What is in the Midpoints kit?

10 questions made by rule with fresh numbers every time it is opened, each with an explanation. Average the coordinates.

Does it cost anything?

A free account opens every kit. Procto AI’s writing runs on a monthly allowance that the free plan includes; a children’s kit uses none of it, because its questions are made by rule.

What happens after the quiz?

The study screen shows the answer and the explanation after each question, then the questions missed, and offers a retry of those. Come back in a few days and take it again: what is still right then is what is known.

Midpoints
For ages 12 to 15.

Average the coordinates.Start the quiz Every kit

What it asks

What is the midpoint of (4, 6) and (0, 0)? Write it like “(3, 4)”.
Average the x-values and the y-values: ((4 + 0)/2, (6 + 0)/2) = (2, 3).
What is the midpoint of (-4, 2) and (2, 4)? Write it like “(3, 4)”.
Average the x-values and the y-values: ((-4 + 2)/2, (2 + 4)/2) = (-1, 3).
What is the midpoint of (-10, 10) and (-4, -8)? Write it like “(3, 4)”.
Average the x-values and the y-values: ((-10 + -4)/2, (10 + -8)/2) = (-7, 1).

The facts

Field: Mathematics
Level: ages 12 to 15
Questions: 10, fresh each time
Shape: Maths expression
Made by: rule, in code, no model
Settings: practice: answers at once, retries without limit, no security

About this kit.

Average the coordinates.

What the mathematics kits are

The mathematics kits run from counting and the first number bonds through tables, fractions, percentages, algebra, geometry, statistics and calculus. The arithmetic kits are made by rule: every time one opens, the numbers are new, so a child can do the same kit every day and never see the same sum twice. The higher kits are written from your own textbook, chapter by chapter, so the questions use your course's notation and methods.

Why they are built this way

Mathematics is learned by doing many problems with feedback, and it is the one subject where a fresh problem can be made by rule without limit. A worksheet has twenty sums; a rule kit has as many as the student has minutes. The explanation after each answer shows the method, so a wrong answer becomes a worked example.

How to use them

For daily practice, open the rule kit for the child's stage and let them do ten minutes; the dashboard shows what they missed. For a course, paste the chapter and let Procto AI write from it, in the show-your-working shape where the method earns marks. Use the estimate shape for measurement and the expression shape for algebra, and set the tolerances.

Made by rule

This kit is made in code: every time it opens, the numbers, words or arrangements are drawn fresh from its rule, so the same kit taken twice is two different quizzes from one rule. There is no answer bank to find, and the practice never runs out. Each question carries its explanation, shown at once in study mode.

The shape: maths expression

An equation or expression typed and checked: algebra, calculus and any answer that is a formula rather than a number.

Expressions, numbers and single-form answers are marked by rule, with tolerances and half-credit tolerances where you set them. A typed expression or chemical equation is compared sign for sign, with spacing ignored, so each form you accept is listed, and a slip that would be forgiven in a word is never forgiven here; working and code are marked by a reader against your rubric, step by step.

Taking it

Open it in study mode for the answer and the explanation after each question, and a retry of only what you missed. Switch to exam mode for the real conditions. It comes due again in a few days; the dashboard shows what is due and what you missed last time. Share it with a code for a class, print it as a paper, or host it on a screen for a room.

Questions.

What is in the Midpoints kit?: 10 questions made by rule with fresh numbers every time it is opened, each with an explanation. Average the coordinates.
Does it cost anything?: A free account opens every kit. Procto AI’s writing runs on a monthly allowance that the free plan includes; a children’s kit uses none of it, because its questions are made by rule.
What happens after the quiz?: The study screen shows the answer and the explanation after each question, then the questions missed, and offers a retry of those. Come back in a few days and take it again: what is still right then is what is known.