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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-FP-IC-G011 markL1 FoundationNon-calculatorDifferentiating

Find the gradient of

y=\arcsin x

at

x=0

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-Q011 markL1 FoundationNon-calculatorIntegrating

\displaystyle\int\frac{dx}{\sqrt{x^2+a^2}}=

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-X011 markL1 FoundationNon-calculatorDifferentiating

Find the gradient of

y=\arctan x

at

x=1

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-X021 markL1 FoundationNon-calculatorIntegrating

Find

\int_0^1\frac{1}{1+x^2}\,dx

exactly.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-0012 marksL2 StandardNon-calculatorDifferentiating

Find

\frac{d}{dx}\arctan(2x)

at

x=0

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-0022 marksL2 StandardCalculatorDifferentiating

Find the gradient of

y=\operatorname{arcosh}x

at

x=2

(to 3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-0032 marksL2 StandardCalculatorIntegrating

Evaluate

\displaystyle\int_0^1\frac{dx}{1+x^2}

(to 4 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-X032 marksL2 StandardNon-calculatorIntegrating

Find

\int_0^{1/2}\frac{1}{\sqrt{1-x^2}}\,dx

exactly.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-X041 markL2 StandardNon-calculatorDifferentiating

Find the gradient of

y=\operatorname{arsinh}x

at

x=\sqrt3

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-0043 marksL3 ExamCalculatorIntegrating

Evaluate

\displaystyle\int_0^{3/2}\frac{dx}{\sqrt{9-x^2}}

exactly (enter to 4 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-X053 marksL3 ExamNon-calculatorIntegrating

Find

\int_0^3\frac{1}{\sqrt{9+x^2}}\,dx

in logarithmic form.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-IC-0054 marksL4 ChallengingCalculatorIntegrating

Show that

\displaystyle\int_0^4\frac{dx}{\sqrt{x^2+9}}=\ln k

and find

k

.

Salam Academy Original Practice · Proposed mark scheme