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Smart Alex Mathematics
Australia
Приєднався 6 кві 2020
Hi and welcome to my channel! I'm June and and I'm a mathematics tutor based in Australia.
I created this channel to help my students and anyone interested in learning mathematics.
My aim is to create a library of of short videos with complementary workbooks that would be beneficial to students, parents and teachers.
Please help support my journey by subscribing to my channel and sharing the resources. Your subscription means so much to me.
Thank you.
#smartalexmathematics
#smartalexcoaching
My new website www.smartalexmathematics.com.au will be launching in 2024.
I created this channel to help my students and anyone interested in learning mathematics.
My aim is to create a library of of short videos with complementary workbooks that would be beneficial to students, parents and teachers.
Please help support my journey by subscribing to my channel and sharing the resources. Your subscription means so much to me.
Thank you.
#smartalexmathematics
#smartalexcoaching
My new website www.smartalexmathematics.com.au will be launching in 2024.
Find Minimum Value of (abs(z/(1-z)))^2 + (abs(z/(1+z)))^2 given abs(z) = 1
#complexnumber
In this video tutorial on complex numbers, we work through an example to show how to find the minimum value of (abs(z/(1-z)))^2 + (abs(z/(1+z)))^2 given z is a complex number with abs(z) = 1.
We make use of z = cos(theta) + i sin(theta) and trigonometric identities to help simplify the expression.
This is part of the Year 12 NSW HSC Extension 2 Mathematics course.
In this video tutorial on complex numbers, we work through an example to show how to find the minimum value of (abs(z/(1-z)))^2 + (abs(z/(1+z)))^2 given z is a complex number with abs(z) = 1.
We make use of z = cos(theta) + i sin(theta) and trigonometric identities to help simplify the expression.
This is part of the Year 12 NSW HSC Extension 2 Mathematics course.
Переглядів: 23
Відео
Circle Locus Question: Find locus of points P(x,y) to Two points A and B where PA = 2*PB
Переглядів 2321 день тому
#locus In this video tutorial, we explain using example how to find the locus of a set of points P(x,y) which moves in such a way where the distance between point P(x,y) and point A(4, 0) is equal to twice the distance between point P(x,y) and point B (1,0). The final locus is a circle.
Congruent Triangles Tests - SSS, AAS, SAS and RHS
Переглядів 39Місяць тому
#congruenttriangles #congruenceoftriangles #congruent In this video tutorial, we explain the four tests used to prove two triangles are congruent. We also work through examples on how to write proofs for proving two triangles are congruent. The four tests are: SSS - all sides equal AAS - two angles and a side equal SAS - two sides equal and included angle equal RHS - right angle, hypotenuse and...
Prove cos 3x, sin 3x and tan 3x Trigonometric Identities using De Moivre's Theorem
Переглядів 111Місяць тому
#complexnumbers #demoivrestheorem #trigonometricidentities In this video tutorial, we explain with examples on how to prove trigonometric identities involving sin3x, cos3x and tan3x using a combination of binomial expansion and De Moivre's theorem. This is part of the NSW Extension 2 Mathematics topic - Complex Numbers
Finding Square Root of Complex Number -5 + 2i
Переглядів 184Місяць тому
#complexnumbers In this video tutorial, we explaing how to find the square root of a complex number using the example -5 @2̈I We use the cartesian coordinate x and y, form a set of non-linear simultaneous equations by equating the real and imaginary parts. We then solve the equations for x and y which we then combine to get the answers for the square roots of the complex number -5 @2i. This is ...
Finding Equation of Straight Line Given Two Points
Переглядів 732 місяці тому
#equationofline #equationofstraightline #linearfunctions In this video tutorial, we work through an example on how to find the equation of a straight line given two points. Question: Find the equation of a line passing through (2, 4) and (-2, -8)
Solving Trigonometric Equation sin(theta) = 0.5
Переглядів 2353 місяці тому
#trigonometricequations #trigonometricfunction In this video tutorial, we explain with examples how to solve basic trigonometric equations: Sin(theta) = ½ Cos(theta) = 0.63 The steps are simplified into three sections: 1. Establish quadrant the angle theta is in based on the sign of the trigonometric functions. 2. Find the related acute angle by solving the trigonometric equation for theta. 3. ...
Finding Angle using Cosine Rule
Переглядів 1313 місяці тому
#cosinerule #trigonometry In this video tutorial, we explain how to use the Cosine Rule for finding unknown angle in a triangle. We cover: - Deriving Cosine Rule Formula for finding angle. - Understanding what each variable in the formula represents. - Examples on how to apply the Cosine Rule to finding unknown angle.
Finding Side Using Cosine Rule
Переглядів 1093 місяці тому
#cosinerule #trigonometry In this video tutorial, we explain how to use the cosine rule for finding unknown side in a triangle. We start off by introducing what each variable in the Cosine Rule represent. We then work through examples on how to apply the Cosine Rule formula to finding unknown side length.
Finding Equation of the Hyperbola from Graph Example 2
Переглядів 3213 місяці тому
#hyperbola #nonlinear #hyperbolicfunctions In this video tutorial, we work through an example to explain how to find the equation of the hyperbola from the graph. We start with the general equation of the hyperbola. From the graph, we can determine the horizontal and vertical asymptotes of the hyperbola. A point is given, which helps us to find the dilation factor. Substituting all these values...
Finding Equation of Hyperbola from Graph
Переглядів 1123 місяці тому
#hyperbola #nonlinear #functions In this video tutorial, we explain how to find the equation of the hyperbola given its graph. To find the equation of the hyperbola, we begin with the general equation of the hyperbola: y = a/(x-h) k a gives us the dilation factor of the hyperbola. h gives us the vertical asymptote of the hyperbola. k gives us the horizontal asymptote of the hyperbola. We can de...
Finding Median from Frequency Distribution Table (Middle Score)
Переглядів 1074 місяці тому
#frequencydistribution #statistics #dataanalysis In this video tutorial, we explain how to calculate the median from the frequency distribution table. The median of a dataset is the middle score when all scores are arranged in ascending order. From the frequency distribution table, we create another column - cumulative frequency which is a running total of all the scores. In addition, we have a...
Finding Mean (Average) from Frequency Distribution Table
Переглядів 684 місяці тому
#statistics #average In this maths video tutorial we explain the concept of how to find the mean (also known as average) from the frequency distribution table.
Solving Non linear Simultaneous Equations (Circle and Straight Line)
Переглядів 2644 місяці тому
#simultaneousequations #nonlinear #algebra #functions In this video tutorial, we work through an example on how to solve non-linear simultaneous equations between two equations - equation of a circle and equation of a straight line. Our simultaneous equations are: (x 3)^2 (y - 4)^2 = 13 x 5y - 4 = 0 We use the substitution method, form a quadratic equation to solve. The solutions to the non-lin...
Solving Non-Linear Simultaneous Equations (Line and Hyperbola)
Переглядів 6214 місяці тому
#simultaneousequations #nonlinear #functions In this video tutorial, we look at how to solve non-linear simultaneous equations using substitution method. Our equations are: x - y = 2 xy = 2 The equations represent a straight line and a hyperbola. We also look at how the solutions correspond to the points of intersection of the two graphs.
Solving Non-Linear Simultaneous Equations (Line and Parabola)
Переглядів 6315 місяців тому
Solving Non-Linear Simultaneous Equations (Line and Parabola)
Solving Basic Trigonometric Equations (Negative Constant)
Переглядів 545 місяців тому
Solving Basic Trigonometric Equations (Negative Constant)
Solving Trig Equation sin x = -1/2 and tan x = -2
Переглядів 735 місяців тому
Solving Trig Equation sin x = -1/2 and tan x = -2
Integrating Rational Functions - When to use Log, Power Rule or Reverse Chain Rule
Переглядів 1015 місяців тому
Integrating Rational Functions - When to use Log, Power Rule or Reverse Chain Rule
Quick Method for Differentiating Logarithmic Functions
Переглядів 366 місяців тому
Quick Method for Differentiating Logarithmic Functions
Differentiation of Logarithmic Functions Examples Part 1 (Using Chain Rule)
Переглядів 636 місяців тому
Differentiation of Logarithmic Functions Examples Part 1 (Using Chain Rule)
Introduction to Present Value of Annuity (PVA) and interest factors (PVIFA)
Переглядів 3256 місяців тому
Introduction to Present Value of Annuity (PVA) and interest factors (PVIFA)
Introduction to Future Value of Annuity (FVA & FVIFA)
Переглядів 1946 місяців тому
Introduction to Future Value of Annuity (FVA & FVIFA)
How to find coefficient of x^6 in binomial expansion of (x-2)^2*(2x-3)^8
Переглядів 7236 місяців тому
How to find coefficient of x^6 in binomial expansion of (x-2)^2*(2x-3)^8
Finding Coefficient of x^3 term in expansion of (2+x^2)(3-2x)^5
Переглядів 6536 місяців тому
Finding Coefficient of x^3 term in expansion of (2 x^2)(3-2x)^5
Solving Exponential Equations Reducible to Quadratics
Переглядів 1057 місяців тому
Solving Exponential Equations Reducible to Quadratics
Solving Equations Reducible to Quadratic Equations x^6 - 26x^3 - 27 = 0
Переглядів 1557 місяців тому
Solving Equations Reducible to Quadratic Equations x^6 - 26x^3 - 27 = 0
Solving Equations Reducible to Quadratics x^4 - 13x^2 + 36 = 0
Переглядів 5687 місяців тому
Solving Equations Reducible to Quadratics x^4 - 13x^2 36 = 0
Solving Quadratic Equation using Completing the Square Method (Non-Monic)
Переглядів 2827 місяців тому
Solving Quadratic Equation using Completing the Square Method (Non-Monic)
Solving Quadratic Equation using Completing the Square Method (Monic)
Переглядів 2427 місяців тому
Solving Quadratic Equation using Completing the Square Method (Monic)
It is good for me and also I think its good for other, so I want to like this question and thank you for this provide 😂😂❤❤❤❤❤
XX - 26X - 27 = 0 * 27 = 1x27=3x9=4,5x6 27 - 1 = 26 = (b) ** 27: 27x27 - 26x27 - 27 729 - 702 - 27 = 0 **. 1: 1x1 - 26x1 - 27 1 - 26 - 27 # 0 -1: (-1x-1)-26(-1)-27 1 +26 - 27 = 0 ***. X' = 27, X" = -1./.
@@ngocdo5687 Thank you for your comment.
4XX - 5X - 9 = 0 *. XX - 1,25X - 2,25 = 0 2,25 = 1x2,25= 1,5x1,5 2,25 - 1 = 1,25 = (b') **. 2,25: 4(2,25x2,25)-5(2,25)-9 20,25 - 11,25 - 9 = 0 ** 1: 4(1x1) - 5x1 - 9 4 - 5 - 9 # 0 -1: 4(-1x-1)-5(-1)-9 4 + 5 - 9 = 0 ***. X' = 2,25 , X = -1 ./.
XX - 13X + 36 = 0 * 36 = 2x18=3x12=4x9 4 + 9 = 13 = (b) **. 4: 4x4 - 13x4 + 36 16 - 52 + 36 = 0 **. 9: 9x9 - 13x9 + 36 81 - 13x9 + 36 = 0 *** X' = 3, X" = 9 ./.
Tyvm
Awesome skill😊
Thanks
Okay I understood the examples...But, WHAT'S THE DIFFERENCE?🙄🤷
Well Explained ..... It really made it way easier to understand... Thank You
y = xx - 2x - 3 , y = 2x - 3 . * 3 = 3x1 , 3 - 1 = 2 = (b) ** 3 : 3x3 - 2x3 - 3 9 - 6 - 3 = 0 ** 1 : 1x1 - 2x1 - 3 1 - 2 - 3 # 0 -1 : (-1x-1) -2(-1) - 3 1 + 2 - 3 = 0 *** x' = 3 , x" = -1 ./.
x - y = 2, xy = 15 . x,y ? * 15 = 1x15 = 3x5 ... 5 - 3 = 2 = x - y ** x = 5 , y = 3 ./.
❤️❤️❤️
You saved my life btw
i feel like i was just raptured this video was incredible
❤
Nice sharing 😊😊😊 love from India 😊
tnx
i finally found thsi video again after years
oh nevermind
Lol
Wow! Thank you for revisiting.
Pretty good👍
Thank you!
Hello thank you ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Yes 😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂
Simple and useful
Those who all watching this bc are willing to learn
Best video on this topic. Great step by step explanation
But what about sin(x)^2
👍👍👍
i needed this
(2x+3y)5
👍
Thanks❤
thank you for the video. it helped me to understand the formula. one more,please i hope you to prove the " (x-1)*x^(-1) <= lnx , thank you please
Great introduction, and step by step explanation, thank you!
> Doesn't actually show how to calculate the Integral of the function squared. Disappointed
that was not the point of the video. Did you also want her teach you to do basic arithmetic operations?
Demonstração incrível.
👏👏❤
Hey can you put quadratic sums in root value
🏩
somebody snoozin in the background
Thank you sir 😊
Sorry mam
How to find the value of r?
When the bases are common u can equate it to the other power and continue as an algebraic equation..👍
What does ASTC stand for and mean?
ASTC is an acronym used to help memorise the signs of trig functions in different quadrants. ASTC stands for All Stations To Central A corresponds to Quadrant 1 where All functions (Sin, Cos and Tan) are positive. S corresponds to Quadrant 2 where only Sin function is positive. T corresponds to Quadrant 3 where only Tan function is positive. C corresponds to Quadrant 4 where only Cos function is positive. Hope that helps.
cheers alex
Good work
THANK YOU SO MUCH!!! THIS WAS SO HELPFUL
I wasn't able to compleheld anything
Thank you🌹🙏
im from the uk but this is really helpful and similar to the a level curriculum, thank you so much! you definitely deserve more credit for these videos!
Thank you so much for your comment. I'm in Australia and it's wonderful to hear that my video is able to help across the globe :)
Thank you madam
👍👍
Thank
thank you so much. ive been looking everywhere for someone to explain hcf in factor tree form since its the easiest method for me.