Algebra 1 Benchmark 2.0
2 nd Semester Benchmark Toolkit
Topic: Rules of Exponents
Simplify the following. Express without any negative exponents.
1. 0
8 x y

4
2.

5
3 5 x y

3
4 x y

3. (5

3 5 2 x y ) 8
7 x y
4.
4 x y 6
Algebra 1 Benchmark 10.0
Simplify the following:
1. ( x
2 
4 x
  x x
3  
6)
Topic: Adding, Subtracting, and Multiplying Polynomials
2. (3 x
  
3)
2
3. ( x

4)( x
2 
3 x

5)
Algebra 1 Benchmark 11.1
Factor the following polynomials:
1. x
2  
30 2. 2 x
2 
3 x

14
Topic: Factoring Polynomials
3. 2 y
3 
8 y
2 
10 y

Algebra 1 Benchmark 11.2
Factor the following polynomials:
1. x
2 
64 2. 25 x
6 
16 y
2
Topic: Factoring Special Polynomials
3. 25 x
2 
40 x

16
Algebra 1 Benchmark 21.0
Graph and label the zeros, axis of symmetry, and vertex. y
 x
2 
2 x

3
Topic: Graphing Quadratics y x
Algebra 1 Benchmark 14.1
1. Solve.
(2 x

3)(3 x
 
0
Topic: Solving Quadratic Equations by Factoring
2. Solve by factoring.
x
2 
4 x

32

Algebra 1 Benchmark Radicals
Simplify the following radicals:
1. 80
2.
81
49
Topic: Simplifying Radicals
3. 8 5

5

2 5
Algebra 1 Benchmark 14.2 Topic: Solving Quadratic Equations by Completing the Square
1. Solve.
(2 x

1)
2 
9
2. Solve by completing the square. x 2 
8 x
 
14
Algebra 1 Benchmark 20.0 Topic: Solving Quadratic Equations by Quadratic Formula
1. Solve by using the quadratic formula.
2 x
2 
3 x
 
1

Algebra 1 Benchmark 22.0
1. How many times does the following graph intersect the x-axis? y
 x
2 
3 x

8
Topic: Discriminant
2. How many solutions does the following quadratic equation have?
5 x
 
2 x
2 
3
Algebra 1 Benchmark 23.0 Topic: Solving Quadratic Word Problems
What if you throw an egg straight up in the air at an initial velocity of 20 ft/sec. How long will it take before it hits the ground, if you released the egg at an initial height of 4 ft? s
 
16 t
2  v t
0
 s
0
, s
0

,
0

,
 final height
Algebra 1 Benchmark 12.0
Simplify the following expressions.
1.
2 x 2 
18 x
2 
2 x

15
Topic: Simplifying Rational Expressions
2. x
2 
10 xy

25 y
2
2 x
2 
10 xy

Algebra 1 Benchmark 13.1
Simplify the following expressions.
1. a a
2


9

6 a
2 
3 a

18
2 a

6
Topic: Multiplying and Dividing Rational Expressions
2. x
3 x
2 
4 x

4

10 x
2 
16 x

9 x
2 
1 x
2 
8 x
Algebra 1 Benchmark 13.2 Topic: Solve and Simplify Rational Expressions/Equations
1. Solve: a
5

2

3 a
7

2
2. Simplify: x
2 x


20

5
5 x

5
Algebra 1 Benchmark 9.1 Topic: Solving Systems by Substitution and Elimination
1. What ordered pair is the solution to this system? 2. What ordered pair is the solution to this system?
(Use substitution) x

2 y

2 y x 1
(Use elimination/linear combinations)
3 x

2 y

2
5 x 3 y
 
1
(__,__) (__,__)

Algebra 1 Benchmark 9.2
1. During the basketball game, there were 300 tickets sold and they made $1,200. The student tickets were $2 and the adult tickets were $5.
How many adult tickets were sold?
Topic: Solving Systems Word Problems
2. Josh has $20 and is saving $5 a day. Sal has
$160 and is spending $2 a day. After how many days will they have the same amount of money?
Algebra 1 Benchmark 9.3
1. equations? (Use graphing) y y
What ordered pair is the solution to this system of
 
2

3 x

1
3
Topic: Graphing Linear Systems of Equations and Inequalities
2. Graph the solution to this system? x
 
1 x

2 y

2
(__,__)