D. √-1 E. −2

A.

A total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f, r, and m? A. rm + 5 = f B. rm − 5 = f C. r + m + 5= f D. rf = m + 5 E. rf = m − 5

B.

For positive integers x and y, x + y = 21. What is the smallest possible value of xy? A. 10 B. 20 C. 38 D. 54 E. 110

B.

For the complex number i such that i^2 = −1, which of the following is equivalent to (i−1)^2/(i+1)^2? A. −2 B. −1 C. 0 D. 1 E. 2

B.

What is the 217th digit after the decimal point in the repeating decimal 0.3456? A. 0 B. 3 C. 4 D. 5 E. 6

B.

For the complex number i such that i^2 = −1, which of the following is equal to i^5 + i^7? A. −2 B. −1 C. 0 D. 1 E. 2

C.

For what values of a is the inequality a^2 ≤ a always true? A. a < 0 B. a > 0 C. 0 ≤ a ≤ 1 D. a > 1 and a < −1 E. The inequality is not true for any value of a.

C.

Gary has turtles, cats, and birds for pets. The number of birds he has is 4 more than the number of turtles, and the number of cats is 2 times the number of birds. Of the following, which could be the total number of Gary's pets? A. 14 B. 18 C. 20 D. 22 E. 26

C.

How many imaginary roots does the function g(x) = x^2 + 1 have? A. 0 B. 1 C. 2 D. 3 E. 4

C.

How many three-digit numbers have an odd number as a tens digit? A. 25 B. 200 C. 450 D. 500 E. 620

C.

If the length of a square's edge is increased by 20%, then the perimeter of the new square will increase by? A. 5% B. 10% C. 20% D. 40% E. 80%

C.

Let n equal 3a + 2b −7. What happens to the value of n if the value of a increases by 2 and the value of b decreases by 1? A. It is unchanged. B. It decreases by 1. C. It increases by 4. D. It decreases by 4. E. It decreases by 2.

C.

There are 45 students signed up for the performance band, while 30 are signed up for the jazz band. If 19 students are signed up for both bands how many students are signed up for only one of the bands? A. 11 B. 16 C. 37 D. 56 E. 75

C.

Which of the following numbers is an imaginary number? A.−32 B. (−5)^2 C. √5 D. √49 E. √-36

D

A company is deciding between two different car models as it updates its fleet of cars. The purchase price for model A is $30,000, and the price for model B is $35,000. However, model A has an average gas mileage of 27 miles per gallon while model B's is 36 miles per gallon. Each car in the fleet drives an average of 20,000 miles each year. If a gallon of gas costs $4, during which year of driving is the extra cost for model B made up by its superior gas mileage? A. Fourth year B. Fifth year C. Sixth year D. Seventh year E. Eighth year

D.

A computer repair person charges $50.00 per hour, plus an additional mileage fee. The charge for mileage varies directly with the square root of the number of miles traveled. If one hour plus 25 miles traveled costs $140.00, what is the total amount charged for one hour plus 36 miles traveled? A. $218.00 B. $196.92 C. $179.60 D. $158.00 E. $143.60

D.

A prize of $m is to be divided evenly among 6 people. In terms of m, which of the following expressions represents the total amount of prize money 2 of the 6 people will receive? A. m/6 B. m/5 C. m/4 D. m/3 E. m/2

D.

After polling a class of 24 students by a show of hands, you find that 9 students play soccer and 21 students play basketball. Given that information, what is the number of students in the class who must play both soccer and basketball? A. 0 B. 1 C. 3 D. 6 E. 9

D.

For every positive 2-digit number, a, with tens digit x and units digit y, let b be the 2-digit number formed by reversing the digits of a. Which of the following expressions is equivalent to a - b? A. 0 B. 9x − y C. 9y − x D. 9(x − y) E. 9(y − x)

D.

Gail made apple jelly and applesauce out of a bushel of apples. If the number of jars of jelly, j, is 3 less than twice the number of jars of applesauce, a, which expression shows the relationship of jars of jelly, j, to the jars of applesauce, a? A. 2j = 2a − 3 B. j − 3 = 2a C. 2j = 3a D. j + 3 = 2a E. ja = 2a

D.

Kate rode her bicycle to visit her grandmother. The trip to Kate's grandmother's house was mostly uphill, and took m minutes. On the way home, Kate rode mostly downhill and was able to travel at an average speed twice that of her trip to her grandmother's house. Which of the following expresses the total number of minutes that Kate bicycled on her entire trip? A. 3m B. 2m C. m+1/2 D. 3m/2 E. m/2

D.

The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a? A. 5(2a + 9) + 2a = 74 B. 5(2a − 9) + 2a = 74 C. (4a + 9) + 5a = 74 D. 2(2a + 9) + 5a = 74 E. 2(2a − 9) + 5a = 74

D.

For any real number a, the equation |x − 2a| = 5. On a number line, how far apart are the 2 solutions for x? A. 2a B. 5 + 2a C. 10a D. 5 E. 10

E.

For every cent increase in price of a pound of apples, the grocery store sells 25 fewer pounds per day. The grocery store normally sells 800 pounds of apples per day at $1.09 per pound. Which of the following expressions represents the number of pounds of apples sold per day if the cost is increased by 3x cents per pound of apples? A. (1.09 + 3x) (800 − 75x) B. 800 − 25x C. 800 − 75(1.09)x D. 800 + 75x E. 800 − 75x

E.

How many different integer values of a/4 satisfy the inequality 1/11 < 2/a < 18? A. 5 B. 4 C. 3 D. 2 E. 1

E.

If a is inversely proportional to b and a = 36 when b = 12, what is the value of a when b = 48? A. 0 B. 1/3 C. 1/4 D. 4 E. 9

E.

If a right triangle has legs of length 5x and x, which of the following expressions represents the length of its hypotenuse in terms of x? A. 2x B. 5x C. x√6 D. 2x√6 E. x√26

E.

If p and q are real numbers such that p > 5 and q > 4, what is the smallest integer larger than the product pq? A. 9 B. 10 C. 19 D. 20 E. 21

E.

If x and y are positive integers such that the greatest common factor of x^2y^2 and xy^3 is 27, then which of the following could y equal? A. 81 B. 27 C. 18 D. 9 E. 3

E.

If x and y are real numbers such that 0 < x < y^2, then which of the following inequalities must be true? A. x<y B. y>0y C. 3x > y^2 D. x<1 E. x < 3y^2

E.