| COLLEGE ALGEBRA
EXAM 3 CG
R2
NAME __________________
SHOW
ALL WORK ON THIS TEST OR ON SEPARATE PAPER.
Circle answers. TURN
IN ALL WORKSHEETS. CALCULATORS
ARE REQUIRED ON THIS TEST. 1.
Solve the systems of equations:
a) 50x
– 9y
= 1
b)
y
= 2x –
4
7x – 2y = – 8
4x – 2y
=
8
2. Solve the system:
3. Solve the system: 3x
+ 2y
+ 5z
= 2 3x + 2y =
– 2 2x – 3y + 2z = – 4 2y – 3z = 1x + 4 + 2z = 2 x – 2y + 2z = 4
4.
Solve the system:
5.
Solve the system: y 2 – 4x 2 = 105 xy = – 12
y = 3x – 5 2x – y
= – 11
6. Evaluate the determinants: a) 7.
Evaluate the determinant:
8.
Solve by Cramer's Rule:
9. Graph the
intersection: x – 2y =
8
x ³
0 –8x + 6y = 32 2x – 3y ³
12 7x
+ 4y > 28
10. Find the remainder if x 7 – 6 x
2 + 3 is divided by x –
1. 11.
Find a quadratic equation whose roots are x
= 5 ± 3i. 12.
Solve for x. Give
irrational roots in radical form:
x 4 – x
3 – 2 x 2 + x
+ 1 = 0
In 13 - 14, find all roots
and multiplicities by synthetic division:
13. x 3 + x 2
– 8 x – 12 = 0 14.
x 4
– 5 x 3 + x
2 + 21 x – 18 = 0 In 15 - 16, sketch the
graphs and give roots: 15. y = (x
– 2)3(x + 3)2(x –
4) 16.
y = x 3 + 2
x 2 – 4 x – 8
In
17 - 20, solve the inequalities. Give
interval notation.
Sketch graphs
when using graphing methods. 17.
| x + 8 | ≥ 6
18. –7x2
+ 40x > –12 (Give exact form!)
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