Linear, Quadratic and Exponential Models Practice

CCSS Algebra Practice

 





This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
1F.LE.1
2F.LE.1b
3F.LE.1
4F.LE.1c
5F.LE.1c
6F.LE.2
7F.LE.3
8F.LE.4
9F.LE.5
10F.LE.5
indicates a modeling standard.

All questions of this quiz illustrate the difficulty of the high school F.LE standards required for all students, including the college and career ready students.



Question 1: Given the exponential functions f(x) = a·2x and g(x) = b·4x, find the values of a and b if both functions intersect in point A of coordinates (1, 2).








Question 2: Which of the functions, f1(x), f2(x) and f3(x) from the table below are quadratic or exponential?

xf1(x)f2(x)f3(x)
1564-1
2732-4
3916-9
4118-16
5134-25
6152-36








Question 3: A bank account was opened with $1,000 and a fixed interest of 5%, compounded yearly. After five years, the interest rate was lowered to 3%, also compounded yearly. What is the balance of the account nine years after the account was opened?








Questions 4 and 5: A new species of frogs is released into a pond. The growth of the population of this new species is modeled by P(t) = a·bt , where t is the time in months following the introduction and a and b are positive unknown numbers. After 2 months, the number of frogs is 45 and 3 months after the release, the number of frogs is 135.

The number of frogs released into the pond is:

The value of the exponential base b is:



Question 6: One thousand dollars is invested in a high yield account that pays an interest rate of 7% compounded annually. The first time the sum in the account is more than triple the sum invested is after years.



Question 7: The table below shows values of functions f(x) = 2x and g(x) = x(x + 100) for x ≥ 1:

xf(x)g(x)
12101
24204
38309
416416
532525


What is the smallest positive non-zero integer x for which f(x) > g(x)?








Question 8:



What is the value of x for which f(x) = 10?








Questions 9 and 10: The ticket prices advertised by an airline agency are given in the table below:

Distance D (miles)Fare F ($)
510371
850405
1530473


Assuming a linear relation between the distances traveled and fares, if F = a·D + b, then:

a = 0.08 b = 250
a = 0.1 b = 280
a = 0.15 b = 290
a = 0.2 b = 300
a = 0.25 b = 320




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