Math 46 Practice Final
(1) Evaluate x + yz if x = 6, y = −3, and z = −2.
(2) Evaluate
15 − x
when x = −3 and y = 4.
y+2
(3) Evaluate the expression (−x2 + y)(y 2 − 3) when x = 3 and y = −2.
(4) Suppose that f (x) = −2x2 − x + 1. Evaluate and simplify f (−4).
(5) Suppose that g(x) =
1 − 2x
. Evaluate and simplify g(5).
3x2
(6) Simplify −9(4x + 8) + 3
(7) Simplify 3(2x − 4) − (4 − x)
(8) Simplify 7(a + b) − 5(2a − b)
(9) Simplify 3(w + 2) − (12 − w)
(10) Perform the operation and simplify if possible: (5y 3 − y − 3) − (−4y 2 + 2y − 8)
(11) Perform the operation and simplify if possible: −3x(5x2 + 6x − 3)
(12) Perform the operation and simplify if possible: (4x − 3)(5x − 2)
(13) Perform the operation and simplify if possible: (5x + 3)2
−3x2 + 5x − 1
2x2
4x2 + 20x + 3
(15) Perform the operation:
x+5
(14) Perform the operation:
(16) Simplify: (−2x3 y 4 )3
(17) Simplify:
10ab5
15a3 b5
(18) Simplify: 2−1 + 3−1
(19) Simplify. Write variables with positive exponents only:
−2x2 y −5 4
10x4 y
(20) Simplify. Write variables with positive exponents only: (−3x−2 y)(2x4 y −3 )
3y
.
− 30y
x2 + 5x − 14
(22) Simplify:
.
x2 − 49
(21) Simplify:
6y 2
(23) Perform the operation and simplify if possible:
2x + 5 6 − x
·
.
x−6
3x
2
(24) Perform the operation and simplify if possible:
(25) Perform the operation and simplify if possible:
(26) Perform the operation and simplify if possible:
(27) Perform the operation and simplify if possible:
(28) Perform the operation and simplify if possible:
4x − 4y x2 + xy
.
· 2
x
y − x2
x2 − y 2
2x2 + 5xy + 3y 2
·
.
x2 + 2x + 1 2x2 + xy − 3y 2
4p − 4
6p2
·
p
9p − 9
4
− 2.
x−3
x−1
x−1
+
.
2
x + 4x + 4 x + 2
(29) Solve the equation: −6(2x − 5) = −3(9 + 4x)
2
5
(30) Solve the equation: − x − = 3
7
7
7x + 3
= −x
(31) Solve the equation:
5
(32) Solve V = lwh for w.
(33) Solve S = 4lw + 2wh for h.
1
(34) Solve V = Ah for h.
3
(35) Solve 3x + 6 − x = 8 + 3x − 6
(36) Solve 4(x + 2) + 1 = 7 − 3(x − 3) + 7x
(37) Solve y = mx + b for x.
(38) Solve y 2 − 5y + 6 = 0
(39) Solve x2 − 2x = 24
(40) Solve |1 + 6x| − 7 = −3.
(41) Solve 5 + |4x| = 21.
(42) Graph the solution on the number line and express the solution in interval notation:
0<x
(43) Graph the solution on the number line and express the solution in interval notation:
x ≥ −2
(44) Graph the solution on the number line and express the solution in interval notation:
−7x + 4 > 3(4 − x)
(45) Graph the solution on the number line and express the solution in interval notation:
5x − 7x ≤ x + 2
3
(46) Graph the solution on the number line and express the solution in interval notation:
x + 4 < 0 or 6x > −12.
(47) Graph the solution on the number line and express the solution in interval notation:
3 ≤ 4x − 3 < 19.
(48) Graph the lines(in this system of equations on the same graph. What is the solution to the system
x+y =7
of equations?
.
x=4
(
x+y =3
(49) Solve the system of equations.
.
x−y =5
(
y = 5x − 3
(50) Solve the system of equations.
.
y = 8x + 4
(
2x − 5y = 1
(51) Solve the system of equations.
.
3x + y = −7
(
2x − 5y = 13
(52) Solve the system of equations.
.
3x + y = 11
(
x − 3y = 2
(53) Solve the system of equations.
.
−2x + 6y = −4
(
3x + y = 4
(54) Solve the system of equations.
.
9x + 3y = 6
(55) Graph the line containing the points (−3, 4) and (5, 0).
2
(56) Graph the line containing the point (−2, 1) with slope m = .
5
(57) Graph the line: x + 8y = 8.
(58) Graph the line: 2x − 3y = 6.
2
(59) Graph the line: y = x + 5.
3
(60) Graph the line: y = −x + 6.
(61) Find an equation of the line with slope 4, through (−3, 4) and write the equation in slope-intercept
form.
(62) Find an equation of the line through (−4, 0) and (6, −1) and write the equation in slope-intercept
form
(63) Find the slope of the line that passing through (−1, 3) and (4, −4).
(64) Find the slope and the y−intercept of the line 8x + y = 0.
(65) Factor completely or state that the expression is prime: y 2 − 64
(66) Factor completely or state that the expression is prime: 2x3 + 8x
4
(67) Factor completely or state that the expression is prime: x3 y 3 + 27
(68) Factor completely or state that the expression is prime: 8x3 − 64
(69) Factor completely or state that the expression is prime: 4y 2 + 4y − 3
(70) Factor completely or state that the expression is prime: 24a3 − 20a2 b − 18ab2 + 15b3
(71) Factor completely or state that the expression is prime: 4x2 y − 4xy − 120y
(72) Factor completely or state that the expression is prime: 5x2 + 9x − 2
(73) Maxine makes twice as much money as Fran. If the total of their salaries is $114,000, find each
woman’s salary.
(74) A family is planning their vacation to Santa Barbara. They will drive a distance of 216 miles.
They plan to average a rate of 72 mph. How long will it take?
(75) The sale price of a sweater is $27 and is 25% off of the original price. What was the original price?
(76) A store advertises a 20% off sale on all items in the store. What is the sale price of a pair of shoes
normally priced at $85?
(77) Two hikers are 11 miles apart and are walking toward each other. They meet in 2 hours. Find the
rate of each hiker is one hiker walks 1.1 mph faster than the other.
x+y+z
. On your first
(78) The average of three exam grades, x, y, and z, is given by the formula
3
two exams, your grades are 86 and 88. What must you get on the third exam to have an average
of 90.
9
(79) Given that F = C + 32 where F is temperature in Fahrenheit and C is temperature in Celcius.
5
The highest temperature on record in Rome, Italy, is 104◦ Fahrenheit. Convert this temperature
to Celcius.
(80) An automobile repair shop charged a customer $440, listing $80 for parts and the remainder for
labor. If the cost of labor is $60 per hour, how many hours of labor did it take to repair the car?
(81) Students at a school raised $350 for a club trip. They want to accumulate $2000 for the trip. What
percent of their goal has been reached?
(82) Find the base and height of a triangle whose height is one more than four times its base if the area
of the triangle is 9.
(83) The largest angle in a triangle measures 9 times the size of the smallest angle. The remaining angle
measures twice the size of the smallest angle. Find the measure of the smallest angle of the triangle.
(84) Can a triangle contain two right angles? Justify your answer.
5
(85) To rent a moving truck from a certain company, there is a base charge to rent the truck per day
and a fee paid per mile the truck is driven. Assume the price include taxes. The base fee is $20
per day and the mileage fee is $0.80 per mile. How many miles can you drive a rental truck if you
use it for one day and have $60 to spend?
(86) Find the missing angles A and E.
50◦
C D
B A
E
35◦
(87) The distance from the earth to the sun is about 93 million miles. Write the number of miles from
the earth to the sun using scientific notation.
(88) The size of a skin cell is about 30 micrometers which is 0.00003 meters. Write the number of meters
a skin cell measures using scientific notation.
5
4
y = f(x)
3
2
1
-1
x
1
2
3
-1
(89) Using the graph above, find f (3).
(90) Using the graph above, for what value(s) of x is f (x) = 3?
4
5