A particle is projected up a rough plane at a given speed. Given the angle of the slope and the coefficient friction, find the distance the particle travels before it comes to instantaneous rest.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ direction but the positive $y$. 

A caravan pulled along by a car. Question uses SUVAT equations and $F=ma$.

Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

Intorduction to proof and existence statements.

Find roots and the area under a parabola

Definite Integrals

rebel

rebelmaths

Rebelmaths

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Simple Indefinite Integrals

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

rebelmaths

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Simple Indefinite Integrals

Indefinite Integrals

rebel

rebelmaths

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

No description given

No description given

Exam test 1/ 2016 past paper

No description given

No description given

No description given

No description given

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Find roots and the area under a curve

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Indefinite Integrals

rebel

rebelmaths

Simple Indefinite Integrals

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.