Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to our series of lessons on how to use your Casio calculator.

In these lessons, we're looking at three of the Casio calculator models.

So let's get started.

By the end of today's lesson you'll be able to use the fx-CG50 to perform calculations with numbers and solve equations numerically.

On the screen you can see some of the keywords we'll be using today.

Feel free to pause the video now while you have a read through them.

Our lesson's broken into two parts.

We're going to begin by solving equations graphically.

Calculators can do a lot numerically, but the fx-CG50 can also solve graphically.

It allows you to draw graphs and then analyse them.

From the main menu, navigate to the graph option and press execute.

You can enter the equation of the graph on this screen using the x theta T button to input the variable X.

When ready, press F6 to draw the graph.

If you've entered the equations for multiple graphs, then the calculator will draw them all.

So you can see here that the equation x squared + 3x + 2 produces the graph shown in blue and the linear equation x + 2 produces the straight line shown in red.

Quick check now, true or false, the calculator can only plot one graph at a time.

Is that true or is that false? Pause the video while you make your choice and don't forget to justify your answer.

You should have said that it's false.

There are actually spaces for up to 20 equations of graphs to be entered.

Once you've drawn your graph or graphs, you can use the G-Solve menu to analyse them.

Pressing shift followed by F5 lets you access G-Solve.

You can find the roots, the maximum/minimum points, the y-intercept, and the points of intersection if you have multiple graphs.

The first point of intersection is when x = -2, y = 0.

The arrows can be used to select the next point.

What are the coordinates of the second point of intersection? Pause the video and write down your answers now.

Well done if you said x is 0, y is 2.

So you wrote down the coordinates, 0, 2.

It's now time for your first task.

Question one, use your calculator to solve these pairs of simultaneous equations.

Pause and do this now.

Question two, for each pair of simultaneous equations, write down what your calculator says when you try to solve them graphically.

Why do you think the calculator gives this output? Pause the video while you work on this now.

Welcome back.

Question three, use your calculator to estimate the solutions to this pair of simultaneous equations to 3 d.

p.

Pause and do this now.

It's time to go through our answers.

For question one I asked you to use your calculator to solve these pairs of simultaneous equations.

Part A I've shown you what you see on the screen when you draw the two graphs.

Remember you can use the arrow keys to navigate to see the point of intersection, but by accessing that G-Solve menu and then selecting the points of intersection, your calculator will just display them for you.

So you can see here it's when x is -4.

5 and when y = to -7.

5.

Part B, where do these two lines intersect? They intersect when x = to 4 and y = to 3.

Question two, for each pair of simultaneous equations asked you to write down what your calculator says when you try to solve them graphically, why do you think it gives this output? So for part A, you would've got not found.

In other words the calculator could not find a solution 'cause there is no point of intersection.

In this instance, it's because the lines are parallel, they have the same gradient.

Part B, the lines have one intersection which the calculator was able to find.

And you can see the values displayed on the screen.

X is 4.

2 and y is -1.

4.

And then in part C, the calculator gives a point of intersection.

But scrolling reveals that there are many points of intersection.

In fact, when we initially look at what our calculator shows us, it looks like there's only one equation shown, but actually it's because the two lines lie on top of each other.

So we have infinitely many solutions.

Question three asked you to use your calculator to estimate the solutions to the pair of simultaneous equations to three decimal places.

We have two possible solutions.

We have one where x = 0.

518 and y is 1.

286.

And the second one is where x = 3.

282 and y = -0.

926.

Well done if you've got both.

It's now time for the second part of the lesson, we're going to look at solving equations numerically.

Aisha points out, "So 'cause it's a graphical calculator, it can only solve equations graphically?" Sam says "Nope, and did you know this calculator can even deal with formulas?" The fx-CG50 allows you to solve equations numerically and evaluate formulas.

From the main menu, navigate to the equation option and press execute.

Once equation has been chosen, you can select solver by pressing F3.

Enter the equation or formula using the alpha button to select different variables as required.

What is the value of a when s = 210, u = 2 and t = 5 for the following formula? We use the alpha key to enter the variables.

You can see here what I've entered into my calculator.

It does not matter that the letters are appearing as capital letters rather than lowercase.

Pressing execute then allows you to set the values for the variables, enter the known values and leave the one you want to find as 0.

So in this case, we want the value of a, so we leave it set to 0.

Pressing solve or F6 then produces the value of the remaining variable.

So we can see here that a is going to be equal to 16.

Quick check now, true or false, the solver mode can only handle linear equations.

Is that true or is that false? And don't forget to justify your answer.

Pause the video and have a go at this now.

Welcome back.

You should of course have said that it's false.

The solver mode lets you determine the value of any variable in a formula.

Our calculator can also solve pairs of linear simultaneous equations.

You can see that option here.

Under equation, we then select simultaneous by pressing F1, we are dealing with simultaneous equations with two unknowns, so we select 2.

Now, your calculator will only accept equations in the form axe + by = c, so it may be necessary to rearrange before inputting.

That's what I've done with the two equations you can see on the screen.

Now you might be thinking, hang on, you had w and h why have you now got x and y? Well, the calculator uses x and y, so it's important that I know which variable x is representing and which variable y is representing.

In this case, x is representing w and y is representing h.

Having put in the coefficients and any constant terms into my calculator, being very careful, of course, with any negative values, I can then press solve or F1 to display both possible values.

I can interpret this as w = 1.

8, remember, x stood for w, and h = -9.

8.

Quick check now, true or false? You can enter any pair of simultaneous equations into the calculator without needing to rearrange.

Is that true or is that false? And don't forget to justify your answer.

Pause the video now please.

Welcome back.

You should of course have said it's false, equations must be in the form axe + by = c, so it may be necessary to rearrange first.

You can solve quadratic equations by selecting equation and then polynomial.

You choose the general form for the polynomial you want to solve.

Let's solve 2x squared + 9x + 4 = 0.

Once we've inputted any coefficients and constant terms into the calculator, being careful of course that it's in the form axe squared + bx + c = 0.

If it's not, you'll need to rearrange first.

We then press solve or F1.

And we can see here the two possible values, x = - 0.

5, and x = -4.

It's now your turn.

For our quick check, use your calculator to find the solution or solutions to x squared + 8x - 20 = 0.

Pause the video and have a go at this now.

Welcome back.

Once you've entered that in you should have seen the x = 2 and x = -10.

It's now time for your final task.

Solve the following pairs of simultaneous equations using your calculator.

Pause the video while you work on question one now.

Question two, calculate the solutions to these quadratic equations.

Pause the video while you work on this now.

It's time to go through our answers.

For question one, you can see the pairs of solutions on the screen now.

I've given them to you as improper fractions and as mixed numbers.

Feel free to pause while you check your work.

Question two ask you to calculate the solutions to these quadratic equations.

Again, feel free to pause the video so you can check your own work.

It's time to sum up what we've looked at today.

Some calculators can perform more than just basic calculations.

The fx-CG50 can solve equations graphically and numerically.

Well done, I hope you've enjoyed learning about some of the functions of your calculator.

I look forward to seeing you for more maths in the future.

Goodbye for now.