Prueba cada modelo con dos o tres puntos de la tabla.
Trampas habituales
Interpretar la pendiente como si fuera el valor inicial.
Ejemplo resuelto
Recta de ajuste $y=3x+2$: para $x=4$ predice 14. Si el valor real es 15, el residuo es $15-14=1$.
Preguntas de ejemplo
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
Pregunta 1
Dificultad fácil≈ 2 min
$x$
0
1
2
3
$y$
5
10
20
40
The table shows four values of $x$ and the corresponding values of $y$. Which equation best models the relationship between $x$ and $y$?
AA. $y=5x+5$
BB. $y=5x2$
CC. $y=2(5)x$
DD. $y=5(2)x$
Ver respuesta y explicación
Respuesta correcta: D. $y=5(2)x$
Explicación
Each time $x$ increases by 1, $y$ doubles $(5, 10, 20, 40)$, which is exponential growth with factor 2 and starting value 5 at $x=0$: $y=5(2)x$.
$y=5x+5$ fits only the first two points (it gives 15 at $x=2$). $y=5x2$ gives 0 at $x=0$. $y=2(5)x$ gives 2 at $x=0$.
Pregunta 2
Dificultad media≈ 1 min
Which of the following equations best models the data in the scatterplot?
AA. $y=1.5x+40$
BB. $y=-1.5x+40$
CC. $y=-1.5x+10$
DD. $y=-0.2x+40$
Ver respuesta y explicación
Respuesta correcta: B. $y=-1.5x+40$
Explicación
The points fall from left to right, so the slope is negative. Moving from about $(2, 37)$ to $(20, 11)$, $y$ decreases about $26$ while $x$ increases $18$, a slope of about $-1.4$. Extending the trend back to $x=0$ gives a $y$-intercept near $40$. So $y=-1.5x+40$ fits best.
$y=1.5x+40$ rises instead of falling. $y=-1.5x+10$ has a $y$-intercept far below the data. $y=-0.2x+40$ is much too flat: at $x=20$ it gives $36$, not about $11$.
Pregunta 3
Dificultad difícil≈ 2 min
The scatterplot shows the weekly practice time $x$, in hours, and the number of puzzles solved $y$ in a timed contest for 12 members of a puzzle club. A line of best fit is also shown. For how many of the 12 members is the actual number of puzzles solved greater than the number predicted by the line of best fit by at least 2?
AA. $2$
BB. $3$
CC. $4$
DD. $5$
Ver respuesta y explicación
Respuesta correcta: B. $3$
Explicación
The line passes through $(0, 3)$ and $(10, 8)$, so it is $y=0.5x+3$. A member counts when $(\text{actual } y)-(\text{predicted } y)\ge 2$. For $(2, 6)$ the prediction is 4, a difference of 2; for $(5, 8)$ it is 5.5, a difference of 2.5; for $(8, 10)$ it is 7, a difference of 3. The only other points above the line, $(1, 4)$ and $(7, 7)$, are just 0.5 above it. So 3 members.
2 counts only points MORE than 2 above the line and leaves out $(2, 6)$, which is exactly 2 above. 4 also counts $(9, 5)$, which is 2.5 BELOW the line. 5 counts every point above the line.