Questions and Answers
What is the next term in the sequence 2, 6, 10?
What is the recursive formula for the sequence 2, 6, 10?
What is the 3007th term of the sequence 2, 6, 10?
What is the simplified form of the expression x^(5/4) × x^(3/4)?
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What is the simplified form of the expression y^(2/3)^(1/2)?
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If f(x) is a function, what is the corresponding function for y = 2f(x)?
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What is the value of f(-3) if f(x) = 5x^2 - 2?
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What is the period of a periodic relation that repeats every 5 units?
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What is the simplified form of 8^(-5/3)?
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What is the domain of the function √(x - 5)?
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What is the exact value of sec(30°)?
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What is the simplified form of the expression -14/42?
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What is the value of x that makes the sequence x - 4, 6, x arithmetic?
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What is the next term in the sequence 1, 3, 7, 15?
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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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Description
Assess your understanding of Grade 11 Functions course with this exam covering various topics, excluding finance.
