You're about to take a big test, the one that could get you into a selective school.

A big part of this test is maths, and we're here to help you conquer it. Think of this as your guide to acing the mathematics section.

It's Not About How "Hard" the Maths Is

Here's a secret: the maths on these tests isn't necessarily super advanced. If you're doing the Year 9 ACER selective school test, they've said that they won't test you on anything past the Year 8 curriculum. So, you probably already know most of the maths concepts you'll see!

But (and this is a big "but"), the test isn't about just spitting out formulas. It's about using those formulas in new and sometimes tricky ways. They want to see if you can really think mathematically.

The Real Challenge: Making Sense of the Questions

The tricky part is figuring out what each question is actually asking you to do. They'll give you information in graphs, charts, tables – things you might not be used to seeing in a maths problem. Your job is to look at that information, figure out what it means, and then decide which maths concept (or concepts!) you need to use to solve the problem.

Think of it Like a Detective Game

Imagine you're a detective. You're given clues (the information in the question), and you have to use your detective tools (your maths knowledge) to solve the case (answer the question).

Example Time!

Let's say you get a table like this:

Wood Type	Plank Width (cm)	Price per Metre ($)
Pine	10	5.00
Oak	15	8.00
Cedar	12	7.00
Maple	10	6.50

And then the question is:

You need to buy wood planks to run along bottom of a rectangular room where the wall meets the floor (see image). The room is 5 metres long and 3 metres wide. Unfortunately, there are cracks in the wall from the floor up. You have measured the smallest crack, which is 6cm (see image). The largest crack is twice the size of the smallest crack. You want the width of your wood plank to precisely cover the largest crack with no overlap. What is the minimum width of wood plank you need, and how much will the wood cost if you are seeking the cheapest option that fulfills this requirement?

Breaking It Down

This question isn't just about one maths idea. It's a mix! Here's how you'd solve it:

Step 1: Calculate the Largest Crack Size: Smallest crack: 6 cm; Largest crack: 2 times the smallest crack = 2 * 6 cm = 12 cm

Step 2: Determine Required Plank Width. The wood plank now needs to be at least 12 cm wide to cover the largest crack.

Step 3: Find the Cheapest Option. We need a plank at least 12 cm wide. Pine and Maple are too narrow. Oak and Cedar are wide enough, but Cedar is cheaper at $7.00 per meter.

Step 4: Calculate Perimeter. You need to find the perimeter of the room (the total length of all the sides). The formula is Perimeter = 2 * (length + width). So, in this case, it's 2 * (5 + 3) = 16 metres.

Step 5: Calculate the Total Cost. Cost = 16 metres * $7.00/metre = $112.00

See? You had to use your knowledge of perimeter, multiplication, and basic numeracy and cost calculations to get the answer.

It's About Depth, Not Just Quantity

To do well on this test, you need to know your maths concepts really, really well. It's not only about memorising tons of formulas (you do need to know formula though!); it's about truly understanding how they work, when they would be useful to you and how to use them in different situations.

Another Example: Putting Your Algebra Skills to the Test

Let's say you learned about the distributive law in class.

You know that a(b + c) = ab + ac. That's great!

But on the test, they might ask you something like this:

A gardener wants to create a rectangular vegetable patch but they’re not yet sure of the exact dimensions. They decide to increase the length of the patch by 3 metres and decrease the width by 2 metres. If the original length was 'x' metres and the original width was 'y' metres, write an expression for the new area of the vegetable patch.

Thinking It Through

Here's how to approach it:

1. New Dimensions: The new length is (x + 3) metres, and the new width is (y - 2) metres.
2. Area Formula: Remember, the area of a rectangle is length * width.
3. Apply Distributive Law: So, the new area is (x + 3)(y - 2). To simplify this, you use the distributive law: (x + 3)(y - 2) = x(y - 2) + 3(y - 2) = xy - 2x + 3y – 6

The Bottom Line

The key to success is practice!

This course will help you build your mathematical concept knowledge of the Year 8 curriculum, but most importantly, we’ll be working with the concepts in various problems to help you develop your problem-solving skills.

The more you work with different types of problems, the better you'll get at figuring out what each question is asking and how to apply your maths knowledge to solve it.

Practice time!

Now, it's your turn to practice.

The questions in this checkpoint are provided to give you an introduction to possible questions you may see in your exam. Don't worry too much as you'll continue to build your skills throughout the course.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has a suggested solutions videos after you complete the question. This video explains to you the steps to take to answer the question and provides tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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