Math Written Exam Demo
Below, you can find sample math written exam based on the selected program.
We recommend reading key terms in the Glossary first.
We recommend reading key terms in the Glossary first.
Written Exam Format
Please read the short version below (1 minute).
Exam in 6 steps
You need:
Exam in 6 steps
- Install proctor app.
- Start exam on Sunday, March 29 at 09:00 UTC (at 13:00 Europe/Astrakhan (+04:00);).
- Solve problems on paper (120 min).
- Get QR code.
- Photograph solutions.
- Upload and finish.
You need:
- computer with camera + mic;
- smartphone with camera;
- stable internet.
Details
- You will get two email links: familiarization and exam.
- Complete all familiarization steps in advance.
- Practice on the same device and network you will use for the exam.
- Install Constructor Proctor and verify camera/microphone beforehand.
- Add the exam to your calendar: Google Calendar or ICS file.
- The exam starts on Sunday, March 29 at 09:00 UTC.
- 13:00 Europe/Astrakhan (+04:00); 10:00 London; 11:00 Venice and Belgrade; 12:00 Nicosia, Kyiv and Moscow; 13:00 Yerevan; 14:00 Almaty and Tashkent; 15:00 Bishkek.
- The exam must be started no later than 09:30 UTC.
- At start, Constructor Proctor opens and checks your device.
- After checks, a secure full-screen browser is launched.
- You have 120 minutes for solving.
- You can solve problems in any order.
- Provide full written solutions on paper in English.
- Calculators, help from others, generative AI, and tab switching are prohibited.
- Smartphone use during solving is prohibited.
- After 120 minutes (or when you click finish), you get a QR code.
- You have 10 minutes for photographing and uploading your solutions.
- Scan the QR code with your smartphone and open the upload page.
- Take photos of all solution pages and upload them.
- Complete the exam in the proctoring app.
- Laptop or desktop: Windows 10+ or macOS 11+ (Big Sur).
- Working camera, microphone, and stable internet (5 Mbit/s).
- Smartphone with camera, internet, and up-to-date browser.
- QR code reader app and ability to use it.
- Linux, Chromebooks, iPads, tablets, and smartphones as main device are not supported.
Devices and software
— Learner guide for Windows: Constructor Proctor Learner Guide and for MacOS: Constructor Proctor Learner Guide.
— Detailed installation instructions:
Windows
- Participation in the written exam requires a laptop or desktop computer (with Windows 10+ or macOS 11+ (Big Sur)) equipped with a working camera and microphone, and a stable internet connection (2Mbit/s).
- A smartphone with a working camera, connected to the internet, with an up-to-date browser is also required. Additionally, you will need a QR code reader app and the ability to use it.
- Detailed computer requirements:
— Learner guide for Windows: Constructor Proctor Learner Guide and for MacOS: Constructor Proctor Learner Guide.
— Detailed installation instructions:
Windows
- Open the learner guide at Constructor Proctor Learner Guide.
- Open the downloaded file once the download completes.
- The Constructor Proctor Desktop Application will complete a brief install and will launch automatically.
- If you’ve used Constructor Proctor before, it will launch automatically, downloading and installing any necessary updates before beginning the System Check.
- Open the learner guide at Constructor Proctor Learner Guide.
- Open the downloaded file once the download completes.
- In the opened window, drag the Constructor Proctor application into the Applications folder.
- Open the Applications folder and run the Constructor Proctor application.
- The Constructor Proctor Desktop Application will complete a brief install and will launch automatically.
- If you’ve used Constructor Proctor before, it will launch automatically, downloading and installing any necessary updates before beginning the System Check.
- You can see examples of exam problems below.
- The problems will be provided in English.
- Detailed solutions must be provided, written on paper in English.
- Correct answers without explanations will receive 0 marks.
- Partial marks will be awarded for incomplete solutions or minor mistakes.
- Proper drawings for geometry problems are highly recommended.
- It is not necessary to solve all problems to pass, but try to solve as many as possible.
- The problems can be solved in any order.
- During the exam, you are allowed to use a pen, pencil, and paper.
- The use of calculators, assistance from others, generative models (ChatGPT, DeepSeek, etc.), or switching between browser tabs is prohibited.
- If needed, you may request translation assistance for any term or ask a question about a problem via the support chat (the "?" button after each problem).
- You will receive an email with two links: one for familiarizing yourself with the interface, and one for the exam.
- It is strongly recommended that you go through all the exam steps using the familiarization link, in order to set up and configure the application in advance and ensure that there are no technical issues with your equipment.
- The exam link can be opened in advance, but the exam can only be started on Sunday, March 29 at 09:00 UTC (13:00 Europe/Astrakhan (+04:00); 10:00 London; 11:00 Venice and Belgrade; 12:00 Nicosia, Kyiv and Moscow; 13:00 Yerevan; 14:00 Almaty and Tashkent; 15:00 Bishkek). Add the event to your calendar or download the ICS file
- The exam must be started no later than 09:30 UTC.
- After the exam begins, you will be directed to the launch page for the Constructor Proctor proctoring application.
- After launching the Constructor Proctor application, it will check your device for a working camera, microphone, absence of a second monitor, internet connection, etc.
- The application will then take your photo.
- After all checks are completed, a secure browser displaying the exam conditions will be launched. The browser will operate in full-screen mode and can only be minimized after the exam is finished. Switching between tabs, navigating to other pages, and taking screenshots is prohibited.
- Using a smartphone during the problem-solving phase is prohibited.
- Examples of problems can be viewed below. The problem interface will be identical to the testing interface.
- After the 120 minutes allotted for recording your solutions (or after clicking the "finish" button), you will receive a QR code with a link to the solution upload page.
- Next, you will need to scan the QR code with your smartphone, open the solution upload page, take photos of all your solutions, and upload them.
- After that, complete the exam within the proctoring application.
- In the event of technical issues, loss of internet connection, etc., you will need to reopen the exam link and restart the proctoring application.
Mathematics Glossary to Prepare for TLF Written Exam
Absolute Value
The non-negative value of a number without regard to its sign.
Acute angle
An angle whose measure is strictly between 0° and 90°.
Angle
A figure formed by two lines or line segments, measured in degrees.
Angle Bisector
A line or ray that divides an angle into two equal parts.
Arbitrary Values
Values chosen for substitution by judgment and not following a specific pattern or rule.
Arithmetic Sequence
A sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
Bounded
A set is called bounded if all of its points are within a certain (finite) distance of each other.
Circumference
The distance around the boundary of a circle.
Coefficient
A number used to multiply a variable, indicated in front of the variable.
Commutative
An operation in which changing the order of the operands does not change the result (e.g., a + b = b + a).
Composite Figure
A shape or figure made up of smaller, simpler shapes.
Composite Function
A function that is formed when one function is applied to the result of another function.
Contradiction
A type of proof that establishes the truth of a statement by assuming the opposite and showing an impossibility.
Decimal Representation
The expression of a number in base-10 numeral system.
Diameter
The length of a straight line segment that extends through the center of a circle and ends at the circumference.
Domain
The set of x-values that are inputs to a function.
Equilateral
A triangle with three equal sides.
Exact Form
A representation of a number that uses radicals, fractions, or constants like pi, without approximating or rounding.
Expansion
The process of multiplying to remove brackets from an expression.
Exponent
A power to which a number is raised.
Factorial
n! is the product of all integers between 1 and n.
Factorise
To express a mathematical expression as a product of its factors.
Fraction
A number that represents a part of a whole, expressed as a quotient.
Greatest Common Factor of two or more numbers
The largest number that divides two or more integer numbers exactly.
Incircle
A circle inscribed within a triangle, tangent to all its sides.
Integers
All whole numbers, both positive and negative.
Interior Angle
An angle inside a polygon.
Irrational Number
A number that cannot be expressed as a fraction of two integers.
Isosceles
A triangle with two equal sides called legs. The side that is not equal is called the base.
Least Common Multiple of two or more numbers
The smallest positive integer that is divisible by all the numbers in question.
Line Segment
A part of a line with two endpoints.
Linear Equations
Equations that form a straight line when graphed, where the highest power is 1.
Logarithm
The exponent by which a base number must be raised to get a given number. For example, log₂(8) = 3 because 2³ = 8.
Magnitude
The size or length of a vector.
Maximum
The highest value in a dataset.
Median (in geometry)
A line segment joining a vertex of a triangle to the midpoint of the opposite side.
Midpoint
The point that divides a line segment into two equal parts.
Minimum
The lowest value in a dataset.
Mode
The most frequently occurring number in a dataset.
Obtuse
An angle measuring between 90° and 180°.
Origin
The point (0,0) where the x and y axes intersect.
Outlier
A data point that significantly differs from other values in a dataset.
Parameters
Constants or variables in a function that define its specific form but not its general nature.
Perimeter
The sum of all sides of a polygon.
Polygon
A closed figure with three or more straight sides.
Power
A number raised to an exponent.
Proof by Induction
A proof method in which each step is justified based on a base case and an induction step.
Quadratic Expressions
Expressions where the highest power is 2.
Quadrilateral
A polygon with four sides and four angles.
Quotient
The result of division.
Range
The difference between the highest and lowest values in a dataset.
Ratio
A relationship between two numbers indicating how many times the first number contains the second.
Regular polygon
A polygon with all sides and angles equal.
Right Angle
An angle of 90°.
Roots of a Polynomial
Values of the variable that satisfy the equation when the polynomial is set to zero.
Scale Factor
The number by which an object is enlarged or reduced.
Scalene
A triangle in which all three sides (and all three angles) are different in length and measure.
Sequence
An ordered list of numbers following a particular pattern.
Slope
A measure of the steepness of a line, usually expressed as the ratio of the vertical change to the horizontal change (rise over run).
Substitution
Replacing a value for a variable.
Subtended
An angle or arc is said to be subtended when it is formed or defined by lines or segments drawn from its endpoints to a point.
Superimpose
To place one object on top of another.
Surd
A number in root or radical form.
System of Inequalities
A set of two or more inequalities with the same variables.
Tangent
A line that touches a circle at exactly one point.
Variable
A quantity that can change in value.
Vertex
The point where two or more edges meet in a polygon.
X-Intercept
The point where a line crosses the x-axis.
Y-Intercept
The point where a line crosses the y-axis.
The non-negative value of a number without regard to its sign.
Acute angle
An angle whose measure is strictly between 0° and 90°.
Angle
A figure formed by two lines or line segments, measured in degrees.
Angle Bisector
A line or ray that divides an angle into two equal parts.
Arbitrary Values
Values chosen for substitution by judgment and not following a specific pattern or rule.
Arithmetic Sequence
A sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
Bounded
A set is called bounded if all of its points are within a certain (finite) distance of each other.
Circumference
The distance around the boundary of a circle.
Coefficient
A number used to multiply a variable, indicated in front of the variable.
Commutative
An operation in which changing the order of the operands does not change the result (e.g., a + b = b + a).
Composite Figure
A shape or figure made up of smaller, simpler shapes.
Composite Function
A function that is formed when one function is applied to the result of another function.
Contradiction
A type of proof that establishes the truth of a statement by assuming the opposite and showing an impossibility.
Decimal Representation
The expression of a number in base-10 numeral system.
Diameter
The length of a straight line segment that extends through the center of a circle and ends at the circumference.
Domain
The set of x-values that are inputs to a function.
Equilateral
A triangle with three equal sides.
Exact Form
A representation of a number that uses radicals, fractions, or constants like pi, without approximating or rounding.
Expansion
The process of multiplying to remove brackets from an expression.
Exponent
A power to which a number is raised.
Factorial
n! is the product of all integers between 1 and n.
Factorise
To express a mathematical expression as a product of its factors.
Fraction
A number that represents a part of a whole, expressed as a quotient.
Greatest Common Factor of two or more numbers
The largest number that divides two or more integer numbers exactly.
Incircle
A circle inscribed within a triangle, tangent to all its sides.
Integers
All whole numbers, both positive and negative.
Interior Angle
An angle inside a polygon.
Irrational Number
A number that cannot be expressed as a fraction of two integers.
Isosceles
A triangle with two equal sides called legs. The side that is not equal is called the base.
Least Common Multiple of two or more numbers
The smallest positive integer that is divisible by all the numbers in question.
Line Segment
A part of a line with two endpoints.
Linear Equations
Equations that form a straight line when graphed, where the highest power is 1.
Logarithm
The exponent by which a base number must be raised to get a given number. For example, log₂(8) = 3 because 2³ = 8.
Magnitude
The size or length of a vector.
Maximum
The highest value in a dataset.
Median (in geometry)
A line segment joining a vertex of a triangle to the midpoint of the opposite side.
Midpoint
The point that divides a line segment into two equal parts.
Minimum
The lowest value in a dataset.
Mode
The most frequently occurring number in a dataset.
Obtuse
An angle measuring between 90° and 180°.
Origin
The point (0,0) where the x and y axes intersect.
Outlier
A data point that significantly differs from other values in a dataset.
Parameters
Constants or variables in a function that define its specific form but not its general nature.
Perimeter
The sum of all sides of a polygon.
Polygon
A closed figure with three or more straight sides.
Power
A number raised to an exponent.
Proof by Induction
A proof method in which each step is justified based on a base case and an induction step.
Quadratic Expressions
Expressions where the highest power is 2.
Quadrilateral
A polygon with four sides and four angles.
Quotient
The result of division.
Range
The difference between the highest and lowest values in a dataset.
Ratio
A relationship between two numbers indicating how many times the first number contains the second.
Regular polygon
A polygon with all sides and angles equal.
Right Angle
An angle of 90°.
Roots of a Polynomial
Values of the variable that satisfy the equation when the polynomial is set to zero.
Scale Factor
The number by which an object is enlarged or reduced.
Scalene
A triangle in which all three sides (and all three angles) are different in length and measure.
Sequence
An ordered list of numbers following a particular pattern.
Slope
A measure of the steepness of a line, usually expressed as the ratio of the vertical change to the horizontal change (rise over run).
Substitution
Replacing a value for a variable.
Subtended
An angle or arc is said to be subtended when it is formed or defined by lines or segments drawn from its endpoints to a point.
Superimpose
To place one object on top of another.
Surd
A number in root or radical form.
System of Inequalities
A set of two or more inequalities with the same variables.
Tangent
A line that touches a circle at exactly one point.
Variable
A quantity that can change in value.
Vertex
The point where two or more edges meet in a polygon.
X-Intercept
The point where a line crosses the x-axis.
Y-Intercept
The point where a line crosses the y-axis.
Contact us:
- info@leaders.tech
- t.me/techleadersbot
- Partner Schools:
- The Island School:
- H-FARM International School:
