SEAMO 2021 — Paper D — Grade 7–8

Evaluate $1/2021+(2020\times2022)/2021-2022$.

Terry scores seventy, eighty and ninety percent on quizzes with twenty, twenty-five and thirty problems. What overall percentage is correct, rounded to the nearest whole number?

Evaluate $\sqrt[3]{\sqrt{30}-\sqrt3}\times\sqrt[3]{\sqrt{30}+\sqrt3}$.

Which figure has the most lines of symmetry?

How many subsets of $\{S,E,A,M,O\}$ contain at least one vowel?

Evaluate $\sqrt{108\times110\times112\times114+16}$.

In a hundred-metre sprint Austin finishes twenty metres ahead of Bob and sixty ahead of Carson. Each keeps a constant speed. How many metres ahead of Carson does Bob finish?

Let U contain $2021$ consecutive nines and V contain $2021$ consecutive threes. Find the remainder of $U^{20}-V^{20}$ divided by eleven.

Count all squares in the grid, each cell being a square.

Eight unit squares form the shown figure. AB divides its area into equal halves. Find MA/NA.

Form N by concatenating integers $1001,1002,\ldots,1021$. Find the greatest power of three dividing N.

Solve $\frac92=2+\frac1{0+\frac1{2+1/x}}$.

Find the constant term in $(2x^2+x^{-3})^{10}$.

ABCD is a unit square, M the midpoint of AB. Find the shaded area.

A fair die is thrown three times, producing a,b,c. Find the probability that $a\gt b\gt c$.

Count nonnegative integer quadruples satisfying $a+b+c+d\le12$.

Two medians of a triangle have lengths twelve and fifteen. Find its maximum possible area.

Given $a/(2b-a)=5$, find $b/(2b-a)$.

Evaluate $\frac1{1\cdot2}+\frac5{2\cdot3}+\frac{11}{3\cdot4}+\cdots+\frac{71}{8\cdot9}+\frac{89}{9\cdot10}$.

ABC is acute. BE is an altitude and CF a median, with $BC=5,BE=CF=4$. Find its area.