SASMO 2027 · Grades 2-3 · SET 015 · 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.

How many squares of side 2 cm are needed to cover a rectangle 24 cm long and 8 cm wide?

Find the perimeter of the notched figure, in centimeters. The outer rectangle is 6 cm wide and 5 cm high. The rectangular notch is 2 cm wide and 1 cm deep.

A box contains 3 red, 4 yellow and 5 blue marbles. Bob draws without looking and without replacing marbles. What is the minimum number of draws that guarantees (a) one blue marble; (b) two yellow marbles; (c) two marbles of the same color? Give the three numbers in order, separated by semicolons.

If the day before yesterday was Friday, how many days are there from today until the next Friday? For example, Monday to Wednesday is counted as two days.

Compute (a) A=1+3+5+7+⋯+17+19; (b) B=1+2+3+4+⋯+19+20. Give A; B.

Four boxes are labeled W, X, Y and Z. W and Z are the same size. W fits inside X, and Y fits inside Z. Which statement is certainly true?

Use the source size model: fitting inside means strictly smaller, equal-sized boxes have interchangeable dimensions, and the given fits can be nested.

What is the largest two-digit number divisible by both 3 and 5?

Find the area of the figure in square centimeters. All corners are right angles; use the lengths shown: 8 cm along the base, outer heights 5 cm and 6 cm, top widths 3 cm and 2 cm, and the 2 cm drop on the right side of the notch.

Find the next number in the pattern 47, 44, 38, 29, 17, …

Continue the intended pattern in which each successive decrease is 3 greater than the previous decrease. A finite sequence can fit other rules.

A caterpillar doubles its length each day and is 32 mm long on day 12. The original languages ask different questions, so answer both: (a) Vietnamese variant: on which day is it 8 mm long? (b) English variant: is it exactly 8 cm long on any whole-number day? Enter the day for (a), then yes or no for (b), separated by a semicolon.

The source English says 8 cm, but its Vietnamese says 8 mm. Both variants are explicit here. Days mean whole-number daily observations; no continuous growth law is assumed.

A hotel porter mixes up 5 keys for 5 rooms. Each key opens exactly one room, and each room has one key. What is the smallest number of key-in-lock trials that is sufficient in the worst case to identify every key?

One trial means trying one key in one room lock. A remaining match may be inferred without trying it, and only identification is required, not physically opening all rooms. The source’s answer-only 24 is unresolved under its unspecified convention; this edition uses the explicit convention above.

A farm has 45 chickens and rabbits altogether. There are 4 times as many chickens as rabbits. Find (a) the number of chickens and (b) the number of rabbits. Enter chickens; rabbits.

A baker has 34 loaves of bread. Every box sold must contain 3 loaves. At most how many complete boxes can the baker sell?

Bart has a pack of M&M’s containing 3 red, 4 yellow and 5 brown candies. He draws without looking and without replacement. What is the smallest number he must draw to guarantee that among the drawn candies there are two of different colors?

Kenny is 26 years old and 8 years older than Sarah. How many years ago was Kenny three times as old as Sarah? The second source occurrence gives the identical question with Sean and John in place of Kenny and Sarah.

In the figure, equal shapes represent equal numbers. What number is hidden by the flower?

The pattern repeats 2, 0, 1, 9: 2, 0, 1, 9, 2, 0, 1, 9, … Find (a) the 22nd number and (b) the 32nd number. Enter (a); (b).

How many squares of all sizes are in the grid? Count squares whose complete sides follow the drawn grid lines.

The figure is made of identical squares of side 1 cm. What is its perimeter in centimeters?

Two squares A and B stand next to each other with their bottom edges aligned, as shown. Their total area is 74 square centimeters. Assuming both side lengths are whole numbers of centimeters, find the perimeter of the combined figure in centimeters.



The source implicitly tests whole-number side lengths but does not state that restriction. It is made explicit before answering; without it, the result is underdetermined.