On a plusieurs ensembles dont les éléments sont des entiers tirés aléatoirement. Il faut faire des opérations élémentaires faisant intervenir  $\cap,\;\cup$ et la notion de complémentaire.

Add, subtract, multiply and divide numerical fractions.

Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

Add, subtract, multiply and divide numerical fractions.

Add, subtract, multiply and divide algebraic fractions.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

No description given

This quiz poses questions on basic probability and statistics.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$. 

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$. Finally, find all solutions of an equation $\mod b$.

No description given

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solve a quadratic equation by completing the square. The roots are not pretty!

No description given

No description given

Questions on graph theory

This question displays one of 10 graphs. It asks the student to either 

(a) count the vertices, or

(b) count the edges, or

(c) state how many vertices a spanning tree would contain, or

(d) state how many edges a spanning tree would contain, or

(e) state the degree of a selected (randomly chosen) vertex.

Students are randomly shown one of two networks. They are shown four sub-networks, and asked to identify which one is a minimum spanning tree for the network. Thus, there are 2 versions of this question.

No description given

Based on an activity tweeted by Richard Perring.