IB Mathematics Applications & Interpretation Topic SL…

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Paper

Level

Difficulty

Question 1

HLPaper 2

View answer

A flare's height is modelled by $h(t)=-t^3+7t^2+2t+1$ , where $h$ is in metres and $t$ is in seconds. In the first two parts, use technology where appropriate.

(a)

Find the time when the flare hits the ground, giving your answer correct to three significant figures.

[4]

(b)

A signal reading is modelled by $P(u)=u^3-4u^2-11u+20$ . Write down an equation whose solutions are the $u$ -values for which the signal reading is $8$ , and solve it.

[4]

(c)

The cost of a subscription is modelled by $C(t)=240(1.09)^t$ , where $C$ is in dollars and $t$ is in years. Find the value of $t$ when the cost reaches $600$ .

[4]

(d)

Hence the first whole year for which the cost exceeds $600$ .

[2]

Question 2

SL & HLPaper 1

View answer

The amount of substrate in a chemical reactor, $S$ , in kilograms, is modelled by $S(t) = -0.5t^3 + 5.75t^2 - 18.25t + 33, \quad 0 \leq t \leq 7,$ where $t$ is the time, in hours, since the start of the reaction.

The chemist records the times at which $S(t)=20$ .

(a)

Write down the initial amount of substrate in the reactor.

[1]

(b)

Find the three values of $t$ at which $S(t)=20$ .

[4]

(c)

Hence the total number of distinct times during the $7$ -hour period at which $S(t)=20$ .

[1]

Question 3

SL & HLPaper 1

View answer

A bakery sells three types of bread: sourdough, multigrain, and rye. The table below shows the number of loaves sold of each type to three customers on a particular day, and the total amount each customer paid.

Customer	Sourdough	Multigrain	Rye	Total ($$$)
Alex	3	2	1	38.00
Brenda	2	4	3	61.00
Cyrus	1	1	4	44.80

Let $x$ , $y$ , and $z$ be the prices, in dollars, of one loaf of sourdough, multigrain, and rye respectively.

(a)

Write down a system of three linear equations in $x$ , $y$ , and $z$ to represent this information.

[2]

(b)

Use technology to solve your system and find the price of each type of bread.

[3]

(c)

Daria buys $5$ sourdough loaves, $3$ multigrain loaves, and $2$ rye loaves.

the total amount Daria pays.

[1]

Question 4

SL & HLPaper 1

View answer

A solid metal sculpture is shaped as a cuboid with length $x$ cm, width $(x+2)$ cm, and height $(x+5)$ cm, where $x>0$ . The volume of the sculpture is $350$ cm $^3$ .

(a)

Show that $x^3 + 7x^2 + 10x - 350 = 0$ .

[2]

(b)

Use technology to solve the equation in part (1) and find the value of $x$ .

[2]

(c)

Hence find the total surface area of the sculpture.

[2]

Question 5

SL & HLPaper 1

View answer

A community theatre sells two types of tickets for its annual play: adult tickets for $ $32$ each and student tickets for $ $15$ each. At one performance, the theatre sold $240$ tickets in total and collected $ $6065$ in ticket revenue.

Let $x$ be the number of adult tickets sold and $y$ be the number of student tickets sold.

(a)

Write down a system of two linear equations in $x$ and $y$ to represent this situation.

[2]

(b)

Use technology to solve your system and find the number of each type of ticket sold.

[2]

(c)

the percentage of all tickets sold that were student tickets.

[2]

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Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Difficulty

Question 1

HLPaper 2

View answer

A flare's height is modelled by $h(t)=-t^3+7t^2+2t+1$ , where $h$ is in metres and $t$ is in seconds. In the first two parts, use technology where appropriate.

(a)

Find the time when the flare hits the ground, giving your answer correct to three significant figures.

[4]

(b)

A signal reading is modelled by $P(u)=u^3-4u^2-11u+20$ . Write down an equation whose solutions are the $u$ -values for which the signal reading is $8$ , and solve it.

[4]

(c)

The cost of a subscription is modelled by $C(t)=240(1.09)^t$ , where $C$ is in dollars and $t$ is in years. Find the value of $t$ when the cost reaches $600$ .

[4]

(d)

Hence the first whole year for which the cost exceeds $600$ .

[2]

Question 2

SL & HLPaper 1

View answer

The chemist records the times at which $S(t)=20$ .

(a)

Write down the initial amount of substrate in the reactor.

[1]

(b)

Find the three values of $t$ at which $S(t)=20$ .

[4]

(c)

Hence the total number of distinct times during the $7$ -hour period at which $S(t)=20$ .

[1]

Question 3

SL & HLPaper 1

View answer

Customer	Sourdough	Multigrain	Rye	Total ($$$)
Alex	3	2	1	38.00
Brenda	2	4	3	61.00
Cyrus	1	1	4	44.80

Let $x$ , $y$ , and $z$ be the prices, in dollars, of one loaf of sourdough, multigrain, and rye respectively.

(a)

Write down a system of three linear equations in $x$ , $y$ , and $z$ to represent this information.

[2]

(b)

Use technology to solve your system and find the price of each type of bread.

[3]

(c)

Daria buys $5$ sourdough loaves, $3$ multigrain loaves, and $2$ rye loaves.

the total amount Daria pays.

[1]

Question 4

SL & HLPaper 1

View answer

A solid metal sculpture is shaped as a cuboid with length $x$ cm, width $(x+2)$ cm, and height $(x+5)$ cm, where $x>0$ . The volume of the sculpture is $350$ cm $^3$ .

(a)

Show that $x^3 + 7x^2 + 10x - 350 = 0$ .

[2]

(b)

Use technology to solve the equation in part (1) and find the value of $x$ .

[2]

(c)

Hence find the total surface area of the sculpture.

[2]

Question 5

SL & HLPaper 1

View answer

Let $x$ be the number of adult tickets sold and $y$ be the number of student tickets sold.

(a)

Write down a system of two linear equations in $x$ and $y$ to represent this situation.

[2]

(b)

Use technology to solve your system and find the number of each type of ticket sold.

[2]

(c)

the percentage of all tickets sold that were student tickets.

[2]

Unlock all 15 questions with a free account

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

IB Mathematics Applications & Interpretation SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank

IB Mathematics Applications & Interpretation SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank

Unlock all 15 questions with a free account

Unlock all 15 questions with a free account

IB Mathematics Applications & Interpretation SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank

IB Mathematics Applications & Interpretation SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank

Unlock all 15 questions with a free account

IB Mathematics Applications & Interpretation (AI) Topic SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank

Unlock all 15 questions with a free account

IB Mathematics Applications & Interpretation (AI) Topic SL 1.8—use of Technology to Solve Systems of Linear Equations and Polynomial Equations Questionbank