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.
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
| Week | Topic | Core Content |
|---|
| 1 | Bearings | Three-figure bearings, directions and navigation. |
| 2 | Loci | Definition, types of loci and construction ideas. |
| 3 | Angles and Circle Geometry | Angles in a circle, arcs and basic circle properties. |
| 4 | Trigonometry | Introduction to sine, cosine and tangent in right-angled triangles. |
| 5 | Heights and Distances | Applying trigonometry to real-life problems. |
| 6 | Construction and Measurement | Simple geometric constructions and accurate measurement. |
| 7 | Revision of the Term | General revision and practice. |
| 8 | End of Term Examination | Assessment 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.
CuemathExtra problem-solving support.
DesmosVisual math exploration.
CBT Practice Test
30 questions | Timed quiz | Corrections appear after submission.
20:00
The email button opens a draft to edwinogielibrary@gmail.com so the score can be sent quickly after submission.
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