School / IB / MATH AA SL / Functions Question practice
Functions About this practice Quadratics, transformations and exponential models.
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What this functions practice helps with Use this IB Mathematics AA SL functions set for quadratic functions, composite and inverse functions, logarithms, exponential growth models, and calculator/non-calculator method marks.
Exponential model example: solve 1200(1.08)^t > 2000 by using logarithms, then round up because t is a complete number of years. Paper 1 style: practise completing the square, inequalities, inverse functions, composite functions, and exact algebra without a calculator. Paper 2 style: practise logarithmic and exponential modelling questions where the calculator supports the final numerical decision. Mathematics AA: Standard Level Functions
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About paper groupings Paper labels are an unofficial, independently authored grouping, applied only where a question's own format genuinely matches a real paper convention (such as IB Mathematics AA's non-calculator/calculator split). They do not reproduce any exam board's real paper numbering or mark allocation, and uncertain questions are labelled general practice instead.
1 The function f(x) = x² − 4x + 7 is defined for all real x. Write f(x) in completed-square form. Hence state the coordinates of the vertex and the minimum value of f. Paper 1 style Easy 3 marks No calculator + 2 Marking analysis: A learner attempts the following task: “The function f(x) = x² − 4x + 7 is defined for all real x. Write f(x) in completed-square form. Hence state the coordinates of the vertex and the minimum value of f.” Their response addresses only this point: “Correctly obtains f(x) = (x − 2)² + 3.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 5 Solve the inequality x² − 5x + 6 ≤ 0. Give your answer using interval notation. Paper 1 style Easy 3 marks No calculator + 6 Marking analysis: A learner attempts the following task: “Solve the inequality x² − 5x + 6 ≤ 0. Give your answer using interval notation.” Their response addresses only this point: “Factorises to (x − 2)(x − 3) ≤ 0.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 7 The function f(x) = 3x − 2 is defined for all real x. Find f⁻¹(x) and state its domain. Paper 1 style Easy 3 marks No calculator + 8 Marking analysis: A learner attempts the following task: “The function f(x) = 3x − 2 is defined for all real x. Find f⁻¹(x) and state its domain.” Their response addresses only this point: “Sets y = 3x − 2 and swaps x and y (or equivalent method).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 9 Let f(x) = 2x + 1 and g(x) = x². Find an expression for the composite function (f ∘ g)(x) and evaluate (f ∘ g)(3). Paper 1 style Easy 3 marks No calculator + 10 Marking analysis: A learner attempts the following task: “Let f(x) = 2x + 1 and g(x) = x². Find an expression for the composite function (f ∘ g)(x) and evaluate (f ∘ g)(3).” Their response addresses only this point: “Substitutes g(x) into f to obtain f(g(x)) = 2x² + 1.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 15 The graph of y = f(x) is transformed to give the graph of y = f(x − 2) + 3. Describe fully the geometric transformation applied to the graph of f. Paper 1 style Easy 2 marks No calculator + 16 Marking analysis: A learner attempts the following task: “The graph of y = f(x) is transformed to give the graph of y = f(x − 2) + 3. Describe fully the geometric transformation applied to the graph of f.” Their response addresses only this point: “Identifies a horizontal translation of 2 units in the positive x-direction.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 17 Solve the equation e^(2x) = 15, giving your answer to three significant figures. Solve the equation e(2x) = 15, giving your answer to three significant figures. Paper 2 style Easy 3 marks Calculator + 18 Marking analysis: A learner attempts the following task: “Solve the equation e^(2x) = 15, giving your answer to three significant figures.” Their response addresses only this point: “Takes the natural logarithm of both sides: 2x = ln(15).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis: A learner attempts the following task: “Solve the equation e(2x) = 15, giving your answer to three significant figures.” Their response addresses only this point: “Takes the natural logarithm of both sides: 2x = ln(15).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 19 Find the largest possible domain of f(x) = √(x − 3), and state the corresponding range. Paper 1 style Easy 3 marks No calculator + 20 Marking analysis: A learner attempts the following task: “Find the largest possible domain of f(x) = √(x − 3), and state the corresponding range.” Their response addresses only this point: “Requires the expression under the root to be non-negative: x − 3 ≥ 0.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 21 The quadratic equation kx² + 4x + 1 = 0 has two equal real roots. Find the value of k. Paper 2 style Easy 3 marks Calculator + 22 Marking analysis: A learner attempts the following task: “The quadratic equation kx² + 4x + 1 = 0 has two equal real roots. Find the value of k.” Their response addresses only this point: “States that for equal roots, the discriminant b² − 4ac = 0.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 29 State the domain of the function f(x) = 1/(x − 3), and write the equations of its vertical and horizontal asymptotes. Paper 1 style Easy 3 marks No calculator + 30 Marking analysis: A learner attempts the following task: “State the domain of the function f(x) = 1/(x − 3), and write the equations of its vertical and horizontal asymptotes.” Their response addresses only this point: “States the domain as all real x except x = 3 (x ≠ 3), since division by zero is undefined.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 31 f(x) = 3x - 5 for x >= 2. Find its inverse and state the domain of the inverse. Paper 1 style Easy 3 marks No calculator + 32 Marking analysis: A learner attempts the following task: “f(x) = 3x - 5 for x >= 2. Find its inverse and state the domain of the inverse.” Their response addresses only this point: “The range of f is y >= 1.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + Self-assessed Not marked yet
Set total 110
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Questions learners ask about this practice Are these official IB questions? No. These are original SubjectScout practice questions for Functions. They are not official past-paper questions or endorsed material.
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