c How will the scores vary between the maximum and minimum scores?
A
aMaxiumum Score: 50 points
Minimum Score: -50 points
B
bEquation:∣m−160∣=50
C
c{-50,-40,-30,-20,-10,0,10,20,30,40,50}
Practice makes perfect
aThe maximum score a team can earn on the math section is when they answer each question correctly. Then they would earn 10 points for each of the 5 questions. With this information, we can calculate the maximum score.
10⋅5=50points
A team would earn the minimum score if they gave an incorrect response to each question. Then they would lose 10 points, which is the same as earning -10 points. Regarding this, we can calculate the minimum score.
-10⋅5=-50points
b Let m1 be the highest score and m2 be the lowest score the McKinley team can have at the end of the math section. From Part A, we know that the maximum score they can earn is 50 and the minimum score is -50. Knowing that they have 160 at the start, we can determine m1 and m2 by adding and subtracting50 from 160.
Looking at the number line, we can write the equation that represents the maximum and minimum scores.
∣m−160∣=50
Let's solve it!
∣m−160∣=50
m−160≥0: m−160=50m−160<0: m−160=-50(I)(II)
m−160=50m−160=-50(I)(II)
(I), (II): LHS+160=RHS+160
m1=210m2=110
Therefore, the maximum score the McKinley team can have at the end of the math section is 210, and the minimum score is 110.
c From Part A, we know that the minimum score is -50 and the maximum score is 50. A team can only earn 10 points for a correct answer, lose 10 points for an incorrect answer, or earn 0 points on an unattempted question. Therefore, the possible scores will be every tenth value between -50 and 50. We can state them as a set.
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