Cofactors Determinant and inverse of a 3x3 matrix.

Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution, no hint given

Simple Indefinite Integrals

Simple Indefinite Integrals

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

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Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

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

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

Elementary Exercises in multiplying matrices. 

Multiplication of $2 \times 2$ matrices.

Linear combinations of $2 \times 2$ matrices. Three examples.

Cofactors Determinant and inverse of a 3x3 matrix.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

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

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Find the dot product and the angle between two vectors

angle between two vectors

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Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

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

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

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

Calculate the hypotenuse of a right triangle, given the other two side lengths.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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