π
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About this video
A Grade 8 Term 3 test worked through: simplifying algebraic expressions, solving equations (one with the unknown in the exponent), angles on straight lines and parallel lines, and the properties of triangles.
What it covers
- Like terms; subtracting one expression FROM another
- Dividing every term by a single term
- Equations by inverse operations, and an exponential equation
- Complements and supplements; angles on a straight line
- Corresponding, alternate and co-interior angles
- Triangles: the angle sum, the exterior angle, classifying
Extra worked examples
✍️ Extra example: simplify (15x⁴ − 10x³ + 5x)/5x
- 115x⁴/5x − 10x³/5x + 5x/5xThe terms on top are unlike, so divide EACH one by the bottom.
- 2= 3x³ − 2x² + 1Divide the numbers; the same letter, so subtract the exponents; the same over the same is 1.
✍️ Extra example: co-interior angles are 2x + 30° and x + 15°. Find x and both angles.
- 1(2x + 30°) + (x + 15°) = 180°Co-int ∠s — each reason is worth a mark.
- 23x + 45° = 180° → x = 45°Collect the like terms, then use the inverses.
- 3The angles are 120° and 60°Substitute: 2(45°) + 30° and 45° + 15°.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Subtract 4x − 5 from 9 + 2x.
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(9 + 2x) − (4x − 5) = 9 + 2x − 4x + 5 = −2x + 14 - 2Solve (3x + 1)/4 = 4.
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3x + 1 = 16 → 3x = 15 → x = 5 - 3Solve 2x − 1 = 32.
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2x − 1 = 25 → x − 1 = 5 → x = 6 - 4Find the complement of 27° and the supplement of 115°.
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90° − 27° = 63°; 180° − 115° = 65° - 5A triangle has angles x + 10°, 2x and 3x − 40°. Find x and classify the triangle.
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6x − 30° = 180° → x = 35° → 45°, 70° and 65°: no equal angles, so scalene
Practise this topic
Download matching Grade 8 papers and worksheets.
