Skip to content

Salam Academy

Sign in Create account

Practise

Question bank

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

Sign in to check answers. Your attempts build your mastery and error book.

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