Grade 11 Functions Exam: Part A
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Questions and Answers

What is the next term in the sequence 2, 6, 10?

  • 16
  • 12
  • 14 (correct)
  • 18

    • What is the recursive formula for the sequence 2, 6, 10?

  • Tn = T1 + (n - 1)d/2
  • Tn = T1 × (n - 1)d
  • Tn = T1 + (n - 1)d (correct)
  • Tn = T1 - (n - 1)d

    • What is the 3007th term of the sequence 2, 6, 10?

  • 16,032
  • 10,026
  • 12,028 (correct)
  • 14,030

    • What is the simplified form of the expression x^(5/4) × x^(3/4)?

    <p>x^2</p> Signup and view all the answers

    What is the simplified form of the expression y^(2/3)^(1/2)?

    <p>y^(1/3)</p> Signup and view all the answers

    If f(x) is a function, what is the corresponding function for y = 2f(x)?

    <p>f(x) = y/2</p> Signup and view all the answers

    What is the value of f(-3) if f(x) = 5x^2 - 2?

    <p>43</p> Signup and view all the answers

    What is the period of a periodic relation that repeats every 5 units?

    <p>5</p> Signup and view all the answers

    What is the simplified form of 8^(-5/3)?

    <p>2√3/3</p> Signup and view all the answers

    What is the domain of the function √(x - 5)?

    <p>{x | x ≥ 5, x ∈ ℝ}</p> Signup and view all the answers

    What is the exact value of sec(30°)?

    <p>2/√3</p> Signup and view all the answers

    What is the simplified form of the expression -14/42?

    <p>-1/3</p> Signup and view all the answers

    What is the value of x that makes the sequence x - 4, 6, x arithmetic?

    <p>8</p> Signup and view all the answers

    What is the next term in the sequence 1, 3, 7, 15?

    <p>31</p> Signup and view all the answers

    Study Notes

    Part A of Grade 11 Functions Exam

    • Exam covers a little bit of everything to ensure students understand the basics of the grade level course
    • No finance section on the exam because it's evaluated separately as a summative

    Question 1: Function Notation

    • f(x) = 5x^2 - 2, find f(-3)
    • Plug in x value in brackets to avoid sign errors
    • Calculation: f(-3) = 5(-3)^2 - 2 = 45 - 2 = 43

    Question 2: Periodic Relation

    • Given a periodic relation, state the period, amplitude, and value of F(11)
    • Period: measure of how long before the relation repeats again
    • Amplitude: height of the function from lowest to highest point
    • Value of F(11): find the height of the function when x = 11
    • Period: 5
    • Amplitude: 6
    • Value of F(11): 1

    Question 3: Exponential Expression

    • Evaluate 8^(-5/3) and express as a fraction in simplified form
    • 8^(-5/3) = 1/(2^5) = 1/32
    • Rationalize the denominator by multiplying top and bottom by √3: 2√3/3

    Question 4: Domain and Range

    • Given √(x - 5), state the domain and range
    • Domain: all x values that can be input into the function (x ≥ 5)
    • Range: all y values that can be output by the function (y ≥ 0)
    • Domain: {x | x ≥ 5, x ∈ ℝ}
    • Range: {y | y ≥ 0, y ∈ ℝ}

    Question 5: Trigonometry

    • Evaluate sec(30°) exactly
    • Use special triangles to find exact value
    • sec(30°) = 1/cos(30°) = 2/√3

    Question 6: Simplifying Rational Expressions

    • Simplify the expression: -14/42, reduce to lowest terms
    • Cancel out common factors: -1/3
    • Simplify a^4/b^2c^3: -a^5/b^2c^(-2)

    Question 7: Restrictions

    • State the restrictions of the expression x/(3x - 6)
    • Find values of x that make the denominator zero (x ≠ 0, x ≠ 2)

    Question 8: Arithmetic Sequence

    • Determine the value of x that makes the sequence x - 4, 6, x arithmetic
    • Find the common difference between terms: 6 - x = x - 4
    • Solve for x: x = 8

    Question 9: Sequence

    • Find the next term in the sequence: 1, 3, 7, 15
    • Identify the pattern: add 2, 4, 8, ...
    • Next term: 15 + 16 = 31

    Question 10: Graph of f(x)

    • Given a point on the graph of f(x), find the corresponding image point
    • Apply mapping rules: y = f(x) -> y = 2f(x) -> x = f^-1(x)

    Question 11: Sequence

    • Given the sequence 2, 6, 10, state the next term
    • Identify the sequence as arithmetic: common difference is 4
    • Next term: 10 + 4 = 14

    Question 12: Recursive Formula

    • State the recursive formula for the sequence
    • Use the formula: Tn = T1 + (n - 1)d
    • Identify the first term (a) and common difference (d): a = 2, d = 4

    Question 13: Term of a Sequence

    • Find the 3007th term of the sequence
    • Use the formula: Tn = a + (n - 1)d
    • Plug in values: a = 2, n = 3007, d = 4
    • Simplify: 2 + 3006(4) = 12,028

    Question 14: Exponent Rules

    • Simplify the expression: x^(5/4) × x^(3/4)
    • Use exponent rules: add exponents when multiplying
    • Simplify: x^(5/4 + 3/4) = x^2

    Question 15: Exponent Rules

    • Simplify the expression: y^(2/3)^(1/2)
    • Use exponent rules: multiply exponents when taking a power
    • Simplify: y^(2/6) = y^(1/3)

    Part A of Grade 11 Functions Exam

    • Covers a wide range of topics to ensure students understand the basics of the grade level course
    • No finance section on the exam, evaluated separately as a summative

    Function Notation

    • To find the value of f(x), plug in the x value in brackets to avoid sign errors
    • Example: f(x) = 5x^2 - 2, find f(-3) = 5(-3)^2 - 2 = 45 - 2 = 43

    Periodic Relation

    • Period: measure of how long before the relation repeats again
    • Amplitude: height of the function from lowest to highest point
    • Example: period = 5, amplitude = 6, value of F(11) = 1

    Exponential Expression

    • Evaluate exponential expressions by simplifying to a fraction in lowest terms
    • Example: 8^(-5/3) = 1/(2^5) = 1/32, rationalize denominator by multiplying top and bottom by √3: 2√3/3

    Domain and Range

    • Domain: all x values that can be input into the function (x ≥ 5)
    • Range: all y values that can be output by the function (y ≥ 0)
    • Example: domain = {x | x ≥ 5, x ∈ ℝ}, range = {y | y ≥ 0, y ∈ ℝ}

    Trigonometry

    • Evaluate trigonometric expressions exactly using special triangles
    • Example: sec(30°) = 1/cos(30°) = 2/√3

    Simplifying Rational Expressions

    • Simplify rational expressions by canceling out common factors
    • Example: -14/42 = -1/3, simplify a^4/b^2c^3 = -a^5/b^2c^(-2)

    Restrictions

    • Find values of x that make the denominator zero (x ≠ 0, x ≠ 2)
    • Example: restrictions of the expression x/(3x - 6)

    Arithmetic Sequence

    • Determine the value of x that makes the sequence arithmetic
    • Find the common difference between terms: 6 - x = x - 4
    • Solve for x: x = 8

    Sequence

    • Identify patterns in sequences: add 2, 4, 8,...
    • Example: find the next term in the sequence: 1, 3, 7, 15, next term = 15 + 16 = 31

    Graph of f(x)

    • Apply mapping rules: y = f(x) -> y = 2f(x) -> x = f^-1(x)
    • Example: find the corresponding image point on the graph of f(x)

    Sequence

    • Identify the sequence as arithmetic: common difference is 4
    • Example: find the next term in the sequence: 2, 6, 10, next term = 10 + 4 = 14

    Recursive Formula

    • Use the formula: Tn = T1 + (n - 1)d
    • Example: identify the first term (a) and common difference (d): a = 2, d = 4

    Term of a Sequence

    • Use the formula: Tn = a + (n - 1)d
    • Example: find the 3007th term of the sequence: 2 + 3006(4) = 12,028

    Exponent Rules

    • Use exponent rules: add exponents when multiplying
    • Example: simplify x^(5/4) × x^(3/4) = x^(5/4 + 3/4) = x^2

    Exponent Rules

    • Use exponent rules: multiply exponents when taking a power
    • Example: simplify y^(2/3)^(1/2) = y^(2/6) = y^(1/3)

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    Assess your understanding of Grade 11 Functions course with this exam covering various topics, excluding finance.

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