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Listed under:  Algebra

### Patterns, primes and Pascal's Triangle

Are you intrigued by patterns? Check out Vi Hart as she explains how to visualise patterns in prime numbers, using Ulam's Spiral. Watch as Vi creates patterns, using Pascal's Triangle to explore relationships in number. See what happens when she circles the odd numbers. What rule does she use to create the final pattern?

### From patterns to equations in three simple steps

Can you write a rule to match a number pattern? See how to use a table to record a number pattern, identify the rule and write an algebraic equation to match.

### The language of algebra

Have you seen mathematical expressions that use numbers and letters? They're called algebraic expressions. See what all this means. Watch how you can substitute a value for 'x' in an algebraic expression. It's easy when you know how!

### The key to finding 'y' is 'x'

Try these two exercises, which require you to substitute values of x into an algebraic equation. Complete the table of values for y for both equations.

### Linear simultaneous equations: elimination

One method of solving linear simultaneous equations is by eliminating either x or y. Start with a straightforward example eliminating one unknown value. In the next example, unknown values x and y are numerically different for each equation. See how you use both elimination and a bit of substituting to find your answer. ...

### Two unknowns: two equations

A written mathematical problem that has two unknowns can be solved using simultaneous equations. See how it's done. The first step is to write the problem as two equations. In these two examples, the equations are linear. The first can be solved using the elimination method. Find out how to set the next two linear equations ...

### Basic rules about linear equations

Want to know how to solve a linear equation? Find out the basics and see how a balance is used to explain how to find an unknown value. Pick up some helpful tips and tricks to find the value of that elusive x, b or d!

### Solving linear simultaneous equations graphically

Linear simultaneous equations can be solved graphically. All you need to do is graph each equation and find the x and y coordinates where they intersect. Then just write these as values for x and y. Watch how it's done. You'll be an expert in no time!

### Linear simultaneous equations and substitution

Do you know how to solve linear simultaneous equations by finding values for x and y? Find out about the substitution method in this clip. See how to rewrite and rearrange one of the linear equations to get a value for x or y. Substitute this value into the second equation. Follow the steps and you'll get a number value ...

### Substitution in algebra

Substitution is when you replace one thing with something else. In algebra, this often means replacing a letter with a given number in order to work out an equation. Using the substitutes given in this video, see if you can work out the equation a+b (l-mn).

### Differential calculus: linear graphs

Observe the linear distance–time graph of a rocket travelling at a constant velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller the rocket's average velocity is equivalent to its instantaneous velocity. Work out how the ...

### Differential calculus: linear and non-linear graphs

Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work ...

### TIMES Module 33: Number and Algebra: factorisation - teacher guide

This is a 17-page guide for teachers. It continues the discussion of factorisation. In particular, the techniques for the factorisation of quadratic expressions are presented.

### Algebra review

This teacher resource is particularly relevant for the topic Functions and graphs of the Australian Curriculum subject Mathematical Methods and will also serve as a review of Australian Curriculum F-10 algebra for existing year 11 subjects that contain material on functions, algebra and calculus. A brief history of algebraic ...

### Applications of differentiation

This is a teacher resource for applications of differentiation consisting of a website and a PDF with identical content. It contains a discussion of graph sketching, related rates of change and the solution of maxima and minima questions.

### Try a cherry slice equation

Need a challenge to write an algebraic formula? This example involves trays of cherry slice! See if you can work out the relationship between the number of slices and the number of trays. Find out what the equation looks like after two pieces of slice from one tray have been eaten.

### Algebra: a piece of cake

Can you write an algebraic equation to relate two variables? See how to write an equation that shows how the number of cakes relates to the cake ingredients of eggs, butter, cocoa, flour, sugar and milk.

### A slice of algebra

Do you know how to write an algebraic equation? In this example we use trays of coconut slice. Find out what the equation looks like after a piece of slice from one tray has been eaten. See how this equation can be used to predict the number of slices to be made.

### Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

### EagleCat: trig-G

Explore the graphs of trigonometric equations in the form: (a) y = a sin[n(x - h)] + k, (b) y = a cos[n(x - h)] + k and (c) y = a tan[n(x - h)] + k. Use sliders or enter values to dilate, reflect and translate the basic trigonometric equations y = sin(x), y = cos(x) and y = tan(x), and observe the changes in the amplitude, ...