ORIENT · CHAPTER 1

ORIENT — Quadrants and Sign Patterns

Think first. Use AI purposefully. Verify always.

01 · DISCOVER

Start with a question.

A point is left of the y-axis and above the x-axis. What can you know before measuring?

Make a prediction before exploring. You do not need a rule yet.

02 · UNDERSTAND

Quadrants and Sign Patterns

The axes divide the plane into four quadrants, numbered anticlockwise from the upper right. A sign describes direction, not the size of a distance. Points on an axis belong to no quadrant.

03 · KEY IDEAS

Key Ideas

I: (+, +). II: (−, +). III: (−, −). IV: (+, −).
x tells left or right; y tells down or up. Read x first, y second.
On x: $(x, 0)$ . On y: $(0, y)$ . The origin is $(0, 0)$ .

04 · VISUALISE

Explore the idea.

One interval = one unit.

Explore, then verify

Point Px: -3y: 2

Drag a point, or focus a slider and use arrow keys.

P(-3, 2). Predict the quadrant, then check.

05 · METHOD

From understanding to a method.

Read the signs in order. Check for a zero first: it means the point is on an axis. Otherwise match the two signs to a quadrant.

06 · ONE WORKED EXAMPLE

Follow each step.

Locate P $(- 3, 2)$ and identify its quadrant.

Move 3 units left and 2 units up.
The sign pair is (−, +).
P is in Quadrant II. Verify that it is above x and left of y.

One interval = one unit.

Read the matching diagram

P(-3, 2). Quadrant II · (−, +)

07 · AIMS METHOD

Your turn to reason.

Attempt independently
Investigate the idea
Make connections
Scrutinise your reasoning

Does $(0, - 4)$ belong to Quadrant III or IV?

Your reasoning

Your written reasoning is not automatically graded or sent anywhere.

08 · AIMS PRACTICE SPRINT

Vary the situation. Keep the idea.

Work through 10 questions on this concept. Select an answer before checking it; use the feedback to revise your reasoning.

Start practice sprint

09 · CHECK & FEEDBACK

Correct answers receive an explanation. Incorrect answers receive a hint and another attempt. This is practice, not an examination.

Review status is self-reported, not a mastery score. Progress is stored only in this browser; no account or tracking service is used.

TEXTBOOK CONNECTION · ORIENT

Now connect with your textbook.

Choose one item. Try it independently, then use an AIMS hint or compare the reasoning.

Textbook Guided Example

Fig. 1.4 · related Think and Reflect →

End-of-Chapter Practice

End-of-Chapter Q2 →

★ AIMS Think+

AT+ · Explore deeper. Reason beyond the routine.

End-of-Chapter ★ Q8 →Also connects to APPLY

Original AIMS explanations linked to verified textbook references. Completion remains untracked.