SASMO 2027 · Grades 4-5 · SET 009 · 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.

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

In the figure, square ABCD has area 36 cm², rectangle CDEF has area 18 cm², and rectangle ADGH has area 48 cm². Find the perimeter of BFEDGH in centimetres.

Different letters stand for different digits from 1 to 9 in the subtraction shown. Find the four-digit number $\overline{GHKE}$.

Find a in the four diamond diagrams.



Use one simple common arithmetic rule for all four diagrams, as intended by the source.

Find a+b+c if $\overline{173a}$ is divisible by 6, $\overline{173b}$ is divisible by 9, and $\overline{173c}$ is divisible by 10. Here a,b,c are digits.

A football hits Miss Cookson’s back. Three suspects are questioned. Alex: “I did not do it.” Ben: “I saw Alex kick that shot.” Cindy: “Alex lied.” Exactly one of them lied. Who kicked the football?



Assume exactly one of these three people kicked the ball. In the solution table T means true and F means false.

The sum 2019+n is divisible by both 5 and 9. Find the smallest value of n. In this question n is a nonnegative integer.

Find all digits x such that $\overline{2x5}$ is divisible by 3. Enter the digits in increasing order, separated by commas.

How many triangles can be formed by choosing three of the six points shown as vertices?

Minh learns 2 English words on Monday, 3 on Tuesday, and one more each day until 8 on Sunday. This weekly schedule repeats. If Minh starts on Monday, on which weekday will the 100th word be learned?

A group of 9 people visits a science centre. An adult ticket costs 10 dollars and a child ticket costs 5 dollars. They pay 70 dollars in total. How many children are in the group?

A square of side 16 cm and a rectangle of breadth 4 cm have the same perimeter. What is the rectangle’s length in centimetres?

Given $16\odot9=8$, $11\odot5=16$ and $3\odot7=5$, calculate $(11\odot(3\odot7))\odot9$.

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

Calculate 17×8+17×12.

A square is partitioned into five squares and one rectangle as shown. The shaded square has area 4 cm². Find the area of the rectangle.

The ratio of Amy’s weight to Hadi’s is 5:11. Hadi loses 16 kg, and their new weight ratio is 3:5. Amy’s weight stays unchanged. What was Amy’s initial weight in kilograms?

Find the 100th term of the digit sequence 1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,… . It is formed by writing the positive integers consecutively and treating each digit as one term.

Variant 1 (worked example): Ten points are given, with no three collinear. How many triangles have vertices among them? Variant 2 (practice paper): Ten points lie on a circle. How many triangles can be formed by choosing any three as vertices? Give the common answer.

The sum of Jack’s and Mark’s ages is 11 years. What will the sum be in 3 years?