Number and algebra practice questions (IB Maths AI)

Sample questions

All 2 free IB Maths AI questions on this topic, from the free IB Maths AI SL Practice Exam. Each answer is behind its own toggle; the whole paper, its PDF and the full answer key are on the exam page.

1. Question 16 marks · Financial mathematics
   Maya invests 8000 USD in a savings account that pays a nominal annual interest rate of 4.2%, compounded monthly. She leaves the money in the account for 5 years. Maya also borrows 15 000 USD to buy a car. The loan charges a nominal annual interest rate of 6%, compounded monthly, and is repaid in equal monthly instalments over 4 years.
   (a)

   Calculate the value of Maya's investment at the end of the 5 years. Give your answer correct to two decimal places.

   [2]
   (b)

   Tom estimates the value of Maya's investment by assuming simple interest of 4.2% per year for 5 years. Calculate the percentage error in Tom's estimate.

   [2]
   (c)

   Find the monthly repayment on the car loan, and hence the total interest Maya pays.

   [2]
   Show answerFrom the free IB Maths AI SL Practice Exam →
2. Question 27 marks · Arithmetic & geometric sequences
   Maya and Tom each start a savings plan on 1 January. Maya saves 40 USD in the first month and increases the amount she saves by 5 USD every month. Tom saves 40 USD in the first month and increases the amount he saves by 8% every month.
   (a)

   Find the amount Maya saves in the twelfth month.

   [2]
   (b)

   Find the total amount Maya saves in the first two years.

   [2]
   (c)

   Find the total amount Tom saves in the first two years.

   [2]
   (d)

   State who saves more over the two years, and by how much.

   [1]
   Show answerFrom the free IB Maths AI SL Practice Exam →

Key terms

The definitions and formulas IB Maths AI expects for number and algebra, typeset as they appear on the paper.

Percentage error

The size of an approximation error relative to the exact value, as a percentage. The absolute value makes it positive whichever way the approximation errs.

$$\varepsilon = \left|\frac{v_A - v_E}{v_E}\right| \times 100\%$$

Arithmetic and geometric sequences

An arithmetic sequence adds a common difference $d$; a geometric sequence multiplies by a common ratio $r$. Sums of the first $n$ terms are in the formula booklet.

$$u_n = u_1 + (n-1)d, \qquad u_n = u_1 r^{n-1}, \qquad S_n = \frac{u_1(r^n - 1)}{r - 1}$$

Compound interest

Growth of a present value at $r$ percent a year, compounded $k$ times a year for $n$ years. The GDC finance app solves for any one unknown (future value, rate, number of periods).

$$FV = PV\left(1 + \frac{r}{100k}\right)^{kn}$$

Depreciation

Compound decay of a value by $r$ percent a year, the same formula as compound interest with the sign of the rate reversed.

$$FV = PV\left(1 - \frac{r}{100}\right)^{n}$$

Annuities and amortisation

Regular payments into or out of an account earning compound interest, such as loan repayments. Solved with the finance solver by entering the number of payments, rate, present value and payments per year.

Scientific notation and significant figures

Numbers written as $a \times 10^k$ with $1 \le a < 10$. Unless told otherwise, final answers are given exactly or to three significant figures, and intermediate values should keep more.

$$a \times 10^k, \qquad 1 \le a < 10, \; k \in \mathbb{Z}$$

Frequently asked questions

Other IB Maths AI topics

• Functions
• Geometry and trigonometry
• Statistics and probability
• Calculus

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