Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Solve complex algebraic equations and inequalities.
• Apply trigonometry to 2D and 3D problems.
• Analyze and interpret data using statistical measures.
• Determine the equation of a straight line.
• Apply Euclidean Geometry theorems with justification.

Lesson summary

This week's focus is on consolidating our understanding of key Grade 11 Mathematics topics in preparation for upcoming assessments. Effective revision isn't just about re-reading notes; it's about actively engaging with the material, identifying areas of weakness, and strengthening your problem-solving skills. Mastery of these topics is crucial, not only for academic success but also because they form the foundation for more advanced mathematical concepts in Grade 12 and beyond.

Lesson notes

Let's dive into the core concepts we'll be revising this week.

A. Algebra: Equations and Inequalities Quadratic Equations: A quadratic equation is of the form ax² + bx + c = 0, where a ≠

0. Solving Methods: Factorization: Look for two numbers that multiply to ac and add up to b. Rewrite the middle term (bx) using these numbers and factor by grouping.

Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a)*. This formula always works, even when factorization is difficult.

Completing the Square: Useful for deriving the quadratic formula and transforming equations into vertex form. Discriminant (Δ = b² - 4ac): Determines the nature of the roots: Δ > 0: Two distinct real roots. Δ = 0: One real (repeated) root. Δ ,

0. Solution: Factorize: (x - 4)(x + 1) > 0 Critical values: x = 4 and x = -1 Test intervals: x 4 x 4. (You can sketch a parabola to visualise this).

Question 2: A ladder 5m long leans against a wall. The foot of the ladder is 2m away from the wall. Find the angle the ladder makes with the ground.

Solution: cos θ = Adjacent / Hypotenuse = 2 / 5 θ = arccos(2/5) ≈ 66.42°* Question 3: The following data represents the ages of players in a soccer team: 18, 19, 20, 21, 22, 22, 23, 24, 25, 26,

2

7. Calculate the interquartile range (IQR).

Solution: First, order the data, which is already done. N =

1

1. Q1 (Lower Quartile): (N+1)/4 = (11+1)/4 =

3. So, Q1 is the 3rd value =

2

0. Q3 (Upper Quartile): 3(N+1)/4 = 3(11+1)/4 =

9. So, Q3 is the 9th value =

2

5. IQR = Q3 - Q1 = 25 - 20 =

5. Question 4: Find the equation of a line that is parallel to y = 3x - 2 and passes through the point (0, 4).

Solution: Parallel lines have the same slope. The slope of the given line is

3. So, the equation of the new line is y = 3x + c. Substitute (0, 4): 4 = 3(0) + c c = 4 Therefore, the equation is y = 3x +

4. Independent Practice (Questions Only)

Solve for x: 3x² + 7x - 6 = 0 Solve the inequality: |2x - 1| < 5 A tower stands on level ground. From a point 50m away from the base of the tower, the angle of elevation to the top of the tower is 30°. Find the height of the tower. In triangle ABC, AB = 8cm, BC = 6cm, and angle ABC = 60°. Find the length of A

C. The marks of 10 students in a test are: 50, 60, 70, 75, 80, 80, 85, 90, 95,

1

0

0. Calculate the range and the median. Find the equation of the line perpendicular to y = -2x + 5 and passing through the point (2, 1). The following data set represents the number of customers visiting a store each day for a week: 25, 30, 28, 35, 40, 32,

2

9. Calculate the mean and standard deviation. In a cyclic quadrilateral ABCD, angle A = 80 degrees. Find angle C. Given circle with centre O. Points A and B are on the circle's circumference. A tangent to the circle touches it at point A. If angle OAB = 50 degrees. Find the angle between the radius (OA) and the tangent at point A. Two trucks leave a depot. Truck A travels 100km North, then 50km East. Truck B travels 75km South, then 60km West. What is the direct distance between the two trucks? (Hint: Use analytical geometry and/or Pythagoras)