Download MAT 0028 Practice for Free Response Final Fall 2011

MAT 0028 - Elementary Algebra
Departmental Final Exam - Practice for Free Response Section
114
-----------------------------------------------------------------------------------------------------------Simplify.
1) [39 - (4 + 6) ÷ 2] - [1 + 24 ÷ 3]
1)
2) (62 - 14) · [(80 + 10 ÷ 5) - (7 · 7 - 5 · 5)]
2)
Solve the equation.
3) -3x + 3(2x - 4) = -5 - 4x
3)
4)
7
1 3
x + = x
4
2 2
4)
5)
4(7 - x)
= x
3
5)
6) -36 - 2x = 12 + 4x
7)
6)
n
= 4 - (-5)
-5
7)
Solve using algebra.
8) The product of a number and -9 is equal to four times the sum of that number and -26.
Find the number.
8)
Write the sentence as a mathematical statement.
9) Negative forty-one is less than negative fourteen.
9)
Use an associative property to complete the statement.
10) (5x + 4y) + 9z =
10)
Use the distributive property to write the expression without parentheses. Then simplify if possible.
11) 7(3z + 6) - 2
11)
Solve the application.
12) A canvas for a mural is in the shape of a right triangle. Before the mural can be painted,
the canvas must be varnished. The base of the mural is 5 meters and the height of the
mural is 11 meters. How many cans of varnish will you need if each can covers 10 square
1
meters? The formula for the area of a right triangle is A = bh.
2
Simplify the expression. Write the result using positive exponents only.
13) (-5x4 y-5 )(2x-1 y)
1
12)
13)
Write the number in scientific notation.
14) 0.000829
14)
Evaluate the expression using exponential rules. Write the result in standard notation.
16 × 104
15)
4 × 106
Find the value of the polynomial at the given replacement values.
16) x3 - 4x2 + 8x when x = 3
15)
16)
Multiply.
17) -5x4 (-10x7 + 6x6 + 5)
17)
Find the product.
18) (4x - 12)(x + 2)
18)
Multiply.
19) (3x + 12)(3x - 12)
19)
20) (5x + 2)2
20)
Divide.
21)
22)
-8x10 + 24x6
21)
-4x2
8x4 y3 + 12x6 y7 - 8x7 y4
4x4 y3
22)
Find the GCF for the list.
23) x4 , x6 , x7
23)
24) x8 y5 , x7 y4 , xy5 , x2 y3
24)
Factor out the GCF from the polynomial.
25) 2x4 y - 10x2
25)
Factor the trinomial completely.
26) 15x2 + 14x - 8
26)
Determine whether the trinomial is a perfect square trinomial.
27) x2 + 12x + 36
27)
2
Factor the trinomial completely.
28) 49x2 + 126x + 81
28)
Solve.
29) The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the
longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of
the triangle.
Factor the polynomial completely. If the polynomial cannot be factored, write ʺprime.ʺ
30) y2 + 24y + 144
29)
30)
Solve.
31) One leg of a right triangle is 7 inches longer than the smaller leg, and the hypotenuse is
8 inches longer than the smaller leg. Find the lengths of the sides of the triangle.
Find the value of the expression for the given replacement value.
x + 3
32)
; x = 2
-3x + 8
Simplify the expression.
7x - 7y
33)
7y - 7x
31)
32)
33)
Multiply or divide as indicated.
81
x2 + 2x
· 34)
9x + 18
8
34)
Perform the indicated operation. Simplify if possible.
8a + 2b 8a - 2b
35)
- 2
2
35)
Name the quadrant or axis in which the point lies.
36) (-15, 16)
36)
Graph the linear equation.
37) x = 2
37)
y
10
5
-10
-5
5
10
x
-5
-10
3
38) x + 8y = -3
38)
y
10
5
-10
-5
5
10
x
-5
-10
39) 5y - 35x = -40
39)
y
10
5
-10
-5
5
10
x
-5
-10
Graph the linear equation by finding and plotting its intercepts.
40) -4x - 16y = 16
40)
y
10
5
-10
-5
5
10
x
-5
-10
Decide whether a line with the given slope is upward sloping, downward sloping, horizontal or vertical.
41) m = -5
41)
4
Use two points on the graph to find the slope of the line.
42)
42)
y
10
5
-10
-5
5
10
x
-5
-10
Find the slope of the line.
43)
43)
y
10
5
-10
-5
5
10
x
-5
-10
Write the equation of the line with the given slope, m, and y -intercept, (0, b).
1
44) m = ; b = 2
4
Use the slope-intercept form to graph the equation.
45) 5x + 2y = 10
44)
45)
y
10
5
-10
-5
5
10
x
-5
-10
Simplify the radical. Assume that all variables represent positive numbers.
46) 245y2
5
46)
47)
x17
36
47)
Add or subtract as indicated.
48) 13 - 3 13
48)
Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables
represent positive numbers.
49)
49) 2 5 + 8 20
6
Answer Key
Testname: MAT 0028 PRACTICE FOR FREE RESPONSE FINAL 114
1) 25
2) 2784
3) 1
4) -2
5) 4
6) -8
7) -45
8) 8
9) -41 < -14
10) 5x + (4y + 9z)
11) 21z + 40
12) 3 cans of varnish
-10x3
13)
y4
40) (0, -1), (-4, 0)
37)
y
y
-10
10
10
5
5
-5
5
-5
-10
-10
y
5
5
10
y
-10
-5
5
10
10
-5
5
22) 2 + 3x2 y4 - 2x3 y
-10
23) x4
-10
39)
-5
-5
y
10
26) (3x + 4)(5x - 2)
27) Yes
28) (7x + 9)2
31) 5 in., 12 in., 13 in.
5
32)
2
10
45)
20) 25x2 + 20x + 4
21) 2x8 - 6x4
29) 20 ft, 48 ft, 52 ft
30) (y + 12)2
5
41) downward
42) 4
43) m = 0
1
44) y = x + 2
4
10
18) 4x2 - 4x - 24
19) 9x2 - 144
24) xy3
25) 2x2 (x2 y - 5)
-5
-5
38)
14) 8.29 × 10-4
15) 0.04
16) 15
17) 50x11 - 30x10 - 25x4
-10
10
-10
5
-10
-5
5
-5
33) -1
9x
34)
8
-10
35) 2b
36) quadrant II
7
10
46) 7y 5
x8 x
47)
6
48) -2 13
49) 18 5