Functions — Free IB MYP4 Mathematics (Standard) Questions

1QuestionFunction notation f(x)Concept Practice

2 marks~3 minCriterion A

A structural engineer models the hypotenuse of a right-triangular roof truss using the function

f(x) = 3x + 5

, where

x

is a design parameter in metres and

f(x)

gives the hypotenuse length in centimetres. Building regulations require the hypotenuse to be no longer than 20 cm for this truss type.

a

Calculate

f(4)

. [1]

b

Justify whether the truss meets the building regulation when

x = 4

. [1]

Solutions

2QuestionLinear functionsConcept Practice

4 marks~6 minCriterion A

A cyclist's journey is shown on the distance–time graph below. The two labelled points are

(1, 15)

and

(3, 45)

, where the horizontal axis shows time in hours and the vertical axis shows distance in kilometres.

a

Interpret what the gradient of the line represents in the context of this journey. [1]

b

Calculate the cyclist's speed in km/h. [1]

c

A cycling event requires competitors to cover at least 40 km in the first 2.5 hours. Justify whether this cyclist meets that requirement. [2]

Solutions

3QuestionRange from graphsConcept Practice

2 marks~3 minCriterion A

A delivery drone travels in a straight line between two checkpoints. Its horizontal distance

x

(in km) from the launch pad satisfies

-2 \leq x \leq 3

. The drone's altitude (in metres) is modelled by

f(x) = 2x + 1

.

a

State the range of

f

for the given domain. [1]

b

The drone must maintain an altitude strictly above

-1

m throughout the journey. Justify whether this safety condition is met. [1]

Solutions

4QuestionInterceptsConcept Practice

4 marks~6 minCriterion A

A city planner models the edge of a new cycle lane using the linear function

y = 2x - 6

, where

x

represents the horizontal distance (metres) from a reference point and

y

represents the lane's vertical position. The graph of this function is shown, with both axes clearly labelled and scaled.

a

Explain how to locate the

x

-intercept from the graph of

y = 2x - 6

. [1]

b

Calculate the

x

-intercept of

y = 2x - 6

, showing all algebraic steps. [2]

c

The cycle lane must begin no more than 2 metres from the reference point. Advise the city planner whether this design meets the requirement, justifying your answer using your result from (b). [1]

Solutions

5QuestionReflectionsConcept Practice

2 marks~3 minCriterion B

A graphic designer uses coordinate geometry to create a reflected logo. The original logo contains the point

P(3, -5)

. The designer reflects the entire logo across the

x

-axis, as shown by the pattern below.

(2,\ 3) \rightarrow (2,\ -3)

(-1,\ 5) \rightarrow (-1,\ -5)

(4,\ -2) \rightarrow (4,\ 2)

Deduce the general rule for reflecting any point

(x, y)

across the

x

-axis. [1]

State the image of

P(3, -5)

after reflection across the

x

-axis. [1]

Solutions

6QuestionCombined transformationsConcept Practice

2 marks~3 minCriterion A

A graphic designer maps logo elements onto a coordinate grid. Triangle

ABC

has vertices

A(2, 1)

,

B(5, 1)

, and

C(3, 4)

. To reposition the logo, the triangle is first translated by the vector

\begin{pmatrix} 3 \\ -2 \end{pmatrix}

, then reflected across the

y

-axis.

a

Calculate the coordinates of vertex

A

after both transformations. [1]

b

The designer requires vertex

A

to land in the second quadrant after both transformations. Justify whether this requirement is met, using the coordinates found in part (a). [1]

Solutions

7QuestionGraphing parabolasConcept Practice

4 marks~6 minCriterion A

A structural engineer models the cross-section of a concrete arch using the equation

y = 2x^2 + 8x + 6

, where

x

is the horizontal distance (metres) from a reference point and

y

is the height (metres) above ground level.

a

State the

y

-intercept of the parabola and deduce the direction in which it opens, justifying your answer using the equation. [2]

b

Calculate the discriminant of

2x^2 + 8x + 6 = 0

and deduce the number of points at which the arch meets ground level. [1]

c

Justify whether this arch design is structurally feasible, given that a valid arch must contact the ground at exactly two distinct points. [1]

Solutions

8QuestionGraphing exponentialConcept Practice

2 marks~3 minCriterion A

A laboratory culture of bacteria begins with 2 000 cells. The population is modelled by

P = 2000 \cdot 3^{t}

, where

t

is the time in hours after the experiment starts and

P

is the number of bacteria.

A biologist states: "At the start of the experiment, the population is already above 1 500 cells."

a

Determine the value of

P

when

t = 0

. [1]

b

Justify whether the biologist's claim is correct. [1]

Solutions

9QuestionInterpret compositeConcept Practice

2 marks~3 minCriterion A

A security camera at position

P = (2, 3)

on a coordinate grid (units in metres) undergoes a composite transformation: a rotation of

90°

clockwise about the origin, followed by a reflection across the

y

-axis.

a

Determine the final coordinates of the camera's image

P''

after both transformations. [1]

b

The camera has a maximum effective range of 3.5 m from the origin. Justify whether the composite transformation places the camera within its effective range. [1]

Solutions

10QuestionPredictionConcept Practice

2 marks~3 minCriterion A

A car travels at a constant speed. A distance–time graph for the journey passes through the origin and the point

(2, 120)

, where distance

d

is measured in kilometres and time

t

in hours.

a

Deduce the equation of the line that models this relationship. [1]

b

The car must complete a 200 km journey within 3 hours. Justify whether the car's speed is sufficient to meet this requirement. [1]

Solutions

11QuestionFunction notation f(x)Assessment Practice

6 marks~9 minCriterion B

A computer network doubles its active nodes each cycle, modelled by

f(x) = 2x + 1

, where one coordination node is added per cycle. Starting from a single seed node, the network state after each cycle is defined by

a_1 = f(1)

,

a_2 = f(a_1)

,

a_3 = f(a_2)

, and so on.

a

Calculate the values of

a_1

,

a_2

,

a_3

, and

a_4

. [2]

b

Deduce a general expression for

a_n

in terms of

n

. [2]

c

A network is considered stable once it exceeds 500 active nodes. Using your expression from part (b), justify whether the network reaches stability within 8 cycles. [2]

Solutions

12QuestionRelation vs functionAssessment Practice

4 marks~6 minCriterion C

A parabolic solar reflector is designed so that its cross-section satisfies the relation

x = y^2 - 2

, where

x

and

y

are measured in metres.

a

Determine the domain and range of this relation. [2]

b

Explain whether this relation represents a function, using the vertical line test. [1]

c

A sensor must be placed at a unique horizontal position for each height

y

. Justify whether the relation

x = y^2 - 2

, as stated, is suitable for this purpose, and state any restriction needed. [1]

Solutions

13QuestionFunction notation f(x)Assessment Practice

2 marks~3 minCriterion D

A taxi company charges a base fare of 3.50 dollars and 2.10 dollars per kilometre. The total cost, in dollars, for a journey of

d

kilometres is modelled by

C(d) = 2.1d + 3.5.

A passenger has a budget of exactly 20.00 dollars.

a

Calculate

C(8)

. [1]

b

Justify whether the passenger can afford the 8 km journey, using both

C(8)

and

C^{-1}(20)

in your reasoning. [1]

Solutions

14QuestionIdentify from equationsAssessment Practice

4 marks~6 minCriterion B

A landscape architect is designing square garden plots. Each plot has a side length of

x

cm, and the usable planting area

y

cm² follows the pattern below.

x

(cm):

1, \ 2, \ 3, \ 4

y

(cm²):

3, \ 7, \ 13, \ 21

a

Calculate the first differences and second differences for the

y

-values. [2]

b

Deduce the type of function (linear or quadratic) that models this data, justifying your answer using the differences found in part (a). [1]

c

The architect needs the usable planting area to exceed 90 cm². Advise the architect whether a plot with side length

x = 6

cm is sufficient to meet this requirement. [1]

Solutions

15QuestionIdentify from graphsAssessment Practice

4 marks~6 minCriterion C

The graph shows a smooth curve with a local maximum at approximately

(-1,\ 4)

and a local minimum at approximately

(2,\ -3)

. The curve falls without bound to the left and rises without bound to the right.

a

Identify the type and degree of the function shown. [1]

b

Deduce the end behaviour of the function, expressing your answer using limit notation as

x \to +\infty

and as

x \to -\infty

. [1]

c

A civil engineer models the cross-section of a valley using this function. She needs the model to capture both a ridge and a trough within the domain. Critique the suggestion that a quadratic function would serve as an equally valid model, using the turning points of the graph as evidence. [2]

Solutions

16QuestionRational functionsAssessment Practice

4 marks~6 minCriterion D

A patient receives a single oral dose of medication. The concentration

C(t)

of the drug in the bloodstream (in mg/L),

t

hours after ingestion, is modelled by

C(t) = \frac{20t}{t^2 + 4}.

a

Calculate

C(2)

. Show all working and state your answer in mg/L. [1]

b

Calculate

C(6)

. Show all working and state your answer in mg/L. [1]

c

The function has a horizontal asymptote at

C = 0

. Critique the use of this model as a reliable representation of drug elimination for an actual patient. [2]

Solutions

17QuestionRange from graphsAssessment Practice

6 marks~9 minCriterion D

A rocket is launched from ground level. Its predicted height

h

(in metres) at time

t

(in seconds) is modelled by

h(t) = -5t^2 + 20t.

Experimental measurements were recorded:

t

(s): 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5

Measured

h

(m): 8.7, 15.2, 18.9, 20.0, 18.5, 15.1, 8.9

a

Calculate the predicted height at each of the seven time values. [2]

b

Compute the absolute difference

|\text{predicted} - \text{measured}|

for each time value, then calculate the mean absolute error (MAE). [2]

c

The launch team will trust the model for future predictions only if the MAE is less than 0.20 m. Advise the launch team whether the model should be used for future predictions, justifying your answer using your result from (b). [2]

Solutions

18QuestionDomain from graphsAssessment Practice

4 marks~6 minCriterion C

A city's water pressure monitoring system records pressure (in bar) as a piecewise linear function of time (in hours) over a 24-hour period. Due to scheduled maintenance, no data is recorded between

t = -1

and

t = 1

.

The graph shows two linear segments:
- Segment 1: from

(-4,\ 2)

(closed circle) to

(-1,\ 5)

(open circle)
- Segment 2: from

(1,\ 3)

(closed circle) to

(4,\ 0)

(closed circle)

a

Justify whether this graph represents a function. [1]

b

Deduce the domain of the function, expressing your answer in interval notation. [1]

c

The monitoring system requires at least 7 hours of combined recorded data to be considered reliable. Advise the network operator whether this session meets the reliability requirement, supporting your answer with calculations. [2]

Solutions

19QuestionRange from graphsAssessment Practice

6 marks~9 minCriterion B

A sports analyst models the height (in metres) of a ball above the ground during a throw using functions of the form

y = a(x - h)^2 + k

, where

x

is horizontal distance (in metres).

Five functions are proposed:

y = x^2

\quad

y = x^2 + 3

\quad

y = (x-2)^2

\quad

y = -x^2 + 5

\quad

y = -2(x+1)^2 - 4

a

Determine the range of each function. [3]

b

Analyse the five ranges to identify a pattern. State a general rule for the range of

y = a(x - h)^2 + k

in terms of

a

and

k

, and explain why

h

does not affect the range. [2]

c

The analyst claims any function with

a < 0

and

k \leq 0

cannot model a ball thrown above the ground. Assess whether this claim is correct. [1]

Solutions

20QuestionPlot quadratic functionsAssessment Practice

6 marks~9 minCriterion B

A structural engineer models the vertical cross-section of a concrete arch using the quadratic function

y = ax^2 + bx + c

, where

y

is the height (in metres) at horizontal position

x

(in metres). Measurements taken at five positions are recorded below.

x

(m):

-2,\ -1,\ 0,\ 1,\ 2

y

(m):

11,\ 6,\ 3,\ 2,\ 3

a

Calculate the first differences and second differences of the

y

-values. [2]

b

Deduce the value of

a

, given that the second difference of a quadratic

y = ax^2 + bx + c

with unit steps equals

2a

. Hence state the equation of the arch. [1]

c

The arch must clear a minimum height of

1.5

m at

x = 3

m to allow vehicles to pass beneath it. Substituting

x = 3

into your equation from part (b), advise the engineer whether the arch is safe for vehicles at that position. [3]

Solutions

21QuestionInterpret graphsAssessment Practice

6 marks~9 minCriterion D

A city council uses the quadratic model

h(t) = -4.9t^2 + 20t + 2

to predict the height (in metres) of a firework shell at time

t

seconds. A real test flight shows the shell explodes at

t = 1.5

s at a height of

18

m.

a

Calculate

h(1.5)

. [2]

b

The model assumes no air resistance and a perfect launch angle. Evaluate the impact of these assumptions on the model's reliability for safety planning. [2]

c

The council sets a minimum safe clearance height of

20

m at

t = 1.5

s. Advise the council whether the model should be used to make this safety decision. [2]

Solutions

22QuestionRecognize shapesAssessment Practice

4 marks~6 minCriterion C

A landscape architect models two fountain jets as parabolas. The first jet follows the path

y = x^2

, where

x

is horizontal distance (metres) and

y

is height (metres). The second jet follows a path that is a vertical translation of the first jet upward by 3 metres.

a

Explain how a vertical translation upward by 3 metres affects the equation of

y = x^2

. [1]

b

Deduce the equation of the second jet and calculate its

y

-intercept. [2]

c

The architect states: "The second jet always stays at least 3 metres above the first jet." Justify whether this statement is correct. [1]

Solutions

23QuestionStretch/compressionAssessment Practice

4 marks~6 minCriterion C

A sports analyst models the vertical height (in metres) of a ball's bounce using the function

f(x) = x^2

, where

x

is time in seconds. A new surface increases all heights by a factor of 3 and reduces the launch height by 2 metres, giving a transformed function

g(x)

.

a

Deduce the equation of

g(x)

. [1]

b

Calculate

g(4)

. [1]

c

The analyst claims: "At

x = 4

seconds, the ball reaches a height above 50 metres, so the surface is unsuitable for regulation play." Advise the analyst whether this conclusion is supported by the model. [2]

Solutions

24QuestionHorizontal shiftsAssessment Practice

4 marks~6 minCriterion D

A coastal engineer models tide height at a port using

h(t) = 3\cos(0.5(t - 2)) + 4

, where

h

is in metres and

t

is hours after midnight. The horizontal shift of 2 hours represents a lag from a reference tide. A vessel requires a minimum depth of 6.5 m to enter the port safely.

a

Deduce the first two times after midnight at which high tide occurs. [2]

b

Advise the port authority which of the two high tide times is more operationally suitable for the vessel to enter, justifying your recommendation with both the mathematical result and a real-world reason. [2]

Solutions

25QuestionSlopeAssessment Practice

4 marks~6 minCriterion B

A city's water authority monitors daily water usage at a treatment plant. The graph shows total water processed (in megalitres) against time (in days), modelled as a straight line passing through the labelled points

(1, 2)

and

(4, 8)

.

a

Calculate the slope of the line using the two labelled points. [1]

b

Show that the slope is constant by calculating the rise and run between a different pair of points on the line. [2]

c

The authority states: "Usage is increasing at a steady rate, so we can reliably forecast demand using this model." Assess whether the mathematical properties of the graph support this statement. [1]

Solutions

26QuestionSlopeAssessment Practice

4 marks~6 minCriterion A

A distance–time graph shows a cyclist's journey from A to D, with coordinates A(0, 0), B(20, 5), C(60, 5), and D(80, 20), where time is in minutes and distance is in kilometres.

a

Calculate the slope of segment AB. [1]

b

Interpret what the slope of segment AB represents in the context of the cyclist's journey. Include appropriate units in your answer. [1]

c

The cyclist must maintain an average speed of at least 0.20 km/min over the entire journey from A to D. Justify whether this condition is met. [2]

Solutions

27QuestionGraphing linesAssessment Practice

4 marks~6 minCriterion D

A city's water authority monitors its reservoir during a drought. Sensors record the water volume relative to a target level, where each unit represents 10 million litres. At week 0 the reservoir is at

-2

units relative to target; by week 4 it is at

1

unit relative to target.

a

Calculate the slope of the line passing through

(0, -2)

and

(4, 1)

. [1]

b

Deduce the equation of the line in the form

y = mx + c

. [1]

c

Interpret what the slope and

y

-intercept reveal about the reservoir's situation, and justify whether the authority should still take action to safeguard the water supply. [2]

Solutions

28QuestionSlope-intercept formAssessment Practice

4 marks~6 minCriterion C

A mobile data plan charges a fixed monthly fee plus a constant rate per gigabyte used. The total cost, in dollars, is modelled by a linear function. The graph passes through

(0, -4)

and

(3, -2)

.

a

Calculate the slope of the line using the two given points. [1]

b

Deduce the equation of the line in slope-intercept form

y = mx + b

. [1]

c

A technician claims the monthly fixed fee is a cost saving of 4 dollars. Justify whether this claim accurately describes the overall pricing structure of the plan. [2]

Solutions

29QuestionGraphing parabolasAssessment Practice

4 marks~6 minCriterion C

A sports analyst models the height of a basketball shot using the equation

y = 2(x - 3)^2 - 8

, where

x

is the horizontal distance (metres) from the player and

y

is the height (metres) relative to the release point. The graph of this parabola is shown.

a

State the coordinates of the vertex of the parabola. [1]

b

Calculate the

x

-intercepts of the parabola. Show your working. [2]

c

The analyst claims the ball lands on the ground at two points either side of the player. Justify whether this claim is valid, using your results from part (b) and the context. [1]

Solutions

30QuestionAxis of symmetryAssessment Practice

6 marks~9 minCriterion B

A water fountain projects a jet of water from a nozzle at ground level. The water follows a parabolic path modelled by

h(x) = ax^2 + bx + c

, where

h

is the height (m) and

x

is the horizontal distance (m). The nozzle is at

x = 0

and the water lands at

x = d

. The designer wants to maximise the horizontal distance

d

the water travels before hitting the ground.

a

State the axis of symmetry of

h(x) = ax^2 + bx + c

and explain what it represents in this context. [2]

b

The designer claims the maximum horizontal distance is achieved when the vertex lies directly above the midpoint of the water's flight. Using the axis of symmetry, show that this requires

-\dfrac{b}{2a} = \dfrac{d}{2}

. [2]

c

A wall is located at

x = 3

m and has height 4 m. The designer proposes the model

h(x) = -x^2 + 6x

. Assess whether the designer's proposal should be accepted. [2]

Solutions

31QuestionFinding vertexAssessment Practice

4 marks~6 minCriterion D

A structural engineer models the cross-section of a cable support arch using the function

f(x) = 3(x - 1)^2 + k

, where

x

is the horizontal distance in metres from a reference point and

k

is an unknown constant. The vertex of the arch is at the point

(1, -3)

.

a

Deduce the value of

k

. [1]

b

Calculate the

y

-intercept of

f(x)

and interpret what this value represents in the context of the arch. [2]

c

The engineer considers adjusting the height of the arch by varying

k

. Justify which values of

k

are structurally valid if the arch must cross ground level (

f(x) = 0

) at two distinct points. [1]

Solutions

32QuestionGraphing exponentialAssessment Practice

8 marks~12 minCriterion D

A pharmaceutical company models the concentration of a drug in a patient's bloodstream as

C(t) = 200 \cdot (0.85)^t

mg/L, where

t

is the time in hours after injection. A nurse records the following measured concentrations:

Time (hours)	1	2	4	6
Measured concentration (mg/L)	170	144	104	75

a

Calculate the predicted concentration at each time point using the model. Present your results alongside the measured values. [2]

b

Calculate the percentage error at each time point using

\% \text{ error} = \frac{|\text{predicted} - \text{measured}|}{\text{measured}} \times 100\%

Round to one decimal place. [2]

c

Advise the nurse whether this model alone is sufficient for making clinical dosing decisions. In your response, discuss at least two limitations of the model and justify your advice by interpreting your percentage error results in a medical context. [4]

Solutions

33QuestionGraphing exponentialAssessment Practice

5 marks~8 minCriterion C

A bacteria culture grows according to

y = 2^x

, where

x

is time in hours and

y

is population in thousands. A researcher models a modified strain using

y = 2^{x+3} - 4

.

a

State the two transformations that map

y = 2^x

onto

y = 2^{x+3} - 4

. [1]

b

A student claims that the point

(0, 1)

on

y = 2^x

maps to

(3, -3)

on

y = 2^{x+3} - 4

. Justify why this claim is incorrect, and determine the correct image of

(0, 1)

. [2]

c

The modified strain is only viable when its population exceeds zero. Deduce the value of

x

at which the population first becomes positive, and assess whether this model is biologically valid from

x = 0

onwards. [2]

Solutions

34QuestionGraphing exponentialAssessment Practice

2 marks~3 minCriterion B

The graph shows two exponential functions: curve A,

y = 2^x

, and curve B,

y = \left(\dfrac{1}{2}\right)^x

.

Explain why the two curves are reflections of each other across the

y

-axis, using the relationship between the two functions. In your answer, state what this means for a general point

(a,\, b)

on curve A. [2]

Solutions

35QuestionInterpret compositeAssessment Practice

6 marks~9 minCriterion B

A factory uses two automated processes to price its products. Process

f

converts a raw material quantity

x

(kg) into a base unit count:

f(x) = 2x + 1

. Process

g

then converts the base unit count into a final price (dollars).

x

: 1, 2, 3, 4 —

f(x)

: 3, 5, 7, 9

x

: 3, 5, 7, 9 —

g(x)

: 9, 15, 21, 27

a

Calculate

g(f(2))

and

g(f(3))

using the tables above. [2]

b

Deduce an algebraic expression for

g(x)

. [2]

c

A bulk order requires 10 kg of raw material. The factory's budget allows a maximum spend of 60 dollars. Advise the factory manager whether the order should proceed, justifying your answer using

g(f(10))

. [2]

Solutions

36Questionf(g(x)) conceptAssessment Practice

2 marks~3 minCriterion D

A clothing store applies a 10% discount followed by an 8% sales tax on all items. Let

x

be the original price in dollars, where

f(x) = 0.9x

represents the discount and

g(x) = 1.08x

represents the tax.

Determine

g(f(x))

and

f(g(x))

, and hence advise the store manager which order of operations to advertise to best serve customer perception. [2]

Solutions

37QuestionEvaluate compositeAssessment Practice

4 marks~6 minCriterion C

The graphs of two functions,

f(x)

and

g(x)

, are shown below.

[Imagine two graphs are shown: one for

f(x)

and one for

g(x)

.

The graph of $f(x)$ is a straight line passing through the points $(0, 1)$ and $(2, 5)$ .
The graph of

g(x)

is a curve passing through the points

(1, 3)

and

(5, 7)

.]

Explain how you would determine the value of

g(f(2))

using these graphs. In your explanation, clearly show the order of operations and state the values you read from each graph at each step. Use complete sentences and proper mathematical notation.

Solutions

38QuestionInterpret contextAssessment Practice

4 marks~6 minCriterion C

A student records the height of a plant each day after it sprouts:

Day ( $n$ )	1	2	3	4
Height (cm)	3	6	11	18

a

Deduce whether the growth is linear or quadratic by calculating the first and second differences. [1]

b

Construct a general formula for the height

h

on day

n

. [2]

c

The student claims the plant will exceed 50 cm before Day 8. Justify whether this claim is supported by the model, and assess whether the formula is a reliable basis for this prediction. [1]

Solutions

39QuestionReal-life modelsAssessment Practice

5 marks~8 minCriterion B

A student records the battery percentage of a phone during a video call.

Time (min):

0, \ 10, \ 20, \ 30, \ 40, \ 50

Battery (%):

100, \ 87, \ 72, \ 55, \ 36, \ 15

a

Calculate the first differences in battery percentage between consecutive intervals. Justify, using these values, why a linear model

P(t) = mt + c

is not appropriate for this data. [2]

b

Using the data points at

t = 0

,

t = 10

, and

t = 20

, derive a quadratic model of the form

P(t) = at^2 + bt + c

. Show your system of equations and solve for

a

,

b

, and

c

. [2]

c

A phone is considered critically low when battery drops below 10 percent. Using your model, determine the time at which this occurs and advise whether the quadratic model should be used to make this prediction. [1]

Solutions

40QuestionPredictionAssessment Practice

6 marks~9 minCriterion D

A city planner is modelling the population growth of a town. Census data shows the population was 10 000 in 2000, 12 000 in 2005, 14 400 in 2010, and 17 280 in 2015. Two models are proposed, where

t

is years since 2000:

Model A (exponential):

P(t) = 10000 \times e^{0.0365t}

Model B (logistic):

\displaystyle P(t) = \frac{50000}{1 + 4e^{-0.05t}}

a

Calculate the predicted population in 2030 using both models. Show all working. [2]

b

Justify which model is more appropriate for long-term population prediction, referring to the structure of each model. [2]

c

The city planner must decide whether to commission a new water treatment plant with capacity for 30 000 residents. Advise the city planner whether either model provides sufficient justification to commission the plant for 2030, identifying one assumption of each model that could affect the reliability of this advice. [2]

Solutions

Functions — Free MYP4 Mathematics (Standard) Practice Questions