Variation and Inequalities
GCE Mathematics

(a) P varies directly as the square of Q and inversely as R. When P = 36, Q = 6 and R = 4. (i) Find the relationship between P, Q and R. (ii) Find the value of P when Q = 10 and R = 25. (…

(a) Given that -3 ≤ x ≤ 5 and -1 ≤ y ≤ 4, find the range of values of: (i) x + y (ii) x - y (iii) xy (b) Solve the following inequalities and represent each solution on a number line: …

If y varies directly as x and y = 15 when x = 3, find y when x = 7.

If p varies inversely as the square of q, and p = 4 when q = 3, find p when q = 6.

A quantity T varies directly as the cube of m and inversely as n. If T = 54 when m = 3 and n = 2, find T when m = 2 and n = 4.

z varies jointly as x and the square root of y. If z = 24 when x = 4 and y = 9, find z when x = 3 and y = 16.

The solution set of $2x + 3 \leq 7$ and $x - 1 > -3$ is

Find the range of values of x for which $3x - 5 > x + 7$.

If $x$ is an integer, find the greatest value of $x$ which satisfies $5 - 3x \geq x - 11$.