Unit notes and practice questions
Everything here is for unit 3 of the Grade 11 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 11 Mathematics page. Open one at a time.
| Operation | Procedure |
|---|---|
| Swapping | Interchanging two rows of a matrix. |
| Scaling | Multiplying a row of a matrix by a non-zero constant. |
| Pivoting | Adding a constant multiple of one row to another row. |
When you use it
Use these three valid transformations to row reduce a matrix to Row Echelon Form or Reduced Row Echelon Form.
Drafted from Grade 11 Mathematics, pages 131-206, then checked twice before it went up
When you use it
Use this rule to compute or expand the inverse of multiplied square matrices.
Watch out
The order of factors reverses in the inverse. Expanding without switching the order is a common mistake.
Drafted from Grade 11 Mathematics, pages 131-206, then checked twice before it went up
When you use it
Use this method to find the inverse of a square matrix or to verify whether it is nonsingular.
Watch out
If row reduction of the augmented matrix produces a row of zeros on the left side, the matrix is singular and has no inverse.
Drafted from Grade 11 Mathematics, pages 131-206, then checked twice before it went up
| Matrix Type | Defining Condition |
|---|---|
| Diagonal | Entries outside the main diagonal are all zero. |
| Scalar | Diagonal matrix where all diagonal entries are equal. |
| Identity | Diagonal matrix where all diagonal entries are 1. |
| Upper Triangular | All entries below the main diagonal are zero. |
| Lower Triangular | All entries above the main diagonal are zero. |
When you use it
Use this reference to classify square matrices based on the patterns of their zero and diagonal entries.
Drafted from Grade 11 Mathematics, pages 131-206, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
What is the y-intercept of the graph of the rational function g(x) = (x + 1) / (x2 + 5x + 6)?
Answer: A (0, 1/6)
Why
To find the y-intercept, evaluate the function at x = 0: g(0) = (0 + 1) / (02 + 5(0) + 6) = 1/6. Therefore, the y-intercept is (0, 1/6).
Question 2
Person A plants 50 flower bulbs in 2 hours, and Person B plants 45 flower bulbs in 3 hours. How many bulbs do they plant together in 1 hour?
Answer: B 40 bulbs
Why
Person A plants 50 / 2 = 25 bulbs per hour. Person B plants 45 / 3 = 15 bulbs per hour. Working together, they plant 25 + 15 = 40 bulbs per hour.
Question 3
Legesse bought 150 USD with 7,500 Birr. At this same rate, how many USD can he buy with 30,000 Birr?
Answer: C 600 USD
Why
Set up the proportion: 150 / 7500 = x / 30000. Solving for x gives x = (150 / 7500) * 30000 = 600 USD.
Question 4
The ratio of boys to girls in a high school is 4 : 5. If the total number of students in the school is 1,260, how many boys are in the school?
Answer: B 560
Why
The total ratio parts are 4 + 5 = 9. The number of boys is (4 / 9) * 1260 = 560.
Question 5
A sample of 80 g of ice cream contains 15 g of fat. How many grams of fat are contained in 350 g of the same ice cream?
Answer: C 65.625 g
Why
Set up the rational equation: x / 350 = 15 / 80. Solving for x gives x = (15 / 80) * 350 = 65.625 grams.
Question 6
What is the horizontal asymptote of the rational function h(x) = x2 / (x2 + 3x + 2)?
Answer: B y = 1
Why
Since the degree of the numerator (2) is equal to the degree of the denominator (2), the horizontal asymptote is the ratio of their leading coefficients: y = 1 / 1 = 1.
Question 7
In the morning, a building that is 20 meters tall casts a shadow 15 meters long. How long is the shadow of a tree that is 10 meters tall at the same time?
Answer: B 7.5 meters
Why
Using the proportion of shadow length to height: shadow / 10 = 15 / 20. Solving gives shadow = (15 / 20) * 10 = 7.5 meters.
Question 8
Two gardeners plant bulbs together at a combined rate of 40 bulbs per hour. Using the work formula W = r * t, how many hours will it take them to plant 160 bulbs?
Answer: C 4 hours
Why
From W = r * t, we have t = W / r = 160 / 40 = 4 hours.
Question 9
What is the equation of the oblique asymptote to the graph of l(x) = (x3 + 1) / (x2 + 4x + 4)?
Answer: A y = x - 4
Why
Using polynomial long division, dividing x3 + 1 by x2 + 4x + 4 gives a quotient of x - 4 plus a remainder of 12x + 17. Therefore, the oblique asymptote is y = x - 4.
Question 10
A mixing tank starts with 100 gallons of water and 5 pounds of sugar. Water is added at 10 gallons per minute, and sugar is added at 1 pound per minute. What is the concentration of sugar in pounds per gallon after 10 minutes?
Answer: B 0.075 pounds per gallon
Why
The concentration function is C(t) = (5 + t) / (100 + 10t). At t = 10, C(10) = (5 + 10) / (100 + 10(10)) = 15 / 200 = 0.075 pounds per gallon.
The app holds 23 questions on this unit, marked as you go. These are the first 10.
Unit 3 runs from page 131 to page 206 of the Ministry of Education edition.
Ministry of Education edition, English, 494 pages
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