Unit 2: Functions

Topic 2.10: Solving Equations Graphically Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.10. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Solve2 marks

2026

Solve

3 (x - 2) = x + 4

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2Solve2 marks

2026

Solve (x − 1)(x + 4) = 0.

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3Show that1 mark

2023

Show that, with

u = e^{x}

, the equation

e^{2 x} - 7 e^{x} + 12 = 0

becomes

u^{2} - 7 u + 12 = 0

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4Solve2 marks

2026

Solve

x^{2} - 7 x + 10 = 0

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5Solve2 marks

2026

Solve

(x - 1) (x + 4) = 0

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6Solve2 marks

2026

Solve x² − 7x + 10 = 0.

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7Show that1 mark

2026

Show that taking logarithms gives

x ln 2 = (x - 1) ln 3

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8Show that1 mark

2023

Show that the equation

5^{x + 1} = 2^{3 x}

can be written as

(x + 1) ln 5 = 3 x ln 2

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9Solve2 marks

2026

Solve 3(x − 2) = x + 4.

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10Solve3 marks

2026

Solve x² + 3 = 7x, giving your answers in exact form.

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11Solve3 marks

2026

Use your GDC to solve x³ − 4x + 1 = 0, giving all solutions to 3 significant figures.

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12Find3 marks

2026

The graphs of y = x² and y = 2x + 8 are drawn. Find the x-coordinates where they meet.

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13Solve3 marks

2026

Solve

x^{2} + 3 = 7 x

, giving your answers in exact form.

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14Solve2 marks

2026

Solve

x^{2} = 4 x

by rearranging to = 0.

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15Find2 marks

2026

Solve

3^{2 x} = 5

, giving an exact answer.

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16Find3 marks

2026

The graphs of

y = x^{2}

and

y = 2 x + 8

are drawn. Find the x-coordinates where they meet.

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17Solve3 marks

2026

Use your GDC to solve

x^{3} - 4 x + 1 = 0

, giving all solutions to 3 significant figures.

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18Solve2 marks

2026

Solve x² = 4x by rearranging to = 0.

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19Determine3 marks

2026

A machine part passes each test independently with probability

0.03

of failing. Determine the least number of tests

n

for which the probability of at least one failure exceeds

0.95

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20Solve3 marks

2026

Solve the equation 2ˣ = 3x + 1 using your GDC, giving answers to 3 s.f.

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