Question
Five pipes labelled, “6 metres in length”, were delivered to a building site. The contractor measured each pipe to check its length (in metres) and recorded the following;
5.96, 5.95, 6.02, 5.95, 5.99.
a.(i) Find the mean of the contractor’s measurements.
(ii) Calculate the percentage error between the mean and the stated, approximate length of 6 metres.[3]
b.Calculate \(\sqrt {{{3.87}^5} – {{8.73}^{ – 0.5}}} \), giving your answer
(i) correct to the nearest integer,
(ii) in the form \(a \times 10^k\), where 1 ≤ a < 10, \(k \in {\mathbb{Z}}\) .[3]
▶️Answer/Explanation
Markscheme
(i) Mean = (5.96 + 5.95 + 6.02 + 5.95 + 5.99) / 5 = 5.974 (5.97) (A1)
(ii) \({\text{% error}} = \frac{{error}}{{actualvalue}} \times 100\% \)
\( = \frac{{6 – 5.974}}{{5.974}} \times 100\% = 0.435\% \) (M1)(A1)(ft)
(M1) for correctly substituted formula.
Allow 0.503% as follow through from 5.97
Note: An answer of 0.433% is incorrect. (C3)
[3 marks]
number is 29.45728613
(i) Nearest integer = 29 (A1)
(ii) Standard form = 2.95 × 101 (accept 2.9 × 101) (A1)(ft)(A1)
Award (A1) for each correct term
Award (A1)(A0) for 2.95 × 10 (C3)
[3 marks]
Question
1 Brazilian Real (BRL) = 2.607 South African Rand (ZAR). Giving answers correct to two decimal places,
(i) convert 300 BRL to ZAR,
(ii) find how many Real it costs to purchase 300 Rand.
▶️Answer/Explanation
Markscheme
Financial accuracy penalty (FP) is applicable where indicated in the left hand column.
1 BRL = 2.607 ZAR
(FP) (i) \(300 \times 2.607 = 782.10 {\text{ ZAR}}\) (A1)
Note: 782.1 is (A0)(FP)
(FP) (ii) \(300 \times \frac{1}{{2.607}} = 115.07{\text{ BRL}}\) (A1)(ft)
Note: Follow through only if processes are reversed. (C2)
[2 marks]
Question
Ben inherits $6500. Ben invests his money in a bank that pays compound interest at a rate of 4.5% per annum.
Calculate the value of Ben’s investment at the end of 6 years. Give your answer correct to 2 decimal places.
▶️Answer/Explanation
Markscheme
\({\text{Ben Amount}} = 6500{\left( {1 + \frac{{4.5}}{{100}}} \right)^6}\) (M1)(A1)
\( = $8464.69\) (A1)
(M1)(A1)(A0) if interest only found (=$1964.69) (C3)
[3 marks]
Question
a.Calculate exactly \(\frac{{{{(3 \times 2.1)}^3}}}{{7 \times 1.2}}\).[1]
b.Write the answer to part (a) correct to 2 significant figures.[1]
c.Calculate the percentage error when the answer to part (a) is written correct to 2 significant figures.[2]
d.Write your answer to part (c) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10{\text{ and }}k \in \mathbb{Z}\).[2]
▶️Answer/Explanation
Markscheme
\(29.7675\) (A1) (C1)
Note: Accept exact answer only.
[1 mark]
\(30\) (A1)(ft) (C1)
[1 mark]
\(\frac{{30 – 29.7675}}{{29.7675}} \times 100\% \) (M1)
For correct formula with correct substitution.
\( = 0.781\% \) accept \(0.78\% \) only if formula seen with \(29.7675\) as denominator (A1)(ft) (C2)
[2 marks]
\(7.81 \times {10^{ – 1}}\% \) (\(7.81 \times {10^{ – 3}}\) with no percentage sign) (A1)(ft)(A1)(ft) (C2)
[2 marks]