Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Questions on vector arithmetic and vector operations, including dot and cross product.

Rearranging simple equations to solve for x.

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A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Scientific Notation

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Scientific Notation

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Converting a percentage to a fraction and decimal.

Is this number divisible by 100? Half the time the number is, half the time it isn't. Steps give the divisibility test and how to count the number of 100s.

Is this number divisible by 125? Half the time the number is, half the time it isn't. Steps give the divisibility test.

Is this number divisible by 250? Half the time the number is, half the time it isn't. Steps give the divisibility test.

Is this number divisible by 20? Half the time the number is, half the time it isn't.

Is this number divisible by 50? Half the time the number is, half the time it isn't. Steps give the divisibility test and a way to determine the number of fifties.

Is this number divisible by 25? Half the time the number is, half the time it isn't. Steps give the divisibility test and a way to determine the number of twenty-fives.

Find the gcd $d$ of two positive integers $a$ and $b$ also find integers $x,y$ such that $ax+by=d$, using the extended Euclidean algorithm.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Find the dot product and the angle between two vectors

A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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Find roots and the area under a parabola