Breaking

QUADRATICS REVISION QUESTIONS

Quadratic Equations Revision

Quadratic Equations Revision – High School Level

1. Factorization

Factor the following quadratic expressions:
  • \( x^2 + 5x + 6 \)
  • \( x^2 - 7x + 12 \)
  • \( 2x^2 + 9x + 10 \)
  • \( 3x^2 - 14x - 5 \)

2. Solving by Factorization

Solve the following equations by factoring:
  • \( x^2 + 3x - 10 = 0 \)
  • \( x^2 - x - 6 = 0 \)
  • \( 4x^2 + 4x - 8 = 0 \)

3. Solving Using the Quadratic Formula

Solve the following using the quadratic formula:
  • \( x^2 - 4x + 1 = 0 \)
  • \( 3x^2 + 2x - 1 = 0 \)
  • \( 5x^2 - 6x + 7 = 0 \)

Use the formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

4. Completing the Square

Solve by completing the square:
  • \( x^2 + 6x + 5 = 0 \)
  • \( x^2 - 10x + 21 = 0 \)

5. Word Problems

  1. A rectangle has a length that is 3 meters more than its width. If the area is 40 m², find the dimensions of the rectangle.
  2. The product of two consecutive integers is 56. Find the integers.
  3. A ball is thrown upwards and its height \( h \) (in meters) after \( t \) seconds is given by \( h = -5t^2 + 20t \). After how many seconds will the ball hit the ground?

6. Mixed Practice

  • Solve: \( x^2 - 2x - 15 = 0 \)
  • Factor: \( 6x^2 + 11x - 10 \)
  • Find the roots of: \( x^2 + 2x + 10 = 0 \)

7. Graphing Quadratic Functions

Sketch the graph of the following quadratic functions. Identify the vertex, axis of symmetry, and the direction the parabola opens (upward or downward).

  • \( y = x^2 - 4x + 3 \)
  • \( y = -2x^2 + 8x - 5 \)
  • \( y = x^2 + 2x + 5 \)

Use the vertex formula: \( x = \frac{-b}{2a} \) and plug into the equation to find the vertex \( (x, y) \).

8. Discriminant Analysis

For each quadratic equation below, find the discriminant \( D = b^2 - 4ac \) and use it to determine the nature of the roots:

  • \( x^2 + 6x + 9 = 0 \)
  • \( x^2 - 3x + 2 = 0 \)
  • \( x^2 + 4x + 8 = 0 \)

Discriminant Rule:

  • \( D > 0 \): Two distinct real roots
  • \( D = 0 \): One real root (repeated)
  • \( D < 0 \): No real roots (complex roots)

GET MORE PAST PAPERS WITH MARKING SCHEMES HERE
Get hired here Vacancies
GET THE MARKING SCHEMES FROM THE GROUPS BELOW

No comments:

Post a Comment