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DSPM 0850 Final Exam Review
Version 3/29/
The actual final will also be multiple choice, but will only have 33 questions.
Evaluate the expression.
- (-4) A) -12 B) 64 C) -64 D) 12
Use the power rule to simplify.
- (y7)^6 A) 6y7^ B) 6y C) y42^ D) y
Use the power rule and the power of a product or quotient rule to simplify the expression.
- (x8y)^2 A) x16y B) x16y C) x10y3^ D) x10y
Use the quotient rule to simplify the expression.
- s10t s2t A) s8t7^ B) s12t C) s8t6^ D) s8t
Simplify.
- If P(x) = x2 + 3x - 2, find P(-5). A) -22 B) 10 C) 8 D) 26
Perform the indicated operations.
- (9x2 + 4x + 4) - (-4x2 - 7) A) 5x2 + 11x + 4 B) 5x2 + 4x - 3 C) 13x2 + 11x + 4 D) 13x2 + 4x + 11
Find the following product.
- (5z + 2) A) 5z2 + 20z + 4 B) 25z2 + 20z + 4 C) 25z2 + 4 D) 5z2 + 4
Find the product using the FOIL method.
- (4x + 10)(4x - 10) A) 16x2 + 80x - 100 B) 4x2 - 80x - 100 C) 16x2 - 100 D) 16x2 - 80x - 100 9. (3y + 4)(5y + 1) A) 8y2 + 5 B) 15y2 + 4 C) 15y2 - 17y + 4 D) 15y2 + 23y + 4
Write the number in scientific notation.
- 6,100, A) 6.1 x 10-6^ B) 6.1 x 105 C) 6.1 x 106^ D) 6.1 x 10-
Write in standard notation.
- 3.78 x 10- A) 0.0000378 B) 0. C) -378,000 D) 0.
Perform the division.
- p2 + 3p - 16p + 6
A) p - 3 B) p - 2 + 3 p + 6
C) p + 3 + (^) p + 6^2 D) p - 3 + (^) p + 6^2
Factor out the GCF from the polynomial.
- 18x3 - 6x2 + 8x A) 2(9x3 - 3x2 + 4x) B) x(18x2 - 6x + 8) C) 2x(9x2 - 3x + 4) D) 2x(9x3 - 3x2 + 4x)
Factor by grouping.
- 10y - 120 + xy - 12x A) (x - 12)(10y + x) B) (y - 12)(10 + x) C) (x - 12)(y + 10) D) (y - 12x)(10 + x)
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
- x2 + 6x - 72 A) (x - 12)(x + 1) B) (x - 12)(x + 6) C) (x + 12)(x - 6) D) prime
- 7x2 + x - 66 A) (7x + 3)(x - 22) B) (7x - 22)(x + 3) C) (7x - 3)(x + 22) D) (7x + 22)(x - 3)
- 18x2 - 63x - 36 A) 9(2x - 1)(x + 4) B) 9(2x + 1)(x - 4) C) (18x - 9)(x + 4) D) prime
- x2 + 14xy + 49y A) (x + 7y)2^ B) (x + 7y)(x - 7y) C) (x - 7y)2^ D) prime
- 64x2 - 9 A) (8x - 3)2^ B) (8x + 3)(8x - 3) C) (8x + 3)2^ D) prime
Solve the equation.
- (x - 9)(x + 6) = 0 A) x = -9, x = 6 B) x = 9, x = -9, x = 6, x = - C) x = 9, x = 6 D) x = 9, x = -
- x2 - 10x = 24 A) x = -12, x = 1 B) x = -12, x = 2 C) x = 12, x = -2 D) x = 12, x = 2
Solve the problem.
- An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h = -16t2 + 48t + 160. When will the object hit the ground? A) 2 sec B) -2 sec C) 160 sec D) 5 sec
Find the function value.
- f(x) = x - 8 3x
; f(-4)
A) - 4 B) 3 C)^13 D) 1
Simplify the rational expression.
- x2 + 14x + 48 x2 + 17x + 72
A) x + 6 x + 9
B) - x2 + 14x + 48 x2 + 17x + 72
C) 14x + 48 17x + 72
D) 14x + 2 17x + 3
Multiply. Simplify if possible.
- 3z 4 œ^
z
A)^21 z
B) 21z
C) 21z z^
D) z 21
- x2 + 11x + 28 x2 + 13x + 36
œ
x2 + 18x + 81 x2 + 16x + 63
A) x + 9 x + 9
B) 1
x + 9
C) 1 D) x + 7 x + 9
Divide. Simplify if possible.
- (x + 2) (x + 2)(5x + 3)
d 5 5x + 3
A) 1 B) 5 (5x + 3)
C)^1 5
D) 5
Perform the indicated operation. Simplify if possible.
- 4 15 + x
A)^13 30
B) x + 13 30 + x
C)^13 15
D) x + 13 15 + x
- 3x x2 - 9x + 20
x2 - 9x + 20
A) 3 x - 4
B) 3
x - 5
C) (^) (x - 5)(x - 4)3(x + 5) D) (^) (x + 5)(x - 4)3(x - 5)
- 36x A) 6x12^ B) 6x C) 6x2^ D) 36x
Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
- 457 A) 457.000 B) 21. C) 21.378 D) 21.
Find the root. Assume that all variables represent nonnegative real numbers.
x A) 2x B) x2^ C) x3^ D) x
Evaluate.
- If f(x) = 2x - 6, find the value of f(11). A) 22 B) 22 C) 16 D) 4
Use radical notation to write the expression. Simplify if possible.
- 361
A)^1
B) 6 C) -^1
D) -
A) 4096 B) 1024
C) 256 D) 16,
Write with positive exponents. Simplify if possible.
- 49-3/ A) 343 B) -
C) - 1
D) 1
Use the properties of exponents to simplify the expression. Write with positive exponents.
- (b5)2/ A) b2/25^ B) b7/ C) b1/2^ D) b
Use rational exponents to write as a single radical expression.
x (^) œ x
A)
x2^ B)
x
C) x8^ D) x
Use the product rule to multiply. Assume all variables represent positive real numbers.
- 12 œ 3 A) 6 B) 2 3 C) 36 D) 3 2
Use the quotient rule to divide and simplify.
A) 1
B)
C) 1
D)
Simplify the radical expression. Assume that all variables represent positive real numbers.
- 75 A) 15 B) 75 C) 5 3 D) 25 3
Add or subtract. Assume all variables represent positive real numbers.
- 18 + 9 32 - 6 98 A) 3 2 B) 30 2 C) -3 2 D) -32 2
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
- 2( 18 + 6) A) 6 + 4 3 B) 6 + 2 3 C) 36 + 2 3 D) 12
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
- 5 13
A) 65 169
B) 65
C) 65
D) 5
A) 6 2 - 6 B) 6 2 - 1
C)^6 2 + 6
D) 6 2 + 6
Solve.
- x + 4 = 5 A) 21 B) 81 C) 29 D) 25
Use the Pythagorean theorem to find the unknown side of the right triangle.
12 20
A) 20 B) 19 C) 16 D) 14
Solve.
- When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the ground is given by the
equation t = h
, where t is measured in
seconds. If an object falls 78.4 meters before it hits the ground, find the time it took for the object to fall. A) 16 seconds B) 5 seconds C) 7 seconds D) 4 seconds
Write in terms of i.
- A) -50i B) i 50 C) 50i D) ± 50
Perform the indicated operation. Write the result in the form a + bi.
- (4 - 8i) + (8 + 2i) A) -12 + 6i B) 12 - 6i C) -4 + 10i D) 12 + 6i
Find the power of i.
- i A) 1 B) -1 C) -i D) i
Use the square root property to solve the equation.
- x2 = 225 A) -16, 16 B) 15 C) 112.5 D) -15, 15
Use the quadratic formula to solve the equation.
- 5x2 + 8x + 1 = 0
A) -4 -^11 10
, -4 +^11
B) -4 -^11
, -4 +^11
C) -4 -^21
, -4 +^21
D) -8 -^11
, -8 +^11
- -4x2 + 3x - 5 = 0
A) 3 -^71
, 3 +^71
B) 3 - i^71
, 3 + i^71
C) -3 - i^71
, -3 + i^71
D) -3 -^71
, -3 +^71
