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Questions and Answers
What number is indicated by point A on the number line?
Which point indicates the number $- rac{1}{3}$?
Which point represents the number $1 rac{1}{2}$ on the number line?
Which two points represent the numbers indicated by P and Q on the number line?
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Which of the following fractions is greater, $ rac{7}{9}$ or $ rac{11}{13}$?
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What is the point of concurrence of the altitudes of a triangle called?
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What is the point of concurrence of the medians of a triangle known as?
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In what ratio does the centroid divide the median?
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Where does the orthocentre of an obtuse-angled triangle lie?
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Which pair correctly matches the point of concurrence with its corresponding triangle element?
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What is the expansion of ext{(}x - 10 ext{)} ext{(}x + 12 ext{)}?
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What is the result of ext{(}m - 3 ext{)} ext{(}m - 7 ext{)}?
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What is the expansion of ext{(}x + rac{1}{3} ext{)} ext{(}x - rac{7}{3} ext{)}?
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Fill in the blank: ext{(}x + 4 ext{)} ext{(}x - 3 ext{)} = $x^2 + (.....)x + (4) \times (.....)$
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What is the simplified result of ext{(}3x - 7y ext{)}^3 + ext{(}3x + 7y ext{)}^3?
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Study Notes
Number Line
- Point A indicates the number 1
- Point D indicates the number -2
- Point Q indicates the number 2
- Point P indicates the number -1
Comparing Numbers
- 7/9 is smaller than 11/13
- -9/13 is smaller than -5/9
- 25/16 is smaller than 71/48
- 4/7 is equal to 16/28
Geometric Concurrence Points
- The orthocentre is the point of concurrence of the altitudes of a triangle
- The circumcentre is the point of concurrence of the perpendicular bisectors of a triangle
- The centroid is the point of concurrence of the medians of a triangle
- The incentre is the point of concurrence of the angle bisectors of a triangle
- The centroid divides the median in the ratio 2:1
Expanding Algebraic Expressions
- (x - 10)(x + 12) = x² - 2x -120
- (m - 3)(m - 7) = m² - 10m + 21
- (x + 1/3)(x - 7/3) = x²- 2 x + 7/9
- (x + 4)(x - 3) = x² + x - 12
- (2x + 5y)(2x + 5y) = 4x² + 20xy + 25y²
Simplifying Algebraic Expressions
- (3x - 7y)³ + (3x + 7y)³ = 54x³ + 882xy²
- (5x - 4y)³ - (5x + 4y)³ = 600x - 128
- (2a - 3b + 4c)² - (2a + 3b - 4c)² = 32ca - 24ab
- (4x - 5y + 6z)² + (4x + 5y - 6z)² = 32x² + 50y² + 72z² - 120yz
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Description
Test your knowledge on number lines, comparing fractions, geometric concurrence points, and algebraic expressions. This quiz covers essential concepts needed for mastering algebra and geometry. Perfect for students looking to reinforce their understanding and skills in these areas.
