2020 CSAT Mathematics (Type Na)

What is the value of ?

For two sets , when , what is the value of ? (where are real numbers.)

What is the value of ?

The diagram shows two functions . What is the value of ?

For two events , Find the value of . (Note that is the complement of .)

For two conditions involving real number : What is the value of positive number such that is a sufficient condition for ?

For the function , when , what is the value of the constant ? (where )

The graph of function is shown in the figure. What is the value of ?

What is the minimum value of the real number such that the graph of the inverse function of and the line intersect at two distinct points?

For the function , what is the value of ?

When the function has local maxima at and , what is the value of ? (where are constants such that )

Two polynomial functions with integer constant terms and coefficients satisfy the following conditions. What is the maximum value of ? (a) (b)

For an arithmetic sequence with first term 50 and common difference -4, let be the sum from the first term to the th term. What is the value of the natural number that maximizes ?

Let be the number of positive divisors of a natural number , and let be all positive divisors of 36. What is the value of ?

From the numbers , allowing repetition, select five numbers that satisfy the following conditions and arrange them in a row. What is the total number of five-digit natural numbers that can be formed? (a) Each odd number is either not selected or selected exactly once. (b) Each even number is either not selected or selected exactly twice.

The sequence satisfies the following conditions for all natural numbers . (a) (b) When , find the value of .

Find the value of .

For a geometric sequence where all terms are positive, Find the value of .

A random variable follows a binomial distribution and . Find the value of .

For a natural number , let be the remainder when the polynomial is divided by . Find the value of .

Given two functions Let be the area of the region enclosed by the graphs of these functions. Find the value of .

Two points P and Q move on a number line. Their positions and at time are given by Find the distance between points P and Q at the moment when their velocities become equal.

A polynomial function satisfies the following conditions. (a) For all real numbers , (b) Given that , find the value of .

Find the number of ways to distribute 6 identical candies and 5 identical chocolates to three students , , and without any remainder according to the following rules: (a) Student receives at least 1 candy. (b) Student receives at least 1 chocolate. (c) The sum of the number of candies and chocolates that student receives is at least 1.

A cubic function with a positive leading coefficient satisfies the following conditions. (a) The equation has exactly 2 distinct real roots. (b) The equation has exactly 2 distinct real roots. Given that and , find the value of .