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 82 of 137 · choose a topic above to narrow them down

SA-9709-P1-QD2-0043 marksL2 StandardCalculatorFormula

Solve

x^2-4x-3=0

, giving your answers in the form

p\pm\sqrt q

. State

p

and

q

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0032 marksL2 StandardCalculatorUnknown constants

Find the values of

k

for which

2x^2+kx+8=0

has equal roots.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD4-0033 marksL2 StandardCalculatorQuadratic

Solve

3-2x-x^2>0

. Give your answer as

a<x<b

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0024 marksL2 StandardCalculatorIntersections

Find the

x

-coordinates of the points where the line

y=2x-1

meets the circle

x^2+y^2=10

, and the

y

-coordinate of the point with negative

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR-0012 marksL2 StandardCalculatorExpanding

Find the coefficient of

x^3

in the expansion of

(2-x)^6

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR-0162 marksL2 StandardCalculatorSum to infinity

A geometric progression has first term

5

and second term

4

. Find its sum to infinity.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR1-0022 marksL2 StandardCalculatorParticular terms

Find the coefficient of

x^2

in the expansion of

(3+x)^4

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR1-0043 marksL2 StandardCalculatorExpanding

Find the first three terms in the expansion of

(2+x)^5

in ascending powers of

x

. Enter them as one expression.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR2-0022 marksL2 StandardCalculatorAP formulae

Find the sum of the first

25

terms of the arithmetic progression

2+5+8+\dots

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR2-0042 marksL2 StandardCalculatorUnknowns

Which term of the arithmetic progression

7,\ 11,\ 15,\dots

is equal to

147

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR3-0022 marksL2 StandardCalculatorGP formulae

Find the sum of the first

6

terms of

1+3+9+\dots

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR3-0033 marksL2 StandardCalculatorGP formulae

Find the sum of the first

8

terms of the geometric progression

5,\ -10,\ 20,\dots

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR4-0012 marksL2 StandardCalculatorProblems

By writing

0.\dot{3}=0.3+0.03+0.003+\dots

as a geometric series, write

0.\dot3

as a fraction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-SR4-0032 marksL2 StandardCalculatorSum to infinity

Find the sum to infinity of the geometric series

9-3+1-\dots

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR-0043 marksL2 StandardCalculatorEquations

Solve

\tan x=2

for

0^\circ\le x\le360^\circ

, giving answers to 1 decimal place.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR-0053 marksL2 StandardCalculatorEquations

Solve

\cos x=-0.4

for

0^\circ\le x\le360^\circ

, giving answers to 1 decimal place.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR-0112 marksL2 StandardCalculatorGraphs

For the curve

y=3\sin2x

, state the maximum value of

y

and the period in degrees.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR-0122 marksL2 StandardCalculatorPrincipal values

Find the exact values, in radians, of

\sin^{-1}\left(-\tfrac12\right)

and

\cos^{-1}\left(-\tfrac12\right)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR1-0021 markL2 StandardCalculatorExact values

Find the exact value of

\tan300^\circ

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-TR2-0022 marksL2 StandardCalculatorTransformations

Find the maximum and minimum values of

y=4-3\sin x

Salam Academy Original Practice · Proposed mark scheme