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.
3 A population is modelled by P(t) = 1200(1.08)^t, where t is the number of complete years after the start of 2026. Find the first value of t for which the population exceeds 2000. Show your method. A population is modelled by P(t) = 1200(1.08)t , where t is the number of complete years after the start of 2026. Find the first value of t for which the population exceeds 2000. Show your method. Paper 2 style Medium 4 marks Calculator + 4 Marking analysis: A learner attempts the following task: “A population is modelled by P(t) = 1200(1.08)^t, where t is the number of complete years after the start of 2026. Find the first value of t for which the population exceeds 2000. Show your method.” Their response addresses only this point: “Sets up 1200(1.08)^t > 2000 or the corresponding equality.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis: A learner attempts the following task: “A population is modelled by P(t) = 1200(1.08)t , where t is the number of complete years after the start of 2026. Find the first value of t for which the population exceeds 2000. Show your method.” Their response addresses only this point: “Sets up 1200(1.08)t > 2000 or the corresponding equality.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 11 Solve the equation log₂(x) + log₂(x − 2) = 3 for x, stating why one algebraic solution must be rejected. Paper 2 style Medium 5 marks Calculator + 12 Marking analysis: A learner attempts the following task: “Solve the equation log₂(x) + log₂(x − 2) = 3 for x, stating why one algebraic solution must be rejected.” Their response addresses only this point: “Uses the log law log₂(x) + log₂(x − 2) = log₂[x(x − 2)].” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 5 marks Calculator + 13 A bacteria culture grows according to N(t) = 500(2)^(t/3), where t is measured in hours. Find the initial population and calculate how long it takes for the population to reach 4000. Paper 2 style Medium 4 marks Calculator + 14 Marking analysis: A learner attempts the following task: “A bacteria culture grows according to N(t) = 500(2)^(t/3), where t is measured in hours. Find the initial population and calculate how long it takes for the population to reach 4000.” Their response addresses only this point: “States the initial population N(0) = 500.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 23 A parabola has vertex (1, −4) and passes through the point (3, 4). Find the equation of the parabola in the form y = a(x − h)² + k. Paper 2 style Medium 4 marks Calculator + 24 Marking analysis: A learner attempts the following task: “A parabola has vertex (1, −4) and passes through the point (3, 4). Find the equation of the parabola in the form y = a(x − h)² + k.” Their response addresses only this point: “Writes the vertex form using the given vertex: y = a(x − 1)² − 4.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 25 A radioactive sample decays according to the model M(t) = 80e^(−0.05t), where M is the mass in grams and t is the time in years. Find the initial mass, and calculate the time taken for the mass to decay to 20 grams. Paper 2 style Medium 4 marks Calculator + 26 Marking analysis: A learner attempts the following task: “A radioactive sample decays according to the model M(t) = 80e^(−0.05t), where M is the mass in grams and t is the time in years. Find the initial mass, and calculate the time taken for the mass to decay to 20 grams.” Their response addresses only this point: “States the initial mass M(0) = 80 g.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 27 Solve the equation 2ln(x) − ln(x − 1) = ln(4) for x, given that x > 1. Paper 2 style Medium 5 marks Calculator + 28 Marking analysis: A learner attempts the following task: “Solve the equation 2ln(x) − ln(x − 1) = ln(4) for x, given that x > 1.” Their response addresses only this point: “Uses the power law to rewrite 2ln(x) as ln(x²).” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 5 marks Calculator + Self-assessed Not marked yet
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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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