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PSAT MATHEMATICS
9-A Basic Arithmetic Concepts
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Set
A collection of “things” that have been grouped together in some way.
“things” – elements or members
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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.
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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
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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
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Example
A = {2, 3, 5, 7}B = {2, 4, 6, 8}
Find the union and intersection of sets A and B.
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Solution Set
The set of all numbers that satisfy the equation.
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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?
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Signed Numbers
Draw a number line from -5 to 5. Mark the following points.
-3 ½ 0.25 π - ¾ |-4|
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Example
How many integers are solutions of the inequality
|x|<5?
A. 0 B. 4C. 8 D. 9 E. infinitely many
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Example
What is the sum of the product and quotient of 8 and 8?
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Example
What is the product of all the integers from -5 to 5, inclusive?
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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
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Integers
Integers Positive integers Negative integers Consecutive integers Consecutive odd integers Consecutive even integers Prime numbers
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Example
If 0<x<3 and 2<y<8, what is the largest integer value of x+y?
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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?
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Example
What is the sum of the largest prime factor of 26 and the largest prime factor of 28?
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Exponents and Roots
Repeated addition of the same number is indicated by multiplication.
Repeated multiplication of the same number is indicated by an exponent.
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Laws of Exponents
54 x 53
56 / 54
(52)3
53 x 63
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Example
If 5a x 5b = 550, what is the average (arithmetic mean) of a and b?
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Example
What is the value of 16¾?
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Perfect Squares
List the squares of 0 to 15.
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Example
What is the circumference of a circle whose area is 10π?
A. 5πB. 10πC. π√10D. 2π√10 E. π√20
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Order of Operations
Parentheses Exponents Multiplication & Division Addition & Subtraction
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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)
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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
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Practice Problems