Home / IBDP Maths AI: Topic : SL 1.6: Approximation: decimal places, significant figures: IB style Questions HL Paper 1

IBDP Maths AI: Topic : SL 1.6: Approximation: decimal places, significant figures: IB style Questions HL Paper 1

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]

a.

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]

a.

\(30\)     (A1)(ft)     (C1)

[1 mark]

b.

\(\frac{{30 – 29.7675}}{{29.7675}} \times 100\% \)     (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]

c.

\(7.81 \times {10^{ – 1}}\% \) (\(7.81 \times {10^{ – 3}}\) with no percentage sign)     (A1)(ft)(A1)(ft)     (C2)

[2 marks]

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