Question

A teacher adjusts the grades of an exam using a curve. If a student's raw score on a test is x, the score based on the curve is given by the function c(x) = 10
`√(x)` .

Five students received raw scores of 49, 42, 55, and 72. What are their scores according to the curve?

Answer 1

70, 65, 74, 85

Explanation:

Given function:

`c(x)=10 √(x)` (where
`x` is the raw score)

Given raw scores:

49, 42, 55, 72

To find the students' scores according to the curve, substitute the raw scores into the equation and solve for
`c(x)`, giving each answer to the nearest whole number:

`c(49)=10 √(49)=10 \cdot 7=70`

`c(42)=10 √(42)=65\: \sf(nearest\:whole\:number)`

`c(55)=10 √(55)=74\: \sf(nearest\:whole\:number)`

`c(72)=10 √(72)=60 √(2)=85\: \sf(nearest\:whole\:number)`

Answer 2

Theirs scores according to graph:

70, 65, 74, 85

• Equation provided: c(x) = 10√x

To find their scores, simplify substitute the raw scores with x

i)

c(49) = 10√49

c(49) = 10(7)

c(49) = 70

ii)

c(42) = 10√42

c(42) = 64.807

c(42) ≈ 65

iii)

c(55) = 10√55

c(55) = 74.162

c(55) ≈ 74

iv)

c(72) = 10√72

c(72) = 84.853

c(72) ≈ 85