IB Maths AI SL 1.1 Number and Algebra Sl Content Questions

Practise IB Mathematics AI SL 1.1 by modelling numbers, sequences, percentages, financial contexts and technology-supported algebra.

Exam points

Represent, convert and check numerical quantities using scientific notation, powers, logarithms, accuracy, bounds and percentage error.
Model arithmetic and geometric sequences or series, calculating terms, finite sums, thresholds, convergence and long-term behaviour.
Apply compound-interest, depreciation, annuity and loan models, comparing rates, payment timing, balances and target periods.
Use integer exponent and logarithm laws to solve equations and interpret logarithmic scales in contextual models.
Use graphing or numerical technology to solve permitted systems and polynomial equations, then select and justify valid roots.
Interpret numerical output with correct units, domains, rounding, parameter meaning and practical reasonableness.

Covered syllabus points

SL 1.1—Scientific notation SL 1.2—Arithmetic sequences and series SL 1.3—Geometric sequences and series SL 1.4—Financial applications SL 1.5—Integer exponents and logarithms SL 1.6—Approximation and error SL 1.7—Amortization and annuities SL 1.8—Technology for equations

[Maximum number: 6]

Zaha is designing a bridge to cross a river. She believes that the weight of the steel needed for this bridge is approximately 53632000 kg .
The exact weight of the steel needed for the bridge is 55625000 kg .

(a)

Find the percentage error in Zaha's approximation.

Zaha's design is used to build five identical bridges.

[ 2 ]

attempt to substitute into percentage error formula

\left|\frac{53632000-55625000}{55625000}\right| \times 100

3.58 (\%) (3.58292…(\%))

Note: Award (M1)A0 for a final answer of -3.58 (\%) or 0.0358 .

(b)

Find the weight of the steel needed for these five bridges, to three significant figures.

[ 1 ]

(c)

Write down your answer to part (b)(i) in the form $a \times 10^{k}$ , where $1 \leq a<10$ , $k \in \mathbb{Z}$ .

[ 3 ]

$2.78 \times 10^{8}$

Note: Award A1 for correct mantissa, consistent with their answer in part (b)(i).

Marking guidance:

Award A1 for a correct exponent, consistent with their answer in part (b)(i).
Award AOAO for answers such as $27.8 \times 10^{7}$ .

[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 $177.587 \ldots$

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)

Question (f)