Solve Equations with Fractions
7K views · Oct 4, 2022
This video first explains the steps to solve an equation with brackets. Then equations with fractions are solved following the steps: 1 - find the lowest common multiple of the denominators 2 - multiply all terms of the equations by the lowest common m
Use the Rational Root Theorem to Find the Zeros, Factor and sketch polynomials - Polynomials Part 1
35K views · Oct 3, 2022
The objectives covered in this video are: 1 - Use the rational root theorem to find the zeros of given polynomials 2 - Use division to factor the given polynomial 3 - Complete the factoring of the polynomial 4 - Find all zeros and their multipliciti
Find the Equation of a Polynomial Given its Graph - Grade 12
1K views · Oct 3, 2022
The x-intercepts are obtained from the graph and used as zeros to write the polynomial in factored form. The multiplicity of the zeros is determined by the shape of the graph around the x-intercept, whether the graph cuts or touches the x-axis. The y-int
Factor and Sketch the Polynomial - x^4 - 5x^3 - 3x^2 + 9x - Grade 12
26K views · Oct 3, 2022
In this video, the rational root theorem is first used to find possible rational zeros. Then the synthetic division of the polynomial is used to completely factor the polynomial and hence its zeros and their multiplicities. The behavior of the polynomial
Find a Polynomial Given two Remainders and a Factor - Grade 12
29K views · Oct 3, 2022
Given two remainders and their corresponding divisors as well as a factor of a polynomial, the solution to find the polynomial is presented. The polynomial is first written as P(x) = x^3 + b x^2 + cx + d since it is a polynomial of degree 3 and its l
Sketch the trigonometric function y = -0.5 sin(4(x+pi/3)) + 2.5 - Grade 12
12K views · Oct 3, 2022
A method based on substitution is used to find the 5 key points of the graph of the trigonometric function y = - 0.5 sin ( 4(x+pi/3) ) + 2.5 and sketch over two periods. The substitution PHI = 4 (x+pi/3) is made and the function is written as y = -
Find the Equation of a Trigonometric Function Given Its Graph - Grade 12
107K views · Oct 3, 2022
In this video, it is shown, through an example, how to find the equation of a trigonometric function, given by its graph. The function suggested is of the form: V(t) = A cos (Bt + C) + D where t is the variable. Formulas to find the parameters A (chose
Sketch the graph of the rational function y = (2x - 4)/(x + 2) - Grade 12
14K views · Oct 3, 2022
The domain, vertical and horizontal asymptotes, x and y intercepts as well as the table of signs of the function y = (2x - 4)/(x + 2) are first discussed, then they are used to sketch its graph. More grade 12 math practice at https://www.analyzemath.co
Solve Rational Inequalities (x+1)/(x+2) - 1 ≥ 1/(x-1) Using Table of Signs - Grade 12
4K views · Oct 3, 2022
In this video, the rational inequality : (x+1)/(x+2) - 1 ≥ 1/(x-1) is solved including detailed steps using the table of signs. The main objectives of the video are 1 - Group all terms and write the inequality in standard form with one side equal
Solve Trigonometric Equation cos(2x) - 2/sec (x) = 2 - Grade 12
14K views · Oct 3, 2022
A trigonometric equation involving multiple angles and a reciprocal trigonometric function is solved showing all steps with details. Trigonometric identities are used to rewrite cos(2x) = 2 cos^2(x) - 1 and 2/sec (x) = 2 cos (x) . The substitution u =
Solve the Logarithmic Equations : ln(x^2+-2) - ln(x-1) = 2 Grade 12
20K views · Oct 3, 2022
In this video, the equation (ln(x^2+-2) - ln(x-1) = 2) including logarithmic functions is solved including all detailed steps and the logarithmic rules used to transform the equation. First, the two logarithms on the left side are grouped using the for
Solve the Exponential Equation 3 * 4^x + 2^x = 30 - Grade 12
132K views · Oct 3, 2022
In this video, an equation with exponential functions of different bases is solved with all detailed steps and rules of exponents used to transform the equation. The expression 4^x is first transformed as (2^2)^x = 2^(2x) = (2^x)^2, hence the exponents a
Verify Trigonometric Identities - Grade 12
63K views · Oct 3, 2022
A trigonometric identity with single and multiple angles is transformed and verified using other basic trigonometric identities. Using basic identities, the left side of the identity is rewritten so that it is exactly written in the same form as the righ
Find the Exact Value of a Trigonometric Function - Grade 12
4K views · Oct 3, 2022
Find the exact value of tan(13 pi / 12) by first expressing the angle in terms of special angles and then using trigonometric formulas. 13 pi / 12 is expressed as 13 pi / 12 = pi + pi/12 and therefore tan(13 pi / 12 ) = tan( pi / 12) pi/12 = pi/3 -
System of a 2 by 2 Linear Equations with Parameter - Grade 10
28K views · Oct 3, 2022
Discuss the solutions of a system of 2 by 2 linear equations 2 x + 6 y = -2 -3 x + a y = 4 including parameter "a" in the second equation. The question is to find the values of parameter "a" for which the system has no solution. Three ways to answer t
long division of polynomials
211K views · Oct 3, 2022
The algorithm for the division of polynomials is presented along with the relationship between the dividend D, the divisor d, the quotient Q, and the remainder R. The result of the division is written as D/d = Q + R/d or D = Q d + R The result of th
Solve Polynomial Inequalities Using Table of Signs
7K views · Oct 3, 2022
Several examples of polynomial inequalities are solved and the solution set is written using inequality symbols, intervals, and graphically on the number line. The inequality is written in standard form with the right side equal to zero and the polynomia
Solve Rational Inequalities Using Table of Signs
6K views · Oct 3, 2022
Several examples of inequalities with rational expressions are solved and the solution set is written using inequality symbols, intervals, and graphically on the number line. The inequality is written in standard form with the right side equal to zero an
Quadratic functions at http://www.analyzemath.com
5K views · Feb 20, 2022
A video-applet that explains the effects of the parameters a, b and c on the graph of a quadratic function of the form f(x) = ax^2 + bx + c. More applets at http://www.analyzemath.com
Rational Functions from www.analyzemath.com
5K views · Feb 20, 2022
A video-applet to investigate the properties of rational functions. More applets may be found at http://www.analyzemath.com
Maximum Area of Rectangle form www.analyzemath.com
5K views · Feb 20, 2022
A video-applet that uses dynamic pictures to explain the problem of maximizing the area of a rectangle given that the perimeter in constant. More applets may be found at http://www.analyzemath.com
Find the Inverse of a Function - Part I
5K views · Feb 20, 2022
A tutorial on to find the inverse of a function given by a formula. From www.analyzemath.com see also http://www.analyzemath.com/stepbystep_mathworksheets/functions/inverse_square_root.html http://analyzemath.com/stepbystep_mathworksheets/functions/inv
Graphical interpretation of First Derivative
958 views · Feb 20, 2022
Graphical interpretation of the first derivative using local tangent http://www.analyzemath.com
interactive unit circle with sin(x), cos(x) and tan(x)
2K views · Feb 20, 2022
Online Interactive unit circle to show the relationship between sin(x), cos(x) and tan(x) on the unit circle and rectangular system of axes at http://www.analyzemath.com/unitcircle/unit_circle_applet.html
Smallest distance from point to a circle
27K views · Feb 20, 2022
Calculate the smallest distance from a point to a circle. More math exploration, tutorials and problems at www.analyzemath.com