ACT PREP MATH

1
ACT PREPMATH

• Pre-Algebra

2
Order of Operations

• PEMDAS (Parentheses, Exponents,
  Multiplication/Division, Addition/Subtraction)

• Try This

(72) x 32 5 ?
(9) x 9 5 81 5 76
3
Adding/Subtracting Fractions

• With addition and subtraction, find a common
  denominator, convert the fraction to the
  equivalent fraction, and proceed with the
  operation.
• To make these difficult, the makers of the ACT
  will use variables or they will show up in word
  problems!

• Try This John and Susan ordered a medium pizza.
  John ate 2/5 of the pizza and Susan ate 1/2 of
  the pizza. How much pizza was left?
• 1/10
• 3/8
• 2/5
• 1/2
• 9/10

4
Multiplying/Dividing Fractions

• Multiplication is straightforward multiply the
  numerators and denominators to get the product.
• With division, we multiply the first fraction by
  the reciprocal of the second fraction.

• Try This A box of cereal holds 2 ¾ cups of
  food. If each serving is 1/8 cup, how many
  servings are in the box of cereal?
• 1/8
• 8
• 12
• 22
• Not enough information is given.

5
Operations with Decimals

• If a question involving decimals shows up on the
  ACT, try estimation. If in your estimation, you
  round down, round up when choosing your answer
  and vice versa.

• Try This The average gas price in San Francisco
  is 3.27 per gallon. If Jan has a car that holds
  13 gallons and she currently has ¼ of a tank
  full, how much money does she need to fill up her
  tank?
• 3.27
• 9.75
• 10.67
• 31.88
• 42.51

6
Absolute Value

• The absolute value of a number is the distance of
  that number from zero. It is the number without
  its sign.

• Try This Evaluate the expression -4 3 -1
• -2
• 6
• 7
• 8
• 10

7
Factors and Divisibility

• You will probably only see one of these on the
  math section.
• It is to your benefit to remember the
  divisibility rules instead of wasting your time
  using the calculator to plug and chug!

• Try This The number 12123 is divisible by
• 3
• 6
• 9
• both 3 and 6
• both 3 and 9

8
Square Roots

• Know the basic square roots like those of 36, 25,
  16, 9, and 4.

• Try This Which of the following is equal to 2v6?
• 3
• 6
• 12
• 24

9
Exponents

• Know the rules of exponentsDO NOT RELY ON THE
  CALCULATOR. You will be wasting your valuable
  time!

• Try This Which of the following is equal to
  (ab)4 ?
• b-3
• a4b
• a4b7
• (ab)7
• ab7
• ab

10
Logarithms

• Know the rules of logs. The calculator only
  works for base 10!
• logb(y)x The log base b of y is the power
  to which we raise b to get y.

• Try This Which of the following is equal to 2
  log 8?
• log 64
• log 16
• log 4
• 64
• 16

11
Ratio and Proportion

• Try This Grandmas famous apple pie recipe calls
  for ½ cup sugar, 3 eggs and 2 cups of peeled
  apples. If we only have 2 eggs, what quantity of
  sugar and apples do we need to complete the
  recipe?
• 2 cups sugar, 1 1/3 cups of apples
• 1/3 cup sugar, 3 cups apples
• 3 cups sugar, 1/3 cup of apples
• 1/3 cup sugar, 1 1/3 cups of apples
• 3 cups sugar, 1/3 cup of apples

12
Percent

• Percent part
• whole

• Try This A class survey indicates that 20 of
  the students like chocolate, 30 of the students
  like caramel, and the remaining students like
  neither. If there are 50 students in the class,
  how many do not like chocolate?
• 10
• 15
• 20
• 40
• 45

13
Linear equations in one variable

• Try This Zack has 3 boxes of oranges plus three
  extra cards to give a total of 24 oranges. Which
  of the following expressions represents this
  statement and what is the value of x?
• 243x3, x8
• 243x3, x7
• 243x-3, x8
• 243x, x8
• 24x3-3x, x7

14
Counting addition

• Total number of outcomes event 1 event 2
  common elements

• Try This The set of numbers A 2,3,4,5,6 and
  the set of numbers B 2,4,7. How many ways are
  there to choose an integer from set A or B?
• 3
• 4
• 5
• 8
• 15

15
Counting - Factorials

• A factorial a number, n!, is the number n times
  n-1 times n-2, etc.
• For example, 3! is 3 x 2 x 1 6

• Try This In how many ways can the letters of
  the word SAME be rearranged?
• 4
• 6
• 16
• 24
• 64

16
Counting - Multiplication

• The multiplication principle can be used to find
  out how we can complete one event followed by
  another, provided the two events are separate.

• Try This There are 2 types of crusts for pizza
  and three possible toping choices and two sauces.
  How many ways can we make a pizza?
• 5
• 6
• 7
• 8
• 12

17
Counting - Permutations

• With a permutation, order matters.

• Try This There are 7 players on the high school
  baseball team. How many possible ways can a
  batting lineup be made if only 3 batters are
  required for the first inning?
• 6
• 12
• 21
• 210
• 5040

18
Counting - Probability

• Probability is the ratio of the number of ways an
  event can occur to the total number of overall
  events. The probability can never exceed 1!

• Try This A glass jar contains 6 red, 5 green, 8
  blue and 3 yellow marbles. If a single marble is
  chosen at random from the jar, what is the
  probability that you do not choose a red marble?
• 6/22
• 5/22
• 8/22
• 3/22
• 16/22

19
Complete the 10 minute drill

• ANSWERS