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SS 1

Revision – Third Term

Mathematics SS 1 Third Term
📌 Welcome to Your Third Term Revision!

This comprehensive revision covers all the topics from the Third Term. Use this to:

  • Review key concepts from each topic
  • Practice with revision questions
  • Prepare for your end-of-term examination
  • Identify areas that need more attention

Topics Covered in Third Term

Week Topic Key Concepts
1 Revision of First & Second Term Number Bases, Modular Arithmetic, Indices, Logarithms, Surds, Sets, Algebra, Equations, Quadratic Equations
2 Graphs I Cartesian plane, quadrants, plotting points, linear graphs, y = mx + c
3 Graphs II Gradient formula, equation of a line, parallel and perpendicular lines
4 Variation I Direct variation (y = kx), inverse variation (xy = k), constant of variation
5 Variation II Joint variation (y = kxz), partial variation (y = ax + b)
6 Geometry I Types of angles, complementary/supplementary, angles on a line, at a point, vertically opposite, parallel lines and transversals
7 Geometry II Types of triangles, sum of angles = 180°, exterior angle theorem, Pythagoras theorem
8 Geometry III Quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite), sum of angles in polygons, interior/exterior angles
Third Term Topics – Summary

Topic 1: Graphs I & II – Summary

🔑 Key Points:
  • Cartesian Plane: x-axis (horizontal), y-axis (vertical), origin (0,0).
  • Quadrants: I(+,+), II(−,+), III(−,−), IV(+,−).
  • Linear Equation: y = mx + c (m = gradient, c = y-intercept).
  • Gradient: m = (y₂ − y₁) / (x₂ − x₁).
  • Parallel Lines: m₁ = m₂.
  • Perpendicular Lines: m₁ × m₂ = −1.

Topic 2: Variation I & II – Summary

🔑 Key Points:
  • Direct Variation: y ∝ x → y = kx (k = y/x).
  • Inverse Variation: y ∝ 1/x → xy = k (k = xy).
  • Joint Variation: y ∝ xz → y = kxz (k = y/(xz)).
  • Partial Variation: y = ax + b (a = rate, b = constant).

Topic 3: Geometry I – Summary

🔑 Key Points:
  • Types of Angles: Acute, Right, Obtuse, Straight, Reflex, Complete.
  • Complementary: Sum = 90°.
  • Supplementary: Sum = 180°.
  • Parallel Lines: Corresponding (equal), Alternate (equal), Co-interior (sum = 180°).

Topic 4: Geometry II – Summary

🔑 Key Points:
  • Types of Triangles: Equilateral, Isosceles, Scalene; Acute, Right, Obtuse.
  • Sum of Angles: ∠A + ∠B + ∠C = 180°.
  • Exterior Angle: = ∠A + ∠B.
  • Pythagoras: a² + b² = c² (right-angled triangle).

Topic 5: Geometry III – Summary

🔑 Key Points:
  • Quadrilaterals: Square, Rectangle, Parallelogram, Rhombus, Trapezium, Kite.
  • Sum of Interior Angles: 360°.
  • Polygon Angles: Sum = (n−2)×180°, Interior = [(n−2)×180°]/n, Exterior = 360°/n.

Key Formulas Summary

Topic Formula Variables
Gradient m = (y₂ − y₁) / (x₂ − x₁) Two points on a line
Equation of Line y = mx + c m = gradient, c = y-intercept
Parallel Lines m₁ = m₂ Same gradient
Perpendicular Lines m₁ × m₂ = −1 Product of gradients = −1
Direct Variation y = kx k = y/x
Inverse Variation xy = k k = xy
Joint Variation y = kxz k = y/(xz)
Partial Variation y = ax + b a and b constants
Sum of Angles (Triangle) ∠A + ∠B + ∠C = 180° Triangle angles
Pythagoras Theorem a² + b² = c² Right-angled triangle
Polygon Interior Sum S = (n−2)×180° n = number of sides
Polygon Exterior Sum Sum = 360° Any polygon

Revision Questions

Test your understanding of all Third Term topics:

Section A: Multiple Choice (Choose the correct option)

  1. The gradient of the line through (1, 3) and (4, 9) is:
    A) 1 B) 2 C) 3 D) 4
  2. If y varies directly as x and y = 12 when x = 3, the constant of variation is:
    A) 3 B) 4 C) 6 D) 9
  3. Two angles that add up to 180° are called:
    A) Complementary B) Supplementary C) Corresponding D) Alternate
  4. The sum of interior angles of a quadrilateral is:
    A) 180° B) 270° C) 360° D) 540°
  5. In a right-angled triangle, 3² + 4² = c². c is:
    A) 5 B) 7 C) 9 D) 12
  6. The equation of a line with gradient 2 and y-intercept 3 is:
    A) y = 2x + 3 B) y = 3x + 2 C) y = 2x − 3 D) y = 3x − 2
  7. If y varies inversely as x and xy = 24, when x = 4, y = :
    A) 4 B) 6 C) 8 D) 12
  8. Parallel lines have:
    A) Different gradients B) Same gradient C) Sum of gradients = −1 D) Product of gradients = −1
  9. An angle of 135° is classified as:
    A) Acute B) Right C) Obtuse D) Reflex
  10. Which of the following is a parallelogram?
    A) Square B) Kite C) Trapezium D) All of the above

Answers: 1-B, 2-B, 3-B, 4-C, 5-A, 6-A, 7-B, 8-B, 9-C, 10-A

Section B: Short Answer Questions

  1. Find the gradient of the line through (−2, 5) and (4, 11).
  2. If y varies directly as x and y = 15 when x = 3, find y when x = 7.
  3. If y varies inversely as x and y = 8 when x = 3, find y when x = 6.
  4. Find the supplement of 65°.
  5. Find the missing angle in triangle ABC if ∠A = 40° and ∠B = 75°.
  6. State the Pythagoras theorem.
  7. Find the sum of interior angles of a pentagon.
  8. Find the exterior angle of a regular hexagon.
  9. Find the equation of a line with gradient 3 passing through (2, 5).
  10. If y = 2x + 5, identify the gradient and y-intercept.

Section C: Calculation Questions

  1. Find the gradient of the line through (1, 2) and (5, 10).
  2. Find the equation of the line through (2, 3) and (4, 7).
  3. If y varies directly as x and y = 18 when x = 6, find y when x = 10.
  4. If y varies inversely as x and y = 12 when x = 4, find y when x = 8.
  5. Find the hypotenuse of a right-angled triangle with sides 5 cm and 12 cm.
  6. Find the missing side of a right-angled triangle with hypotenuse 25 cm and one side 7 cm.
  7. Find the sum of interior angles of a hexagon.
  8. Find the interior angle of a regular octagon.
  9. In a parallelogram, one angle is 65°. Find the other three angles.
  10. If y varies jointly as x and z, and y = 36 when x = 3 and z = 4, find y when x = 5 and z = 6.

Answers to Section B

1. m = (11−5)/(4−(−2)) = 6/6 = 1

2. k = 15/3 = 5, y = 5x → when x=7, y = 35

3. k = 8×3 = 24, xy = 24 → when x=6, y = 4

4. Supplement = 180° − 65° = 115°

5. ∠C = 180° − 40° − 75° = 65°

6. a² + b² = c² (c is the hypotenuse)

7. (5−2) × 180° = 3 × 180° = 540°

8. 360°/6 = 60°

9. y − 5 = 3(x − 2) → y = 3x − 1

10. Gradient = 2, y-intercept = 5

Answers to Section C

1. m = (10−2)/(5−1) = 8/4 = 2

2. m = (7−3)/(4−2) = 4/2 = 2, y − 3 = 2(x−2) → y = 2x − 1

3. k = 18/6 = 3, y = 3x → when x=10, y = 30

4. k = 12×4 = 48, xy = 48 → when x=8, y = 6

5. c² = 5² + 12² = 25 + 144 = 169 → c = 13 cm

6. a² + 7² = 25² → a² = 625 − 49 = 576 → a = 24 cm

7. (6−2) × 180° = 720°

8. Interior = [(8−2)×180°]/8 = 1080°/8 = 135°

9. Opposite angles are equal: 65°, 115°, 65°, 115°

10. k = 36/(3×4) = 3, y = 3xz → when x=5,z=6, y = 3×5×6 = 90

Examination Preparation Tips

📌 Tips for Success:
  • Review all formulas – make a formula sheet and memorise them.
  • Understand key definitions – be able to explain concepts in your own words.
  • Practice calculations – work through all examples and assignment questions.
  • Know your graphs – plotting points, finding gradient, equation of a line.
  • Practice variation problems – direct, inverse, joint, and partial.
  • Geometry concepts – angles, triangles, quadrilaterals, polygons.
  • Pythagoras theorem – be comfortable with finding missing sides.
  • Time management – allocate time for each section during the exam.
  • Read questions carefully – identify what is being asked before answering.

Board Summary

╔════════════════════════════════════════════════════════════════════════════╗ ║ SS1 MATHEMATICS – THIRD TERM REVISION ║ ╠════════════════════════════════════════════════════════════════════════════╣ ║ ║ ║ WEEKS 2-3: GRAPHS ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Cartesian plane: x-axis, y-axis, origin ║ ║ • y = mx + c: m = gradient, c = y-intercept ║ ║ • Gradient: m = (y₂−y₁)/(x₂−x₁) ║ ║ • Parallel: m₁ = m₂; Perpendicular: m₁ × m₂ = −1 ║ ║ ║ ║ WEEKS 4-5: VARIATION ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Direct: y = kx; Inverse: xy = k; Joint: y = kxz; Partial: y = ax+b ║ ║ ║ ║ WEEK 6: GEOMETRY I – ANGLES ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Complementary: 90°, Supplementary: 180° ║ ║ • Angles on a line: 180°, at a point: 360° ║ ║ • Parallel lines: Corresponding (equal), Alternate (equal), Co-interior ║ ║ ║ ║ WEEK 7: GEOMETRY II – TRIANGLES ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Sum of angles = 180°, Exterior = sum of opposite interior ║ ║ • Pythagoras: a² + b² = c² ║ ║ ║ ║ WEEK 8: GEOMETRY III – QUADRILATERALS & POLYGONS ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Quadrilaterals: Square, Rectangle, Parallelogram, Rhombus, ║ ║ Trapezium, Kite ║ ║ • Polygons: Sum interior = (n−2)×180°, Exterior = 360° ║ ║ ║ ╚════════════════════════════════════════════════════════════════════════════╝
✅ Good luck with your examination!

Remember to stay calm, read all questions carefully, and show your working clearly. You've got this! 💪

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