Algebra 2 Summer Review Assignment
This assignment should serve as a review of some of the Algebra skills necessary for success in Algebra 2. Our hope is that this review will keep your mind mathematically active during the summer, identify weaknesses in Algebra, if they exist, and prepare you for the fun and challenging year ahead. We expect that you come to class knowing this material and ready to continue learning Algebra. Answer all questions on separate paper. SHOW ALL WORK. This assignment will be collected for a grade on the first day of school.
Enjoy your summer!!
I. Solve the systems of equations.
1) 5x + 4y = 6 2) -2x + y = 8 3) -x + 2y = 11 4) 3x - 2y = 5
-2x - 3y = -1 y = -3x – 2 3x - 2y = -13 -6x + 4y = 7
II. Solve the linear equations.
1) -4(3 - x) = 2(x + 6) 2) 2(3x + 6) + 8 = 6x 3) 3x - 2(x + 1) = 0
4) 3(x + 2) + 1 = 2x + 7 + x
III. Factor.
1) x2 - x - 72 2) 7x3 - 4x2 + 8x 3) a2 + 20a + 64
4) 10m3n2 - 15m2n - 25m 5) x2 - 64 6) 2x2 + 9x – 5 7)
IV. Solve the quadratic equations.
1) r2 + 10r - 9 = 0 2) p2 + 6p = 0 3) m2 – 3m = 10
4) (2x + 1)(x + 3) = 0 5) x2 = 4x + 32 6) 2t2 – 3t - 2 = 0
7) x2 = 16 8) n2 + 5n - 1 = 0
V. Write the equation of the following lines (use y = mx+b).
1) through ( 0, -1 ) with m = -1 2) through ( -2, 3 ) with m =
3) through ( 3, -1 ) with m = 0 4) vertical, through ( 5, 4 )
5) through ( 2, 3 ) and ( 7, -2 ) 6) through ( 3, 4 ) and ( -2, 4 )
VI. Solve.
1) 2) 3) 4) 5)
VII. Find the solution for the given matrix operations.
1) A + B= 2) A – B 3) -2C
VIII. 1) Find the area of a rectangle with L = 2x + 3 and W = x - 2
2) Find the area of a square with s = 2x + 5
3) The area of a square with side 2x - 1 is 49. Find x
4) A baseball diamond is a square 90 feet on each side.
How far is it from 1st to 3rd base?
5) Find the diagonal of a rectangle with L = 40 and W = 55.
6) An isosceles right triangle has leg = 4 cm. What is the length of the hypotenuse?
7) A 30 - 60 -90 triangle has shortest leg = 4 cm.
Find the measure of the other sides.
8) A 30 -60 -90 triangle has longest leg = 5. Find the measure of the other sides.
IX. Simplify.
1) ( -3x2 + 4x - 7 ) + ( 2x2 - 7x + 8 )
2) ( 39a4 - 4a3 + 2a2 - a - 7 ) - ( 10a4 + 3a3 - 2a2 - a + 8 )
3) 4) -3xy3 (x - 2y) 5) (3x2 + x - 1) (2x - 3)
6) ( 8a3b2 ) ( 2a-4 b-5 ) 7) (-3x2y3z )3 8) ( 15a4b2c )0
9) 10) 11)
X. Graph each function and find the following properties for each.
Domain, Range, Increasing/Decreasing Interval(s), Minimum, Maximum, x-intercepts/zeros, and y-intercepts.
1) y = -x + 4 2) 2x + 3y = 12 3) y = (x - 2)2 + 1
4) y = x2 + 6x + 1 5) y = 2(2)x
XI. Simplify the following fractions.
1) 2) 3)
XII. Divide.
1) 2) 3)