Test statistics allow us to quantify how close things are to our expectations or theories. Instead of going on our gut feelings, they allow us to add a little mathematical rigor when asking the question: “Is this random… or real?” Today,...

Get ready to crush the AP Physics 1 exam with this complete 30-minute review of the entire course! This video covers every major topic from Units 1 through 8, including kinematics, dynamics, energy, momentum, rotation, harmonic motion,...

We just looked at some simple ways to solve systems of differential equations, via modeling and elimination. But there are other methods, some of which involve matrices. This will require that we remember some concepts from linear...

Pupil outcome: I can describe a translation using column notation and carry out the translation of a point. Key learning points: - It can be helpful to choose a vertex and translate that. - Once all the vertices have been translated, the...

Pupil outcome: I can use the fx-991CW to perform calculations with numbers and solve equations numerically. Key learning points: - Some calculators can perform more than just basic calculations. - The fx-991CW can convert between...

Pupil outcome: I can describe a situation using algebraic symbols. Key learning points: - A conjecture about a generalisation can be expressed algebraically. - The algebraic expression can be used to test the conjecture. - Substituting...

Pupil outcome: I can generate coordinate pairs using the equation of a circle in the form x^2 + y^2 = r^2 and then draw the graph. Key learning points: - A table of values can be useful to identify coordinate pairs which satisfy the...

Pupil outcome: I can recognise that an arithmetic sequence can be shown graphically and how this relates to the equation of a linear graph and use this to find the n^th term formula. Key learning points: - The n^th term rule can be...

Pupil outcome: I can use my knowledge of non-linear graphs to solve problems. Key learning points: - The shape of the graph can be used to identify the form of its equation. - Sketching the graph can help when solving problems. - Problem...

Pupil outcome: I can fluently write general algebraic forms for different number properties. Key learning points: - The divisibility tests can be used to help write general algebraic forms of multiples. - By understanding the general...

Pupil outcome: I can interpret and draw more real-life graphs. Key learning points: - Not all real-life graphs can be drawn using sections of different linear graphs. - The graphs are models, which means that we want them to be useful.

Pupil outcome: I can find the equation of a radius of a circle. Key learning points: - The equation of a circle gives the coordinates of the centre of the circle. - Using this and the coordinates of a point on the circle, you can...

This video discusses center-radius form of a circle. There are multiply ways to write the equation of the circle, but this is the most common form of it. In order to write this equation, you only need to know the center (h,k) and the...

We've looked at a few simple examples of first-order differential equations and how to solve them. Now let's take a look at exact first-order differential equations.

We just got our feet wet with separable differential equations, so now let's look at something slightly trickier. Solving linear first-order differential equations will require a little bit more effort, involving something called an...

In this video, a teacher reveals the mathematical logic behind three popular number tricks involving doubling, adding, and subtracting digits. Viewers are encouraged to use their logic and math skills to solve these puzzles and share...

In this next episode, Mr. P guides us through the culmination of electromagnetic knowledge – Maxwell's equations. After a quick recap of Gauss's law and its magnetic counterpart, the class dives into Faraday's law of induction, unveiling...

This is the fifth video on the equations of lines and planes video series. In this video we derive the vector equation of a plane, the scalar equation of a plane and parametric equations of a plane in space.

In this video, the teacher explains how to solve a quadratic equation that has no real solutions using the quadratic formula. The video also covers a review of imaginary and complex numbers, as well as a common mistake to avoid when...

Before the method of completing the square was developed, only very limited types of quadratic equations could be solved. This method eliminated those limitations, allowing the solutions of any quadratic equation to be found. As...

In this video, the teacher explains how to solve quadratic equations using the quadratic formula. They highlight common mistakes to avoid, such as squaring negative numbers and correctly identifying the coefficients.

A quadratic function can be written in general form or in vertex form. But given a quadratic function in one of these forms, how can we convert to the other form? This lecture shows how conversion formulas between these two forms can...

In this video, the teacher explains how to find the center and radius of a circle when the equation is in general form. By using the process of completing the square, the teacher demonstrates how to transform the equation into standard...

In this lesson, students will learn how to graph shifted exponential and logarithmic functions by considering the spread of an Internet video. They will understand how changing the base affects the rate of growth or decay, and how...