math revision T05 - pranaya

TOPIC 5: MEASUREMENT

W1AB: CAS Skills Part 1

Simple calculations:

Click the grey calculator icon to create a new document. Then, just type the expression you want to solve, and solve it.

Solving equations with a CAS:

To solve equations on the CAS,

• Press ‘menu’

• Press ‘3: Algebra’

• Press ‘1: Solve’

• Type the equation in the bracket, and put a comma, then the pronumeral to solve for next to it.

  e.g. solve(x+2=5,x)

NOTE: you can also type ‘solve’ in the calculator, but this might take a long time, since the keyboard layout is not QWERTY.

Solving inequalities on the CAS:

To solve inequalities, do the same thing that you would do for equations, but use the inequality signs (ctrl + =)

e.g. solve(9–2*x<25,x)

NOTE: you need to put 2*x if you want to do 2x in the CAS.

W2AB: Length, Perimeter and Circumference

If units are in the question, you MUST put them in the answer. You don’t have to include units if the unit isn’t specified.

PERIMETER OF A CIRCLE = 2πr or πd (r = radius, d = diameter).

SECTORS: A sector is a fraction of a circle. The fraction can be found by θ/360 (θ = angle of the sector)

PERIMETER OF A SECTOR: θ/360 × πd + 2r

NOTE: if the question doesn’t specify the number of decimal places the final answer needs to be rounded off, then put the answer in terms of pi.

W3AB: Area of 2D shapes:

AREA OF A TRIANGLE = 1/2 x b x h (b = base, h = height)

AREA OF A SQUARE = l² (l = length)

AREA OF A CIRCLE = πr² (r = radius)

AREA OF A RECTANGLE = l x w (l = length, w = width)

AREA OF A TRAPEZIUM = 1/2 (a+b)h (a = top length, b = bottom length, h = height)

AREA OF A KITE/RHOMBUS = xy/2 (x = horizontal length, y = vertical length)

AREA OF A PARALLELOGRAM: = b x h (b = base, h = height)

Composite shapes:

To find areas of composite shapes, you need to break them down into simpler shapes, and find the area of the shapes.

W4AB: Total Surface Area

Total surface area:

The total surface area of a 3D shape can be found by adding up the area of all the sides of the shape.

TSA of a cuboid = 2(wl)+2(wh)+2(lh)

TSA of a cylinder = 2πr²+2πrh

TSA of a cube = 6l²

Composite solids:

Composite solids are basically like composite shapes, but with 3D shapes. You find the total surface area of them by eliminating common faces.

e.g. if there is a cylinder on top of a cuboid, you have to subtract the area of the circular face of the cylinder from the area of the top face of the cuboid.

W5AB: Volume of Prisms and Cylinders

What are prisms?

Prisms are solids that have a constant cross section

AREA OF A PRISM = cross section x length

What are cylinders?

Cylinders are solids with a constant circular cross section.

AREA OF A CYLINDER = same as area of a prism

What is a cross section?

A cross section is a two-dimensional shape that results from cutting a solid.

Why is it important for us to identify the cross-section before calculating the volume of prisms and cylinders?

Finding the cross section is important, because finding the area of it will help find the volume of the prism/cylinder.

Do pyramids have a cross section?

No, it does not, since the cross-section is inconsistent.

VOLUME OF A PRISM = cross section x height

VOLUME OF A CYLINDER = πr²h (r = radius)

VOLUME OF A CONE = πr²h/3 (r = radius, h = height)

W6AB: Unit Conversions

Linear unit conversions:

Square unit (area) conversions:

Cubic units (volume) conversions:

Liquid conversion:

1cm³ = 1mL

1m³ = 1kL

W7AB: CAS skills Part 2

Factorising with the CAS:

To factorise an expression, you need to do the following steps:

• Click ‘menu’, then ‘3: Algebra’ and ‘2: Factorise’

• Put the expression in the brackets, followed by ‘,x’

• Press ‘enter’

NOTE: The function won’t work if you don’t put ‘,x’ next to the expression.

You can also type out ‘factor’, but it will take a while.

Expanding with the CAS:

To expand an expression, you need to do the following steps:

• Click ‘menu’, then ‘3: Algebra’ and ‘3: Expand’

• Put the expression in the brackets

NOTE: You need to put * between each bracket

W8AB: Transposing Formulae

Transposing with a CAS:

To transpose an equation, use the solve function, and the pronumeral that you need to make the subject next to the comma.

e.g. d = s*t (make s the subject)

solve(d=s*t,s)