Review ACT PREP Math

Review ACT PREP Math

Algebraic Functions

Multiple Choice

With the complex number $i$ , where  $i=\sqrt{-1}$  , consider the expression  $i^n$  , where n can be any randomly chosen positive integer between 1 and infinity.  What is the percent chance that a given value of  $i^n$  in this expression will be a positive real number? 

• 25%

• 33%

• 50%

• 66%

• 75%

Multiple Choice

 $x+3$  is a factor of  $x^4+x^3-11x^2-nx+30$  if n equals what?

• 3

• 5

• 8

• 12

• 17

Multiple Choice

 $x+3$  is a factor of  $x^4+x^3-11x^2-nx+30$  if n equals what?

• 3

• 5

• 8

• 12

• 17

Multiple Choice

If $f\left(x\right)=3x^2$ and $g\left(x\right)=7x-2$  , what is  $g\left(f\left(2\right)\right)$  ? 

• 24

• 40

• 82

• 432

• 588

Multiple Choice

The sum of x and 2 is less than or equal to the product of -5 and x. Which of the following is equivalent to this expression?

• 
  

  $x\le-\frac{1}{3}$
  

• $x+2\ge-5x$

• $x-2<5x$

• $x\le\frac{4}{5}$

• $x\ge2-5x$

Multiple Choice

If x and y are directly proportional and

 $y=4$  when $x=2$  , what is the value of x when y is 12?

• 3

• 4

• 6

• 9

• 16

Multiple Choice

What value of c in this equation would cause the equation to have only imaginary solutions?

 $x^2+5x+c=0$  

• -3

• 0

• 1

• 2

• 8

Multiple Choice

 $\frac{\log_28+\log_327}{\log_416}=?$  

• 2

• 3

• 8

• 12

• 24

Multiple Choice

Which of the following correctly expresses the statement: x is less than or equal to the product of 3 and y?

• 
  

  $x\le3y$
  

• $x\ge3y$

• $x<3+y$

• $x<3y$

• $x\le\frac{3}{y}$

Multiple Choice

What will the dimensions of a matrix be that is the product of a 3 x 2 matrix and a 2 x 5 matrix?

• 2 x 2

• 3 x 2

• 2 x 3

• 3 x 5

• 5 x 3

Multiple Choice

If g(x) = −1/2 f(x), for all values of x, which of the following is a true statement describing the graph of g in comparison with the graph of f, shown below?

• It is narrower and opens downward.

• It is narrower and opens upward.

• It is the same width but opens upward.

• It is wider and opens downward.

• It is wider and opens upward.

Multiple Choice

In the xy-coordinate system, line k passes through points (-5m, 0) and (0, 2m). Which of the following is a possible equation of line k?

• $y=-\frac{5}{2}x+2m$

• $y=\frac{2}{5}x-5m$

• $y=\frac{5}{2}x+2m$

• $y=\frac{2}{5}x+2m$

• $y=-\frac{2}{5}x-5m$

Multiple Choice

In the standard (x,y) coordinate plane, what is the slope of a line that is perpendicular to 4x − 6y = 14?

• $-4$

• $-\frac{3}{2}$

• $-\frac{2}{3}$

• $\frac{3}{2}$

• $4$

Multiple Choice

A survey of a high school track team asked the 40 members how many hours per week (rounded to the nearest hour) they spend running outside of team practices. The 40 responses are summarized in the histogram below. To the nearest hundredth of an hour, what is the average number of hours spent running for the 40 respondents?

• 2.75

• 2.90

• 3.25

• 3.40

• 6.00

Multiple Choice

The average (arithmetic mean) of two numbers is 4x. If one of the numbers is y, then the value of the other number is

• $x-4y$

• $4x+4y$

• $8x-4y$

• $4y-8x$

• $8x-y$

Multiple Choice

Students in an 11th grade history class are randomly divided into three teams of five students for a history trivia contest. Each student takes a trivia test with 100 total points, and their scores are posted below. The team with the highest average score (rounded to the nearest whole number) wins the contest.

Which of the following is closest to the percent of individual trivia test scores that are at or above 80 points?

• 10%

• 33%

• 60%

• 67%

• 80%

Multiple Choice

If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?

• 36

• 47

• 48

• 49

• 72

Multiple Choice

The average of x and t is y. If s = 2y, what is the average of s, x, and t in terms of y?

• 3y

• 2y

• $\frac{5y}{3}$

• $\frac{4y}{3}$

• y

Multiple Choice

Which of the following equations expresses the relationship between x and y in the table?

•  $y=10x+1$  

•  $y=2x-1$  

•  $y=-x+45$  

•  $y=-3x+53$  

•  $y=-7x+81$  

Multiple Choice

On a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. If there are 60 juniors on the team, how many students in total are on the team?

• 90

• 140

• 150

• 180

• 210

Multiple Choice

A company has 40 executives and 120 customer service representatives. If these are the only employees, what percentage of the employees are executives?

• 20%

• 25%

• 33%

• 40%

• 80%

Multiple Choice

In the Antares Corporation, ³/₇ of the managers are female. If there are 42 female managers, how many managers in total are there?

• 18

• 24

• 60

• 66

• 98

Multiple Choice

In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. To date, Sam has won 14 of his 18 matches. Of Sam’s 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament?

• 4

• 5

• 6

• 7

• 8

Multiple Choice

After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

• $215

• $220

• $225

• $240

• $245

Multiple Choice

Which of the following numbers is between  $\frac{3}{5}$  and  $\frac{5}{7}$ ? 

•  $\frac{1}{2}$  

•  $\frac{3}{7}$  

•  $\frac{8}{9}$  

•  $\frac{19}{35}$  

•  $\frac{47}{70}$