Name: _________________________________________
9H Test Review (Aims 50 – 58)
Directions: Work on loose-leaf!
1) Simplify the following radicals.
a)
b)
c)
d)
√150
√147
√60
√1200
e) √252
f) √405
g) √192
h)
10  50
5
2) Rewrite the following expressions by completing the square:
a) 𝑥 2 − 13𝑥 + 12
c) 3x 2  6 x  2
2
b) 𝑥 − 0.2𝑥 − 0.6
d) 6 x2  11x  10
3) Solve the following quadratic equations by factoring.
a) 2𝑥 2 − 4𝑥 = 0
d) 14𝑥 2 − 19𝑥 = 3
b) 𝑥 2 − 6𝑥 + 5 = 0
e) 9 − 4𝑥 2 = 0
c) 3x3 – 12x2 = 0
f) 2𝑥 2 = 9𝑥 + 5
g) 4 − 5𝑥 + 𝑥 2 = 0
h) −5𝑥 2 − 9𝑥 + 2 = 0
4) Solve the following quadratic equations by completing the square. Leave all answers in
simplest radical form when necessary.
a) 𝑥 2 + 6𝑥 + 1 = 0
b) 𝑥 2 − 10𝑥 + 13 = 0
c) 2𝑥 2 + 4𝑥 + 1 = 0
d) 3𝑥 2 + 30𝑥 + 74 = 0
5) Solve the following quadratic equations using the quadratic formula. Leave all answers in
simplest radical form when necessary.
a) 𝑥 2 + 3𝑥 − 7 = 0
c) −4𝑥 2 + 19𝑥 = −30
b) −𝑥 2 + 5𝑥 + 2 = 0
d) 5𝑥 2 − 8𝑥 − 3 = 0
6) Solve each word problem using an algebraic solution.
a) Find three consecutive integers such that the square of the first exceeds the sum of the
second and third by 45.
b) Find three consecutive even integers such that the product of the two smaller exceeds the
largest by 38.
c) The length of a rectangle is 1 less than 4 times its width. Find the dimensions of the
rectangle if the area is 33 square units.
d) A rectangle has a width and length whose dimensions are in a ratio of 3:8. Find the
dimensions of the rectangle if the area is 96 square units.
e) The perimeter of a rectangle is 52 units and the area is 168 units squared. Find the
dimensions of the rectangle.
f) The length and width of a rectangular picture is 10in by 4in respectively. A picture frame
of uniform width is placed around the picture. The new area of the picture and the frame
is 112 square inches. Find the width of the picture frame.