SL 1.8—Use of technology to solve systems of linear equations and polynomial equations - IB Questionbank | RevisionDojo

SL 1.8—Use of technology to solve systems of linear equations and polynomial equations Questionbank

Practice SL 1.8—Use of technology to solve systems of linear equations and polynomial equations with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

Solve for $x$ by using technology.

$2 x^{2}+4 x=7$

[2]

$x^{3}+4 x^{2}=6-x$

[3]

$2 x(x-1)=x+5$

[2]

Question 2

SLPaper 2

Use technology to solve for $x$ :

$2^{x}=x+3$

[3]

$x^{2}-\frac{5}{x}=0$

[2]

$x=\sqrt{5}-\sqrt{x}$

[2]

Question 3

SLPaper 2

Use technology to solve for $x$ :

$x+\sqrt[3]{x}+4=0$

[2]

$2 x^{2}-\sqrt{x+1}=0$

[3]

$x^{4}+2^{-x}-30=0$

[3]

Question 4

SLPaper 2

Solve the systems of linear equations using technology.

$\left\{ \begin{aligned} 3.2x - 5.4y &= -25 \\ 1.1x + 2.7y &= 23.3 \end{aligned} \right.$

[3]

$\left\{ \begin{aligned} 13a + 12b &= 104.5 \\ 14a - 5b &= 28.3 \end{aligned} \right.$

[3]

Question 5

HLPaper 1

Intersection of three planes

Find the coordinates of the point of intersection of the planes defined by the equations $x + y + z = 3$ , $x - y + z = 5$ and $x + y + 2z = 6$ .

[5]

Question 6

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 3x - 7y + z = -39 \\ 7x + 2y - z = 44 \\ -x + 7y - 5z = 55 \end{cases}$

[3]

$\begin{cases} 5a + 7b = 19 \\ 8b - 3c = 7 \\ 9a + 4c = 21 \end{cases}$

[3]

Question 7

SLPaper 2

The sum of three integers $A, B$ and $C$ is 20. The sum of $2 A$ and $3 B$ is 41. The value of $A$ is 7 more than the value of $C$ .

Write down 3 linear equations in $A, B$ and $C$ .

[3]

Find the numbers $A, B$ and $C$ .

[3]

Question 8

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 2x - 5y - 7z = -21 \\ x - 4y + 3z = 44 \\ x - y + z = 12 \end{cases}$

[3]

$\begin{cases} -x - y + z = -11 \\ 5x - 2y + 11z = -28 \\ x + 3y - 4z = 30 \end{cases}$

[3]

Question 9

HLPaper 2

Write down the inverse of the matrix $A = \begin{pmatrix} 1 & -3 & 0 \\ 2 & 0 & 1 \\ 4 & 1 & 3 \end{pmatrix}$ .

[2]

Hence or otherwise solve the system of equations: $\begin{aligned} x - 3y &= 1 \\ 2x + z &= 2 \\ 4x + y + 3z &= -1 \end{aligned}$

[4]

Question 10

SLPaper 2

Solve the following systems of linear equations using technology.

Solve the system:

\begin{cases} 3x + 7y = 41 \\ 5y - 2x = 21 \end{cases}

[3]

Solve the system:

\begin{cases} 9a + 2b = 29.5 \\ 2a + 7b = 29.5 \end{cases}

[3]

Paper

Level

Question 1

SLPaper 2

Solve for $x$ by using technology.

$2 x^{2}+4 x=7$

[2]

$x^{3}+4 x^{2}=6-x$

[3]

$2 x(x-1)=x+5$

[2]

Question 2

SLPaper 2

Use technology to solve for $x$ :

$2^{x}=x+3$

[3]

$x^{2}-\frac{5}{x}=0$

[2]

$x=\sqrt{5}-\sqrt{x}$

[2]

Question 3

SLPaper 2

Use technology to solve for $x$ :

$x+\sqrt[3]{x}+4=0$

[2]

$2 x^{2}-\sqrt{x+1}=0$

[3]

$x^{4}+2^{-x}-30=0$

[3]

Question 4

SLPaper 2

Solve the systems of linear equations using technology.

$\left\{ \begin{aligned} 3.2x - 5.4y &= -25 \\ 1.1x + 2.7y &= 23.3 \end{aligned} \right.$

[3]

$\left\{ \begin{aligned} 13a + 12b &= 104.5 \\ 14a - 5b &= 28.3 \end{aligned} \right.$

[3]

Question 5

HLPaper 1

Intersection of three planes

Find the coordinates of the point of intersection of the planes defined by the equations $x + y + z = 3$ , $x - y + z = 5$ and $x + y + 2z = 6$ .

[5]

Question 6

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 3x - 7y + z = -39 \\ 7x + 2y - z = 44 \\ -x + 7y - 5z = 55 \end{cases}$

[3]

$\begin{cases} 5a + 7b = 19 \\ 8b - 3c = 7 \\ 9a + 4c = 21 \end{cases}$

[3]

Question 7

SLPaper 2

The sum of three integers $A, B$ and $C$ is 20. The sum of $2 A$ and $3 B$ is 41. The value of $A$ is 7 more than the value of $C$ .

Write down 3 linear equations in $A, B$ and $C$ .

[3]

Find the numbers $A, B$ and $C$ .

[3]

Question 8

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 2x - 5y - 7z = -21 \\ x - 4y + 3z = 44 \\ x - y + z = 12 \end{cases}$

[3]

$\begin{cases} -x - y + z = -11 \\ 5x - 2y + 11z = -28 \\ x + 3y - 4z = 30 \end{cases}$

[3]

Question 9

HLPaper 2

Write down the inverse of the matrix $A = \begin{pmatrix} 1 & -3 & 0 \\ 2 & 0 & 1 \\ 4 & 1 & 3 \end{pmatrix}$ .

[2]

Hence or otherwise solve the system of equations: $\begin{aligned} x - 3y &= 1 \\ 2x + z &= 2 \\ 4x + y + 3z &= -1 \end{aligned}$

[4]

Question 10

SLPaper 2

Solve the following systems of linear equations using technology.

Solve the system:

\begin{cases} 3x + 7y = 41 \\ 5y - 2x = 21 \end{cases}

[3]

Solve the system:

\begin{cases} 9a + 2b = 29.5 \\ 2a + 7b = 29.5 \end{cases}

[3]

Paper

Level

Question 1

SLPaper 2

Solve for $x$ by using technology.

$2 x^{2}+4 x=7$

[2]

$x^{3}+4 x^{2}=6-x$

[3]

$2 x(x-1)=x+5$

[2]

Question 2

SLPaper 2

Use technology to solve for $x$ :

$2^{x}=x+3$

[3]

$x^{2}-\frac{5}{x}=0$

[2]

$x=\sqrt{5}-\sqrt{x}$

[2]

Question 3

SLPaper 2

Use technology to solve for $x$ :

$x+\sqrt[3]{x}+4=0$

[2]

$2 x^{2}-\sqrt{x+1}=0$

[3]

$x^{4}+2^{-x}-30=0$

[3]

Question 4

SLPaper 2

Solve the systems of linear equations using technology.

$\left\{ \begin{aligned} 3.2x - 5.4y &= -25 \\ 1.1x + 2.7y &= 23.3 \end{aligned} \right.$

[3]

$\left\{ \begin{aligned} 13a + 12b &= 104.5 \\ 14a - 5b &= 28.3 \end{aligned} \right.$

[3]

Question 5

HLPaper 1

Intersection of three planes

Find the coordinates of the point of intersection of the planes defined by the equations $x + y + z = 3$ , $x - y + z = 5$ and $x + y + 2z = 6$ .

[5]

Question 6

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 3x - 7y + z = -39 \\ 7x + 2y - z = 44 \\ -x + 7y - 5z = 55 \end{cases}$

[3]

$\begin{cases} 5a + 7b = 19 \\ 8b - 3c = 7 \\ 9a + 4c = 21 \end{cases}$

[3]

Question 7

SLPaper 2

The sum of three integers $A, B$ and $C$ is 20. The sum of $2 A$ and $3 B$ is 41. The value of $A$ is 7 more than the value of $C$ .

Write down 3 linear equations in $A, B$ and $C$ .

[3]

Find the numbers $A, B$ and $C$ .

[3]

Question 8

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 2x - 5y - 7z = -21 \\ x - 4y + 3z = 44 \\ x - y + z = 12 \end{cases}$

[3]

$\begin{cases} -x - y + z = -11 \\ 5x - 2y + 11z = -28 \\ x + 3y - 4z = 30 \end{cases}$

[3]

Question 9

HLPaper 2

Write down the inverse of the matrix $A = \begin{pmatrix} 1 & -3 & 0 \\ 2 & 0 & 1 \\ 4 & 1 & 3 \end{pmatrix}$ .

[2]

Hence or otherwise solve the system of equations: $\begin{aligned} x - 3y &= 1 \\ 2x + z &= 2 \\ 4x + y + 3z &= -1 \end{aligned}$

[4]

Question 10

SLPaper 2

Solve the following systems of linear equations using technology.

Solve the system:

\begin{cases} 3x + 7y = 41 \\ 5y - 2x = 21 \end{cases}

[3]

Solve the system:

\begin{cases} 9a + 2b = 29.5 \\ 2a + 7b = 29.5 \end{cases}

[3]

Paper

Level

Question 1

SLPaper 2

Solve for $x$ by using technology.

$2 x^{2}+4 x=7$

[2]

$x^{3}+4 x^{2}=6-x$

[3]

$2 x(x-1)=x+5$

[2]

Question 2

SLPaper 2

Use technology to solve for $x$ :

$2^{x}=x+3$

[3]

$x^{2}-\frac{5}{x}=0$

[2]

$x=\sqrt{5}-\sqrt{x}$

[2]

Question 3

SLPaper 2

Use technology to solve for $x$ :

$x+\sqrt[3]{x}+4=0$

[2]

$2 x^{2}-\sqrt{x+1}=0$

[3]

$x^{4}+2^{-x}-30=0$

[3]

Question 4

SLPaper 2

Solve the systems of linear equations using technology.

$\left\{ \begin{aligned} 3.2x - 5.4y &= -25 \\ 1.1x + 2.7y &= 23.3 \end{aligned} \right.$

[3]

$\left\{ \begin{aligned} 13a + 12b &= 104.5 \\ 14a - 5b &= 28.3 \end{aligned} \right.$

[3]

Question 5

HLPaper 1

Intersection of three planes

Find the coordinates of the point of intersection of the planes defined by the equations $x + y + z = 3$ , $x - y + z = 5$ and $x + y + 2z = 6$ .

[5]

Question 6

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 3x - 7y + z = -39 \\ 7x + 2y - z = 44 \\ -x + 7y - 5z = 55 \end{cases}$

[3]

$\begin{cases} 5a + 7b = 19 \\ 8b - 3c = 7 \\ 9a + 4c = 21 \end{cases}$

[3]

Question 7

SLPaper 2

The sum of three integers $A, B$ and $C$ is 20. The sum of $2 A$ and $3 B$ is 41. The value of $A$ is 7 more than the value of $C$ .

Write down 3 linear equations in $A, B$ and $C$ .

[3]

Find the numbers $A, B$ and $C$ .

[3]

Question 8

SLPaper 2

Solve the systems of linear equations using technology.

$\begin{cases} 2x - 5y - 7z = -21 \\ x - 4y + 3z = 44 \\ x - y + z = 12 \end{cases}$

[3]

$\begin{cases} -x - y + z = -11 \\ 5x - 2y + 11z = -28 \\ x + 3y - 4z = 30 \end{cases}$

[3]

Question 9

HLPaper 2

Write down the inverse of the matrix $A = \begin{pmatrix} 1 & -3 & 0 \\ 2 & 0 & 1 \\ 4 & 1 & 3 \end{pmatrix}$ .

[2]

Hence or otherwise solve the system of equations: $\begin{aligned} x - 3y &= 1 \\ 2x + z &= 2 \\ 4x + y + 3z &= -1 \end{aligned}$

[4]

Question 10

SLPaper 2

Solve the following systems of linear equations using technology.

Solve the system:

\begin{cases} 3x + 7y = 41 \\ 5y - 2x = 21 \end{cases}

[3]

Solve the system:

\begin{cases} 9a + 2b = 29.5 \\ 2a + 7b = 29.5 \end{cases}

[3]