SEAMO 2016 — Paper C — Grade 5–6

Evaluate $100-98+96-94+\cdots+8-6+4-2$.

Find the missing number: $4,6,10,14,22,26,34,(\quad),46,\ldots$.

In pentagon $ABCDE$, $AB=BC=CD=DE=AE$. Find $\angle y$ at $C$ as shown.

Heavy traffic reduces Mr Wang’s speed by $20\%$. By what percentage does the time for the same journey increase?

How many paths from $A$ to $B$ pass through $X$ in the grid? Move only down and right.

Jane walks from home to school. Her brother cycles out to deliver her forgotten pencil case. After receiving it, Jane takes another $4$ minutes to reach school; her brother reaches home at the same time. Cycling speed is three times walking speed. How long is Jane’s whole walk?

Two fair dice are rolled. What is the probability that the sum of their upper faces is $8$?

A bag contains $8$ red, $7$ white, $5$ yellow, $3$ blue and $2$ black balls. Draw without looking or replacement. What is the least number guaranteeing four balls of one colour?

The average ages of $m$ teachers and $n$ engineers are $32$ and $40$. Their combined average age is $35$. Find $m+n$.

Chicken nuggets are sold only in boxes of $4$ or $7$. What is the largest number of nuggets that cannot be bought?

The diagram shows three successively inscribed squares and two circles. The largest square has side $14$ cm. Find the area of the smallest square.

On the number line, $2a=3b-8$. Find $2c+d$. The marked positions are shown.

Evaluate $\frac12+\frac1{2\times2}+\frac1{2\times2\times2}+\cdots+\frac1{2^8}$.

In triangle $ABC$, $D,E,F$ are midpoints of $CE,AF,BD$ respectively. The area of $ABC$ is $56\text{ cm}^2$. Find the area of $DEF$.

Find the $2016$th digit after the decimal point in $5/7$.

Whole numbers $r,s,t,u$ satisfy $2^r3^s5^t7^u=252$. Find $r+2s+3t+4u$.

How many triangles can be formed with any three of the seven marked points as vertices?

Evaluate $\frac{2016}{2016^2-2015\times2017}$.

John cuts away one sixth of a pizza. The remaining curved circumference is $15\pi$ inches. Find the original diameter in inches.

A shop has $200$ kg of oatmeal. On day one it sells half, day two one third of the remainder, day three one quarter, and so on through day $199$, when it sells $1/200$ of the remainder. How many kilograms remain?