IB Mathematics AI HL 1.1 Number and Algebra Question Bank

Practise IB Mathematics AI HL 1.1 by extending number-and-algebra models, sequences, finance and symbolic reasoning with technology.

Exam points

Analyse sequences, series, growth and decay models while interpreting parameters and long-term behaviour.
Use financial mathematics and technology to compare assumptions, rates, repayments and sensitivity.
Combine symbolic reasoning with graphing or calculator checks and justify approximation choices.

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: 5]

A bakery sells egg tarts in boxes. Each box contains 6 tarts. On a particular morning, the bakery has 400 freshly baked tarts. The number of tarts remaining, after n boxes have been sold, forms an arithmetic sequence, $u_{n}=u_{1}+(n-1) d$ .

(a)

Write down the value of d.

[ 1 ]

(b)

Find the value of $u_{1}$ .

[ 1 ]

(c)

Find the greatest number of boxes the bakery can sell that morning.

[ 3 ]

attempt to solve $394-6(n-1) \geq 0$ OR $400 \div 6$

Note: Accept equality or any inequality with zero seen, graphical approach to find zero, use of table/list to find zero.
( n< ) $66.6666 \ldots$
( n= ) 66
(A1)
A1

Note: If 400 is given as the answer in (b) then n=67 in part (c).

[Maximum number: 2]

Nanthana is completing an exploration on multiplication using complex numbers. She considers a geometric sequence where $u_{1}=9$ and $r=\frac{2}{3}+\frac{2}{3} \mathrm{i}$ .

(a)

Write down the value of

[ 2 ]

(i)

$\quad u_{2}$ .

[ 1 ]

$\left(u_{2}=\right) 6+6 \mathrm{i} \quad \boldsymbol{A} \mathbf{1}$

(ii)

$u_{3}$ .

Nanthana claims that the sequence $\left|u_{1}\right|,\left|u_{2}\right|,\left|u_{3}\right|, \ldots$ also forms a geometric sequence.

[ 1 ]

$\quad\left(u_{3}=\right) 8 \mathrm{i} \quad \boldsymbol{A} \mathbf{1}$

All question bank results loaded

Covered syllabus points

1.1 Number and algebra - SL content question 1

Question (a)

Question (b)

Question (c)

1.1 Number and algebra - SL content question 2

Question (a)

Question (b)

Question (c)

1.1 Number and algebra - SL content question 3

Question (a)

Question (i)

Question (ii)