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IB Maths AI HL 1.1 Number and Algebra Sl Content Questions

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

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

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 notationSL 1.2—Arithmetic sequences and seriesSL 1.3—Geometric sequences and seriesSL 1.4—Financial applicationsSL 1.5—Integer exponents and logarithmsSL 1.6—Approximation and errorSL 1.7—Amortization and annuitiesSL 1.8—Technology for equations

Question 1

[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, un=u1+(n−1)du_{n}=u_{1}+(n-1) d.

Question (a)

(a)

Write down the value of d.

[ 1 ]

Question (b)

(b)

Find the value of u1u_{1}.

[ 1 ]

Question (c)

(c)

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

[ 3 ]

Question 2

[Maximum number: 2]

Nanthana is completing an exploration on multiplication using complex numbers. She considers a geometric sequence where u1=9u_{1}=9 and r=23+23ir=\frac{2}{3}+\frac{2}{3} \mathrm{i}.

Question (a)

(a)

Write down the value of

[ 2 ]

Question (i)

(i)

u2\quad u_{2}.

[ 1 ]

Question (ii)

(ii)

u3u_{3}.

Nanthana claims that the sequence ∣u1∣,∣u2∣,∣u3∣,…\left|u_{1}\right|,\left|u_{2}\right|,\left|u_{3}\right|, \ldots also forms a geometric sequence.

[ 1 ]

Question 3

[Maximum number: 19]

Give your answers in parts (a), (d)(i), (e) and (f) to the nearest dollar.
Daisy invested 37000 Australian dollars (AUD) in a fixed deposit account with an annual interest rate of 6.4 % compounded quarterly.

Question (a)

(a)

Calculate the value of Daisy's investment after 2 years.

[ 3 ]

Question (b)

(b)

After m months, the amount of money in the fixed deposit account has appreciated to more than 50000 AUD.

Find the minimum value of m, where m∈Nm \in \mathbb{N}.

[ 4 ]

Question (c)

(c)

Daisy is saving to purchase a new apartment. The price of the apartment is 200000 AUD.
Daisy makes an initial payment of 25 % and takes out a loan to pay the rest.

Write down the amount of the loan.

[ 1 ]

Question (d)

(d)

The loan is for 10 years, compounded monthly, with equal monthly payments of 1700 AUD made by Daisy at the end of each month.

For this loan, find

[ 5 ]

Question (i)

(i)

the amount of interest paid by Daisy.

[ 2 ]

Question (ii)

(ii)

the annual interest rate of the loan.

[ 3 ]

Question (e)

(e)

After 5 years of paying off this loan, Daisy decides to pay the remainder in one final payment.

Find the amount of Daisy's final payment.

[ 3 ]

Question (f)

(f)

Find how much money Daisy saved by making one final payment after 5 years.

[ 3 ]
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