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

rebelmaths

Statistics and probability. Questions asking student to calculate and interpret Pearson and Spearman correlation coefficients.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Curl of a vector field.

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

Polar form of a complex number.

Practice to decide which quadrant a complex number lies in.

Complex number multiplication & division

modulus & argument of a complex number

Calculating the square root of a complex number using De Moivre.

Calculating complex numbers raised to an natural number exponent

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

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.