SEAMO 2021 — Paper C — Grade 5–6

Find the missing number in the three circles shown.

Form a three-digit number by choosing three distinct digits from $0,2,3,5,8$. What is the probability that it is even?

Square $BDEF$ is inside right triangle $ABC$, as shown. Given $AE=10$ cm and $EC=15$ cm, find the shaded area in square centimetres.

Define $m\ominus n=m^2-n^2$. Evaluate $(2021\ominus2020)\ominus(2020\ominus2019)$.

An item yields a profit of $180$ dollars when sold at a $10\%$ discount, and a loss of $240$ dollars at a $20\%$ discount. Find its cost price.

In the diagram, $\angle A=72^\circ$. The bisectors of $\angle ABC$ and exterior angle $\angle ACE$ meet at $D$. Find $\angle D$.

A two-digit number $\overline{ab}$ is descending when $a\gt b$. How many descending two-digit numbers are there?

The circle has diameter $AB=14$ and centre $O$. A semicircle with diameter equal to the left half of the horizontal diameter is unshaded, as shown. Find the shaded area, using $\pi=22/7$.

Study $1=1^2$, $1+3=2^2$, $1+3+5=3^2$, and so on. Find the largest odd $n$ for which $1+3+5+\cdots+n\lt 300$.

A whole number $m\lt 100$ makes the mean of $m,99,100,101,102,103,104$ a whole number. Find the sum of all possible $m$.

Put seven identical bean bags into four labelled baskets A–D, with at least one in each. How many ways?

Abel lies on Monday, Tuesday, Wednesday and tells the truth otherwise. Bernice lies on Thursday, Friday, Saturday and tells the truth otherwise. On which weekday can both say “I lied yesterday”?

Count all triangles in the figure.

Evaluate $(1+\frac12)(1-\frac13)(1+\frac14)(1-\frac15)\cdots(1+\frac1{2020})(1-\frac1{2021})$.

Find the smallest positive integer $k$ such that $2^{69}+k$ is divisible by $31$.

Find the units digit of $13^{243}+17^{381}+4^{2021}$.

Parallelogram $ABCD$ has perimeter $75$ cm. $AE\perp BC$, $AE=14$ cm; $AF\perp CD$, $AF=16$ cm. Find its area.

A triangle has whole-number side lengths and perimeter $27$ cm. How many different triangles are possible?

Remove all multiples of $3$ or $7$ from the positive odd numbers, leaving $1,5,11,13,17,19,23,25,29,31,37,41,\ldots$. Find the $2021$st term.

At $8{:}00$ am two dogs run towards each other from towns $3600$ m apart at $350$ and $450$ m/min. After one minute they both reverse, run two minutes, reverse and run three, and so on, increasing each leg by one minute. When do they meet?