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Algebra B1 Midterm Study Guide
Graph each system of equations. Then determine whether each
system has no solution, one solution, or infinitely many. If the
system has one solution, name it.
1.
y
1
x 1
2
y  x  2
3.
y
1
x 1
2
y
1
x3
2
2.
y  x2
y  3 x  2
Use substitution to solve each system of equations. If the
system does not have exactly one solution, state whether it has
no solution or infinitely many.
4.
x  4y
4 x  y  75
5.
y  x 1
y  3x  9
6.
5x  2 y  2
y  3x  2
Use elimination to solve each system of equations.
7.
4x  5 y  1
 4 x  2 y  10
8.
7 x  y  15
 3 x  y  7
9.
4 x  2 y  14
6 x  2 y  20
Use elimination to solve each system of equations.
10.
6 x  2 y  16
3x  4 y  17
11.
9 x  2 y  11
 3 x  4 y  7
12.
4 x  2 y  6
x  3y  9
Solve each system of inequalities by graphing.
13.
14.
y
1
x2
2
y
2
x 1
3
y2
y  3x  1
15.
y
1
x3
4
x3
Simplify.
16.
(6 x 2 y 3 )( x15 y 21 )
18.
2 x y  8x y 
3
4 4
2
17.
 5x
10
y4z2

3
9 2
Simplify. Assume that no denominator is equal to zero.
19.
j 15
j7
21.
3
x



6
20.
 a7
 5
b
22.
 j 4c0 f 5 


6
 jf

2
Express each number in standard notation.
23.
3.278 *10 5
Express each number in scientific notation.
24.
24,000,000
Find the degree of each polynomial.
25.
3x 4 y 3  11x 2 y 4  21x 5
Arrange the terms of each polynomial so that the powers of x
are in descending order.
26.
 7 x 2 y 4 2 x 3 y 2  8 x 7
Find each sum or difference.
27.
28.
29.
20abc  4xy  7df    12xy  8abc  5df 
6x  4x  12  4x  2x  10
8x y  4xy  8  5x y  11xy  19
2
3
2
3
Simplify.
30.
4 x5 x  3  13x 2
31.

3x6 x  2  x 3x 2  4 x  2

Solve.
32.
xx  3  17  xx  6  28
Find each product.
33.
x  3x  5
35.
5x  24x  4
34.
4x  23x  5
Find the prime factorization of each integer.
36.
 108
Find the GCF of each set of monomials.
37.
12 jk 2 ,18 j 2k 2 ,24 jf
Factor each polynomial.
38.
9 x 2  54 x
39.
25a 2b 2  30ab3
41.
8 x 2  16 x  0
43.
x2  4x  5
45.
x 2  10 x  25  0
47.
2 x 2  11x  15
50.
5 x 2  3x  2  0
Solve each equation.
40.
xx  28  0
Factor each trinomial.
42.
x 2  7 x  10
Solve each equation.
44.
x2  6x  5  0
Factor each trinomial.
46.
4 x 2  25 x  6
48.
8 x 2  10 x  3
Solve each equation.
49.
8 x 2  32 x  24  0