IB · Mathematics: Applications & Interpretation SL & HL · Topic

Number & Algebra: IB Mathematics: Applications & Interpretation questions and answers

10 free IB Mathematics: Applications & Interpretation Number & Algebra questions written in the style of IB Mathematics: Applications & Interpretation papers, each with its answer and mark scheme. 2 of them are A* challenge questions, built to catch the mistakes strong students still make.

This topic covers Standard form & errors, Sequences & series, Financial mathematics, Exponents & logarithmic scales, Systems of equations, Complex numbers, Matrices & eigenvalues. Work through the questions below, then generate a full Number & Algebra paper with a fresh set every time.

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Number & algebra sub-topics

Standard form & errorsSequences & seriesFinancial mathematicsExponents & logarithmic scalesSystems of equationsComplex numbersMatrices & eigenvalues

Number & algebra practice questions

Question 1Structured · 6 marksA* challenge

Lena has $150000 in a retirement account earning 3% per year, compounded monthly. She withdraws $2000 at the end of each month.

(a)

Find the number of complete months for which she can make the full withdrawal.

[3]
(b)

Find the monthly withdrawal that would make the money last exactly 25 years.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)83 months
TVM: PV = −150000, PMT = 2000, FV = 0, I% = 3 (M1)(A1)
83 months A1
3
(b)$711.32
N = 300, FV = 0 (M1)
solving for PMT (M1)
$711.32 A1
3
Question 2Structured · 14 marksA* challenge

Sara invests $40000 at 4.5% per year compounded annually. Inflation is 2.5% per year.

(a)

Find the value of the investment after 10 years.

[2]
(b)

Find the real value of the investment after this time.

[3]
(c)

Instead, Sara saves $250 at the end of each month at 4.5% per year compounded monthly. Find the value after 10 years.

[3]
(d)

Find the monthly saving needed to reach $62000 in 10 years under the monthly plan.

[3]
(e)

Compare the two plans, considering the total amount invested.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$62118.78
TVM or formula (M1)
$62118.78 A1
2
(b)$48759.78
real rate 2% (A1)
TVM with the real rate (M1)
$48759.78 A1
3
(c)$37799.52
N = 120, PMT = −250, PV = 0 (M1)(A1)
$37799.52 A1
3
(d)$410.06
FV = 62000 (M1)
solving for PMT (M1)
$410.06 A1
3
(e)comparison
plan 1 invests $40000 A1
plan 2 invests $30000.00 A1
valid comparison with reason R1
3
Question 3Structured · 5 marks

Let A = 4 32 2 and B = 23 −614 −2.

(a)

Find det A, and explain why A−1 exists.

[2]
(b)

Find the matrix X such that AX = B.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2
det A = 2 A1
det A ≠ 0 R1
2
(b)2 −35 2
X = A−1B (M1)
use of GDC (M1)
2 −35 2 A1
3
Question 4Structured · 7 marks

Kai takes out a loan of $180000 at a nominal annual interest rate of 4.8%, compounded monthly. The loan is repaid with equal monthly payments over 25 years.

(a)

Find the monthly payment.

[3]
(b)

Find the total interest paid.

[2]
(c)

Find the amount still owed after 13 years.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$1031.39
N = 300, I% = 4.8, PV = 180000, FV = 0, P/Y = C/Y = 12 (M1)(A1)
$1031.39 A1
3
(b)$129418.36
300 × 1031.39 − 180000 (M1)
$129418.36 A1
2
(c)$112734.34
TVM with N = 156, solving for FV (M1)
$112734.34 A1
2
Question 5Structured · 4 marks

z = −3 + 4i.

(a)

Find the modulus and argument of z.

[2]
(b)

Find z3, giving your answer in the form reiθ.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)5.00; 2.21
5.00 A1
2.21 A1
2
(b)125e6.64i
r3, 3θ (M1)
correct A1
2
Question 6Structured · 4 marks

A city’s population of rabbits is 5000 and increases by 4% each year.

(a)

Find the population after 10 years.

[2]
(b)

Find the number of complete years until the population first exceeds double its initial value.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)7401
un = u1rn (M1)
7401 A1
2
(b)18
equation or GDC table (M1)
18 A1
2
Question 7Structured · 5 marks

A cinema sells adult, child and senior tickets at $x, $y and $z respectively.

DayAdultsChildrenSeniorsTotal takings ($)
1362013495
222245329
3361222526
Table 7.1
(a)

Write down a system of three equations to represent this information.

[2]
(b)

Find the price of each type of ticket.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)equations
one correct equation, e.g. 36x + 20y + 13z = 495 A1
all three correct A1
2
(b)$9, $4, $7
use of GDC to solve (M1)
x = 9, y = 4 A1
z = 7 A1
3
Question 8Structured · 6 marks

Ana invests $5000 in an account that pays a nominal annual interest rate of 2.5%, compounded monthly.

(a)

Find the value of the investment after 5 years, to the nearest dollar.

[3]
(b)

Find the number of complete years needed for the investment to exceed $7500.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$5665
N = 60, I% = 2.5, PV = −5000, P/Y = C/Y = 12 (M1)(A1)
$5665 A1
3
(b)17 years
FV = 7500, solve for N (M1)
N = 195 (A1)
17 years A1
3
Question 9Structured · 5 marks

The pH of a solution is given by pH = −log10[H+], where [H+] is the hydrogen ion concentration in mol dm−3.

(a)

Find [H+] for a solution with pH 3.7. Give your answer in standard form.

[2]
(b)

Find how many times greater [H+] is in a solution of pH 3.7 than in a solution of pH 5.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2.00 × 10−4
10−3.7 (M1)
2.00 × 10−4 A1
2
(b)20.0
10−3.710−5 (M1)
101.3 (A1)
20.0 A1
3
Question 10Structured · 4 marks

A cinema sells adult, student and child tickets.

3 adult, 2 student and 1 child ticket cost $38; 1 adult, 3 student and 2 child tickets cost $38; 2 adult, 1 student and 4 child tickets cost $36. Find the price of each ticket.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
adult $6, student $8, child $4
three equations (M1)
GDC solution (M1)
two correct A1
all three A1
4

Other IB Mathematics: Applications & Interpretation topics

FunctionsGeometry & trigonometryStatistics & probabilityCalculus

Frequently asked questions

What is in IB Mathematics: Applications & Interpretation Number & Algebra?

In the SL & HL syllabus, Number & Algebra covers Standard form & errors, Sequences & series, Financial mathematics, Exponents & logarithmic scales, Systems of equations, Complex numbers, Matrices & eigenvalues.

Where can I get Number & Algebra questions with mark schemes?

This page has 10 Number & Algebra questions with answers. For more, the free generator on mentorriyaz.in builds a new Number & Algebra paper with a full mark scheme each time you click.

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in