ACT Mathematics Guide

Circumference/Perimeter of a Circle formula

2πr

On a map, 1/2 inch represents 12 actual miles. Two towns that are 5 inches apart on this map are how many actual miles apart? F) 120 G) 60 H) 30 J) 24 K) 12

Any time you get a problem like this telling that this many units(in this case inches) equals this many units(in this case miles), proportions are the way to solve it. (see picture for solution and steps)

An on-demand movie service charges $5 per month, plus $2 for each movie rented. Which of the following equations models the relationship between M, the number of movies rented per month, and T, the total monthly cost, in dollars, for the service? F) M = 5 + 2T G) M = 2 + 5T H) T= 2 + 5M J) T = 2 + 5M K) T = (5 + 2)M

Think of this format: y = mx + b T = y = total M = # of movies rented per month T = total monthly cost The movie service charges $5 per month. That itself is the subscription without having rented any movies yet. It costs $2 to rent each movie. T = 2M + 5 or T = 5 + 2M

Winter Fun Ski Resort sells only 2 types of tickets - adult and student. On Monday, the resort sold 200 tickets, 1 to each skier. The resort collected a total of $6,000 in ticket sales on Monday. The price of an adult ticket is $50 and the price of a student ticket is $25. How many adult and student tickets were sold on Monday? F) 40 adult tickets and 160 student tickets G) 80 adult tickets and 120 student tickets H) 100 adult tickets and 100 student tickets J) 120 adult tickets and 80 student tickets K) 160 adult tickets and 40 student tickets

With problems like this, you have to set up a system of equations. 200 tickets were sold, and you're using the 2 types of tickets described in the problem, so that's the first equation: a + s = 200 A for adult tickets and s for student tickets For the second equation, that deals in the ticket prices so, 50a + 25s = 6000 since $6,000 is the amount of money made from the tickets in total. The second equation is because its $50 for each adult ticket and $25 for each student ticket and $6000 is the total. I solved this system of equations using substitution.

Caden had exactly 45 plants to sell. After Day 1 of his sale, he had exactly 42 plants left. After Day 2, Caden had exactly 39 plants left. After Day 3, he has exactly 36 plants left. Assuming Caden will continue to sell plants at that daily rate, how many of these plants will he have left at the end of Day 6? A) 33 B) 27 C) 24 D) 6 E) 3

You have to see the pattern here. The number gets subtracted by 3 each day, which means 3 plants get sold per day. (See picture for solution and steps)

Time formula

distance/velocity

In parallelograms, adjacent angles are

supplementary

Diagonals bisect each other in parallelograms, so

the center of the diagonals is a midpoint

Midpoint Formula

x¹ + x²/2, y¹ + y²/2,