SQA Advanced Higher Mathematics of Mechanics Mathematical Techniques for Mechanics overview quiz quiz

a number (scalar)

a vector

a unit vector

a matrix

their sum is zero

their scalar product is zero

their magnitudes are equal

their components are equal

$1$

$7$

$5$

$\sqrt{7}$

$8$

$1$

$5$

$4$

$2\cos 2t$

$\cos 2t$

$-2\cos 2t$

$2\sin 2t$

$3e^{3t} + c$

$\tfrac{1}{3}e^{3t} + c$

$e^{3t} + c$

$\tfrac{1}{3}e^{t} + c$

differentiate again

ignore any constant

add a constant fixed by an initial condition

divide by the time

$5\sin 5t + c$

$-\tfrac{1}{5}\sin 5t + c$

$\sin 5t + c$

$\tfrac{1}{5}\sin 5t + c$

$v\dfrac{dv}{dx}$

$\dfrac{dv}{dt}$

$\dfrac{dx}{dt}$

$\dfrac{d^2v}{dt^2}$

a sum of derivatives

$g(v)\,dv = h(t)\,dt$

a second-order equation

a product of two unknowns

$v = v_0 + kt$

$v = v_0 e^{kt}$

$v = v_0 e^{-kt}$

$v = v_0 - kt$

$\mathbf{F} \times \hat{\mathbf{d}}$

$|\mathbf{F}| + 1$

$\dfrac{\mathbf{F}}{\hat{\mathbf{d}}}$

$\mathbf{F}\cdot\hat{\mathbf{d}}$

perpendicular

parallel

equal

both zero

$t^3$

$4t^3$

$\tfrac{1}{5}t^5$

$4t^4$