SEAMO 2027 - Paper B - SET 09 - Self-study

SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.

In mathematics, $3^1=3$, $3^2=3\times3=9$, $3^3=3\times3\times3=27$, $3^4=3\times3\times3\times3=81$, … . What is the ones digit of $33^{33}$?

A square number is obtained by multiplying a whole number by itself: $1\times1=1$, $2\times2=4$, $3\times3=9$, … . Find the first square number after 2022.

The product of a number multiplied by itself is called a square number. $1260\times m$ is a square number. Find the smallest possible value of $m$.

For self-study, m is a positive integer, as intended by the choices. The source does not explicitly state this domain.

In mathematics, $2^1=2$, $2^2=2\times2$, $2^3=2\times2\times2$, … . Find the digit in the ones place of $3^{10}$.

Find the number of consecutive zeros in $15\times24\times25\times30$.

Some teenagers are questioned by the traffic police.

Adrian: “I have a driving license.”

Ben: “I do not know how to drive.”

Chris: “Ben does not know how to drive.”

Only one person is telling the truth. Which conclusion can we make?

Use the ordinary puzzle assumption that a person holding a driving license knows how to drive.

The values on opposite faces of a die add up to 7. The diagram shows cardboard that can be folded into a die. How many dots should there be on faces A, B and C?

Find $m$ in $1+2+3+4+\cdots+m=253$.

What is the largest 4-digit number that is a common multiple of 5 and 8?

The blueberry cheesecake is missing from the fridge. Mrs Wong questions her four children.

Jack: “I did not take the cake.”

Wilson: “Jack is lying.”

Chloe: “Wilson is lying.”

Sarah: “Wilson took the cake.”

Only one of them told the truth. Who took the cheesecake?

Evaluate $1-2+3-4+5-6+7-\cdots-2018+2019$.

Find the value of $12345654321\times(1+2+3+4+5+6+5+4+3+2+1)$.

Given $s\ominus t=5\times t-3\times s$, compute $4\ominus5$.

How many digits are there in $111\,111\,111\times111\,111\,111$?

The printed answer key is inconsistent with this printed expression. Answer the expression exactly as shown; each factor contains nine ones.

Divide the figure into 4 identical shapes of equal areas using only straight lines.

The source gives no lengths or angle markings. For the intended self-study construction, treat the pictured trapezoid as half a regular hexagon: its parallel bases have ratio 2:1 and each sloping side equals the shorter base. The original figure is retained; do not measure the scan. Submit a drawing or an unambiguous description of your dividing segments.

A number m is divided by 10, then 80 is added. The result is multiplied by 3. Finally 85 is subtracted, giving 200. Find m.

Evaluate $1-2+3-4+5-6+\cdots+2023-2024+2025$.

The figure shows 3 squares and a circle. The area of the largest square is $84\text{ cm}^2$. Find the area of the shaded region, in square centimetres.

Read the intended incidences in the diagram: the circle is inscribed in the outer square, the middle square is inscribed in the circle, and the shaded square joins the middle square’s side midpoints.

Every 5 minutes, the algae covering a pond doubles in area. Within 1 hour, the whole surface is covered. How long would it take to cover the pond if we started with twice as much algae? Give the time in minutes.

Interpret “within 1 hour” as becoming completely covered at exactly 60 minutes, as intended by the source key; each doubling occurs after 5 minutes.

Forty students took a mathematics test with 3 questions. The numbers answering questions 1, 2 and 3 correctly were 25, 28 and 31, respectively. At least how many students answered all 3 correctly?