AISAAC-MATHEMATICS Show all working

Answer ALL questions

1. (a) (Fractions and Approximation) Determine the EXACT value of:

(i) ( 2 3

4 − 5

2

5 ) ÷ ( 2 3

4 − 5

2

5 )

(ii) 24.5! − 2.8935 + 20

giving your answer correct to 2 significant figures and 2 decimal places.

(iii) Write the number 0.00009384567 AND 432190 in standard form. (Consumer Arithmetic)

(b) BDS$ means Barbados dollars and EC$ means Eastern Caribbean dollars.

(i) Karen exchanged BDS $2000.00 and received EC $2700.00. Calculate the value of one BDS$ in $EC$.

(ii) If Karen exchanged EC $432.00 for BDS$, calculate the amount of BD$$ which Karen would receive.

[Assume that the buying and selling rates are the same.] (c) A credit union pays 8% per annum compound interest on all fixed deposits. A customer

deposited $24 000 in an account. Calculate the TOTAL amount of money in the account at the end of five years.

(d) John deposited $2000 into Republic Bank at a rate of 5% for 3 years. Calculate his interest. (e) Jane deposited $10000 into Republic Bank and the money grew to $12, 000 at a rate of 2%.

How long did her deposit take to reach that amount?

-MATHEMATICS Show all working 2

2. (a) (Substitution) Given that 𝒂 = −𝟏,𝒃 = −𝟐 𝑎𝑛𝑑 𝒄 = 𝟑, find the value of:

(i) 𝑎 − 𝑏 + 𝑐

(ii) 𝑎! − 𝑐! − (2𝑎𝑏)!

(iii) −2𝑎𝑏𝑐

(iv) +2𝑎𝑏𝑐 (v) 𝑎 − 𝑏 + 2𝑐𝑏

(vi) 2𝑎𝑏 − 𝑎𝑏 + 𝑐

(vii) 6𝑎 − 𝑏 + 4𝑐

(viii) (𝑎 − 𝑏)! + 2𝑐!

(ix) 𝑎! − 𝑏! − 𝑐!

(b) (Simplify) the following: (i) −8𝑥𝑦! − 3𝑎𝑏! − 13𝑥𝑦! + 9𝑎𝑏!

(ii) −5𝑥 + 4𝑥 + 𝑦

(iii) 9𝑥 − 4𝑦 + 3𝑧

(vii) 6𝑎 − 6𝑏 − 3𝑎 − 4𝑏

(viii) 2𝑐 − 3𝑎 − 4𝑐

(ix) 3𝑎!𝑏 − 5𝑏! − 8𝑐! + 4𝑎!𝑏

(c) (Binary Operation) An operation is defined by 𝒂 ∗ 𝒃 = 3𝑎𝑏 − 2𝑎𝑏 + 𝑏!.

Calculate the exact value of (i) 2 ∗ 3 (ii) 4 ∗−1 (iii) −5 ∗−2 (iv) 0 * 5 (v) (2 ∗ 3) ∗ −4

End of Assignment