Study Island – Algebra
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1. Solve the system of equations.
y = x+4
y = x2 + 9x + 19
A. (3, 7) and (5, 9)
B. (-3, -7) and (-5, -9)
C. (-3, 1) and (-5, -1)
D. (-3, -1) and (-5, 1)
2. The height in feet of an object above the ground t seconds after being projected into the sky is shown by the
function below.
Which statement best describes the term 6?
the velocity of the object
A.
B.
C.
D.
the time before the object hit the ground
the highest point the object reached
the initial height of the object
3. Ted is building a square-shaped deck around a tree in his backyard. The empty area which holds the tree is in
the shape of a square with a side length of 5 feet, and the deck has a side length that is x ft longer.
Which of the following inequalities could be used to solve for x if Ted wants the area of the deck to be at least
171 square feet?
x2 + 10x - 171 > 0
A.
B.
C.
D.
x2 + 10x + 171 > 0
x2 + 10x - 171 < 0
x2 + 10x + 171 < 0
4. Simplify the following expression.
(2x - 6)2
A. 4x2 + 24x + 36
B. 4x2 - 36
C. 4x2 - 24x + 36
D. 4x2 + 36
5. The length of a rectangle is 3 units less than 6 times its width. The area of the rectangle is 131 square units.
Which of the following equations can be used to find w, the width of the rectangle?
A. 7w - 3 = 131
B. 6w2 - 3w = 131
C. 7w - 18 = 131
D. 6w2 - 18w = 131
6. A company installs circular swimming pools. Each pool has a radius of 10 feet. The company also tiles the
area around the pool in such a way that the tiles form a square with at least 4 feet of tile extending from the edge
of the pool. The situation is shown in the following figure.
A customer wants their tiled area to be no larger than 100 square feet. Which of the following inequalities can
be used to solve for the length x?
x2 + 36x + 424 - 100 < 0
A.
B.
C.
D.
x2 + 36x + 224 - 100 > 0
x2 + 36x + 424 - 100 > 0
x2 + 36x + 224 - 100 < 0
7. Factor the polynomial below.
x2 + 7x + 12
A. (x - 3)(x + 4)
B. (x - 3)(x - 4)
C. (x + 3)(x - 4)
D. (x + 3)(x + 4)
8. Susie bought a rectangular rug for her living room that had a square pattern. Each square on the rug has a side
length of s inches. The length of the rug was 2 inches longer than than 8 times the length of one side of one
square in the pattern. She found the area of the rug in square inches with the equation shown below.
Which statement best describes the term (48s2)?
the width of the rug
A.
B.
C.
D.
the area of the rug that is covered by squares
the perimeter of the squares on the rug
the area of the rug that is not covered by squares
9. Solve the system of equations.
y = x+3
y = x2 + 10x + 21
A. (3, 6) and (6, 9)
B. (-3, -3) and (-6, 0)
C. (-3, 0) and (-6, -3)
D. (-3, -6) and (-6, -9)
10.
A.
B.
C.
D.
11.
A.
B.
C.
D.
12. Simplify the following expression.
(8m - 3n)(7m + 9n)
A. 15m + 12n
B. 56m2 + 93mn - 27n2
C. 56m2 + 51mn - 27n2
D. 56m2 - 27n2
13. Walter owns a small online business that makes and sells jewelry. The revenue function of Walter's small
business can be shown by the function below, where x represents the number of days in business.
Which statement best describes the constant term?
a profit of $12 per jewelry piece sold
A.
B.
C.
D.
a daily profit of $453
a start-up cost of $453
a $12 cost of operation per day
14. Solve the following equation for x.
x(x - 2) = 48
A. x = -6; x = 8
B. x = -6; x = -8
C. x = 6; x = 8
D. x = 6; x = -8
15. Simplify the following expression.
A.
B.
C.
D.
16. Solve the following equation for x.
4x2 - 117 = 5x2 + 22x
A. x = 13; x = 9
B. x = -9; x = 13
C. x = -13; x = -9
D. x = 9; x = -13
17. Simplify the following expression.
(-4x - 5) + (3x2 + 6x + 4)
A. 3x2 + 2x - 1
B. -3x2 + 2x - 9
C. 10x - 1
D. 3x2 + 10x - 1
18. Simplify the following expression.
(-7x + 2) - (3x2 - 2x - 8)
A. -3x2 - 5x + 10
B. -3x2 - 10x + 16
C. 3x2 - 5x + 10
D. 3x2 - 5x + 6
19.
A.
B.
C.
D.
20. Solve for x.
A.
B.
C.
D.