1. Math: Pre-algebra & Algebra
ACT 1-on-1 Curriculum
Math: Pre-algebra & Algebra

2. Math Section at a Glance
ACT Math
Math Section at a Glance
Math Directions:
60 questions
60 minutes
Three sections of
questions:
Pre-Algebra/ Elementary Algebra
24 questions
Intermediate Algebra/ Coordinate Geometry
18 questions
Plane Geometry/ Trigonometry
DIRECTIONS: Answer each question and then plug in the matching bubble on your answer sheet.
Do not stay on problems that you are struggling with. Answer the questions you know first; then go back complete the other problems as time permits.
Calculators are allowed on this section of the test. Note that some of the problems can be answered without a calculator.
Note: unless the questions explain something differently, assume the following.
1. Figures, graphs and charts may not be drawn to actual measurements.
2. Linear data, figures and shape are represented in a plane.
3. A straight, 180° line will be introduced as a line.
4. Arithmetic mean will be introduced as an average.

3. ACT Math The Basics – Math
Concepts range from pre-algebra up to algebra II and trigonometry
There are only 4 trigonometry questions
Questions are generally in order of difficulty
To answer all questions, you need to work generally at a pace of one minute per question

4. ACT Math General Strategies Write down your work! Pace yourself
Do not just go to your calculator to find the answer. Write it down.
If you work it out, you can review the steps to get the right answer if you make a mistake.
Pace yourself
It is easy to lose track of time on one problem.
Do not spend too much time on any one problem.
Read the questions carefully!
This is a way to avoid easy mistakes.
Pick & Plug
Use the answer choices to help you solve the problem.
Oddball Answers are OK
In math, many times the odd answer out is the correct one.
Assign Values to Variables
If a question has numerous variables, assign a consistent numerical value to help you solve it.
To help on pick & plug and number substitution (assigning values to variables) use an example or two. These could include p. 172 #34 (numb. Sub), p. 169 #21, p. 169 #23.

5. Word Problems – Pre-Algebra/Elementary Algebra
ACT Math
Word Problems – Pre-Algebra/Elementary Algebra
Translate words into an equation or statement that you can solve.

6. Word Problems – Pre-Algebra/Elementary Algebra
ACT Math
Word Problems – Pre-Algebra/Elementary Algebra
50 is what percent of 450?
21 is 6 more than what number?
8 is 5 less than half of what number?
21 more than what number is five times the number?
In discussing percents, also hit on percent increase and decrease. Emphasize the need to read the question carefully.
Two situations that are common on the ACT: % discount of a clothing item or a dinner tip.

7. Mean, Median, and Mode – Pre-Algebra/Elementary Algebra
ACT Math
Mean, Median, and Mode – Pre-Algebra/Elementary Algebra
Mean:
Mean is the average of a list of numbers.
Median
The middle number between a list of numbers is the median.
If the list has an even set of numbers, the median is the average of the two middle values.
Mode
The number that occurs the most in a list of numbers is the mode.

8. Primes, Multiples, and Factors– Pre-Algebra/Elementary Algebra
ACT Math
Primes, Multiples, and Factors– Pre-Algebra/Elementary Algebra
Primes:
A prime number is only divisible by one and itself.
Special rules:
1 is not a prime number.
2 is the only even prime number.
Factors:
Factors are numbers that you multiply together to get a product.
Multiples:
Multiples are formed by multiplying a given number by the counting numbers.
Greatest Common Factor (GCF) and Least Common Multiple (LCM)
Greatest common factor is the largest factor of a set of numbers.
Least Common Multiple is the smallest common multiple of a set of numbers.

9. Distance – Pre-Algebra/Elementary Algebra
ACT Math
Distance – Pre-Algebra/Elementary Algebra
For distance problems, remember that:
Distance= Rate x Time
Use the given units to help on this.
Many will use miles and hours.

10. Surface Area Conversions
ACT Math
Measurements – Pre-Algebra/Elementary Algebra
For measurement questions, identify the units that are used.
You need to remember some basic conversions:
Length Conversions
12 inches (in.) = 1 foot (ft.)
3 ft. = 36 in. = 1 yard (yd.)
5280 ft. = 1760 yd. = 1 mile (mi.)
Surface Area Conversions

11. Absolute Value – Pre-Algebra/Elementary Algebra
ACT Math
Absolute Value – Pre-Algebra/Elementary Algebra
Absolute value is the number of integers a number is away from zero.
|-5| = 5
For difficult absolute value questions, account for the positive and negative values of a variable when the variable is between the brackets.
Note how to solve an equation like this |x-5|=2. Solve for both the positive and negative numbers.

12. Probability– Pre-Algebra/Elementary Algebra
ACT Math
Probability– Pre-Algebra/Elementary Algebra
Probability of x: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑡ℎ𝑎𝑡 𝑎𝑟𝑒 𝑥 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Combinations: For these problems, multiply the numbers provided by each other.
Permutations: For these problems, order matters. To find the answer, multiply the number of items by one less for each placement.
Emphasize that for combinations, order does not matter. For permutations, order matters. Create an example of this. For combinations, one possible example is to say: you are getting dressed and are choosing between 3 pairs of shoes, 4 pairs of pants, and 6 shirts. How many combinations do you have?
For permutations, an example is: you have 5 paintings that are hung in your living room. Each painting can only take up one spot. How many different orders can the paintings be hung in?

13. Exponents and Roots– Pre-Algebra/Elementary Algebra
ACT Math
Exponents and Roots– Pre-Algebra/Elementary Algebra
Remember rules for simplifying expressions with exponents:
𝑥 𝑎 * 𝑥 𝑏 = 𝑥 𝑎+𝑏
( 𝑥 𝑎 ) 𝑏 = 𝑥 𝑎∗𝑏
𝑥 −𝑎 = 1 𝑥 𝑎
𝑥 𝑎 𝑥 𝑏 = 𝑥 𝑎−𝑏
𝑥 = 𝑥 1 2
In these, emphasize the first 2—when you multiply exponents with the same base, you add. When you raise an exponent to a power, you multiply.

14. Ratios and Proportions – Pre-Algebra/Elementary Algebra
ACT Math
Ratios and Proportions – Pre-Algebra/Elementary Algebra
Ratios are comparisons between two variables.
Solving Ratio Problems:
Write down both ratios as fractions, setting them equal to one another.
Verify that your units match on both sides of the equation.
Use cross-multiplication to solve the problem.
Do an example on the board.

15. Series – Pre-Algebra/Elementary Algebra
ACT Math
Series – Pre-Algebra/Elementary Algebra
Arithmetic sequences are separated by a common number, called a common term or difference.
Example: 28, 24, 20, 16 is a arithmetic sequence with a difference of -4.
Geometric sequences are separated by a common ratio that is either multiplied or divided by the previous number.
Example: 2, 6, 18, 54 is a geometric sequence with a ratio of 3.

16. Simplifying Algebraic Expressions – Pre-Algebra/Elementary Algebra
ACT Math
Simplifying Algebraic Expressions – Pre-Algebra/Elementary Algebra
These test if you can simplify or manipulate algebraic expressions.
Remember the order of operations: PEMDAS.
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
Remember the distributive property.
A(b+c) = ab + ac

17. Pre-Algebra/Elementary Algebra
ACT Math
Pre-Algebra/Elementary Algebra
Work on the following Practice Problems from 61D:
# 1
# 24
# 3
# 27
# 4
# 32
# 5
# 35
# 6
# 39
# 14
# 43
# 15
# 16
Use problems from the sheet in your handout. You can assign one per student, cherry pick certain problems, or have them work through them all.

18. System of Equations – Intermediate Algebra
ACT Math
System of Equations – Intermediate Algebra
System of equations provide a pair of equations with two variables for which you have to solve.
One way to solve for x is to add or subtract the equations to eliminate one of the variables.
Another way to solve for x is by substitution, where you solve for one of the variables and plug it into the other equation.

19. Solving & Factoring Quadratic Equations – Intermediate Algebra
ACT Math
Solving & Factoring Quadratic Equations – Intermediate Algebra
Multiplying binomials:
Use FOIL to multiply binomials: First, Outer, Inner, Last.
Example: (x+5)(x-3)
Solving quadratics by factoring:
Factor x2+5x+6.

20. Functions – Intermediate Algebra
ACT Math
Functions – Intermediate Algebra
Functions are a way of restating y=ax+b as f(x) = ax+b.
To solve functions, you substitute x for some number or variable.
Example: f(x) = x2+2x-4. What is f(3)?

21. Inequalities – Intermediate Algebra
ACT Math
Inequalities – Intermediate Algebra
In an inequality, one of the sides of the equation is greater than the other.
Solve inequalities similar to the way you solve linear equations.
One note on solving inequalities: if you multiply or divide by a negative number, you must flip the sign.

22. Matrices – Intermediate Algebra
ACT Math
Matrices – Intermediate Algebra
Matrix questions occasionally pop up on the ACT.
Adding and subtracting matrices:
To add or subtract matrices, add or subtract corresponding numbers.
Multiplying matrices:
Take the first row of the first matrix and the first column of the second matrix and multiply the corresponding numbers.
Determinant:
The determinant is found by subtracting the product of the diagonals.
Use the packet to help illustrate this or do an example on the board. If you have geometry students scared by this, encourage them to save matrix problems for last.

23. Logarithms – Intermediate Algebra
ACT Math
Logarithms – Intermediate Algebra
The basic form of a logarithm:
Logb y = x means bx = y
Logarithmic identities:
Logb (xy) = Logb x + Logb y
Logb (x/y) = Logb x - Logb y
Logb (xd) = d Logb x

24. ACT Math Intermediate Algebra
Work on the following Practice Problems from 61D:
# 10
# 11
# 12
# 21
# 34
# 57
Use problems from the sheet in your handout. You can assign one per student, cherry pick certain problems, or have them work through them all.