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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2730 questions · page 31 of 137 · choose a topic above to narrow them down

SA-9709-P2-AL-G012 marksL1 FoundationCalculatorEquations

Solve the equation

|3x-2|=7

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0143 marksL1 FoundationCalculatorParametric

A curve has parametric equations

x=t^2

y=2t

. Find the gradient of the curve at the point where

t=2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-G012 marksL1 FoundationCalculatorStandard derivatives

Differentiate

y=e^{3x}+\ln(2x)

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-IN-0012 marksL1 FoundationCalculatorStandard integrals

Find

\displaystyle\int\frac{1}{2x+3}\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-IN-0033 marksL1 FoundationCalculatorExact integrals

Find the exact value of

\displaystyle\int_0^1e^{2x}\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-IN-G012 marksL1 FoundationCalculatorStandard integrals

Find

\displaystyle\int\left(e^{4x}+\frac3x\right)dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0022 marksL1 FoundationCalculatorSimple

The solution of

|x-3|<2

a<x<b

. Find

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0042 marksL1 FoundationCalculatorRemainder theorem

Find the remainder when

x^3-4x^2+2x+5

is divided by

(x-3)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0083 marksL1 FoundationCalculatorLinear factors

Express

\dfrac{5x+1}{(x-1)(x+2)}

in the form

\dfrac{A}{x-1}+\dfrac{B}{x+2}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL1-0012 marksL1 FoundationCalculatorGraphs

For the graph of

y=|2x+4|

, state the

x

-coordinate of the vertex and the

y

-intercept.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL2-G012 marksL1 FoundationCalculatorSimple

The solution of

|x-1|<3

a<x<b

. Find

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL4-G012 marksL1 FoundationCalculatorLinear factors

Express

\dfrac{3}{(x+1)(x-2)}

in the form

\dfrac{A}{x+1}+\dfrac{B}{x-2}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-G013 marksL1 FoundationCalculatorExpanding

Expand

(1+x)^{-1}

in ascending powers of

x

, up to and including the term in

x^3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-G012 marksL1 FoundationCalculatorEquations

Solve the equation

|2x-3|=5

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0012 marksL1 FoundationCalculatorArithmetic

Express

(2-3i)^2

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0043 marksL1 FoundationCalculatorPolynomial roots

Solve the equation

z^2-4z+13=0

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0142 marksL1 FoundationCalculatorPolar form

Express

z=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)

in the form

x+iy

, giving exact values.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0011 markL1 FoundationCalculatorArithmetic

Express

(4+3i)+(2-5i)-(1-i)

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0022 marksL1 FoundationCalculatorArithmetic

Express

(3+2i)(4-i)

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX2-0011 markL1 FoundationCalculatorModulus–argument

Find

|5-12i|

Salam Academy Original Practice · Proposed mark scheme