Pertanyaan:
1) A law firm seeks to recruit top-quality experienced lawyers. The total package offered is the sum of three separate components: a basic salary which is 1.2 times the candidate’s current salary together with an additional $3000 for each year worked as a qualified lawyer and an extra $1000 for every year that they are over the age of 21.
Work out a formula that could be used to calculate the total salary, S, offered to someone who is A years of age, has Eyears Ey of relevant experience and who currently eams SN. Hence work out the salary offered to someone who is 30 years old with five years’ experience and who currently earns $150 000.
2) Write down a formula for each situation
a) A plumber has a fixed call-out charge of $80 and has an hourly rate of $60. Work out the total charge, C, for a job that takes / hours in which the cost of materials and parts is SK
a) An airport currency exchange booth charges a fixed fee of $10 on all transactions and offers an exchange rate of 1 dollar to 0.8 euros. Work out the total charge. C (in $) for buying x euros.
b) A firm provides 5 hours of in-house training for each of its semi-skilled workers and 10 hours of training for each of its skilled workers. Work out the total number of hours, H, if the firm employs a semi-skilled and b skilled workers
c) A car hire company charges SC a day together with an additional Sc per mile Work out the total charge, $X, for hiring a car for d days and travelling m miles during that time.
Without using a calculator, evaluate
(a) 10(- 2)(b)(- 1)(- 3)(c)(- 8) / 2 * (d)(- 5) = (- 5)
(e) 24 + (- 2)(t)(- 10)(- 5)(f)(- 6) * 5(- 1)
3) Without using a calculator, evaluate
(a) 5 – 6(b) – 1 – 2(c) * 6 – 17(d) – 7 + 23
(e ) – 7 – (- 6)(t) – 4 – 9(g) * 7 – (- 4)(h) – 9 – (- 9)
(i ) 12 – 43(j) * 2 + 6 – 10
4) Without using a calculator, evaluate
(a) 5×2-13 (b) 5x (1-4)
(c) 1 – 6 * 7(d) – 5 + 6 +3( ) 2x (-3)2 ( (f) – 10 + 22
(g) (- 2) * 2 – 5 * 6 + 1(i)
5) Simplify each of the following algebraic expressions
(a) 2 x Px Q (b) /x8 (c) 3 x x x y
(d) 4 x gx wxz (e) bx b (f) kx 3xk
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Bukti:
1. Law Firm Salary Formula
Formula: S = 1.10C + 3,000Y
Explanation: The total salary (S) is calculated from the current salary (C) plus a performance bonus (10% of C) and an experience bonus ($3,000 per year).
Answer: $180,000
2. Car Repair, Currency Exchange, and Travel Costs
Car Repair: C = 60t + P
Explanation: The total cost (C) is the labor cost ($60 per hour, t) plus the cost of parts (P).
Currency Exchange: C = 10 + 1.3E
Explanation: The total cost (C) is a fixed fee of $10 plus the cost of the euros (E) at an exchange rate of 1.3.
Travel Costs: C = 5x + 10y + Gm
Explanation: The total cost (C) is the rental car fee ($5 per day, x), the training cost ($10 per hour, y), and the gas cost (G per mile, m).
3. Integer Arithmetic
Explanation: This problem tests the addition and subtraction of positive and negative numbers. Subtracting a negative number is the same as adding a positive one.
(a) 24
(b) 43
(c) -11
(d) -35
(e) -69
4. Order of Operations (BODMAS/PEMDAS)
Explanation: This problem follows the order of operations (BODMAS/PEMDAS) rule: Multiplication and Division are done before Addition and Subtraction.
(a) -14
(b) -6
(c) -5
5. Simplifying Algebraic Expressions
Explanation: This problem requires you to combine like terms (terms with the same variable).
(a) 3y (Combine the ‘x’ terms and the ‘y’ terms)
(b) 6a^2b^2c (Combine the numbers and the like variables)
(c) 12gwzb^2k^2 (Combine the numbers and the like variables)