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Teacher:	Prof. JM	Section:	AS Mathematics Grade 11
Date:	Week	Grade	Grade 11

Quadratic Inequalities

Learning Objectives		Understand how to solve quadratic inequalities by factoring and analyzing the sign of the quadratic expression. Learn how to represent the solution of quadratic inequalities using interval notation. Develop the ability to identify the nature of the roots and use graphical methods to solve quadratic inequalities.
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Student Materials: Name:.......................Grade.................... Solving Quadratic Inequalities Quadratic Inequalities Worksheet Question 1: Solve the inequality \( x^2 - 5x + 6 \leq 0 \) Question 2: Solve the inequality \( x^2 + 3x - 4 > 0 \) Question 3: Solve the inequality \( x^2 - 2x - 8 \geq 0 \) Question 4: Solve the inequality \( x^2 + 4x + 3 < 0 \) Question 5: Solve the inequality \( x^2 - 7x + 10 \geq 0 \) Question 6: Solve the inequality \( x^2 - 6x + 5 < 0 \) Question 7: Solve the inequality \( x^2 + 2x - 15 \leq 0 \) Question 8: Solve the inequality \( x^2 - 4x + 3 > 0 \) Question 9: Solve the inequality \( x^2 + 5x - 6 \geq 0 \) Question 10: Solve the inequality \( x^2 + 6x + 9 \leq 0 \) Answer Keys: Answer 1: \( x \in [2, 3] \) Answer 2: \( x \in (-\infty, -4) \cup (1, \infty) \) Answer 3: \( x \in (-\infty, -2] \cup [4, \infty) \) Answer 4: \( x \in (-3, -1) \) Answer 5: \( x \in (-\infty, 2] \cup [5, \infty) \) Answer 6: \( x \in (1, 5) \) Answer 7: \( x \in [-5, 3] \) Answer 8: \( x \in (-\infty, 1) \cup (3, \infty) \) Answer 9: \( x \in (-\infty, -6] \cup [1, \infty) \) Answer 10: \( x = -3 \)	Student Materials: Show detailed steps here
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Student Materials:

Question 1: Solve the inequality \( x^2 - 5x + 6 \leq 0 \)

Question 2: Solve the inequality \( x^2 + 3x - 4 > 0 \)

Question 3: Solve the inequality \( x^2 - 2x - 8 \geq 0 \)

Question 4: Solve the inequality \( x^2 + 4x + 3 < 0 \)

Question 5: Solve the inequality \( x^2 - 7x + 10 \geq 0 \)

Question 6: Solve the inequality \( x^2 - 6x + 5 < 0 \)

Question 7: Solve the inequality \( x^2 + 2x - 15 \leq 0 \)

Question 8: Solve the inequality \( x^2 - 4x + 3 > 0 \)

Question 9: Solve the inequality \( x^2 + 5x - 6 \geq 0 \)

Question 10: Solve the inequality \( x^2 + 6x + 9 \leq 0 \)

Answer 1: \( x \in [2, 3] \)
Answer 2: \( x \in (-\infty, -4) \cup (1, \infty) \)
Answer 3: \( x \in (-\infty, -2] \cup [4, \infty) \)
Answer 4: \( x \in (-3, -1) \)
Answer 5: \( x \in (-\infty, 2] \cup [5, \infty) \)
Answer 6: \( x \in (1, 5) \)
Answer 7: \( x \in [-5, 3] \)
Answer 8: \( x \in (-\infty, 1) \cup (3, \infty) \)
Answer 9: \( x \in (-\infty, -6] \cup [1, \infty) \)
Answer 10: \( x = -3 \)

Student Materials:

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