EduNinja

[Maximum number: 3]

The Scheveningen Ferris wheel's lowest point is 8 m above sea level, and its highest point is 45 m above sea level.

Calculate the total number of revolutions that the Ferris wheel has made. Give your answer in the form $a \times 10^{k}$ where $1 \leq a<10$ and k is an integer.

4 (revolutions per hour) seen OR 32 (revolutions per day) seen $(4 \times 8 \times 3000=) 96000$

[Maximum number: 18]

A marathon is a race over a distance of 42.19 km .

(a)

Write down 42.19 km correct to the nearest kilometre.

[ 3 ]

$42(\mathrm{~km})$

(b)

Find the percentage error if 42.19 km is rounded to the nearest kilometre.

Rolando and Davi are training to run a marathon. They both start their training in the same week.
Rolando runs 6 km in the first week, 8 km in the second week and 10 km in the third week. In each subsequent week he runs 2 km further than the previous week.

[ 3 ]

$\quad(\varepsilon=)\left|\frac{42-42.19}{42.19}\right| \times 100 \%$
0.450 (\%) (0.450343...(\%))

Note: Award (M1) for correct substitution of their part (a)(i) into percentage error formula.

(c)

Find the week during which Rolando runs 42 km .

[ 3 ]

METHOD 1 attempt to substitute into arithmetic sequence formula
$42=6+(n-1) \times 2$ OR 42=2 n+4
( n= ) 19

METHOD 2
list of any consecutive terms ending on/above 42
at least two correct terms (not including 6, 8 and 10)
( n= ) 19

(d)

Find the total distance that Rolando runs in the first 10 weeks.

Davi runs 3 km in the first week. In each subsequent week he runs 20 % further than the previous week. These distances form the terms of a geometric sequence.

[ 2 ]

METHOD 1
$\left(S_{10}=\right) \frac{10}{2}(2 \times 6+(10-1) 2)$ $150(\mathrm{~km})$

METHOD 2
summing (some) correct terms up to 24 OR list of correct cumulative values $6+8+10+\ldots+24$ OR $6,14,24,36 \ldots$ $150(\mathrm{~km})$

(e)

Find the first week during which Davi runs more than 42 km .

[ 4 ]

(d) METHOD 1
$3(1.2)^{n-1}$

Note: Award (A1) for correct substitution into geometric sequence formula.
comparing their geometric expression to 42
e.g. $3(1.2)^{n-1}>42$ OR $3(1.2)^{n-1}=42$ $(n=) 15.4747 \ldots$ seen OR $38.5175 \ldots$ and $46.2210 \ldots$ seen (from table)

16 (weeks)

METHOD 2

List of values see. At least 3, 3.6, 4.32 etc
$38.5175 \ldots$ and $46.2210 \ldots$ seen

16 (weeks)

(f)

Find the first week that the total distance that Davi has run, since the start of training, exceeds 150 km .

[ 3 ]

METHOD 1 attempt to substitute into geometric series formula

Note: FT their r from (d).

150<\frac{3\left(1-1.2^{n}\right)}{1-1.2} \text { OR } 150=\frac{3\left(1-1.2^{n}\right)}{1-1.2} \text { OR } 13.1520 \ldots

14 (weeks)

METHOD 2
evidence using tables in GDC or adding the first 14 terms both crossover values seen, e.g $145.589 \ldots$ and $177.587 \ldots$

IB Maths AI SL 1.1 Number and Algebra Sl Content Topic Practice

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IB Maths AI SL 1.1 Number and Algebra Sl Content Topic Practice

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Question 1

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)

Question (f)