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) Calculate 20.7.
Answer/Explanation
Ans: 1.62 or 1.62…
(b) Find the value of x in each of the following.
(i) 2x= 128
Answer/Explanation
Ans: 7
(ii) 2x × 29 = 213
Answer/Explanation
Ans: 4
(iii) 29 ÷ 2x = 4
Answer/Explanation
Ans: 7
(iv) \(2^{x} = \sqrt[3]{2}\)
Answer/Explanation
Ans: \(\frac{1}{3}oe\)
(c) (i) Complete this table of values for y = 2x.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 0.125 | 0.5 | 2 | 4 | 8 |
Answer/Explanation
Ans:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 0.125 | 0.25 oe | 0.5 | 1 | 2 | 4 | 8 |
(ii) On the grid, draw the graph of y = 2x for –3 ≤ x ≤ 3.
Answer/Explanation
Ans: Correct curve
(iii) Use your graph to solve 2x= 5.
Answer/Explanation
Ans: 2.3
(iv) Find the equation of the line joining the points (1, 2) and (3, 8).
Answer/Explanation
Ans: y = 3x – 1 oe 3 term equation
(v) By drawing a suitable line on your graph, solve 2x– 2 – x = 0.
Answer/Explanation
Ans: –1.7 to –1.5 and 2
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