# ACT Math Lesson 1: Pre-Algebra

## Overview to ACT Math Section

### Test Basics

The ACT Math test consists of  questions that must be answered within a -minute time limit. That leaves only  minute per question, with many questions involving extensive reading and calculation.

All of the math questions are -choice, questions.

### ACT Math Section Distribution

#### Because the ACT is a very standardized test, the distribution of questions across the different math skills is quite consistent.For fun, can you match each subject with its most likely number of questions.

• Pre-algebra
14
• Elementary Algebra
10
• Intermediate Algebra
9
• Coordinate Geometry
9
• Plane Geometry
14
• Trigonometry
4

### Scoring

You will receive a score from  to  for the math section as a whole and three sub-scores from 1 to 18, one for categories of Pre-algebra and Elementary Algebra, one for categories of Intermediate Algebra and Coordinate Geometry, and one for categories Plane Geometry and Trigonometry.

Monitoring how you performed on each Subscore category will help you focus in on those areas you need to focus additional practice.

On actual test day, though, you worry too much about your final subscores. Just focus on getting as many questions right as you can, regardless of the categories they are in.

### Test Organization

#### The questions do not appear in any easily decipherable order.Unlike some other standardized tests, they do not go from easy to hard, and they do not go by category. Since your goal is to get the greatest possible number of questions right, you should not worry about going out of order or skipping questions that seem too hard.Remember time is limited: If a quick glance at a question tells you that it isn’t for you (maybe because it looks hard or because it just has a lot of reading), don’t hesitate to move on to the next one.Hopefully, you’ll be able to go back and properly attack it after working through all the easier questions. But don't make one difficult question cost you the potential to answer three or four other questions correctly later on.

• I should never move on from a difficult question on the ACT-- I need to be perfect!
• Math questions on the ACT are divided by category

### Strategy

• There is no guessing penalty on the SAT
• We recommend that you bubble in the answers immediately

### Test Strategy Hypotheticals

• If you have solved a question and are certain it’s correct,
cross out the problem number to let yourself know not to return to that question.
• If you have determined an answer for a question but are unsure whether it is correct,
write down the answer with a question mark next to it. If time permits, you can return to the problem and try again, but if you run out of time, you at least have an answer.
• If you are all but certain that you cannot solve a problem
write down your best guess and underline it.
• When time is about to run out,
fill in answers for any questions you have not done. It does not matter whether you have even read the questions; never omit on the ACT. Your score is based only on the number of questions right, and there is no deduction for incorrect answers.

## Basic math problems:

These questions are straightforward math questions with very few words. Asking you to calculate the remainder when 85 is divided by 7 or to factor a polynomial are examples of such questions.

## Basic math problems “in settings”:

By “in settings,” the ACT generally means word problems. An example of such a problem might involve calculating the floor area of a rectangular living room. In other words, the problem is a basic rectangle problem but in a specific, real-world context. Not all problems in this category will be quite that simple, but they are not too much more difficult.

## Very challenging problems:

These problems are straightforward math questions with very few words, but they are harder than the questions in the first category. For example, a question in the first category might ask you the area of a rectangle while a problem in this category might ask you to find the area of a more complicated triangle.

## Very challenging problems “in settings”:

In case you haven’t guessed by now, these are the harder word problems that require complex calculations within a specific, real-world context.

## Question sets:

In these situations a number of questions, usually from 2 to 4, all relate to a single diagram or situation. Individual questions within this category may also fall into one of the categories above.

• 5
• 6
• 12
• 15
• 18

• 12
• 15
• 18
• 21
• 24

• 7
• 11
• 15
• 18
• 22

## Direct proportions

Two variables, x and y, are said to be directly proportional when the ratio of x:y is constant. So no matter by how much x or y changes, the other variable must change at the same rate, which means the ratio of x to y always stays the same, which means x1/y1=x2/y2

• 9
• 13
• 15
• 21
• 25

• 3/16 inch
• 1/4 inch
• 5/16 inch
• 3/8 inch
• 716 inch

• 0.001
• 0.02
• 0.05
• 0.1
• 0.3

# Inversely proportional

In addition to direct proportions, you will encounter another type of proportion, inverse proportion. For direct proportions, two values change at the same rate; if x increases, then y must increase.

In direct contrast, with inversely proportional types, when x increases, y must decrease, which means their product is a constant.

So, two variables, x and y, are said to be inversely proportional when the product xy is constant, which can be expressed as:

x1y1=x2y2

If x and y are inversely proportional and x=12 when y=4, when y=6 the value of x is  ?

• A.1.2
• B.1.8
• C.3.0
• D.5.0
• E.6.5

• 6
• 6.3
• 6.9
• 7.8
• 8.5

### New Value = ( 1 ± Percentage Change ) × Old Value

For the above calculation, you will use the minus sign when there is a percentage decrease and a plus sign when it is percentage decrease.

You should have no problem using algebraic operations to derive this formula based on the percentage formulas introduced previously.

Try it for yourself.

• 25
• 50
• 66
• 75
• 80

### Inverted Percentage Change

#### This formula works both ways as long as you are given one of two values and a percentage change. Try a related inverted problem:

In a department store, a dress is marked "25% Off," and the sale price is \$75. The original price of the dress is dollars

### Inverted Percentage Change

#### Let's try one markup variation:

Facing the increasing costs of maintaining the property, a landlord decides to increase the rent by 10%. If the current rent is \$2,000 per month for the tenant, the new rent cost for the tenant is dollars.

The extra amount you need to pay is  dollars.

• 40
• 45
• 50
• 55
• 60

### Basic Operations

#### Basic Operations are the old chestnuts : Addition, Subtraction, Multiplication, and Division.You will not see basic operations questions such as “What is 1008/14-1008/36 equal to?” on the ACT. Instead, you will need to determine which particular operations will be needed to solve a question by comprehending the relationships between different values in the question.Once you establish these relationships, you use your knowledge of grade-school math to quickly produce the correct answer. Just be careful to get your relationships clear and avoid silly, sloppy mistakes in calculations. Often, these questions will involve multiple computations, so even though they are simple at the level of understanding, they can lead careless students astray.

Vehicle A averages 14 miles per gallon of gasoline, and Vehicle B averages 36 miles per gallon of gasoline. At these rates, Vehicle A needs  more gallons of gasoline than Vehicle B to make a 1008-mile trip.

## Problem Set

### Problem Set 1-5

1.A coffee maker from company 𝐴 makes 6 liters of coffee per hour, and a coffee maker from company 𝐵 makes 4 liters of coffee per hour. If Adam makes coffee with two coffee makers from company 𝐴 for two hours, how many hours does Beth need to make the same amount of coffee with three coffee makers from company 𝐵?

2.What is the least common multiple of 15, 20, and 25?

3. |2|1−2|−3|3−4||=?

4.Alfred, Beth, and Charles shared a chocolate bar that had a volume of 6 cubic inches. Alfred had 2 cubic inches of chocolate, Beth had 1 of the remaining chocolate, and Charles had the rest.What is the ratio of Alfred’s share to Beth’s share to Charles’s share?

5.At a certain travel agency, the number of male customers in May of a certain year increased10% from the previous month, and the number of female customers in that same May decreased8% from the previous month. The number of total customers in May increased by 48 from theprevious month and was 2,148. How many male customers were there that May?

### Problem Set 6-10

6.At an electronics store, a particular TV is purchased from a warehouse and is marked up 40%.The store then decides to reduce the price of the TV by \$900, leaving the store with 10% profit.

What is the original price of the TV from the warehouse?

A.\$1,000

B.\$2,000

C.\$3,000

D.\$4,000

E.\$5,000

7. A class on a field trip to a park finds identical benches. If 5 students are seated on each bench,there are 3 students standing. However, when they try to seat 6 students on each bench, there is one empty bench and one bench with 4 students on it. How many students are there?

A.57

B.58

C.59

D.60

E.61

8.It takes Alfred 24 days to do a certain job by himself. It takes Ben 15 days to complete the same job. If Alfred works on the job for 16 days, and Ben takes over, how many days does it takeBen to finish the job?

A.5

B.6

C.7

D.8

E.9

9.There are three consecutive odd integers with the property that the sum of the largest and the smallest numbers is 38 less than 4 times the remaining number. What is the middle number?

A.17

B.19

C.21

D.23

E.25

10.What is the least common denominator of the fractions 1/43/10, and 2/21

A.70

B.140

C.210

D.420

E.700