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Question

Difficulty Hard

Source:

ENEM

A store decides to reward its customers. Each customer will receive one of the six possible gifts available, according to their arrival order at the store. The gifts to be distributed are: a ball, a keychain, a pen, a soda, an ice cream, and a CD, in that order. The first customer at the store receives a ball, the second receives a keychain, the third receives a pen, the fourth receives a soda, the fifth receives an ice cream, and the sixth receives a CD. The seventh receives a ball, the eighth receives a keychain, and so on, according to the order of the gifts. The one-thousandth customer will receive as a gift a:

Sequence Terms

Difficulty Hard

Question

Question

Difficulty Easy

Source:

Teachy

Imagine you have 432 candies and want to separate them into containers of 100, 10, and individual units to facilitate counting. How would you make this separation? Explain your answer by showing how the number 432 can be decomposed into powers of 10.

Composition and Decomposition of Natural Numbers into Powers of 10

Difficulty Easy

Question

Question

Difficulty Medium

Source:

Teachy

Consider the linear system below:
2x + 3y = 10
5x - 4y = -7
Transform this linear system into a matrix form using a matrix A and a column vector X, representing the unknowns. Write down the resulting matrix equation and inform what is the dimension of matrix A.

Linear Systems: Written by Matrices

Difficulty Medium

Question

Question

Difficulty Very Hard

Source:

Teachy

Consider a Cartesian coordinate system where a point P has coordinates (a, b) and a point Q has coordinates (c, d). The absolute value of a number is defined as its distance from the origin of this system. If point P is in the second quadrant and point Q is in the fourth quadrant, with a, b, c, and d being integers, and it is known that the absolute difference between the y coordinates of P and Q is 15, determine the value of a - c, knowing that a < 0 and c > 0.

Absolute Value and Modulus

Difficulty Very Hard

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