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Questions, mark schemes and solo study

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4,800+ questions with real mark schemes across twelve curricula, a generator that turns any of them into a fresh variant, and a room designed for the hours between lessons.

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01Question banks & generator 02A question, with its mark scheme 03The Focus Room 04Tests that grade themselves →

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Quadratics — IB AA HL · Paper 1
Generate
Question 1 · 5 marks

The quadratic x² + kx + 9 = 0 has exactly one real root. Find the possible values of k.

Question 2 · 6 marks

The curve y = 2(x − 3)² − 5 has vertex V. (a) Write down the coordinates of V. (b) Find where the curve meets the x-axis.

Question 3 · 7 marks

Given f(x) = x² − 6x + 11, express f in the form (x − a)² + b and hence state the range of f.

Real mark schemes

Marked the way the examiner marks it.

Every question in the bank carries the method and accuracy marks in order — not just a final answer. Students see exactly where the marks are won, one step at a time, and you can generate a similar question from any of them.

Q1 Exam Structured · 6 marks ✦ Similar
A function h satisfies h′(x) = e2x + 4.
(a)Find[2 marks]
Find ∫(e2x + 4) dx.
(b)Find[4 marks]
Given that h(0) = 10, find h(x).
Show walkthrough
(a)2 marks
ANSWER12e2x + 4x + C
M1∫e2x dx = 12e2x  and  ∫4 dx = 4x.
A1∫(e2x + 4) dx = 12e2x + 4x + C.
(b)4 marks
ANSWERh(x) = 12e2x + 4x + 9.5
M1h(x) = 12e2x + 4x + C.
M1h(0) = 12e0 + 4(0) + C = 12 + C.
A112 + C = 10  ⇒  C = 9.5.
A1h(x) = 12e2x + 4x + 9.5.

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Focus room
AA SL
Focus
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15 · 25 · 50 focus5 · 10 break
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SCENE 16
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DrillReviewMock
◎ Today's focus: 3.6 Trig Identities5.4 Rules & Tangents4.7 Distributions
Medium No GDC 3 marks
Part (a)
Show that (1 − cos 2x) / sin 2x = tan x, where defined.
Show a hint Reveal full solution Hint 1 of 3
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