SASMO 2027 · Grades 4-5 · SET 011 · 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 two-digit numbers have a tens digit greater than their units digit?

A big box holds 12 marbles and a small box holds 6 marbles. Eighty-four marbles are put into 10 boxes. How many big boxes are there?



Assume every box used is filled to capacity, as in the source solution.

Team A can repair a road alone in 45 days. Working together, teams A and B complete $\frac{7}{12}$ of the work in 15 days. Team A then leaves for other projects. How many more days does B need to finish the road? Assume constant work rates.

If the five-digit number $\overline{2a344}$ is divisible by 3, how many possible values of this number are there? Here a is a digit.

Choose one digit from each group {1,4,7}, {2,5,8}, {3,6,9}. Arrange the three chosen digits in any order. How many resulting three-digit numbers are divisible by 6?

Which number should be removed from 1,3,5,7,9,11,13,15,17,19 so that the remaining nine numbers have sum 89?

How many triangles are there in the following figure?

Find the value of $\frac35+\frac8{11}+\frac25+\frac79+2\frac{44}{21}+\frac{11}9+\frac3{11}-3\frac2{21}$. The notation $2\frac{44}{21}$ means $2+\frac{44}{21}$, as in the source.

Which figure A–E is the mirror reflection of the given star? The mirror is to its right.

In one month, three Fridays fall on even-numbered dates. What day of the week is the 14th of that month?

Every side of every hexagon in the figure is 3 cm. What is the perimeter, in cm, of the combined figure?

On an island, every native is either a Valak, who always tells the truth, or a Laka, who always lies. A visiting couple hires a native helper. They see another native, and the husband asks the helper to find out which group that native belongs to. The helper returns and reports, “He said that he is a Laka.” The wife concludes that the helper is dishonest and dismisses him. Is her conclusion correct? Explain why.

If $\overline{1a58}$ is divisible by 3, how many possible values of this four-digit number are there? a is a digit.

Nine identical circles are inscribed in the square as shown. The square has side 60 cm. Find the total shaded area in cm². Use π=3.14.

Alex arranges 30 squares in a row, coloured black and white following the pattern shown. How many more black squares than white squares are there?



Continue the repeating colour block shown in the source; the finite picture alone could allow other patterns.

Find the next fraction: $\frac13,\ \frac12,\ \frac59,\ \frac7{12},\ \frac35,\ldots$

Use the source’s intended pattern: equivalent fractions can be written with numerators and denominators each forming an arithmetic sequence. Finite sequences can otherwise have other continuations.

If the five-digit number $\overline{5435A}$ is divisible by 9, what is the digit A?

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.



Enter a number only.

Heidi has three different toy bears and wants to place them in one row on her desk. In how many ways can she arrange them?

Fill the grid with four shapes (circle, triangle, square, pentagon) and numbers 1,2,3,4 so that every row and every column contains each shape once and each number once. What shape belongs at the question mark? Enter the shape name.



Answer only the shape; the number is not requested. Shapes and numbers each obey their own no-repeat rule.