SEAMO 2027 - Paper B - SET 04 - 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.

Find the area of the shaded region, in m².

Interpret the pictured frame as having a uniform width of 1 m on all four sides. Only the left and bottom widths are explicitly labelled in the source.

A mathematics test has 15 questions. Each correct answer earns 8 marks; each wrong answer loses 4 marks. John scores 72 marks. How many questions did he answer wrongly?

Assume John answered all 15 questions; the source does not specify how unanswered questions are treated.

How many ways can an insect climb from A to C, passing through B, along the lines shown?

Count paths that do not revisit any vertex or retrace a line. The source does not explicitly state this finite-path convention.

Meredith has the diagram below. Each box above two adjacent boxes contains their sum. What is the maximum number of odd numbers she can write in the boxes?

ABCD is a rectangle. H lies on AD, and E, F and G are the midpoints of AB, BC and CD respectively. The area of ABCD is 40 cm². Find the total area of the shaded regions, in cm².

Jonathan averages 79 marks in his first four mathematics tests. What must he score in the fifth test to raise his average to 82?

Emelie averages 85 marks in her first three science tests. What must she score in the fourth test to raise her average to 87?

The sum of five consecutive odd numbers is 1125. Find the largest number.

Find the perimeter of the figure below, in centimetres.

The area of a circle is $\pi r^2$, where $\pi=\frac{22}{7}$ and r is the radius. Find the area of the shaded region.

There are 14 children at a party. Each child shakes hands with every other child exactly once. How many handshakes occur?

Two identical 7 cm × 3 cm rectangles overlap as shown. Find the area of the resulting figure, in cm².

The numbers 1 to 7 are placed in the circles, each once. The three numbers on each of the three branches have sum 14. Find m.

A bag contains 5 red, 4 yellow and 3 black balls. Blindfolded, you draw one ball at a time without replacement. What is the minimum number of draws that guarantees at least 3 balls of the same colour?

Find the remainder when the number formed by writing 2024 copies of the block 123 consecutively is divided by 11. That number is 123123123…123123.

Elaine averages 90 in her first three English tests. She scores 96 in the fourth test. What is her average over all four tests?

ABCD is a square of side 5 cm. B, C and E lie on one straight line, with CE = a. Shaded region y is 5 cm² larger than shaded region x. Find a.

A double-decker bus has 66 seats. At the first stop 1 commuter boards, at the second 2 board, at the third 3 board, and so on. At which stop will all seats be taken?

Assume the bus initially has no passengers, nobody gets off, and each commuter takes one seat.

Children are divided into two groups. Group A has 20 more boys than girls. Group B has 12 more girls than boys. Girls make up 45% of all the children. How many boys are there altogether?

In the 3 × 3 magic square shown, every row, column and diagonal has the same sum. Find A + B + C + D.