Unit notes and practice questions
Everything here is for unit 1 of the Grade 10 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 10 Mathematics page. Open one at a time.
When you use it
Use this when finding the domain of a function with a fraction or a square root, such as f(x)=4/(x-3) or g(x)=sqrt(x-2).
Watch out
Exclude the value that makes the denominator zero, but keep the value that makes the inside of a square root zero. For 4/(x-3) exclude x equal to 3. For sqrt(x-2) write x greater than or equal to 2, not x greater than 2.
Drafted from Grade 10 Mathematics, pages 1-64, then checked twice before it went up
When you use it
Use this when sketching the graph of a relation given by an inequality such as y < x + 2 or y ≥ 3x - 4.
Watch out
Use a broken line for < or > and a solid line for ≤ or ≥. Getting the line type wrong loses marks even when the shaded side is correct.
Drafted from Grade 10 Mathematics, pages 1-64, then checked twice before it went up
| Quadrant | Sign of x | Sign of y |
|---|---|---|
| I | + | + |
| II | - | + |
| III | - | - |
| IV | + | - |
When you use it
Use this when plotting a point or deciding which quadrant a point with given coordinates lies in.
Watch out
Read x first, then y. The point (-2, 2) lies in Quadrant II, not Quadrant IV.
Drafted from Grade 10 Mathematics, pages 1-64, then checked twice before it went up
When you use it
Use this when a set of ordered pairs or a table is given and you must decide whether it describes y as a function of x.
Watch out
Repeated identical pairs such as (1, 5) written twice do not break a function. The test fails only when the same first element is paired with two different second elements, as in (5, 3) and (5, 8).
Drafted from Grade 10 Mathematics, pages 1-64, then checked twice before it went up
When you use it
Use this to find the vertex and axis of symmetry of a parabola, or to sketch it quickly once the square is completed.
Watch out
The sign inside the bracket is reversed in the vertex. For (x+3)^2+2 the vertex is (-3, 2), not (3, 2).
Drafted from Grade 10 Mathematics, pages 1-64, 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
In which quadrant does the point T(-5, -3) lie?
Answer: C Quadrant III
Why
In Quadrant III both coordinates are negative. The x-coordinate of T is -5 and the y-coordinate is -3, so T lies in Quadrant III.
Question 2
A function is a relation in which no two distinct ordered pairs have the same first element. Which of these sets is a function?
Answer: B {(6, 7), (1, 9), (-1, 7), (0, 0), (4, -4)}
Why
In set B the first elements are 6, 1, -1, 0 and 4. None of them repeats, so no two pairs share the same first element. In sets A, C and D, some first element (2, 3, or 5) is paired with two different second elements, so they are not functions.
Question 3
Let the function be f(x) = 1 - 3x. What is the value of f(2)?
Answer: A -5
Why
Replace x with 2: f(2) = 1 - 3(2) = 1 - 6 = -5.
Question 4
Find the range of the relation with ordered pairs (-2, 1), (-1, 0), (0, 0), (4, 2), (3, 5).
Answer: B {1, 0, 2, 5}
Why
The range is the set of second components. These are 1, 0, 0, 2 and 5. Writing each value once gives {1, 0, 2, 5}. The set {-2, -1, 0, 3, 4} is the domain, not the range.
Question 5
Let f(x) = 2x + 4 and g(x) = 3x - 1. Find (f + g)(2).
Answer: B 13
Why
First find (f + g)(x) = (2x + 4) + (3x - 1) = 5x + 3. Then (f + g)(2) = 5(2) + 3 = 10 + 3 = 13.
Question 6
Let f(x) = x2 - 1 and g(x) = x - 2. Find (f + g)(3).
Answer: C 9
Why
Work out each function separately. f(3) = 32 - 1 = 8 and g(3) = 3 - 2 = 1. So (f + g)(3) = f(3) + g(3) = 8 + 1 = 9. Option A, 7, is what you get if you subtract instead of add.
Question 7
For the linear function f(x) = 3x - 6, which point is the x-intercept of the graph?
Answer: A (2, 0)
Why
The x-intercept is where y = 0. Put 0 = 3x - 6, so 3x = 6 and x = 2. The x-intercept is (2, 0). The point (0, -6) is the y-intercept, not the x-intercept.
Question 8
Let R be the relation of all ordered pairs (x, y) of real numbers where y is greater than x. Which ordered pair belongs to R?
Answer: B (1.1, 1.11)
Why
For a pair to belong to R, its second number must be greater than its first number. For (1.1, 1.11), 1.11 is greater than 1.1, so it belongs. In (4, 3) and (2, 1) the second number is smaller. In (7, 7) the two numbers are equal, so y is not greater than x.
Question 9
Let R be the relation of all ordered pairs (x, y) of real numbers with y2 = x. Which statement is correct?
Answer: B R is not a function, because (4, 2) and (4, -2) both belong to R.
Why
Both (4, 2) and (4, -2) satisfy y2 = x, because 22 = 4 and (-2)2 = 4. A function cannot have two different ordered pairs with the same first element. So R is not a function. Being a curve does not make a relation a function, and the sign of x is not the reason.
Question 10
Find the domain of the function f(x) = √(x - 2).
Answer: A x ≥ 2
Why
The expression under the square root must not be negative, so x - 2 ≥ 0. This gives x ≥ 2. The domain is the set of real numbers greater than or equal to 2.
The app holds 12 questions on this unit, marked as you go. These are the first 10.
Unit 1 runs from page 1 to page 64 of the Ministry of Education edition.
Ministry of Education edition, English, 373 pages
Temari turns this chapter into timed practice and marks it as you go, with an AI tutor to explain anything that did not land.
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