PSAT MATHEMATICS

9-A Basic Arithmetic Concepts

Set

A collection of “things” that have been grouped together in some way.

“things” – elements or members

Example

If A is the set of states in the United States, then _____________ is an element of A.

If B is the set of letters in the English alphabet, then _____ is a member of B.

If C is the set of even integers, then ___ is in C.

Union

The union of two sets, A and B, is the set consisting of all the elements that are in A or B or both.

A U B

Intersection

The intersection of two sets, A and B, is the set consisting of only the elements that are in both A and B.

A B U

Example

A = {2, 3, 5, 7}B = {2, 4, 6, 8}

Find the union and intersection of sets A and B.

Solution Set

The set of all numbers that satisfy the equation.

Example

If C={-2, -1, 0, 1, 2} and D is the set that consists of the squares of each of the elements of C, how many numbers are elements of D?

Signed Numbers

Draw a number line from -5 to 5. Mark the following points.

-3 ½ 0.25 π - ¾ |-4|

Example

How many integers are solutions of the inequality

|x|<5?

A. 0 B. 4C. 8 D. 9 E. infinitely many

Example

What is the sum of the product and quotient of 8 and 8?

Example

What is the product of all the integers from -5 to 5, inclusive?

Example

Which of the following are equal to (-1)25?I. (-1)100 II. -(1)100 III. - (-1)100

A. I only B. II only C. III only D. II and III only E. I, II, and III

Integers

Integers Positive integers Negative integers Consecutive integers Consecutive odd integers Consecutive even integers Prime numbers

Example

If 0<x<3 and 2<y<8, what is the largest integer value of x+y?

Example

If the remainder when a is divided by 7 is 2 and the remainder when b is divided by 7 is 4, what is the remainder when ab is divided by 7?

Example

What is the sum of the largest prime factor of 26 and the largest prime factor of 28?

Exponents and Roots

Repeated addition of the same number is indicated by multiplication.

Repeated multiplication of the same number is indicated by an exponent.

Laws of Exponents

54 x 53

56 / 54

(52)3

53 x 63

Example

If 5a x 5b = 550, what is the average (arithmetic mean) of a and b?

Example

What is the value of 16¾?

Perfect Squares

List the squares of 0 to 15.

Example

What is the circumference of a circle whose area is 10π?

A. 5πB. 10πC. π√10D. 2π√10 E. π√20

Order of Operations

Parentheses Exponents Multiplication & Division Addition & Subtraction

Practice

1. 10 + 4 x 2 2. (10 + 4) x 2 3. 16 ÷ 2 x 4 4. 16 ÷ (2 x 4) 5. 10 + 15 ÷ (2 + 3) 6. 100 – 22 (3 + 4 x 5)

Example

Which of the following is equivalent to for all nonzero numbers x?

A. x + 1 B. x5 C. x5 + 1D. x + x4 E. x16

€

x 5 + x 4

x 4

Practice Problems