ACT Math

What is the reciprocal of - 1/4?

-4

0

0 is an even number. 0 is neither positive or negative. Anything multiplied by 0 is 0. 0 raised to any power is 0. Anything raised to the 0 power is 1.

1. In the number, 0.191919, what digit is coming next?

1

What is the opposite reciprocal of 2?

- 1/2

Radical

Another world for the root sign

Absolute Value

The distance from zero on the number line

1. Write 3 as a fraction.

3/1

1. What is the least common multiple of 9 and 12?

36

1. What is the least common multiple of 24 and 48?

48

1. In the number 0.1666, what digit is coming next?

6

1. What is the greatest common factor of 27 and 45?

9

1. What is the greatest common factor of 9 and 36?

9

Irrational

A number that can be expressed as a decimal but not a fraction

Rational

A number that can be expressed as the ratio of two other numbers, making a fraction

Prime

A number that has itself and 1 as its only factors

Exponent/Power

A number that indicates how many times to multiply a base by itself

Decimal

A way of expressing a fraction in which numbers are divided by ten, hundred, thousand, and other powers of ten

Fraction

A way of expressing the division of numbers by stacking one over the other.

Integers

All real numbers other than decimals or fractions

Divisible

An integer can be divided by another integer evenly, with no fraction or decimal left over

If x is the least odd prime number and y is the least positive integer multiple of 10, what is the difference between x and y? a. 3 b. 7 c. 11 d. 15 e. 17

B. Take this problem in bite-size pieces. If x is the least odd prime number, x must be 3. If y is the least positive integer multiple of 10. y must be 10. The difference between these two numbers is therefore 10-3=7. If you selected (E), be careful, you may have through that 20 was the first integer multiple of 10, but the first multiple of any number is that number itself.

In the complex numbers, where i^2=-1, which of the following is equal to the result of squaring the expression (i + 4) a. 4i b. 16i c. 15 + 8i d. i + 16 e. 17-18i

C. Although this problem involves an imaginary number, you can still use traditional FOIL method to find the answer. You are asked to square the expression, so do so, and remember to multiply the First, Outer, Inner, and Last terms. (1+4)(1+4)= 1^2 +8i +16. None of the answer choices look quite like this, but remember i^2= -1, so substitute this term: i^2 +81 +16= -1 +8i +16= 8i +15

There are 600 school children in the Lakeville district. If 54 of them are high school seniors, what is the percentage of high school seniors in the Lakeville district? a. .9% b. 2.32% c. 9% d. 11% e. 90%

C. First, we need to figure out what percent 54 is of 600. It's pretty small, definitely way less than 50%, so we can eliminate (E) right off the bat. Now, think about easy percentages that you know-10 and 25%-and start from there. What's 10% of 600 is 60. Let's get rid of (D). Now, we know that 54 is pretty close to 60, so we want something close to 10% but slightly less, and the only possible answer is (C).

Distinct

Different

Even

Divisible by 2

Number

Everything

1. Is 12 a multiple or factor of 24?

Factor

Factor

Integers that multiply together to make a given product. A number's factors are always smaller than or the same as that number.

Negative

Less than 0

Odd

NOT divisible by 2

Order of Operations

Parentheses, Exponents, Multiplications, Division, Addition, Substraction

Digits

The integers 0 through 9

Reciprocal

The inverse of a number-flip the numerator and denominator

Greatest Common Factor

The largest factor common to two numbers

Remainder

The number left over when a number is not divisible by another number

1. Is 8 one of the factors of 64?

Yes

Real

Zero, all positive and negative integers, fractions, decimals, and roots

Each member in a club had to choose an activity for a day of volunteer work. 1/3 of the members chose to pick up trash. 1/4 of the remaining members chose to paint fences. 5/6 of the members still without tasks chose to clean school buses. The rest of the members chose to plant trees. IF the club has 36 members, how many of the members chose to plant trees? a. 3 b. 6 c. 9 d. 12 e. 15

A. Total 36 members. Know 1/3 of those members chose to pick up trash. 1/3 of 36 is 12. (36-12= 24) Of the 24 members left 1/4 chose to paint fences. 1/4 of 24 is 6. (24-6=18) Of the 18 left 5/6 chose to clean buses. 5/6 of 18 is 15. (18-15=3 ) Which leaves you with 3 students to plant trees.

Least Common Multiple

The smallest multiple common to two numbers

When a number and its reciprocal are multiplied, what is the product?

1

1. List the factors of 12. 2. List the first four multiples of 12.

1. 1, 2, 3, 4, 6, 12 2. 12 ,24, 36, 48

1. List the factors of 30. 2. List the first four multiples of 30.

1. 1, 2, 3, 5, 6,10, 15, 30 2. 30, 60, 90, 120

(-81, -19, -9, -6, -1/4, -0.15, 0, 1.75, 2, 3, 12,16, 81) 1. List all the positive numbers. 2. List all the negative integers. 3. List all the odd integers. 4. List all the even integers. 5. List all the positive, even integers in consecutive order. 6. List all the numbers that are neither positive nor negative.

1. 1.75, 2, 3, 12, 16, 81 2. -81, -19, -9, -6 3. -81, -19, -9, 3, 81 4. -6, 0, 2, 12,16 5. 2, 12, 16 6. 0

(A prime number is any number with only two distinct factors: 1 and itself.) 1. What are the single digit prime numbers? 2. What is the only even prime number? 3. Is 1 a prime number?

1. 2, 3, 5, 7 2. 2 3. No, it does not have two distinct factors.

The prime factorization of a number is the reduction of a number to its prime factors. Find the prime factorization of a number by using a factor tree. 1. What is the prime factorization of 36? 2. What is the sum of all the prime factors of 36? 3. What is the product of all the distinct prime factors of 36?

1. 2x2x3x3 or x 2^2x3^2 2. 10(2+2+3+3) 3. 6(2x3)

1. How many times does 2 go into 15 evenly? 2. How much is left over? 3. What is 15 divided by 2?

1. 7 2. 1 3. 7 R 1 (7 remainder 1)

(number, integer, positive, negative, even, odd, consecutive, reciprocal, remainder) 1. Which terms describe the number 6? 2. Which terms describe the number - 1/5? 3. Which terms describe the number 0? 4. When 14 is divided by 3, it has a ____________________________ of 2. 5. The _______________________ of -1/4 is -4. 6. The numbers 2, 4, 6, are listed in _______________order, but the numbers 3, 1, 14 are not.

1. Number, Integer, Positive, Even 2. Number, Negative 3. Number, Integer, Even 4. Remainder 5. Reciprocal 6. Consecutive

1. Write 0.5 as a fraction

1/2

What is the least possible sum of three distinct prime numbers between 10 and 20? a. 30 b. 39 c. 41 d. 45 e. 60

C. The prime number between 10 and 20 are as follows: 11, 13, 17, 19. You want the least sum of three distinct numbers, so the only possible answer is 11 +13 +17= 41. If you chose (B), you may have missed the word distinct.

What is the product of the distinct prime factors of 54? a. 2 b. 3 c. 6 d. 11 e. 54

C. You'll need to find the prime factorization of 54, so use a factor tree. In using this tree, you'll find the prime factorization of 54= 6x9=(2x3)x(3x3)= 2 x 3^3. The distinct prime factors of 54, therefore, are 2 and 3. The product of these two numbers is 6. If you chose (E), you may have missed the word distinct! Read Carefully!

Positive

Greater than 0

Consecutive

In increasing order

Multiple

The product of an integer and another integer. A number's multiples are always larger than or the same as that number.

Sum

The result of addition

Quotient

The result of division

Product

The result of multiplication

Difference

The result of subtraction

Imaginary

The square (or any other even) root of a negative number

Opposite

Two numbers that have the same magnitude but are opposite in signs. That is, two numbers with the same distance from zero on the number line, but one is positive and the other negative.

What is the value of 3x^2+5x-7 when x=-1 a. -15 b. -9 c. -1 d. 5 e. 15

b. First replace x with -1. 3(-1)^2+5(-1). When working with negative numbers or fractions, make doubly sure that you use parentheses. If not, it will mess you up. Use your calculator to get -9.