SASMO 2027 · Grades 4-5 · SET 003 · Self-study

Editorial self-study SET for 2027; not an official SASMO 2027 examination. Known source years remain in individual attributions. Time: 90 minutes. Platform scoring starts at 0: Q1–15 are worth 2 points each; Q16–25 are worth 4 points each; wrong and blank answers score 0; maximum 70. Official SASMO scoring instead starts at 15, deducts 1 for an incorrect Section A answer and has a maximum of 85. Verified means editorially checked; assumptions, source errors and mathematical uncertainty are disclosed where relevant.

The radius of the circumscribing circle is 3 cm. Find the area of the shaded region, in cm².



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Diagram convention: the four inner circles are congruent, each passes through the centre of the outer circle and is internally tangent to it at one of four equally spaced points. Overlap lenses are unshaded. These geometric relationships are implicit in the source drawing.

ABCD is a square. E is the midpoint of AD and F is the midpoint of BC. The shaded area is 10 cm². What is the area of square ABCD, in cm²?



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The day before yesterday was Sunday. How many days are there from today until Saturday? For example, Monday to Wednesday is counted as two days. Enter the number of days.

Source variants: the lesson asks an open question. Grade 4 mock paper 2 offers A. 2; B. 3; C. 4; D. 5; E. None of these. Grade 5 mock paper 2 offers A. 5; B. 4; C. 3; D. 2; E. None of these.



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Brett is 18 years old. Daisy is half as old as Brett. Omar is 7 years older than Daisy. How old is Omar? Enter his age in years.



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Each row, each column and each of the two diagonals in the table have the same sum. Find (B − A ÷ C) × D.



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In the addition XYZ + YZ + Z = ???, equal letters represent equal digits and different letters represent different digits. Each question mark may be any digit. What is the greatest possible sum? XYZ is a three-digit number, YZ is a two-digit number, and the result shown has three digits.



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The figure is formed by overlapping two rectangles, one 5 cm × 8 cm and the other 7 cm × 9 cm. The overall width is 13 cm and overall height is 9 cm, as shown. Find the area enclosed by the figure, in cm².



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The figure is formed from identical small squares and has total area 275 cm². Find its perimeter in cm. Enter the number.

The lesson version is open-ended. The mock-paper variant offers A. 220 cm; B. 200 cm; C. 150 cm; D. 120 cm; E. None of these.



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How many three-digit odd numbers can be formed using the digits 1, 2, 3, 4 and 5, without repeating a digit within a number?



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Mary has 50 notes altogether, in denominations of 1, 2 and 5 dollars. Their total value is 150 dollars. The number of 2-dollar notes equals the number of 5-dollar notes. How many 1-dollar notes does she have?

How many more whole squares must be shaded so that the shaded region covers half the total area?

The operator □ acts on two numbers as shown: 17 □ 29 = 23; 19 □ 11 = 15; 31 □ 7 = 19. Find 13 □ 23.



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Pattern convention: use the same simple arithmetic rule suggested by all three examples, as intended by the source.

Every digit of a seven-digit multiple of 3 is 0, 2 or 3. There are more 3s than 0s, and each of 0, 2 and 3 occurs at least once. What is the sum of its digits?



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Find the next number: 3, 5, 9, 17, 33, ...



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Continue the simple consistent pattern in the successive differences, as intended in the source.

The source states: February 2, 2018 is Wednesday. Under that stated premise, what day of the week is February 28, 2018? Enter the weekday in English or Vietnamese.



Source-error notice: the stated weekday does not match the real calendar. Treat it as a hypothetical premise for this question.

Two teams plant trees. Team 1 has three fewer people than Team 2 but plants 15 more trees. Each person in Team 1 plants 5 trees, and each person in Team 2 plants 3 trees. How many people are in each team? Enter Team 1, Team 2, in that order, separated by a comma.

Each small square in the diagram has area 4 cm². Find the shaded area, in cm².



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Different letters represent different digits in DAD × 5 = GLAD. Find the four-digit number GLAD. Leading digits are nonzero.



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How many three-digit numbers with distinct digits can be formed using 0, 1, 2 and 3?



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How many integers from 16 to 2017 inclusive are divisible by 5?



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