Parametric Equations — Drills
Parametric Equations has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 7 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Radius — Centre to edge. Half the diameter.
- Slope — How much y changes for each 1 that x increases.
- Parabola — The U-shaped graph of a quadratic function.
- Roots — The x values where y = 0.
- Cosine — cos θ = adjacenthypotenuse.
- Pythagorean identity — sin2θ + cos2θ = 1.
- Continuous — A function you could draw without lifting the pen — no holes, jumps or blow-ups.
Point
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For x=4t+2, y=t2, find x when t=6.
Worked answer
26
4(6)+2 = 26
Problem 2
For x=5t+0, y=t2, find y when t=3.
Worked answer
9
32 = 9
Elimination
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Eliminate t from x=2t, y=t2+4. Give y in terms of x.
Worked answer
x^2/4+4
t = x2
y = x24+4
Problem 2
Eliminate t from x=3t, y=t2+3. Give y in terms of x.
Worked answer
x^2/9+3
t = x3
y = x29+3
Circle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For x=3cos t, y=3sin t, find x2+y2.
Worked answer
9
9(cos2 t+sin2 t) = 9
Problem 2
For x=5cos t, y=5sin t, find x2+y2.
Worked answer
25
25(cos2 t+sin2 t) = 25
Projectile
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A ball has y = 96t - 16t2. At what time does it return to the ground?
Worked answer
6
t(96-16t)=0
t = 9616 = 6
Problem 2
A ball has y = 32t - 16t2. At what time does it return to the ground?
Worked answer
2
t(32-16t)=0
t = 3216 = 2
Peak
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A ball has y = 96t - 16t2. At what time is it highest?
Worked answer
3
Roots at t=0 and t=6
Halfway: t = 3
Problem 2
A ball has y = 32t - 16t2. At what time is it highest?
Worked answer
1
Roots at t=0 and t=2
Halfway: t = 1
Largest
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For x=8cos t, what is the largest value x can take?
Worked answer
8
8(1) = 8
Problem 2
For x=2cos t, what is the largest value x can take?
Worked answer
2
2(1) = 2