SAT Math - Advanced Math

This course provides an overview of mixture problems in algebra. The next section includes the concept of exponents and exponential growth or decay of a function. The next section includes the concept of polynomial, sum and difference of polynomials, multiplication of polynomials, a brief idea on long division of division of polynomials. It also involves the brief idea on rational expression and operations on the expression. The last section provides a complete idea on radicals, conjugate, rationalization with examples.

10 topics

335 lectures

Educators

LL

Course Curriculum

1 videos

75 videos

SAT Math - Geometry

20 videos

SAT Math - Trigonometry

30 videos

SAT Math - Quadratics

45 videos

SAT Math - Advanced Math

40 videos

SAT Math - Probability and Statistics

25 videos

73 videos

4 videos

22 videos

SAT Math - Advanced Math Lectures

SAT Math - Advanced Math

Mixture Problems - Overview

A mixture is a combination of two or more substances in which the components retain their respective chemical identities. In other words, a mixture is a physical mixture, not a chemical mixture.

Lily An

SAT Math - Advanced Math

Mixture Problems - Example 1

A mixture is a combination of two or more substances in which the components retain their respective chemical identities. In other words, a mixture is a physical mixture, not a chemical mixture.

Lily An

SAT Math - Advanced Math

Mixture Problems - Example 2

A mixture is a combination of two or more substances in which the components retain their respective chemical identities. In other words, a mixture is a physical mixture, not a chemical mixture.

Lily An

SAT Math - Advanced Math

Mixture Problems - Example 3

A mixture is a combination of two or more substances in which the components retain their respective chemical identities. In other words, a mixture is a physical mixture, not a chemical mixture.

Lily An

SAT Math - Advanced Math

Mixture Problems - Example 4

A mixture is a combination of two or more substances in which the components retain their respective chemical identities. In other words, a mixture is a physical mixture, not a chemical mixture.

Lily An

SAT Math - Advanced Math

Exponential Growth and Decay - Overview

In mathematics, exponential growth is a type of growth in which the change in some value is proportional to its current value. The value of this constant of proportionality is the growth rate of the value. The concept of exponential growth is useful in many areas of mathematics, particularly in elementary algebra, calculus, and discrete time financial mathematics.

Lily An

SAT Math - Advanced Math

Exponential Growth and Decay - Example 1

In mathematics, exponential growth is a type of growth in which the change in some value is proportional to its current value. The value of this constant of proportionality is the growth rate of the value. The concept of exponential growth is useful in many areas of mathematics, particularly in elementary algebra, calculus, and discrete time financial mathematics.

Lily An

SAT Math - Advanced Math

Exponential Growth and Decay - Example 2

In mathematics, exponential growth is a type of growth in which the change in some value is proportional to its current value. The value of this constant of proportionality is the growth rate of the value. The concept of exponential growth is useful in many areas of mathematics, particularly in elementary algebra, calculus, and discrete time financial mathematics.

Lily An

SAT Math - Advanced Math

Exponential Growth and Decay - Example 3

In mathematics, exponential growth is a type of growth in which the change in some value is proportional to its current value. The value of this constant of proportionality is the growth rate of the value. The concept of exponential growth is useful in many areas of mathematics, particularly in elementary algebra, calculus, and discrete time financial mathematics.

Lily An

SAT Math - Advanced Math

Exponential Growth and Decay - Example 4

In mathematics, exponential growth is a type of growth in which the change in some value is proportional to its current value. The value of this constant of proportionality is the growth rate of the value. The concept of exponential growth is useful in many areas of mathematics, particularly in elementary algebra, calculus, and discrete time financial mathematics.

Lily An

SAT Math - Advanced Math

Polynomial Long Division - Overview

In computer science and mathematics, polynomial long division is a method for dividing one polynomial by another. The method is a generalization of the long division of integers. It is used to divide polynomials over a field, which may be either the field of the rational numbers, or the field of the real numbers. The algorithm is similar to the Euclidean algorithm for integers. It is a recursive algorithm, and is well suited for implementation in a computer algebra system.

Lily An

SAT Math - Advanced Math

Polynomial Long Division - Example 1

In computer science and mathematics, polynomial long division is a method for dividing one polynomial by another. The method is a generalization of the long division of integers. It is used to divide polynomials over a field, which may be either the field of the rational numbers, or the field of the real numbers. The algorithm is similar to the Euclidean algorithm for integers. It is a recursive algorithm, and is well suited for implementation in a computer algebra system.

Lily An

SAT Math - Advanced Math

Polynomial Long Division - Example 2

In computer science and mathematics, polynomial long division is a method for dividing one polynomial by another. The method is a generalization of the long division of integers. It is used to divide polynomials over a field, which may be either the field of the rational numbers, or the field of the real numbers. The algorithm is similar to the Euclidean algorithm for integers. It is a recursive algorithm, and is well suited for implementation in a computer algebra system.

Lily An

SAT Math - Advanced Math

Polynomial Long Division - Example 3

In computer science and mathematics, polynomial long division is a method for dividing one polynomial by another. The method is a generalization of the long division of integers. It is used to divide polynomials over a field, which may be either the field of the rational numbers, or the field of the real numbers. The algorithm is similar to the Euclidean algorithm for integers. It is a recursive algorithm, and is well suited for implementation in a computer algebra system.

Lily An

SAT Math - Advanced Math

Polynomial Long Division - Example 4

In computer science and mathematics, polynomial long division is a method for dividing one polynomial by another. The method is a generalization of the long division of integers. It is used to divide polynomials over a field, which may be either the field of the rational numbers, or the field of the real numbers. The algorithm is similar to the Euclidean algorithm for integers. It is a recursive algorithm, and is well suited for implementation in a computer algebra system.

Lily An

SAT Math - Advanced Math

Complex and Imaginary Numbers - Overview

In mathematics, a complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. The complex number system is the basis of complex analysis, a branch of mathematics.

Lily An

SAT Math - Advanced Math

Complex and Imaginary Numbers - Example 1

In mathematics, a complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. The complex number system is the basis of complex analysis, a branch of mathematics.

Lily An

SAT Math - Advanced Math

Complex and Imaginary Numbers - Example 2

In mathematics, a complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. The complex number system is the basis of complex analysis, a branch of mathematics.

Lily An

SAT Math - Advanced Math

Complex and Imaginary Numbers - Example 3

In mathematics, a complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. The complex number system is the basis of complex analysis, a branch of mathematics.

Lily An

SAT Math - Advanced Math

Complex and Imaginary Numbers - Example 4

In mathematics, a complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. The complex number system is the basis of complex analysis, a branch of mathematics.

Lily An

SAT Math - Advanced Math

Rational Expressions - Overview

In mathematics, a rational expression is an expression constructed from the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. A rational expression is an expression that can be written as the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. Rational expressions are often used to represent fractions, in which case they are commonly called rational fractions.

Lily An

SAT Math - Advanced Math

Rational Expressions - Example 1

In mathematics, a rational expression is an expression constructed from the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. A rational expression is an expression that can be written as the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. Rational expressions are often used to represent fractions, in which case they are commonly called rational fractions.

Lily An

SAT Math - Advanced Math

Rational Expressions - Example 2

In mathematics, a rational expression is an expression constructed from the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. A rational expression is an expression that can be written as the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. Rational expressions are often used to represent fractions, in which case they are commonly called rational fractions.

Lily An

SAT Math - Advanced Math

Rational Expressions - Example 3

In mathematics, a rational expression is an expression constructed from the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. A rational expression is an expression that can be written as the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. Rational expressions are often used to represent fractions, in which case they are commonly called rational fractions.

Lily An

SAT Math - Advanced Math

Rational Expressions - Example 4

In mathematics, a rational expression is an expression constructed from the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. A rational expression is an expression that can be written as the ratio of two polynomials, or the quotient of two polynomials. Rational expressions can also be formed by multiplying two polynomials. Rational expressions are often used to represent fractions, in which case they are commonly called rational fractions.

Lily An

SAT Math - Advanced Math

Radicals - Overview

Radical or root is a function that "gives the ratio of a quantity to a power of another quantity". In other words, it is a function that "gives the roots of a function, or, if the roots are complex numbers, gives their ratios to a given number". The concept of root is used in many areas of mathematics, including algebra, calculus, geometry, number theory, and statistics.

Lily An

SAT Math - Advanced Math

Radicals - Example 1

Radical or root is a function that "gives the ratio of a quantity to a power of another quantity". In other words, it is a function that "gives the roots of a function, or, if the roots are complex numbers, gives their ratios to a given number". The concept of root is used in many areas of mathematics, including algebra, calculus, geometry, number theory, and statistics.

Lily An

SAT Math - Advanced Math

Radicals - Example 2

Radical or root is a function that "gives the ratio of a quantity to a power of another quantity". In other words, it is a function that "gives the roots of a function, or, if the roots are complex numbers, gives their ratios to a given number". The concept of root is used in many areas of mathematics, including algebra, calculus, geometry, number theory, and statistics.

Lily An

SAT Math - Advanced Math

Radicals - Example 3

Radical or root is a function that "gives the ratio of a quantity to a power of another quantity". In other words, it is a function that "gives the roots of a function, or, if the roots are complex numbers, gives their ratios to a given number". The concept of root is used in many areas of mathematics, including algebra, calculus, geometry, number theory, and statistics.

Lily An

SAT Math - Advanced Math

Radicals - Example 4

Radical or root is a function that "gives the ratio of a quantity to a power of another quantity". In other words, it is a function that "gives the roots of a function, or, if the roots are complex numbers, gives their ratios to a given number". The concept of root is used in many areas of mathematics, including algebra, calculus, geometry, number theory, and statistics.

Lily An

SAT Math - Advanced Math

Polynomials - Overview

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x^2-2x+4.

Lily An

SAT Math - Advanced Math

Polynomials - Example 1

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x^2-2x+4.

Lily An

SAT Math - Advanced Math

Polynomials - Example 2

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x^2-2x+4.

Lily An

SAT Math - Advanced Math

Polynomials - Example 3

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x^2-2x+4.

Lily An

SAT Math - Advanced Math

Polynomials - Example 4

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x^2-2x+4.

Lily An

SAT Math - Advanced Math

Exponents - Overview

Exponentiation is the raising of a number (the base) to a power (the exponent). For example, 2^3 is the third power of 2, because 2^3 = 2×2×2. The exponent is the number of times the base is multiplied by itself as a factor. Exponentiation by integer exponents can be visualized as stacking a set of objects onto a set of objects.

Lily An

SAT Math - Advanced Math

Exponents - Example 1

Exponentiation is the raising of a number (the base) to a power (the exponent). For example, 2^3 is the third power of 2, because 2^3 = 2×2×2. The exponent is the number of times the base is multiplied by itself as a factor. Exponentiation by integer exponents can be visualized as stacking a set of objects onto a set of objects.

Lily An

SAT Math - Advanced Math

Exponents - Example 2

Exponentiation is the raising of a number (the base) to a power (the exponent). For example, 2^3 is the third power of 2, because 2^3 = 2×2×2. The exponent is the number of times the base is multiplied by itself as a factor. Exponentiation by integer exponents can be visualized as stacking a set of objects onto a set of objects.

Lily An

SAT Math - Advanced Math

Exponents - Example 3

Exponentiation is the raising of a number (the base) to a power (the exponent). For example, 2^3 is the third power of 2, because 2^3 = 2×2×2. The exponent is the number of times the base is multiplied by itself as a factor. Exponentiation by integer exponents can be visualized as stacking a set of objects onto a set of objects.

Lily An

SAT Math - Advanced Math

Exponents - Example 4

Exponentiation is the raising of a number (the base) to a power (the exponent). For example, 2^3 is the third power of 2, because 2^3 = 2×2×2. The exponent is the number of times the base is multiplied by itself as a factor. Exponentiation by integer exponents can be visualized as stacking a set of objects onto a set of objects.

Lily An