SEAMO X 2019 — Paper C — Grade 5–6

How many small squares does the straight line cross in the $2019$th figure of the pattern?

A pencil costs five dollars and a pen three dollars. John spends forty-five dollars on $x$ pencils and $y$ pens. Find two sets of values $(x,y)$.

Weights of $1,2,4,8,16$ grams can be placed only on one end of a balance. How many different positive masses can be measured?

Maomao’s watch loses two minutes every actual hour. She sets it correctly at eight am. What is the actual time when it shows noon?

A special operation is defined by $5\times2=5+6=11$, $3\times4=3+4+5+6=18$, $6\times3=6+7+8=21$. Evaluate $1\times9+2\times9+\cdots+9\times9$ using this operation.

A circle of circumference one metre rolls without slipping around the outside of a square of perimeter four metres. How many full turns does it make in one circuit?

The mean score of Alan and Ben is $2.5$ marks above the mean of Alan, Ben and Charles. The mean of Ben and Charles is $1.5$ below the three-person mean. Ben scored $93$. Find Charles’s score.

Cindy has twelve sticks of different lengths. What is the minimum length in centimetres of the longest stick if no three form a triangle?

Profit is $25\%$ when a racket is sold at its labelled price. The number sold increases by another $1.5$ times when the labelled price is discounted “at $90\%$”. Find the percentage increase in total profit.

SEAMO X took place on January $19$, $2019$, written $20190119$, whose digit sum is $23$. How many days in $2019$ have a date digit sum of $23$?

Two semicircles have diameters on line $CD$. The chord $AB\parallel CD$ has length $12$ cm and is tangent to the smaller semicircle, as shown. Find the shaded area using $\pi=3.14$.

Given $1-\dfrac1{r+\dfrac1{s+\dfrac1{t+\dfrac1{u+1/s}}}}=\dfrac1{1+\dfrac1{2+\dfrac1{2+\dfrac1{3+1/3}}}}$, find $r+s+t+u$.

Square $ABCD$ has side four cm. $E$ is the midpoint of $BC$, and $DC=4DF$. Find the shaded triangle formed above the intersection of $AE$ and $BF$.

Mark starts at $A$, Nina at $B$, and jog back and forth between them at $300$ and $240$ m/min. $AB=2400$ m and both run thirty minutes. (a) How many times do they meet? (b) How far from A is their closest meeting to A?

Consecutive whole numbers $a,b,c$ satisfy $15\mid a$, $17\mid b$, $19\mid c$. Find their values.