Find the dot product and the angle between two vectors

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

rebelmaths

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Calculate the midpoint of two points.

This question aims to assess the student's understanding of the difference between biased and unbiased events and also to assess the student's understanding of the fact that the experimental probability tends towards the theoretical probability as the number of trials increases.

Given sequences with missing terms, find the common difference between terms.

Represent a given probability to a decimal, fraction or percentage.

Graphing exponentials with a base between 0 and 1 and no transformations take place.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

rebelmaths

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

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

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

Find a regression equation.

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

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

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Represent a given probability to a decimal, fraction or percentage.

Paired t-test to see if there is a difference between responses after treatment.

Convert figures for car engine sizes between cc (cm^3), litres, and m^3.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

Identifying y=mx+b given two points

Calculate the midpoint of two points.

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

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