Grade 9 Mathematics Final Exam Review Flashcards

Exam Overview

• Exam Date: Friday, June 7, 2024, 9:00 – 10:30 AM
• Total Pages: 14
• Materials: Graphing calculator permitted.
• Instructions: All fractions must be reduced to lowest terms. Unless stated otherwise, answers should be correct to three significant figures.

Exam Format

• Part A - Multiple Choice:
  • 8 questions.
  • 16 marks total.
  • Circle the most correct response (A, B, C, or D).
  • No work needs to be shown.
• Part B - Short Response:
  • 10 questions; complete 7.
  • 21 marks total.
  • Cross out the three questions not to be corrected.
  • All work must be shown.
• Part C - Long Response:
  • 5 questions; complete 4.
  • 24 marks total.
  • Cross out the question not to be corrected.
  • All work must be shown.

Unit 1: Sets and Venn Diagrams (Chapters 4 and 6)

Multiple Choice

1. Identifying Irrational Numbers

   • Question: Which number is irrational?
   • Options:
     • A) 3.6
     • B) -√169
     • C) 7 \frac{1}{3}
     • D) -145.34567890134901 … (non-repeating, non-terminating decimal)
   • Correct Answer: D

2. Set Theory Statements

   • Question: Which statement is true?
   • Options:
     • A) Z \subseteq N (Integers are a subset of Natural Numbers)
     • B) R \subseteq Q (Real Numbers are a subset of Rational Numbers)
     • C) Z \subseteq Z^+ (Integers are a subset of Positive Integers)
     • D) Q \subseteq R (Rational Numbers are a subset of Real Numbers)
   • Correct Answer: D

Short Answer

1. Rugby and Hockey

   • Context: Class of 40 students, 19 play rugby, 20 play hockey, 8 play neither.
   • Tasks:
     • a. Display information on a Venn diagram.
     • b. Determine the number of students who play rugby.
     • c. Determine the number of students who do not play hockey.
     • d. Determine the number of students who play at least one of the sports.
     • e. Determine the number of students who play one and only one of the sports.
     • f. Determine the number of students who play rugby, but not hockey.

2. Astronomy and Oceanography

   • Context: Class of 30 students, 19 study Astronomy, 17 study Oceanography, 15 study both.
   • Tasks:
     • a. Display this information on a Venn diagram.
     • b. Determine the number of students who study at least one of the subjects.
     • c. Determine the number of students who study Astronomy, but not Oceanography.
     • d. Determine the number of students who study exactly one of the subjects.
     • e. Determine the number of students who study neither subject.

Long Answer

1. Universal Set and Subsets

   • Universal Set U: Positive integers less than 16.
   • Subset A: Integers that are multiples of 3.
   • Subset B: Integers that are factors of 32.
   • Tasks:
     • a. List the elements of subsets A and B.
     • b. Show A and B on a Venn diagram.
     • c. List the elements of:
       • i. A ∩ B
       • ii. B'
       • iii. A ∪ B
       • iv. (A ∪ B)'
     • d. Find:
       • i. n(A) (number of elements in A)
       • ii. n(A ∪ B) (number of elements in A ∪ B)
       • iii. n(A' ∩ B) (number of elements in A' ∩ B)
       • iv. n(B') (number of elements in B')

Unit 2: Algebraic Expansion and Factorisation (Chapters 2 and 3)

Multiple Choice

1. Coefficient Identification

   • Question: State the coefficient of 3xyz^2
   • Options: A) 3 B) x C) y D) z^2
   • Correct Answer: A

2. Coefficient Identification

   • Question: State the coefficient of -u^24v^3
   • Options: A) -u B) 24 C) -1 D) v
   • Correct Answer: C

3. Expansion and Simplification

   • Question: Expand and simplify: (x − 3)(1 − x)(3x + 2)
   • Options:
     • A) x^2 + 7x − 6
     • B) -3x^3 + 12x^2 − 9x + 2
     • C) 3x^3 + 14x^2 + 17x − 6
     • D) -3x^3 + 10x^2 − x − 6
   • Correct Answer: D

Short Answer

1. Factorisation

   • a) -6x^2 + 42x + 48
   • b) 12a^2 − 108
   • c) 5m^2 + 3m − 2
   • d) 49 + 14w + w^2
   • e) 121 − b^2c^4
   • f) 14p^2 + 42p − 8p − 24

2. Complete Factorisation

   • a) 12a + 36ab
   • b) 42x^2y − 25x^3y^2 + 15xy^3

3. Simplification

   • a) 12x^2 − 3 + 7y − 5y − 10 + 8x^2 − y
   • b) 2(x − 2) − 5x + 6

Long Answer

1. Binomial Expansion

   • Use binomial expansion to evaluate (5x − y)^5
   • Pascal’s triangle coefficients: 1, 5, 10, 10, 5, 1

Unit 3: Surds and Other Radicals (Chapter 7)

Multiple Choice

1. Simplifying Radicals

   • Question: If \sqrt{\frac{1}{7}} = k\sqrt{7}, what is the value of k?
   • Options: A) 7 B) \frac{1}{7} C) 0.7 D) \sqrt{\frac{1}{7}}
   • Correct Answer: B

2. Simplest Form of Radical

   • Question: What is \sqrt{28} written in simplest form?
   • Options: A) 7\sqrt{2} B) 2\sqrt{14} C) 2\sqrt{7} D) 4\sqrt{7}
   • Correct Answer: C

Short Answer/Long Answer

1. Simplification of Surds

   • a) (\sqrt{10})^3
   • b) (5)^4
   • c) (\frac{1}{\sqrt{11}})^2
   • d) 3\sqrt{7} − 5\sqrt{13} + 4 − \sqrt{7} + 2(\sqrt{7} − \sqrt{13})
   • e) 3\sqrt{2}(7\sqrt{2} − 4\sqrt{5} + 6)
   • f) \frac{\sqrt{33}}{\sqrt{3}}
   • g) \frac{4\sqrt{6}}{\sqrt{18}}
   • h) -3\sqrt{288}
   • i) (\sqrt{5} + 1)(\sqrt{5} − 1)
   • k) -(3 − 5\sqrt{3})^2
   • l) \frac{1}{\sqrt{15}}
   • m) \frac{1}{2\sqrt{11}}

Unit 4: Pythagoras’ Theorem (Chapter 8)

Multiple Choice

1. Right Angle Triangle Side Lengths

   • Question: Which of the following could NOT be the side lengths of a right angle triangle?
   • Options:
     • a. 9, 12, 15
     • b. 8, 15, 17
     • c. 2, \sqrt{10}, \sqrt{14}
     • d. \sqrt{26}, 3, 6
   • Correct Answer: d

2. Hypotenuse Length

   • Question: What is the length of the hypotenuse of a right angle triangle with sides 15 cm and 8 cm?
   • Options: a. 17 cm b. \sqrt{17} cm c. 23 cm d. 289 cm
   • Correct Answer: a

Short Answer

1. Cell Tower Guy Wire

   • Guy wire attached 12 m from the base, tower 47 m high. Find the length of the guy wire.

2. Rectangular Field Diagonal

   • Dimensions 352m by 144 m. How much farther to walk along the length and width instead of the diagonal?

Long Answer

1. Extension Ladder

   • Ladder rests 4 m up a wall. Extended 0.8 m, now rests 1 m further up the wall. How long is the extended ladder?

Unit 5: Quadratic Equations (Chapter 12)

Multiple Choice

1. Number of Solutions Using Discriminant

   • Question: Using the discriminant, determine how many solutions for x will the following quadratic equation have: x^2 − 4x + 6 = 0
   • Options: a. One b. Two c. Zero d. Three
   • Correct Answer: c

2. Solving Quadratic Equation

   • Question: Solve the following quadratic equation for x: \frac{x+5}{4} = \frac{9−x}{x}
   • Options: a. -3 or 12 b. 3 or -12 c. -6 or 6 d. 18 or -2
   • Correct Answer: b

Short Answer

1. Solving Trinomials

   • a) x^2 − 7x − 18 = 0
   • b) x^2 − 12x + 27 = 0

2. Solving Binomials

   • a) m^2 − 100 = 0
   • b) 5a^2 − 125 = 0

3. Solving Trinomials

   • a) 3a^2 + a − 2 = 0
   • b) 8a^2 + 2a − 6 = 0

Long Answer

1. Number and Its Square

   • The sum of a number and its square is 42. Find the number.

2. Rectangle Dimensions

   • A rectangle has length 5 cm greater than its width. If it has an area of 84 \,cm^2, find the dimensions of the rectangle.

3. Right Angled Triangle

   • A right angled triangle has hypotenuse 1 cm longer than two times the length of the shortest side. The other side is 7 cm longer than the shortest side. Find the length of each side of the triangle.

Unit 6: Coordinate Geometry (Chapter 13)

Multiple Choice

1. Positive Slope

   • Which diagram shows a line with a positive slope?

2. Point on a Line

   • Question: Which of the following points lies on the line x + 4y − 6 = 0?
   • Options: A) (0,2) B) (2,1) C) (3, \frac{1}{4}) D) (1, \frac{1}{2})
   • Correct Answer: B

Short Answer

1. Equation of a Line

   • Determine the equation of the line in the diagram below. Write the answer in general form and slope intercept form.

2. Graphing a Line

   • Graph a line segment through the point (-2,1) that has a slope of 3.

3. Slope of Line Segment

   • The slope of line segment AB is −\frac{2}{3}. The coordinates of the end points are A(4, 0) and B(-2, y). Determine the value of y.

Long Answer

1. Triangle Vertices

   • Points D(3, -1), E(1, 8), F(-6, 1) are the vertices of a triangle.
     • a) Plot the triangle on a grid.
     • b) Find the length of each line segment.
     • c) What type of triangle is it? Why?

2. Parallel and Perpendicular Lines

   • a) Write the equation of the line through P(2, 4) that is parallel to the line shown. Include a sketch of this line in your answer.
   • b) Write the equation of the line through P(2, 4) that is perpendicular to line NK. Include a sketch of this line in your answer.

3. Perpendicular Bisector

   • Find the equation of the perpendicular bisector of line AB such that A(3, 8) and B(7, 2).

Unit 7: Trigonometry (Chapter 17)

Multiple Choice

1. Unknown Side Length

   • Determine the length of the unknown side in the following triangle. (The triangle is not drawn to scale.)
   • a. 8.34 cm b. 9.71 cm c. 3.37 cm d. 22.28 cm

2. Unknown Angle Measure

   • Find the measure of the unknown angle in the following triangle. (The triangle is not drawn to scale.)
   • a. 30.96° b. 36.87° c. 53.13° d. 59.04°

Short Answer

1. Tree and Shadow

   • If a tree casts a shadow 8 m long when the sun is at an elevation of 60˚, how tall is the tree?

2. Flagpole Ropes

   • A flagpole 17 m high is supported by three ropes which meet the ground at angles of 55˚. Determine the total lengths of the three ropes.

Long Answer

1. Grand Canyon

   • A point on the north rim is 2,158 metres above sea level. A point on the south rim is 1,812 metres above sea level. The canyon is 975 metres wide. What is the angle of depression from the north rim to the south rim?

2. Athlete Running

   • An athlete ran for 2.5 hours in the direction 164° at a speed of 14 \,kmh^{-1}.
     • a. Draw a fully labeled diagram of the situation.
     • b. Find the distance traveled by the athlete.
     • c. How far
       • i) east
       • ii) south
     • of the starting point is the athlete?

Unit 8: Statistics (Chapter 20)

Multiple Choice

1. Finding x in a Mean

   • Question: Find x if 7, 15, 6, 10, 4, and x have a mean of 9.
   • Options: A) 7 B) 12 C) 8 D) 14
   • Correct Answer: B

2. Quantitative Continuous Variable

   • Question: Which of the following is considered a quantitative continuous variable?
   • Options:
     • A) The number of cousins a person has
     • B) Favourite type of apple
     • C) The percentage of people with asthma
     • D) The height of 2 year old children
   • Correct Answer: D

Short Answer

1. Test Scores

   • Test scores (out of 40) for 20 students are given.
     • a) Determine the five-number summary for the data.
     • b) Draw a box plot for the data.

2. Basketball Squad Heights

   • A frequency table for the heights of a basketball squad is given.
     • a) Construct a histogram for the data.
     • b) What is the modal class? Explain what this means.
     • c) Describe the distribution of the data.
     • d) Determine the:
       • i. Mean
       • ii. Median
       • iii. Q1
       • iv. Q3

Long Answer

1. History Exam Scores

   • History exam scores with frequencies are given.
     • a) Complete the cumulative frequency table.
     • b) Draw a cumulative frequency graph of the data.
     • c) Find the median mark from your graph.
     • d) How many students score less than 75?
     • e) If the pass mark was 55, how many students failed?

2. Mathematics Examination Marks

   • Mathematics examination marks obtained by students are given.
     • a) Identify:
       • i) The minimum score.
       • ii) The maximum score.
       • iii) The median score.
       • iv) The upper quartile
       • v) The lower quartile
     • b) What is the range of these scores?
     • c) What is the interquartile range of these scores?
     • d) What is the mean of these scores?
     • e) What is the mode of the scores?

Formulas

• Slope: m = \frac{y2−y1}{x2−x1}
• Distance: \sqrt{(x2 − x1)^2 + (y2 − y1)^2}
• Midpoint: (\frac{x1+x2}{2} , \frac{y1+y2}{2})
• Slope Intercept Form: y = mx + b
• General Form: Ax + By = C
• Parallel lines: same slopes
• Perpendicular lines: negative reciprocals
• Area of a rectangle: A = b × h
• Area of a triangle: A = \frac{b×h}{2}
• Pythagoras’ Theorem: a^2 + b^2 = c^2
• Quadratic Formula: x = \frac{−b±\sqrt{b^2−4ac}}{2a}
• Discriminant: Δ = b^2 − 4ac
• Trigonometry Right Angle;
  • sin(θ) = \frac{opp}{hyp}
  • cos(θ) = \frac{adj}{hyp}
  • tan(θ) = \frac{opp}{adj}