PIMSO 2022 - Mathematics - Grade 7 / Secondary 1 - National Round

Consider all the numbers from 1 to 1200. How many of these numbers are NOT divisible by either 2, 5, or 7?

Consider the base-20 system using the first 20 letters of the Alphabet below.



How will you write $3000_{10}$ using this base-20 system?

Using the base-20 system in #2, what is RAF minus LBC in binary system?

Context from Question 2: A=0, B=1, ..., T=19 in base 20.

Enter digits only, without a base subscript.

Convert your answer in #3 into the base-3 system.

Context: Question 3 asks for RAF minus LBC, using A=0, B=1, ..., T=19 in base 20.

Enter digits only, without a base subscript.

What is the sum of this series up to its 2020th term? $$\frac19+\frac1{18}+\frac1{30}+\frac1{45}+\cdots$$

Pattern convention: continue the denominators using consecutive-factor products.

If we divide the product of 1 × 2 × 3 × 4 × 5 × ⋯× 770 by 773, what will be the remainder?

In the 2022 PIMSO Math National examination, a student attempted 23 questions and got 45 points. If for every correct answer 3 points were awarded and for every wrong answer 1 point was deducted, then how many answers were wrong?

At the end of a meeting, seven students shake hands with each other once. How many handshakes will be there altogether?

Robert is at 10th position from the top. In the class of 50 students, there are 26 students between Migs and Robert. How many students are there in between Migs and the last student in the class?

My mother is three times older than my sister. My father is 30 years older than me. I was 5 years old when my sister was born. If the present age of my sister is 15 years, then the difference between my mother’s and father’s age is ____.

Interpretation note: “three times older” is taken to mean “three times as old”.

11, 202, 3443, 9779 and 88,888 are examples of palindromic numbers. How many two- digit, three-digit and four-digit palindromic numbers less than 2022 are there?

Complete the series: 13, 25, 1, 37, –11, ___.

Pattern convention: alternate addition and subtraction with the successive positive multiples of 12.

Simplify: $$2023\left[\frac1{2\times1}+\frac2{3\times4}+\frac3{4\times9}+\frac4{5\times16}+\cdots+\frac{2021}{2022\times2021^2}+\frac{2022}{2023\times2022^2}\right].$$

If $P=\{p,i,m,s,o\}$ and $C=\{c,i,s,m,o\}$ then $\mathfrak R=\{x\mid x\text{ is a subset of }P\}$ and $\mathfrak F=\{y\mid y\text{ is a subset of }C\}$. Let N be the number of subsets in $\mathfrak R$ and M be the number of subsets in $\mathfrak F$. Let X be the number of common elements of $\mathfrak R$ and $\mathfrak F$. Find $N+M-X$.

Interpretation note: count the subsets of P and C that are elements of the displayed power sets.

Simplify $\left[\frac{(2-1.999\ldots)^{10}}{64}\right]^2\left[\frac{(2+1.999\ldots)^{10}}{32}\right]^2$.

Simplify: 1,111 + 2,212 + 3,313 + 4,414 + 5,515 + 6,616 + 7,717 + 8,318 + 9,419 + 10,520 + 11,621 + 12,722 + 13,823 + 14,924

If r and s are roots of the quadratic equation $x^2-x-1=0$, find $r+s$.

What is the sum of the roots of $ax^2-2022x-2023=0$ if $a=2$?

___________ is the point of intersection of the angle bisectors of a triangle.

A rectangle lies on 2 intersecting identical circles such that the points of intersection of the 2 circles are also intersected by the rectangle. The radii of the circles are 37 mm each while the width of the rectangle is 70 mm. What is the distance between the centers of the 2 circles?