Arithmetic

To do well on the PSAT, you need to feel comfortable with most topics of basic arithmetic. The first five sections of Chapter 7 provide you with a review of the basic arithmetic operations, sign numbers, fractions and decimals, rations, precents, and averages. The solution to more than one-third of the math questions on the PSAT depend on your knowing the Key Facts of arithmetic.

A set is a collection of elements or members that have been grouped together in some way.
A union is a set consisting of two sets and is represented by A U B
The intersection of two sets is the set only consisting of those elements that are in both A and B, it is represented by the symbol ∩
The Solution Set of an equation the set of all numbers that satisfy the equation.
The Absolute Value of a number is the distance between the 0 and the number.
Consecutive Integers are two or more integers written in sequence in which each integer is 1 more than the preceding one.
PEMDAS is the order in which is used to perform more than one operation.

Fractions and Decimals

Several questions on the PSAT involve fractions or decimals. Even if you are using a calculator that has fraction capabilities, it is very important that you understand how to do them without a calculator

To compare two fractions, use your calculator to convert them to decimals and then compare them
Use a calculator to save time and avoid careless errors.
Reduce fractions before multiplying them together.
The reciprocal of any nonzero number x, is the number 1/x.
A mixed number is a number which consists of an integer followed by a fraction. It is an abbreviation for the sum of the number and the fraction.

Percent and Ratios

The word percent means hundredths. We use the percent symbol % to express the word “percent.” For example, “15 percent” means “15 hundredths” and can be written with a % symbol, as a fraction, or as a decimal: 15/100 = .15

A ratio is a fraction that compares two Quantities that are measured in the same units. One quantity is a numerator of a fraction, and the other quantity is a denominator. It was just a fraction. It can be reduced or converted to a decimal or percent.

The percent increase of a quantity is the actual increase divided by the original amount multiplied by 100%.
The percent decrease of quality is the actual decrease divided by the original amount, times 100%.
In any ratio problem write the letter X after each number and use some given information to solve for X. Solve it like you would solve an equation or inequality.
Our rate is a fraction that compares to quantities measured in different units. The word per often appears in rate problems. MPH, dollars per week, cents per ounce children per classroom and so on.

Algebra

For the PSAT you need to know only a small part of the algebra normally taught in a high school algebra class course and none of the material taught in an intermediate or advanced course. Polynomials, solving equations, solving inequalities are all important in the PSAT.

A monomial is any number or variable or product of numbers and variables.
A polynomial is a monomial, or the sum of two or more monomials. Each monomial that makes up the polynomial is called a term of the polynomial.
Two terms are called like terms, if they have exactly the same variables and exponents. But they can only defer in their coefficients.
The only terms of a polynomial that can be combined are like terms.
For solving equations and inequalities, when you have to solve for one variable in terms of the others, treat all the others as if their numbers.
To solve for systems of equations add or subtract them. If there are more than two equations, add them.
All distance problems on the PSAT involve one of three variations of the same formula. Distance equals rate x time.

Geometry

Although about 30% of the math questions on the PSAT involve geometry, you need to know only a relatively small number of facts, far fewer than you would learn in a geometry course. And of course, you don't need to provide proofs.

An angle is formed by the intersection of two line segments, rays, or lines.
The point of an interception is called the vertex.
If two or more angles form a straight angle, the sum of their measures is 180 degrees.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
In any triangle, the longest side is opposite the largest angle, the shortest side is opposite, the smallest angle, and sides with the same length of opposite angles with the same measure.
Right triangles are triangles that have one right angle and two acute ones.
The side opposite the 90-degree angle is called the hypotenuse.
An altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side.
A quadrilateral is a polygon of four sides every.
Every quadrilateral has two diagonals.
The sum of any quadrilateral is 360 degrees.

Miscellaneous

About 90% of the questions on the PSAD are on arithmetic, algebra and geometry. The remaining 10% of the questions are on Michelini's topics, such as probability sequences, data interpretation and functions.

The probability that an event will occur is a number between zero and one, usually written as a fraction, which indicates how likely it is that the event will happen.
Probably is always written in fractions, but can be converted into other forms.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.
A geometric sequence is a sequence in which the ratio between any two consecutive terms is the same.
A repeating sequence is a sequence in which a certain number of terms repeat indefinitely.
A line graph indicates how one or more quantities change over time. The horizontal axis usually marked off in units of time.
A circle graph is another way to present data in a circle graph, which is sometimes called a pie chart. The circle is divided into sectors, with each size of each sector exactly proportional to the quantity represents.
A function is a rule that assigns to each number in one set, a number in another set.

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Mathematics: Review of PSAT Mathematics

Arithmetic

A set is a collection of elements or members that have been grouped together in some way.
A union is a set consisting of two sets and is represented by A U B
The intersection of two sets is the set only consisting of those elements that are in both A and B, it is represented by the symbol ∩
The Solution Set of an equation the set of all numbers that satisfy the equation.
The Absolute Value of a number is the distance between the 0 and the number.
Consecutive Integers are two or more integers written in sequence in which each integer is 1 more than the preceding one.
PEMDAS is the order in which is used to perform more than one operation.

Fractions and Decimals

To compare two fractions, use your calculator to convert them to decimals and then compare them
Use a calculator to save time and avoid careless errors.
Reduce fractions before multiplying them together.
The reciprocal of any nonzero number x, is the number 1/x.
A mixed number is a number which consists of an integer followed by a fraction. It is an abbreviation for the sum of the number and the fraction.

Percent and Ratios

The percent increase of a quantity is the actual increase divided by the original amount multiplied by 100%.
The percent decrease of quality is the actual decrease divided by the original amount, times 100%.
In any ratio problem write the letter X after each number and use some given information to solve for X. Solve it like you would solve an equation or inequality.
Our rate is a fraction that compares to quantities measured in different units. The word per often appears in rate problems. MPH, dollars per week, cents per ounce children per classroom and so on.

Algebra

A monomial is any number or variable or product of numbers and variables.
A polynomial is a monomial, or the sum of two or more monomials. Each monomial that makes up the polynomial is called a term of the polynomial.
Two terms are called like terms, if they have exactly the same variables and exponents. But they can only defer in their coefficients.
The only terms of a polynomial that can be combined are like terms.
For solving equations and inequalities, when you have to solve for one variable in terms of the others, treat all the others as if their numbers.
To solve for systems of equations add or subtract them. If there are more than two equations, add them.
All distance problems on the PSAT involve one of three variations of the same formula. Distance equals rate x time.

Geometry

An angle is formed by the intersection of two line segments, rays, or lines.
The point of an interception is called the vertex.
If two or more angles form a straight angle, the sum of their measures is 180 degrees.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
In any triangle, the longest side is opposite the largest angle, the shortest side is opposite, the smallest angle, and sides with the same length of opposite angles with the same measure.
Right triangles are triangles that have one right angle and two acute ones.
The side opposite the 90-degree angle is called the hypotenuse.
An altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side.
A quadrilateral is a polygon of four sides every.
Every quadrilateral has two diagonals.
The sum of any quadrilateral is 360 degrees.

Miscellaneous

The probability that an event will occur is a number between zero and one, usually written as a fraction, which indicates how likely it is that the event will happen.
Probably is always written in fractions, but can be converted into other forms.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.
A geometric sequence is a sequence in which the ratio between any two consecutive terms is the same.
A repeating sequence is a sequence in which a certain number of terms repeat indefinitely.
A line graph indicates how one or more quantities change over time. The horizontal axis usually marked off in units of time.
A circle graph is another way to present data in a circle graph, which is sometimes called a pie chart. The circle is divided into sectors, with each size of each sector exactly proportional to the quantity represents.
A function is a rule that assigns to each number in one set, a number in another set.