Name_________________________________
9H Common Core Algebra – Mixed Review #5
Date________________
Directions: Complete work on a separate piece of loose-leaf!
1. Let A = 3x2 + 4x – 6 and
B = 2x3 + 3x2 + 1, write answers in standard form by simplifying:
b) A – B
a) A + B
c) A x B
d) A subtracted from B
2. Factor the following expression completely:
a) 18x – 8x3
b) 60y3 – 18y2 – 6y
c) 4x3 – x
d) x3y – xy + 5x2y – 5y
e)12x5 – 20x4 + 3x3
f) 5n2 + 5n – 360
3. Is -2x-3 + x2 + x – 4 a polynomial? Explain your answer
4. a) For what value(s) of p is x2 + px + 81 a perfect square trinomial?
b) For what value(s) of m is x2 + 2x + m a perfect square trinomial?
5. Solve each of the following quadratic equations and round your answer to the nearest hundredth:
a) 12n2 = 60
b) 3y2 – 144 = 40
c) 2(x – 5) 2 – 10 =24
6. Write an equation in standard form that has the given roots:
a) -3 or 7
b) 3 or 3/4
c) 0 or -1 or 5/6
7. Solve by using the quadratic formula. Give the solution in simplified radical form.
a) -m2 – m + 10 = 10m – 1
b) 4x2 + 13 = 16x
c) 3d2 – 8d + 3 =0
8. Solving by completing the square. Give the solution in simplified radical form.
a) 2x2 – 12x + 4 = 0
b) -3x2 – 8x + 4 = 0
c) 3x2 + 6x + 1 = 0
9. The length and width of a rectangle are represented by consecutive even integers. The area of the rectangle is
224 square inches. What are the length and width?
10. Leah is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed
is 34 square feet. Write and solve and equation to determine the width of the flower bed, to the nearest tenth of a
foot.
11. A rectangular picture measures 6 inches by 8 inches. Steve wants to build a wooden frame for the picture so that the
framed picture takes up an area of 100 square inches on his wall. The pieces of wood that he uses to build the frame all have
the same width. Determine the width of the pieces of wood used for the frame to the nearest tenth of an inch.
12. Brian’s rectangular patio measures 9 feet by 12 feet. He wants to increase the patio’s dimensions so its area
will be twice the area it is now. He plans to increase both the length and the width by the same amount, x. Find x
to the nearest hundredth of a foot.
13. The hypotenuse of a right triangle is 25 m long. The length of one leg is 10 m less than twice the other. Find
the length of each leg.