Question
A company employed 300 workers when it started and now employs 852 workers.
(a) Calculate the percentage increase in the number of workers.
(b) Of the 852 workers, the ratio part-time workers : full-time workers = 5:7.
Calculate the number of full-time workers.
(c) The company makes 40600 headphones in one year.
Write this number
(i) in words,
(ii) in standard form.
(d) In one month, the company sells 3000 headphones.
Of these, 48% are exported, \(\frac{3}{8}\)are sold to shops and the rest are sold online.
Calculate the number of headphones that are sold online.
(e) One year, sales increased by 15%. The following year sales increased by 18%.
Calculate the overall percentage increase in sales.
Answer/Explanation
1(a) 184
1(b) 497 2
1(c)(i) Forty thousand six hundred
1(c)(ii) \(4.06\times 10^{4}\)
1(d) 435
1(e) 35.7
Question
(a) Write as a single fraction in its simplest form
\(\frac{x+3}{x-3}-\frac{x-2}{x+2}\)
(b)\(2^{12}\div 2^{\frac{k}{2}}=32\)
Find the value of k.
k = ………………………………………….
(c) Expand and simplify.
(y+3)(y-4)(2y-1)
………………………………………….
(d) Make x the subject of the formula.
\(x=\frac{3+x}{y}\)
x = ………………………………………….
Answer/Explanation
(a)\(\frac{10x}{(x-3)(x+2)}\) or\( \frac{10x}{x^{2}-x-6}\) final answer
(b) 14
(c) \(2y^{3}-3y^{2}-23y+12 \)final answer
(d)\(x=\frac{3}{y-1}\) final answer
Question
(a) Write as a single fraction in its simplest form
\(\frac{x+3}{x-3}-\frac{x-2}{x+2}\)
(b)\(2^{12}\div 2^{\frac{k}{2}}=32\)
Find the value of k.
k = ………………………………………….
(c) Expand and simplify.
(y+3)(y-4)(2y-1)
………………………………………….
(d) Make x the subject of the formula.
\(x=\frac{3+x}{y}\)
x = ………………………………………….
Answer/Explanation
(a)\(\frac{10x}{(x-3)(x+2)}\) or\( \frac{10x}{x^{2}-x-6}\) final answer
(b) 14
(c) \(2y^{3}-3y^{2}-23y+12 \)final answer
(d)\(x=\frac{3}{y-1}\) final answer