Functions — Free IB MYP5 Mathematics (Standard) Questions

1QuestionFunction notation f(x)Concept Practice

4 marks~6 minCriterion A

A city's temperature on a winter morning is modelled by the linear function

f(x)

, where

x

is the time in hours after midnight and

f(x)

is the temperature in °C. The graph of

f(x)

passes through

(-1, 4)

and

(3, -2)

.

a

Explain how to read

f(-1)

and

f(3)

directly from the graph, stating both values. [1]

b

Calculate

f(3) - f(-1)

. [1]

c

Interpret the value found in part (b) in the context of the temperature model, and justify whether the temperature is rising or falling over this time interval. [2]

Solutions

2QuestionDefinition of a functionConcept Practice

2 marks~3 minCriterion C

A school nurse records the ages and heights of students in MYP 5. Two students are both 15 years old; one is 162 cm tall and the other is 178 cm tall.

Let

f: A \to H

represent the mapping from student age

a \in A

(years) to height

h \in H

(cm), where

A = \{14, 15, 16, 17, 18\}

and

H

is the set of plausible student heights in centimetres.

Justify whether

f

qualifies as a function, using the data above as evidence. [2]

Solutions

3QuestionQuadratic functionsConcept Practice

4 marks~6 minCriterion A

A landscape architect models the cross-section of a decorative arch using the function

y = x^2

. The design is adjusted for a new location, giving the function

y = (x - 3)^2 + 2

, where

x

and

y

are measured in metres.

a

Describe the transformations applied to the graph of

y = x^2

to obtain the graph of

y = (x - 3)^2 + 2

. [2]

b

Deduce the coordinates of the vertex and the equation of the axis of symmetry of

y = (x - 3)^2 + 2

. [1]

c

The arch must have its lowest point at least 1.5 m above ground level and no more than 4 m horizontally from

x = 0

. Justify whether the adjusted design satisfies both conditions. [1]

Solutions

4QuestionInterpret graphsConcept Practice

4 marks~6 minCriterion A

A car travels along a straight road. Its motion is shown on the distance–time graph below.

The graph passes through the points

(0, 0)

,

(5, 25)

, and

(10, 40)

, where time is in seconds and distance is in metres.

a

Calculate the speed of the car during the first 5 seconds. [1]

b

Calculate the speed of the car during the final 5 seconds. [1]

c

The road has a posted average-speed limit of 3.5 m/s for the full 10-second stretch. Calculate the car's average speed for the entire journey and justify whether the speed limit is exceeded. [2]

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

6QuestionReflectionsConcept Practice

4 marks~6 minCriterion A

A graphic designer is creating a symmetrical logo using triangle

ABC

with vertices

A(0, 0)

,

B(2, 3)

, and

C(4, 1)

. The triangle is reflected over the line

x = 2

to produce triangle

A'B'C'

, which forms the mirror half of the logo.

a

Deduce the coordinate rule for reflecting any point

(x, y)

over the line

x = 2

. [1]

b

Determine the coordinates of

A'

,

B'

, and

C'

. [2]

c

The designer claims the combined shape of triangle

ABC

and triangle

A'B'C'

is perfectly symmetrical about

x = 2

. Justify whether this claim is correct. [1]

Solutions

7QuestionPoint-slope formConcept Practice

4 marks~6 minCriterion A

A delivery company charges a fixed connection fee plus a constant rate per kilometre. A driver records that a 1 km trip costs 2 dollars and a 4 km trip costs 8 dollars.

a

Calculate the rate of change (cost per kilometre) using the two data points. [1]

b

Deduce the equation of the cost function in the form

y = mx + b

, where

x

is distance in kilometres and

y

is total cost in dollars. [2]

c

The company advertises "no connection fee." Justify whether this claim is accurate. [1]

Solutions

8QuestionGraphing parabolasConcept Practice

4 marks~6 minCriterion A

A sports analyst models the height of a basketball shot (in metres) using the function

f(x) = -x^2 + 4x + 12

, where

x

is the horizontal distance (in metres) from the player.

a

Determine the equation of the axis of symmetry of the parabola. [1]

b

Deduce the coordinates of the vertex of the parabola, showing your method. [2]

c

The basketball hoop is positioned at a height of 15 m and a horizontal distance of 3 m from the player. Justify whether the shot reaches the hoop, using the model to support your answer. [1]

Solutions

9QuestionGrowthConcept Practice

2 marks~3 minCriterion C

A population of bacteria doubles every hour. A researcher models the population using

y = a \cdot b^x

, where

x

is time in hours. The population is 4 000 at

x = 1

and 8 000 at

x = 2

.

a

Deduce the value of

b

, the growth factor, showing your method. [1]

b

Interpret what the value of

b

means in the context of this bacterial population. [1]

Solutions

10QuestionDecayConcept Practice

4 marks~6 minCriterion A

A radioactive substance decays according to the model

y = 80(0.5)^{t/5}

, where

y

is the mass in grams and

t

is the time in years. The graph passes through the points

(0, 80)

,

(5, 40)

, and

(10, 20)

.

a

Deduce the half-life of the substance from the graph. [1]

b

Calculate the mass remaining after 15 years. [1]

c

A laboratory requires at least 15 g of the substance to conduct a valid experiment. Advise the laboratory whether the experiment can be conducted after 15 years, justifying your answer with reference to your calculated value. [2]

Solutions

11QuestionEvaluate compositeConcept Practice

2 marks~3 minCriterion A

The mapping diagram below shows how the functions

f(x)

and

g(x)

map values. Find the value of

g(f(3))

.

Solutions

12QuestionFunction notation f(x)Assessment Practice

6 marks~9 minCriterion B

A mobile data plan charges a fixed monthly fee plus a constant rate per gigabyte (GB) used. Recorded charges are:

Data used (GB)	1	2	3	4	5
Monthly charge (dollars)	7	10	13	16	19

The total monthly charge is modelled by

f(x) = ax + b

, where

x

is the number of GB used.

a

Deduce the values of

a

and

b

, and hence state the formula for

f(x)

. [3]

b

The plan advertises a maximum possible charge of 40 dollars per month. Justify whether this claim is consistent with a customer who uses 12 GB. [2]

c

Interpret the meaning of

f(0)

in this context. [1]

Solutions

13QuestionEvaluating functionsAssessment Practice

2 marks~3 minCriterion D

A small business models its weekly production cost using

C(x) = 5x + 20

, where

x

is the number of items produced and

C(x)

is the cost in dollars.

a

Calculate

C(10)

and

C(25)

. [1]

b

The business considers scaling production to 1000 items per week. Justify whether the linear model

C(x) = 5x + 20

is a reliable predictor of costs at this scale. [1]

Solutions

14QuestionQuadratic functionsAssessment Practice

6 marks~9 minCriterion B

A landscape architect models the cross-section of a curved garden bed using a quadratic function

y = ax^2 + bx + c

, where

y

represents the height (cm) of the bed at horizontal position

x

(m).

Measurements taken at equal intervals give:

x

(m):

0, \ 1, \ 2, \ 3, \ 4

y

(cm):

3, \ 6, \ 11, \ 18, \ 27

a

Calculate the first differences and second differences of the

y

values. [2]

b

Deduce the values of

a

,

b

, and

c

, and state the equation of the quadratic function. [2]

c

The architect requires the garden bed to reach a height of at least 40 cm. Justify whether this condition is met within the measured interval

0 \leq x \leq 4

. [2]

Solutions

15QuestionIdentify from graphsAssessment Practice

2 marks~3 minCriterion C

A biologist records two measurements of a growing plant over

x

weeks:

- Plant height (cm), modelled by

y = 2x + 5

- Leaf area (cm²), modelled by

y = x^2 + 3

a

Identify which equation models plant height and which models leaf area, giving a reason for each. [1]

b

A classmate claims both measurements could equally well be modelled by a linear function for the first four weeks. Justify whether this claim is valid, and explain what this means for the biologist's conclusions about long-term growth. [1]

Solutions

16QuestionRational functionsAssessment Practice

5 marks~8 minCriterion D

A hospital monitoring system tracks a patient's drug concentration using the model

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

, where

x

is time in hours after administration (

x > 3

) and

g(x)

is concentration in mg/L. The parent function is

f(x) = \dfrac{1}{x}

.

a

State the equations of the vertical and horizontal asymptotes of

f(x)

. [1]

b

Explain how each transformation applied to

f(x)

shifts the asymptotes to produce those of

g(x)

, stating the equation of each asymptote of

g(x)

. [2]

c

The system triggers a safety alert when concentration remains above 2 mg/L. Justify whether the safety alert ever automatically clears for

x > 3

, using the horizontal asymptote of

g(x)

as the basis for your reasoning. [2]

Solutions

17QuestionRange 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

18QuestionRange from graphsAssessment Practice

5 marks~8 minCriterion C

A hospital monitoring system records a patient's oxygen saturation level,

f(x)

(%), over a 24-hour period. The piecewise function

f(x)

is represented by the graph below.

The graph consists of three parts:
- a horizontal segment at

y = 4

for

-5 \leq x < -2

, with a closed circle at

(-5, 4)

and an open circle at

(-2, 4)

- a downward-opening parabola with vertex

(0, 3)

, passing through

(-2, 1)

and

(2, 1)

, with closed circles at both endpoints
- a curve for

x > 2

starting at

(2, 1)

with a closed circle, decreasing toward the asymptote

y = -1

as

x \to \infty

, never reaching

y = -1

a

State the

y

-value produced by the horizontal segment and identify whether it is included in the range. [1]

b

Deduce the set of

y

-values contributed by the parabola and by the asymptotic curve, showing your reasoning for each endpoint. [2]

c

Interpret the complete range of

f(x)

in interval notation, and justify whether the gap in the range gives cause for clinical concern about the reliability of the monitoring data. [2]

Solutions

19QuestionRange from graphsAssessment Practice

4 marks~6 minCriterion A

A structural engineer models the vertical clearance beneath four cable-stay bridge sections using quadratic functions. Each function gives height

y

(metres) at horizontal position

x

(metres), with the vertex representing the lowest or highest point of the cable profile.

The four cable profiles are:

f(x) = x^2

, vertex

(0,\ 0)

, opens upward

g(x) = x^2 + 3

, vertex

(0,\ 3)

, opens upward

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

, vertex

(2,\ 0)

, opens upward

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

, vertex

(-1,\ 4)

, opens downward

a

State the range of each function. [1]

b

Analyse the relationship between the vertex

y

-coordinate, the direction of opening, and the range of each profile. Deduce a general rule connecting the sign of

a

and the vertex

y

-coordinate

k

to the range of

a(x-h)^2 + k

. [2]

c

A new bridge section requires a cable profile

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

whose height never exceeds

-3

m relative to the reference datum, so the range must be

(-\infty,\ -3]

. Construct a valid function

m(x)

satisfying this condition, and justify whether a cable profile with range

(-\infty,\ -3]

is physically safe for vehicles passing beneath the bridge. [1]

Solutions

20QuestionRange from graphsAssessment Practice

3 marks~5 minCriterion D

A drone delivery company models the height of a package above ground during a short flight using the function

h(t) = t^2 - 4t + 3

, where

h

is the height in metres and

t

is the time in seconds. The graph of

h(t)

shows a parabola with vertex

(2, -1)

that opens upwards.

a

Deduce the range of

h(t)

. [1]

b

The package must remain at or above ground level (

h \geq 0

) throughout the flight. Justify whether this model is physically valid, using your answer to part (a). [2]

Solutions

21QuestionPlot 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

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

23QuestionPlot quadratic functionsAssessment Practice

4 marks~6 minCriterion D

A landscape architect models the cross-section of a decorative arch using the function

y = (x - 3)^2 + 2

, where

x

and

y

are measured in metres. The parent function is

y = x^2

.

a

State the coordinates of the vertex of

y = (x - 3)^2 + 2

and write down the equation of its axis of symmetry. [2]

b

Explain the two transformations that map the graph of

y = x^2

onto the graph of

y = (x - 3)^2 + 2

. [1]

c

The arch must clear a pathway centred at

x = 3

that is 4 metres wide and 2.5 metres tall. Advise the architect whether the arch satisfies both clearance requirements, supporting your advice with calculations. [1]

Solutions

24QuestionStretch/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

25QuestionStretch/compressionAssessment Practice

6 marks~9 minCriterion D

A graphic designer is resizing a logo for a billboard and a business card. The logo's outline is defined by vertices

A(2,\ 1)

,

B(6,\ 1)

,

C(7,\ 4)

, and

D(1,\ 4)

. The designer applies a vertical stretch by factor

2.5

, followed by a horizontal compression by factor

0.4

.

a

Determine the coordinates of the transformed vertices

A'

,

B'

,

C'

, and

D'

after both transformations are applied in the given order. [2]

b

Calculate the area of the original logo and the area of the transformed logo. Show that the two areas are equal, and explain why this result occurs. [2]

c

Advise the designer whether this transformation is suitable for both media, justifying your answer with reference to the effect of non-uniform scaling on the logo's proportions and the significance of the equal-area result. [2]

Solutions

26QuestionSlopeAssessment 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

27QuestionGraphing linesAssessment Practice

4 marks~6 minCriterion D

A city's water authority monitors reservoir levels during a drought. Sensors show the water volume is decreasing at a constant rate. At the start of monitoring (week 0), the reservoir holds

-2

units relative to the target level, and by week 4 it holds

1

unit relative to the target level, where each unit represents 10 million litres.

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 advise the authority whether action is still required to safeguard the water supply. [2]

Solutions

28QuestionParallel & perpendicularAssessment Practice

2 marks~3 minCriterion C

A city planner is designing two straight pedestrian pathways that must cross at a right angle to ensure safe sightlines at the intersection.

The first pathway has a slope of

m_1 = \dfrac{2}{3}

.

a

Deduce the slope of the second pathway. [1]

b

The planner states: "A steeper crossing angle improves pedestrian safety." Justify whether the slopes of the two pathways satisfy the planner's safety condition. [1]

Solutions

29QuestionAxis 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

30QuestionStandard formAssessment Practice

4 marks~6 minCriterion C

A road engineer models the cross-section of a speed bump using the function

f(x) = 2x^2 - 8x + 6

, where

x

is the horizontal distance in metres from a reference point and

f(x)

is the height in metres. The graph of

f(x)

is provided.

a

State the coordinates of the

y

-intercept of

f(x)

. [1]

b

Find the

x

-intercepts of

f(x)

by solving

f(x) = 0

. [1]

c

A colleague proposes the alternative model

g(x) = x^2 - 4x + 3

. Justify whether

f(x)

or

g(x)

produces the steeper speed-bump profile, and advise the engineer which model to select if road safety regulations require the steepest possible cross-section. [2]

Solutions

31QuestionVertex formAssessment Practice

6 marks~9 minCriterion D

A company models its daily profit

P

(in dollars) from selling a product at a price of

x

dollars per unit using the quadratic function

P(x) = -2(x - 50)^2 + 5000.

a

Interpret the vertex of

P(x)

to state the maximum daily profit and the price per unit at which it occurs. [1]

b

The break-even points occur when

P(x) = 0

. Solve

-2(x - 50)^2 + 5000 = 0

to find the two prices at which the company breaks even. [2]

c

The company is considering setting the price at either 20 dollars or 80 dollars per unit. Calculate

P(20)

and

P(80)

, then advise the company which price to set, justifying your recommendation with reference to both the mathematical result and one limitation of the model. [3]

Solutions

32QuestionGraphing 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

33QuestionCompare growthAssessment Practice

2 marks~3 minCriterion D

A social media post goes viral. The number of shares is modelled by two competing predictions: a linear model

f(x) = 2x + 1

and an exponential model

g(x) = 2^x

, where

x

is the number of days after posting and the output is in thousands of shares.

A campaign is considered successful if it exceeds 10 thousand shares by day 5.

a

Calculate

f(5)

and

g(5)

. [1]

b

Both models predict a successful campaign. Justify which model a campaign manager should rely on for long-term planning, and defend your choice using the day-5 values and the growth behaviour of each model. [1]

Solutions

34QuestionEvaluate compositeAssessment Practice

6 marks~9 minCriterion B

A computer simulation models the spread of a notification through a network. At each step, every active node activates exactly one new node and remains active. The number of active nodes at step

n

is modelled by

f(x) = 2x + 1

, applied repeatedly from

x_1 = 1

. The sequence is defined by

x_{k+1} = f(x_k)

for all positive integers

k

.

a

Calculate the first five terms of the sequence. [2]

b

Deduce a formula for

x_n

in terms of

n

, showing clearly how the pattern in part (a) leads to your general expression. [2]

c

Prove by mathematical induction that your formula holds for all positive integers

n

. [2]

d

The network has a capacity of 1000 active nodes. Using your formula, advise the network administrator at which step they should intervene to prevent the capacity being exceeded, justifying your answer with reference to the simulation. [2]

Solutions

35QuestionInterpret compositeAssessment Practice

2 marks~3 minCriterion D

A toy factory models the painting cost

C

(in dollars) of a car as a function of its surface area

A

(in cm²), and the surface area as a function of a single dimension

d

(in cm), such that

A(d) = 6d^2

and

C(A) = 0.05A

.

a

Explain how the composite function

C(A(d))

models the total painting cost in terms of dimension

d

, showing the chain of dependence

d \rightarrow A \rightarrow C

. [1]

b

Interpret what a doubling of dimension

d

means for the painting cost, and justify whether this composite model is sufficient for a factory manager to use when pricing larger car models. [1]

Solutions

36QuestionEvaluate compositeAssessment Practice

4 marks~6 minCriterion C

The graphs of two functions,

f(x)

and

g(x)

, are shown below.

[The image should show two graphs on the same coordinate plane.

f(x)

is a curve passing through points (0, 2), (1, 3), (2, 4), (3, 3), and (4, 2).

g(x)

is a straight line passing through points (0, 1), (1, 2), (2, 3), and (3, 4).]

Explain how you would use the graphs to estimate the value of

f(g(2))

. Show your reasoning and state the approximate final value.

Solutions

37QuestionReal-life modelsAssessment Practice

4 marks~6 minCriterion B

A student compares two savings plans. The total saved (in dollars) at the end of each week is recorded below.

Week (

n

): 1, 2, 3, 4, 5

Plan A (

S

): 50, 100, 150, 200, 250

Plan B (

S

): 50, 105, 170, 245, 330

a

Deduce the type of pattern (linear or quadratic) for each plan and derive a formula for total savings

S

after

n

weeks. [2]

b

Construct a prediction for the total savings under each plan after 10 weeks. [1]

c

Advise the student which savings plan to follow over a 52-week year, supporting your recommendation with calculated evidence. [1]

Solutions

38QuestionReal-life modelsAssessment Practice

6 marks~9 minCriterion C

A concert venue models ticket sales using a linear demand function

Q = aP + b

, where

P

is the price in dollars per ticket and

Q

is the number of tickets sold.

Price $P$ (dollars)	20	60
Quantity $Q$ (tickets)	800	400

a

Deduce the values of

a

and

b

, and write down the demand function

Q(P)

. [2]

b

Construct the revenue function

R(P) = P \cdot Q(P)

, expressing it in the form

R(P) = \alpha P^2 + \beta P

. [2]

c

The venue manager claims that setting a ticket price of 40 dollars maximises revenue. Justify whether this claim is correct, showing full working to support your conclusion. [2]

Solutions

39QuestionPredictionAssessment Practice

2 marks~3 minCriterion D

A ski slope is modelled by the line

y = 2x + 1

, where

x

is the horizontal distance (m) and

y

is the vertical height (m).

Safety regulations state that a ski slope must make an angle of less than 60° with the horizontal to be classified as a beginner slope.

Justify whether this slope qualifies as a beginner slope. [2]

Solutions

40QuestionInterpret contextAssessment Practice

6 marks~9 minCriterion A

A taxi company charges a fixed flag-fall fee plus a constant rate per kilometre travelled. The table below shows sample fares.

Distance (km)	1	3	5
Total cost (dollars)	7.50	14.50	21.50

a

Deduce the rate of change and the flag-fall fee, and hence write the general formula for the total cost

C

(in dollars) in terms of distance

d

(in km). [3]

b

A rival company charges according to

C = 4.20d + 2.00

. Construct a calculation to determine the distance at which both companies charge the same fare. [1]

c

A passenger must travel 8 km and has exactly 32.00 dollars. Advise the passenger which company to use, justifying your recommendation with numerical evidence. [2]

Solutions

Functions — Free MYP5 Mathematics (Standard) Practice Questions