Live practice

A body moves in one direction under a source of constant power. To which power of time is its displacement proportional?

One card is drawn from a standard deck. Find the probability that it is a red king or a black queen.

For one fair die, find the probabilities of a prime, a number at least 3, a number at most 1, a number above 6, and a number at most 6.

Series A has mean 40 and standard deviation 5; series B has mean 50 and standard deviation 7. Which is more consistent?

Find the centroid of the triangle with vertices (1,2,3), (4,5,6) and (7,8,9).

Find the 12th term of the GP 3,6,12,… .

Use binomial reasoning to decide which is larger: (1.1)¹⁰⁰⁰⁰ or 1000.

If \(\frac{1}{6}\)!+\(\frac{1}{7}\)!=\(\frac{x}{8}\)!, find x.

The product \(A\times A\) has 9 elements and contains \((-1,0)\) and \((0,1)\). Determine \(A\) and list \(A\times A\).

Determine whether each pair defines equal sets:

1. \(\{a,b,c,d\}\) and \(\{d,c,b,a\}\)
2. \(\{4,8,12,16\}\) and \(\{8,4,16,18\}\)
3. \(\{2,4,6,8,10\}\) and positive even integers at most 10
4. multiples of 10 and \(\{10,15,20,25,30,\ldots\}\)