Solving arithmetic progressions using simultaneous equations

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$ I $ intervalo compacto, $ g: I \ rightarrow I, \; g (x) = ax ^ 3 + bx ^ 2 + cx + d $. Encuentre puntos estacionarios, máximos locales y globales y mínimos de $ g $ en $ I $

Add, subtract, multiply and divide algebraic fractions.

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.

Add, subtract, multiply and divide algebraic fractions.

A resource for Business students to practise calculating Normal probabilities and finding $Z$-values. 

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

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

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. 

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

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Add, subtract, multiply and divide algebraic fractions.

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Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

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.

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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.

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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.