SEAMO 2027 - Paper B - SET 12 - 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.

What is the first number in the 10th row of the array shown?

Continue the consecutive positive odd numbers, with row lengths 1, 3, 5, 7, … as displayed.

The average of 5 whole numbers is 20. When one of the numbers is changed to 18, the new average is 18. What was the original value of that number?

Two numbers A and B have sum 42. When A is multiplied by 5 and B by 3, the new sum is 182. Find A.

Evaluate $1-2+3-4+5-6+\cdots+2017-2018+2019$.

How many triangles are there in the figure?

Alan writes the integers 1, 2, 3, 4, 5, …, 173. How many times does the digit 7 occur altogether?

How many dots will there be in the 8th figure?

Continue the same illustrated hexagonal construction for later figures.

There are 30 questions in a mathematical competition. All questions must be answered. A correct answer earns 5 marks and a wrong answer loses 2 marks. If Alan scores 122 marks, how many questions does he answer correctly?

Car A leaves Town X one hour before Car B leaves Town Y. Car A travels at 96 km/h and Car B at 80 km/h. Five hours after Car A starts, it catches up with Car B. What is the distance between Town X and Town Y, in kilometres?

As shown in the original diagram, both cars travel in the same direction along the same straight road, with Y ahead of X; they maintain the stated speeds until meeting.

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 $33^{33}$?

How many numbers are in the sequence $4,10,16,22,28,\ldots,64$?

Find the possible values of A and B, respectively, in the five-digit number $\overline{7A36B}$ so that it is divisible by both 5 and 9.

The sum of the five numbers in the outlined cross is 85. Find the middle number when a cross of the same shape contains five numbers with sum 125.

Move the same cross-shaped outline within the continued seven-column array; the five positions keep the same relative arrangement.

How many squares are there altogether in the diagram?

The diagram shows a rectangle of length 36 cm. It contains two shaded regions and 7 identical small rectangles. Find the area of one small rectangle, in square centimetres.

Moving only right or down along the grid lines, how many paths go from A to B while passing through X?

The figure consists of 3 layers of cubes, each \(2\times2\times2\) cm. Find the total area of the visible surfaces from the top and sides, in square centimetres.

Count all exposed top and vertical side surfaces, including sides hidden behind the drawing, but exclude the underside. The layers are complete 3-by-3, 2-by-2 and 1-by-1 square layers as intended by the source figure.

Find the sum of all the digits in the product $11111\times99999$.

The sum of Alice’s age and her uncle’s age is 33 years. In 3 years, her uncle will be twice her age. How old is Alice this year?

Many years ago, February had 5 Saturdays. On which day of the week was the last day of that year?

Enter the weekday in English or Vietnamese.

Enter only the weekday name, with no sentence or punctuation. Unrecognized text forms require manual checking and are ungraded by the offline checker.