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Edwin Ogie Library | Book Spotlight Build Before You Promise: The Inner Work Behind a Lasting Commitment Lasting commitment requires more than good intentions. It asks you to understand yourself, confront difficult patterns, and prepare for the responsibilities your promises will bring. By Edwin Ogie • Edwin Ogie Library There is a difference between wanting a lasting relationship and preparing yourself to sustain one. The desire may be sincere. The feelings may be strong. The future may look promising. Yet a meaningful commitment can still expose parts of us that we have never taken the time to understand. Sometimes, people make promises based on what they feel today without fully examining the habits, expectations, fears, and unresolved difficulties they will carry into tomorrow. They imagine the future they want but spend little time preparing for the responsibilities that future will demand. This...
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SS 3 Mathematics Third Term Full Web Book | Edwin Ogie Library

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JSS 3 Mathematics Third Term Full Web Book | Edwin Ogie Library

JSS 3 Mathematics Third Term Full Web Book

A complete third-term mathematics learning page for JSS 3. Each topic is explained thoroughly with step-by-step examples, quick brain tests, external learning links, and a 30-question CBT quiz with corrections at the end.

Home / Library Collections / JSS 3 Mathematics / Third Term
Third Term Scheme of Work

Scheme of Work Overview

The third term of JSS 3 Mathematics develops geometry, bearings, loci, trigonometry and heights and distances. It also includes final revision for exam readiness.

How to use this page: read each topic carefully, study the examples, answer the brain tests, and then attempt the full-term CBT quiz.
JSS 3 Mathematics Third Term Scheme of Work
WeekTopicCore Content
1BearingsThree-figure bearings, directions and navigation.
2LociDefinition, types of loci and construction ideas.
3Angles and Circle GeometryAngles in a circle, arcs and basic circle properties.
4TrigonometryIntroduction to sine, cosine and tangent in right-angled triangles.
5Heights and DistancesApplying trigonometry to real-life problems.
6Construction and MeasurementSimple geometric constructions and accurate measurement.
7Revision of the TermGeneral revision and practice.
8End of Term ExaminationAssessment and correction.
Topic 1

Bearings

Bearings are ways of describing direction using angles measured clockwise from North. They are written in three figures, such as 045° or 270°.

North

The starting direction for bearings.

Clockwise

Bearings are measured clockwise.

Three figures

Write all bearings as 000° to 360°.

Worked examples

Example 1

Question: What is the bearing of East from North?

Step 1: Start from North.

Step 2: Turn clockwise to East.

Step 3: Answer: 090°.

Example 2

Question: What is the bearing of South from North?

Step 1: Start at North.

Step 2: Turn clockwise to South.

Step 3: Answer: 180°.

Example 3

Question: What is the bearing of West from North?

Step 1: Start at North.

Step 2: Turn clockwise to West.

Step 3: Answer: 270°.

Example 4

Question: Write 45° as a three-figure bearing.

Step 1: Add a zero in front.

Step 2: The bearing becomes 045°.

Step 3: Answer: 045°.

Example 5

Question: A direction is 120° from North clockwise. State it as a bearing.

Step 1: Write the angle as a three-figure number.

Step 2: 120 already has three digits.

Step 3: Answer: 120°.

Example 6

Question: What is the opposite bearing of 030°?

Step 1: Add 180°.

Step 2: 030° + 180° = 210°.

Step 3: Answer: 210°.

Quick Brain Tests

1. Bearing of East?

090°.

2. Bearing of South?

180°.

3. Bearing of West?

270°.

4. Three-figure bearing of 5°?

005°.

5. Bearings are measured from?

North.

Topic 2

Loci

A locus is the set of all points that satisfy a given condition. Loci help us understand positions that are equally distant from objects or lines.

Point

A fixed location in space.

Distance

Loci often depend on equal distance.

Boundary

A locus may form a line or curve.

Worked examples

Example 1

Question: What is the locus of points equidistant from a fixed point?

Step 1: Think of all points same distance from the point.

Step 2: They form a circle.

Step 3: Answer: a circle.

Example 2

Question: What is the locus of points equidistant from two points?

Step 1: Consider the set of points at equal distance.

Step 2: It is the perpendicular bisector of the line joining the points.

Step 3: Answer: perpendicular bisector.

Example 3

Question: What is the locus of points equidistant from a straight line?

Step 1: Think of a parallel line at equal distance.

Step 2: The locus is a line parallel to the original line.

Step 3: Answer: parallel lines.

Example 4

Question: A point moves so that it stays 3 cm from a fixed point. What locus is formed?

Step 1: Equal distance from one point forms a circle.

Step 2: The radius is 3 cm.

Step 3: Answer: a circle of radius 3 cm.

Example 5

Question: Where is the locus of points 2 cm from a line AB?

Step 1: Equal distance from a line suggests a parallel line.

Step 2: The locus is a line parallel to AB at 2 cm away.

Step 3: Answer: a parallel line 2 cm away.

Example 6

Question: What is the locus of points equidistant from the ends of a line segment?

Step 1: Recall the special line for two points.

Step 2: It is the perpendicular bisector.

Step 3: Answer: perpendicular bisector.

Quick Brain Tests

1. Locus means?

Set of all points satisfying a condition.

2. Points equidistant from a fixed point form?

A circle.

3. Equidistant from two points?

Perpendicular bisector.

4. Equidistant from a line?

Parallel line.

5. Locus is about?

Position of points.

Topic 3

Angles and Circle Geometry

Circle geometry studies the properties of angles, arcs and chords inside a circle. It is an important foundation for senior secondary geometry.

Radius

Line from center to circle.

Chord

Line joining two points on a circle.

Arc

Part of the circumference.

Worked examples

Example 1

Question: What is the radius of a circle?

Step 1: Recall the definition.

Step 2: It is the line from the center to the circumference.

Step 3: Answer: radius.

Example 2

Question: What is a chord?

Step 1: Look for a line joining two points on the circle.

Step 2: That line is a chord.

Step 3: Answer: chord.

Example 3

Question: What is the angle at the center compared with angle at the circumference subtending the same arc?

Step 1: Recall the circle theorem.

Step 2: The angle at the center is twice the angle at the circumference.

Step 3: Answer: 2 times.

Example 4

Question: What is a semicircle?

Step 1: Think of half a circle.

Step 2: A semicircle is half of a circle.

Step 3: Answer: half a circle.

Example 5

Question: What do equal chords of a circle imply?

Step 1: Consider their distances from the center.

Step 2: Equal chords are equally distant from the center.

Step 3: Answer: equal distance from the center.

Example 6

Question: What is the circumference?

Step 1: Identify the boundary of the circle.

Step 2: The boundary is the circumference.

Step 3: Answer: the perimeter of a circle.

Quick Brain Tests

1. Line from center to circle?

Radius.

2. Line joining two points on circle?

Chord.

3. Half a circle?

Semicircle.

4. Boundary of circle?

Circumference.

5. Angle at center compared to angle at circumference?

Twice as large.

Topic 4

Trigonometry

Trigonometry in a right-angled triangle studies the relationship between the sides and angles. The basic ratios are sine, cosine and tangent.

Sine

Opposite / Hypotenuse.

Cosine

Adjacent / Hypotenuse.

Tangent

Opposite / Adjacent.

Worked examples

Example 1

Question: State the formula for sine.

Step 1: Remember the side ratio.

Step 2: Sine = opposite / hypotenuse.

Step 3: Answer: SOH.

Example 2

Question: State the formula for cosine.

Step 1: Remember the side ratio.

Step 2: Cosine = adjacent / hypotenuse.

Step 3: Answer: CAH.

Example 3

Question: State the formula for tangent.

Step 1: Remember the side ratio.

Step 2: Tangent = opposite / adjacent.

Step 3: Answer: TOA.

Example 4

Question: If opposite = 3 and hypotenuse = 5, find sin θ.

Step 1: Use sine = opposite / hypotenuse.

Step 2: sin θ = 3/5.

Step 3: Answer: 3/5.

Example 5

Question: If adjacent = 4 and hypotenuse = 5, find cos θ.

Step 1: Use cosine = adjacent / hypotenuse.

Step 2: cos θ = 4/5.

Step 3: Answer: 4/5.

Example 6

Question: If opposite = 6 and adjacent = 2, find tan θ.

Step 1: Use tangent = opposite / adjacent.

Step 2: tan θ = 6/2.

Step 3: Answer: 3.

Quick Brain Tests

1. Sine ratio?

Opposite / hypotenuse.

2. Cosine ratio?

Adjacent / hypotenuse.

3. Tangent ratio?

Opposite / adjacent.

4. SOH stands for?

Sine = Opposite / Hypotenuse.

5. A right-angled triangle is required?

Yes.

Topic 5

Heights and Distances

Heights and distances are solved using trigonometry in real-life situations such as buildings, towers, trees and hills. The main idea is to form a right-angled triangle and apply trigonometric ratios.

Angle of elevation

Angle measured upward from the horizontal.

Angle of depression

Angle measured downward from the horizontal.

Trigonometry use

Helps find unknown heights or distances.

Worked examples

Example 1

Question: A tree casts a shadow of 4 m. If the angle of elevation is 45°, find the height.

Step 1: Use tan 45° = height / shadow.

Step 2: tan 45° = 1, so height = 4 m.

Step 3: Answer: 4 m.

Example 2

Question: A ladder leans against a wall. If the base is 3 m and the angle is 60°, find the height using tan 60° ≈ 1.73.

Step 1: tan 60° = height / 3.

Step 2: height = 3 × 1.73.

Step 3: Answer: 5.19 m.

Example 3

Question: A tower is seen at an angle of elevation of 30°. If the distance from the tower is 10 m, find height using tan 30° ≈ 0.58.

Step 1: tan 30° = height / 10.

Step 2: height = 10 × 0.58.

Step 3: Answer: 5.8 m.

Example 4

Question: A man observes the top of a pole at an angle of 45°. If he is 8 m from the pole, find height.

Step 1: tan 45° = height / 8.

Step 2: Since tan 45° = 1, height = 8 m.

Step 3: Answer: 8 m.

Example 5

Question: If the angle of depression is used from a tower to a car, what triangle is formed?

Step 1: Visualize the line of sight.

Step 2: A right-angled triangle is formed.

Step 3: Answer: right-angled triangle.

Example 6

Question: Why are heights and distances important?

Step 1: They help us measure things we cannot easily reach.

Step 2: They are used in construction, navigation and surveying.

Step 3: Answer: to find unknown lengths in real life.

Quick Brain Tests

1. Angle measured upward?

Angle of elevation.

2. Angle measured downward?

Angle of depression.

3. tan 45°?

1.

4. Real-life use of heights and distances?

Surveying / construction.

5. Triangle used is?

Right-angled triangle.

Topic 6

Construction and Measurement

Construction and measurement involve drawing accurate geometric figures with ruler, compass and protractor. This topic builds precision, order and careful mathematical practice.

Compass

Used to draw circles and arcs.

Protractor

Used to measure angles.

Ruler

Used to measure lengths.

Worked examples

Example 1

Question: Draw a line segment 6 cm long.

Step 1: Use the ruler to mark 6 cm.

Step 2: Draw a straight line between the marks.

Step 3: Answer: a 6 cm line segment.

Example 2

Question: Construct a 90° angle.

Step 1: Draw a baseline.

Step 2: Use a protractor to mark 90°.

Step 3: Draw the second arm.

Example 3

Question: Draw a circle of radius 4 cm.

Step 1: Open the compass to 4 cm.

Step 2: Place the needle on the center point.

Step 3: Rotate the compass to form a circle.

Example 4

Question: Construct the perpendicular bisector of a line segment.

Step 1: Draw the segment.

Step 2: Use compass arcs from both ends with equal radius.

Step 3: Join the intersections to form the perpendicular bisector.

Example 5

Question: Construct a 60° angle.

Step 1: Draw a base line.

Step 2: Use protractor to mark 60°.

Step 3: Join the point to form the angle.

Example 6

Question: Why is accurate construction important?

Step 1: It ensures correct shapes and measurements.

Step 2: It is useful in engineering and design.

Step 3: Answer: accuracy and correctness.

Quick Brain Tests

1. Tool for circles?

Compass.

2. Tool for angles?

Protractor.

3. Tool for length?

Ruler.

4. Angle at square corner?

90°.

5. Construction needs?

Accuracy.

External Resources

Recommended learning links

These links support wider learning and improve discoverability around the topic.

Google Search: JSS 3 Third Term
Search related materials and practice questions.
Google AI
AI-assisted learning support.
Google AI Get Started
Explore AI learning support.
Khan Academy Math
Free math lessons and practice.
Math Is Fun
Simple explanations and drills.
BBC Bitesize Maths
Revision support for maths topics.
Cuemath
Extra problem-solving support.
BYJU'S Maths
Concept explanations and examples.
GeoGebra
Interactive math visualization.
Desmos
Visual math exploration.
NRICH Maths
Rich thinking tasks.
WolframAlpha
Computation and verification tool.

CBT Practice Test

30 questions | Timed quiz | Corrections appear after submission.

20:00
Send Score by Email
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Quiz Result

The email button opens a draft to edwinogielibrary@gmail.com so the score can be sent quickly after submission.

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