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UNIT #9 – ROOTS AND IRRATIONAL NUMBERS
REVIEW QUESTIONS
Part I Questions
1. Which of the following is the value of
(1) 16
(3) 40
(2) 5
(4) 13
36  2 25 ?
2. The expression 3 20 is equivalent to
(1)
60
(2) 12 5
(3) 6 5
(4) 6 10
3. If f  x   10  x  4 then f 12  
(1) 8
(3) 6
(2) 6
(4) 12
4. Which of the following is an irrational number?
(1) 5
(2)
4
9
(3) 10
(4)
8
3
5. Which of the following sums would represent an irrational number?
(1)
3 1

4 2
(2) 3  2
(3)
(4)
25  49
3
1

2
25
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
6. Given the function g  x   x  4 , which of the following values of x cannot be in the domain of g?
(1) x  1
(3) x  5
(2) x  2
(4) x  12
7. The function f  x   x  a  b is graphed on the grid below. Which of the following is the sum of a and b?
(1) 7
(3) 1
(2) 2
(4) 5
8. Which of the following is the solution set to the equation  x  2   25 ?
2
(1) 2, 5
(3) 3, 3
(2) 7, 3
(4) 5, 5
9. The solution set to  x  4   20 is
2
(1) x  4  2 5
(3) x  4  4 5
(2) x  6 5
(4) x  2 5
10. Over which of the following intervals is the function f  x   x  3  2 always increasing?
(1) x  3
(3) x  2
(2) x  3
(4) x  2
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
11. Which of the following equations has the same solutions as x 2  10 x  3  0 ?
(1)  x  5   3  0
(3)  x  5   22  0
(2)  x  10   3  0
(4)  x  10   3  0
2
2
2
2
12. When solving the equation x 2  20 x  11  0 using the method of completing the square, which of the
following quantities must be added to form a perfect square trinomial?
(1) 40
(3) 80
(2) 100
(4) 400
13. Which of the following represents the solutions to the equation x 2  6 x  4  0 ?
(1) x  4 and 6
(3) x  3  5
(2) x  3  10
(4) x  3  2 5
14. The positive solution to the quadratic equation 10 x 2  11x  6  0 is
(1) x  11  6
(3) x 
3
2
(2) x  6  11
(4) x 
2
5
15. If f  x   3 x  5  6 then f  3 
10
3
(1) 4
(3) 
(2) 8
(4) 2
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
Free Response Questions
16. Graph the function f  x   x  3  1 on the grid below. Show the table that you created by hand or using
your calculator. Then, state its domain and range.
Table:
Domain:
Range:
17. Give an example of a non-integer rational number and an irrational number.
Non-integer Rational Example
Irrational Number
If you added your two numbers, would the sum be rational or irrational?
18. The graph of f  x   x is shown below along with the
graph of g  x  . Determine a formula for the function
f  x  x
y
g  x .
g  x
x
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
19. Solve the following equation for all values of x.
2  x  5   13  31
2
20. Solve the following equation for all values of x. Express your answers in simplest radical form.
 x  2
5
2
 7  16
21. Solve the following quadratic equation for all values of x using the method of completing the square.
x2  8x  5  0
22. Algebraically determine the solutions to the equation shown below. Round your answers to the nearest
hundredth.
3 x 2  10 x  5  0
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
1 2
x  2 x  3 is shown graphed. Algebraically, find the value of the positive zero of this
2
y
function. Express your answer to the nearest tenth.
23. The parabola y 
x
24. Evin graphs the parabola y  x 2  4 x  7 and finds that it has no x-intercepts. Explain how you can verify
Evin's result algebraically by solving for the zeroes of the function.
25. Consider the function f  x   3 x  2  1 .
y
(a) Graph the function on the axes to the right.
x
(b) Over what interval is f  x   0 ?
COMMON CORE ALGEBRA I, UNIT REVIEWS – UNIT #9
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015