Practise

Question bank

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

TopicSkillDifficulty

13 questions

SA-9709-P3-LE5-0031 markL1 FoundationCalculatorModels

A population is modelled by

P=200e^{0.03t}

. Find

P

when

t=10

, to the nearest whole number.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-G012 marksL1 FoundationCalculatorLinear forms

y=kx^n

. The graph of

\ln y

against

\ln x

is a straight line with gradient

2

and intercept

0.7

. Find

n

, and

k

correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-Q011 markL1 FoundationCalculatorLinear forms

To test whether data fit

y=ka^x

, you should plot

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SA-9709-P3-LE-Q031 markL1 FoundationCalculatorLinear forms

To test whether

y=kx^n

, you should plot

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0114 marksL2 StandardCalculatorLinear forms

Variables

x

and

y

satisfy

y=kx^n

. The graph of

\ln y

against

\ln x

is a straight line through

(1,\,2.5)

and

(3,\,6.5)

. Find

n

, and

k

correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0153 marksL2 StandardCalculatorModels

A population is modelled by

N=500e^{0.04t}

, where

t

is in years. Find the time taken for the population to reach

1500

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0012 marksL2 StandardCalculatorLinear forms

y=ka^x

. The graph of

\ln y

against

x

is a straight line with intercept

0.5

and gradient

0.3

. Find

k

and

a

, each correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0023 marksL2 StandardCalculatorFinding constants

y=kx^n

. The graph of

\lg y

against

\lg x

is a straight line through

(1,3)

and

(3,7)

. Find

n

and

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0042 marksL2 StandardCalculatorModels

The mass of a radioactive sample is

m=50e^{-0.1t}

grams after

t

days. Find its half-life, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0124 marksL3 ExamCalculatorLinear forms

Variables

x

and

y

satisfy

y=ka^x

. The graph of

\ln y

against

x

is a straight line through

(0,\,1.2)

and

(4,\,3.0)

. Find

k

and

a

, each correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0053 marksL3 ExamCalculatorModels

A cup of tea cools according to

T=20+60e^{-0.05t}

, where

T

is in °C and

t

in minutes. Find the time taken to cool to

50

°C, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0064 marksL4 ChallengingCalculatorFinding constants

A car is worth $5000 when new and $4000 after

3

years. Its value is modelled by

V=Ae^{kt}

. Find

A

, and

k

correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE5-0074 marksL4 ChallengingCalculatorFinding constants

Two points,

(2,12)

and

(4,48)

, lie on the curve

y=kx^n

. Find

n

and

k

Salam Academy Original Practice · Proposed mark scheme