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Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

Useful for a review of the base 10 number system before introducing different bases and also just ensuring students understand how the base 10 system works.

Useful for a review of the base 10 number system before introducing different bases and also just ensuring students understand how the base 10 system works.

Divisor is a two digit number. There is a remainder which we express as a decimal by continuing the division process. No rounding is required by design (another question will include rounding off).

Divisor is a two-digit number. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

Issues: alignment in columns in the working - not sure what to do about it

Decimal divided by a decimal. Multiply by a power of ten to get an integer divisor. Long and short division process. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to some number of decimal places.

Decimals addition algorithm. 2 and 3 digit numbers. Carrying.

Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

rebelmaths

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm checks that the student's answer differs from the expected answer by a multiple of $2\pi$.

The number entry part in this question has an alternative answer which is marked correct if the student's number satisfies an equation specified in the custom marking algorithm.

Two functions given in words. Write down the function definition. The numbers in the function definitions are randomised.

Convert a random number of cubic metres into cubic centimetres

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Shows how the "give a number which satisfies an equation" part type can be used to makr the student's number correct if it satisfies an equation of the form $f(x) = 0$.

Examples of the following custom part types: Yes/no, List of numbers, Give a numerical input for an expression, Number entry modulo.

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.

The numbers and letters are all randomised.

Part of HELM Book 1.3

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Student must calculate distance swum in km given number of laps of 50m pool, days of week and weeks in term. These variables are randomly selected.