spain-selectividad

Papers (16)
2025
selectividad__matematicas-II_modelo 7
2024
selectividad__matematicas-II_modelo 7
2023
selectividad__madrid_matematicas-II 8 selectividad__madrid_matematicas-II_extraordinaria 8
2022
selectividad__madrid_matematicas-II 8 selectividad__madrid_matematicas-II_extraordinaria 8
2021
selectividad__madrid_matematicas-II_extraordinaria 8 selectividad__madrid_matematicas-II_ordinaria 8
2020
selectividad__madrid_matematicas-II_extraordinaria 8 selectividad__madrid_matematicas-II_ordinaria 7
2019
selectividad__madrid_matematicas-II_extraordinaria 4 selectividad__madrid_matematicas-II_ordinaria 4
2018
selectividad__madrid_matematicas-II_extraordinaria 4 selectividad__madrid_matematicas-II_ordinaria 4
2017
selectividad__madrid_matematicas-II_extraordinaria 4 selectividad__madrid_matematicas-II_ordinaria 4
2017 selectividad__madrid_matematicas-II_ordinaria

4 maths questions

Q1 3 marks Simultaneous equations View
Given the following system of equations $\left\{ \begin{array} { l } 2 x + a y + z = a \\ x - 4 y + ( a + 1 ) z = 1 \\ 4 y - a z = 0 \end{array} \right.$
a) (2 points) Discuss depending on the values of the real parameter $a$.
b) ( 0.5 points) Solve the system for $a = 1$.
c) ( 0.5 points) Solve the system for $a = 2$.
Q2 3 marks Vectors 3D & Lines Multi-Part 3D Geometry Problem View
Given the points $P ( 1 , - 2,1 ) , Q ( - 4,0,1 ) , R ( - 3,1,2 ) , S ( 0 , - 3,0 )$, it is requested:
a) (1 point) Find the equation of the plane containing $\mathrm { P } , \mathrm { Q }$ and R.
b) (1 point) Study the relative position of line $r$, which passes through points P and Q, and line $s$, which passes through R and S.
c) (1 point) Find the area of the triangle formed by points $\mathrm { P } , \mathrm { Q }$ and R.
Q3 2 marks Applied differentiation Applied modeling with differentiation View
A medicine is administered to a patient and t hours later the blood concentration of the active ingredient is given by $c ( t ) = t e ^ { - t / 2 }$ milligrams per milliliter. Determine the maximum value of $c ( t )$ and indicate at what moment this maximum value is reached. Knowing that the maximum safe concentration is $1 \mathrm { mg } / \mathrm { ml }$, indicate whether there is risk to the patient at any time.
Q4 2 marks Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer) View
Given the function $f ( x ) = \frac { x ^ { 2 } + x + 6 } { x - 2 }$, it is requested:
a) ( 0.5 points) Determine its domain and vertical asymptotes.
b) ( 0.5 points) Calculate $\lim _ { x \rightarrow \infty } \frac { f ( x ) } { x }$.
c) (1 point) Calculate $\int _ { 3 } ^ { 5 } f ( x ) d x$.