Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

In the Gaussian integer ring $\mathbb{Z}[i]$ , find the remainder $r=r_1+r_2i$, where $a \gt 0,\;b \gt 0$ , on dividing $a+bi$ by $c+di$ .

Expand $(ax+b)(cx+d)$.

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

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Find the remainder when dividing two polynomials, by algebraic long division.

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

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Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Expansion of two brackets

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Expand $(ax+b)(cx+d)$.

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rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths

Rearranging equations by multiplying or dividing: One step

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Instructions on inputting ratios of algebraic expressions.

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Algebra word problems using area and perimeter.

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Given two ordered sets of vectors $S,\;T$ in $\mathbb{R^5}$ find the reduced echelon form of the matrices given by $S$ and $T$ and hence determine whether or not they span the same subspace.

Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.