Algebra Enrichment
2nd Semester Final Exam Review
Name ___Key_________________
DO ALL WORK AND ANSWERS ON A SEPARATE SHEET OF PAPER. CIRCLE FINAL
ANSWERS.
Show all work. Round all answers to the nearest tenth.
Chapter 5
1) Find the x-intercepts and the y-intercepts. Then graph the line.
A) 6x – 4y = 24
X: ( 4 , 0)
Y: (0, -6 )
B) y =
−2
𝑥
3
-4
X: ( -6 , 0)
Y: (0, -4 )
2) Find the slopes of the following.
A) (-3, 5) & (4, -9)
B) (4, 0) & (-2, 10)
C) Line c
D) Line d
c
A) -2
B) 5/3
C) 6/5
D) 0
7 = 7x + 4x + 7
<b>answ er:</b
3) Find the slope and the y-intercept of each line. Then graph each line.
2
−1
A) 𝑦 = 5 𝑥 – 3
B) 𝑦 = −3𝑥
C) 𝑦 = 4 𝑥 + 2
d
D) 𝑦 = 2𝑥 + 4
Ch 8
4. Graph each system of equation. Then determine whether the system has one, no or infinitely
many solutions. If the system has one solution, name it.
a) y = -x
y = 2x -6
(2, -2)
b) 2x + 4y = 2
3x + 6y = 3
infinitely many
c) 3x + y = 2
2x + y = 3
(-1, 5)
5. Use substitution to solve each system of equations.
a) 3x – 2y = -7
y=x+4
(1, 5)
b) 2x – 6y = 5
y=x+3
(-23/4, -11/4)
6. Use elimination to solve each system of equations.
a) x + y = 4
x–y=7
(5.5, -1.5)
b) -2x + y = 5
2x + 3y = 3
(-2, 2)
c) 5r – 3s = 17
2r – 3s = 9
(8/3, -11/9)
7. Solve each system of equations
a) y = 3x
x+y=4
(1, 3)
b) x + 4y = -8
x – 4y = -8
(-8, 0)
c) 2x – 5y = -16
3y = 2x + 12
(-18, -4)
8. Find two numbers whose sum is 26 and whose difference is 42.
x + y = 26, x – y = 42; answers: 34 and 8
Ch 9
9. Simplify
a) (3t 4 )(5t 4 )
b) (9 x 2 y 3 )( 2 xy 4 )
c) (2 x 3 y 3 )( 8xy5 ) 4
15t8
-18x3y7
−8921𝑥 7 𝑦 23
4 3
36 x y
24 x 7 y 2
2 3 3
d) (c d )
e)
f)
 6x 6 y 5
6x 2 y
c6d9
6x2y2
-4x/y3
10. Write using only positive exponents in simplest form.
(4 x 2 ) 3
j 9 k 2
2 4 1
a)
b) x y z
c)
m 1
3x  4
𝑥 10
𝑦4
𝑚
2
9
192
𝑥 𝑧
𝑗 𝑘2
 12 x 2 y 6
d) x 0 y 2 a 4
e)
18 x 7 y 7
𝑦2
−2𝑦
4
𝑎
3𝑥 5
11. Express in scientific notation.
a) 56,000
b) 0.0069
c) 369.23  10 6
5.6 x 103
6.9 x 10−3
3.6923 x 10−7
12. Express in standard notation.
a) 3.40  10 3
b) 2.394  10 4
3400
23,940
13. Express the result in scientific notation.
c) 2.03  10 5
0.0000203
(6  10 9 )(7  10 9 )
6  10
b)
1.2  10 6
(2  10 3 )
5 x 107
2.1 x 104
14. Find the degree of 2 x 9 y 7  6 xy  3x
7
15. Arrange in descending order with respect to y.
a)
a) 3xy 4  8 x 3 y  x 4 y 3  4 xy 2  3
3xy4 + x4y3 – 4xy2 – 8x3y + 3
b)  4 x 3 y  2 xy4  9  x 2 y 2
2xy4 + x2y2 – 4x3y – 9
16. Simplify the sum or difference.
a) (3x  7 y  6 z )  (8 x  y  5 z )
–5x + 6y – 11z
c) (3x 2  5 x  2)  (3x 2  4 x  4)
x+6
b) (2a 4  2)  (9a 4  8a  4)
11a4 + 8a – 6
d) (2 x 3  7 x  2)  (3x 3  5 x 2  4 x  4)
5x3 – 5x2 – 11x + 6
17. Find the product.
a) 3ab(3b 2  9ab  9a 2 )
-9ab3 + 27a2b2 + 27a3b
c) (2x – 5)(x – 9)
2x2 – 23x + 45
e) ( j  5) 2
j2 + 10j + 25
g) (3x  7 y ) 2
9x2 – 42xy + 49y2
b) 5x 3 (2 x 4  2 x 3  6 x  7)
10x7 – 10x6 + 30x4 – 35x3
d) ( x  5)( x 2  4 x  2)
x3 – 9x2 + 18x + 10
f) (c  4) 2
c2 – 8c + 16
h) (5x + 6)(5x –6)
25x2 – 36
Ch 10
18. Give the prime factorization of the following in exponential form.
a) 245
b) 365
c) 270
2
5·7
5·73
2·33·5
19. Find the greatest common factor of 24a 5 b 2 and  64a 4 b
8a4b
20. Factor completely
a) 7 x 4  35 x 3
7x3(x + 5)
b) 16 x 5  24 x 8
8x5(2 – 3x3)
c) x 2  2 x  80
(x + 10)(x – 8)
e) 16 y 2  9
(4y – 3)(4y + 3)
h) x 2  11x  18
(x + 9)(x + 2)
k) x 2  12 x  36
(x – 6)(x – 6)
d) x 2  6 x  5
(x + 5)(x + 1)
g) 16 x 2  40 x  25
(4x + 5)(4x + 5)
j) 3 x 2  x  4
(3x + 4)(x – 1)
21. Solve for x.
a) x 2  2 x  48
x = 8 and -6
f) 49m 2  81n 2
(7m – 9n)(7m + 9n)
i) 2 x 2  5 x  12
(2x + 3)(x – 4)
b) x 2  x  6  0
x = -3 and 2
c) 3x 2  6 x  2  0
x = -2.3 and .3 (not factorable, use quad.
formula or solve by graphing)
Ch. 11
22. Find the equation of the axis of symmetry of the following.
a) y  4 x 2  16 x  2
b) y  x 2  6 x
c) y  4 x 2  10
x=2
x = -3
x=0
2
23. Find the coordinates of the vertex of y  2 x  2 x  2
(0.5, 2.5)
24. Solve the quadratic by graphing.
a) x 2  2 x  15  0
b) x 2  8 x  16  0
c)  x 2  3x  4  0
5 and -3
4
4 and -1
25. What type of graph is y  2  4 x
a) quadratic
b) linear
c) exponential growth
d) exponential decay
26. Simplify
a) 45
b) 108
c) 75
6 3
5 3
Answers: 3 5
27. What is the vertex of the graph?
10
a.
b.
c.
d.
8
6
4
2
-10 -8
-6 -4
-2
2
4
6
8
( .5, 5.25)
(3,-6)
0
x = -3
10
-2
-4
-6
-8
-10
28. Graph y  x 2  8x  7
#28)
29. Solve by using the quadratic formula.
a) 5 x 2  x  2  0
b) 4 x 2  x  5  0
a)
1  41 1  41
,
10
10
b) 5/4 and -1