Unit 2: Functions
Topic 2.7: Solving Quadratics Questions
Practice 20 exam-style questions for IB Math AA SL Topic 2.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Solve2 marks
2026• Aimnova practice — 2.7.3
Solve (x − 1)(x − 5) > 0.
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2026• Aimnova practice — 2.7.2
Find the discriminant of 3x² − 5x + 2 and state the number of real roots.
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2026• Aimnova practice — 2.7.1
Solve x² + 2x − 15 = 0.
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2026• Aimnova practice — 2.7.1
Solve (x − 3)² = 16.
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2026• Aimnova practice — 2.7.3
Solve the inequality x² − 4 < 0.
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2026• Aimnova practice — 2.7.2
Show that x² + 2x + 5 = 0 has no real roots.
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2026• Aimnova practice — 2.7.1
Solve x² + 6x + 9 = 0.
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2026• Aimnova practice — 2.7.2
The equation x² − 6x + k = 0 has two equal roots. Find the value of k.
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2026• Aimnova practice — 2.7.3
Solve x² − 2x − 8 ≥ 0.
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2026• Aimnova practice — 2.7.3
Find the values of x for which x² + x − 6 < 0.
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2026• Aimnova practice — 2.7.3
Solve x² + 3x − 10 ≤ 0.
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2026• Aimnova practice — 2.7.3
Solve x² > 9.
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2026• Aimnova practice — 2.7.1
Solve 2x² − 5x − 4 = 0, giving your answers to 3 significant figures.
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2026• Aimnova practice — 2.7.1
Solve x² = 5x by first rearranging to = 0.
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2026• Aimnova practice — 2.7.1
Solve 3x² − 7x + 2 = 0.
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2026• Aimnova practice — 2.7.1
Solve x² − 4x − 1 = 0, giving your answers in exact (surd) form.
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2026• Aimnova practice — 2.7.2
Show that the line y = 4x − 7 does not meet the curve y = x² + 1.
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2026• Aimnova practice — 2.7.2
The equation 2x² + (k)x + 8 = 0 has two distinct real roots. Find the set of values of k.
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2026• Aimnova practice — 2.7.3
Solve 12 − x − x² ≥ 0.
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2026• Aimnova practice — 2.7.2
Find the value of c for which the line y = 2x + c is tangent to the curve y = x² + 3.
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