Practice Problems for the final exam.
Objective #1: Simplify expressions containing rational exponents. (Text sections: R7 and 6.2)
a) Evaluate 163/4d) Write as a simplified rational exponent
b) Evaluate 5x1/2 when x = 9e) Simplify (x 2/5)3
c) Simplify x3/2 x ¼
Objective #2: Perform operations on and simplify radicals.
(Text sections: 6.1, 6.3, 6.4)
a) Simplify b) Simplify
c) Add d) Multiply
e) Multiply e) Multiply
Objective #3: Perform operations on and simplify rational expressions.
(Text sections: 5.1, 5.2)
a) Simplify b) Simplify
c) Subtract d) Subtract
e) Multiply
Objective #4: Solve quadratic equations with real solutions, including the use of the quadratic formula( two questions). (Text sections: 4.8, 7.2)
a)r2 + 8r = -5c) 3x2 – 5x + 1 = 0
b)a2 – 1 = 4ad) 4x2 = 9x + 2
e)
Objective #5: Solve rational equations. (Text section: 5.5)
a) b)
c) d)
Objective #6: Solve absolute value equations of the form |ax + b|=c. (Text section: 1.6)
a) |3x – 7| + 5 = 9b) | 4 –x | = 12
c) 3|2x – 1| = 15d) |-6x – 5| = -3
e) |8x| + 4 = 1
Objective #7: Solve radical equations of the form: (Text section: 6.6)
a) b)
c) d)
Objective #8: Solve compound linear inequalities. (Text section: 1.5)
a)3x – 1 4 or c) -15< 4x + 5 21
b)-2x < 8 and x+1 < -5x + 19d) 2(x-1)> 6 or x >7
Objective #9: Solve systems of linear inequalities in two variables. (Text section 3.7)
Graph the following system of inequalities
a) y > 3x + 1b) x + 2y 12c) 2 x – y
y -2x +6 2x + y 12 x + y – 4
d) 2x y
x + 2y 8
Objective #10: Solve systems of linear equations in two and three variables.
(Text sections: 3.1-3.3, Appendix B)
a) Solve b) Solve c) Solve
2x – y – 4z = -12 2x – y + z = 5 7x – 4y = -31
2x + y + z = 1 6x + 3y – 2z = 10 5x + 2y = -10
x + 2y + 4z = 10 x – 2y + 3z = 5
d) Solvee) Solve f) Solve
3x + 2y = 12 3x + 2y = -2 8x – 2y = 12
y = 2x – 16 -6x – 4y = 4 y = 4x + 6
Objective #11: Formulate and apply an equation, inequality or system of linear equations to a contextual (real-world) situation. (Text sections: 1.3, 1.4, 3.3, 3.4)
a)Larry’s Hardware sold 45 paint brushes, one kind sold for $8.50 each while another sold for $9.75 each. In all $398.75 was taken in for the brushes. How many of each were sold?
b)Daniela goes to the bank and gets change for $80 dollars consisting of $5 and $1 bills. If there are 28 bills in all, how many of each kind of bill are there?
c)Tom and Jerry made $120 selling books last month. Tom sold 4 dollars more than triple Jerry’s amount. How much did each make in sales?
d)A 168 ft. long rope is cut into two pieces. One piece is 6 times longer than the other. How long is each piece?
e)A long-distance telephone call using Phone Company A cost 10 cents for the first minute and 8 cents for each additional minute. The same call using Phone Company B costs 16 cents for the first minute and 6 cents for each additional minute. For what length phone calls is Company B less expensive?
Objective #12: Solve and evaluate literal equations, including nonlinear equations. (Text sections: 1.2, 5.7)
a) Solve for bd) Solve Ax + By = C for y
b) Solve for pe) Solve T = B + Bqt for B
c) Solve for h
Objective #13: Formulate and apply nonlinear literal equations to a contextual (real-world) situation. (Text sections: 4.8, 5.6, 6.6, 6.7)
a)A ball is dropped from the top of building. The height of a ball at a given time is given by the equation h = 800 – 16t2 , where h is the height in feet and t is the time in seconds. How many seconds will it take the ball to reach a height of 224 feet?
b)The time required for a number of people to build a brick wall can be found using the formula T= 35/P, where T is the time in hours and P is the number of people. How long will it take 10 bricklayers to build the wall?
c)The speed a car was traveling before an accident can be calculated using the formula , where s is the speed in mph and L is the length in feet of the skid mark the car creates. If the car was traveling 40 miles per hour, how long will the skid mark be?
Objective #14: Graph linear and quadratic equations. (2 questions)
(Text sections: 2.1, 2.2, 2.5)
a)Graph e) Graph 3x + 5x = -30
b)Graph 4x – 6y = 24f) Graph f(x) = -2x2 + 2
c)Graph f(x) = x2 + 4xg) Graph y = x2 – 6x - 16
d)Graph h) Graph f(x) = x2 + 2x – 15
Objective #15: Determine equations of lines, including parallel and perpendicular lines.
(Text sections: 2.5, 2.6)
a)Find the equation of a line with a slope of 5 and a y-intercept of -8
b)Find the equation of a line with a slope of 2/3 and passing through the point (9,1)
c)Find the equation passing through points (-3, 2) and (9, -1)
d)Find the equation of a line that passes through (-3, 4) and is perpendicular to the line whose slope is 4.
e) Find the equation of a line that is parallel to the line whose slope is 4/3 and contains thepoint (4, -5)
Objective #16: Determine whether given relationships represented in multiple forms are functions. (Text section: 2.2)
For each set of ordered pairs below, identify whether the set is a function.
Set ASet BSet CSet DSet E
(3, 7)(5, 3) (9, 3)(4, 3)(5, 2)
(3, 8)(8, 9) (7, 3)(7, 2)(3, -7)
(3, 9)(6, 4) (-11,3)(-3, 6)(9, 8)
(3, 11)(11,2) (0, 3)(4, -8)(0, -7)
(3, 12)(-5,-8)(12,3)(0, 5)(5, 9)
Which graphs below are functions?
a b c d e
Objective #17: Determine domain and range from the graph of a function. (Text section: 2.3)
Below are graphs of functions. What are the domain and range of the each function?
a b c
d e
Objective #18: Formulate and apply the concept of a function to a contextual (real-world) situation. (Text sections: 2.3, 2.6, 4.1, 4.8)
a)The function C(x) = 8x + 1200 is used to find the cost in dollars of producing x radios. How much will it cost the company to produce 120 radios?
b)The function C(x) = 8x + 1200 is used to find the cost in dollars of producing x radios. How many radios were produced if it cost the company $1880?
c)A gun shoots a bullet in the air. The function H(t) = 300t – 16t2 is used to show how high the bullet has traveled in feet after t seconds. How high is the bullet 8 seconds after the bullet has been fired?
d)Melton Corporation bought a fax machine for $750. The value depreciates at a constant rate each month. Five months later the fax machine costs $625. Formulate a linear function V(t) of the fax machine after t months.
e)A cable service charges a $35 installation fee and $20 per month for basic service. Formulate a linear function for the total cost C(t) for t months of cable TV service.
Objective #19: Interpret slope in a linear model as a rate of change. (Text section: 2.5)
a)Water is being poured into a water tank at a constant rate. After 3 minutes the water level is 8 inches. After 7 minutes the water level is 22 inches. At what rate is the water level rising?
b)The graph below shows the value of a computer after each year of use. Based on the graph what is the rate of change of the cost of the computer?
c)The graph below shows the average cost of a formal wedding since 1986. Based on the graph below find the rate of change of the average cost for a formal wedding
Objective #20: Apply formulas of perimeter, area, and volume to basic 2- and 3-dimensional figures in a contextual (real-world) situation. (2 questions) (Text sections: Geometry supplement 6.2, 6.3, 6.4, 6.5)
a)A carpenter is to build a fence around a 9-m by 12-m garden. The fence costs $3.15 per meter. What will the cost of the fence be?
b)A plot of land is 45 m by 38 m. A house 22 m by 8 m is to be built on the lot. How much area is left over for a lawn?
c)The diameter of the earth at the equator is about 7920 miles. What is the circumference of the Earth at the equator rounded to the nearest tenth of a mile.
d)A 360 ft3 water storage tank is in the shape of a rectangular box. It is 15 ft long and 8 ft wide. How tall is the tank?
e)A water storage tank is in the shape of a circular cylinder. If the tank has a diameter 8 meters, what is the volume of the tank?
Objective #21: Apply the Pythagorean Theorem to various contextual (real-world) situations. (Text section: 6.7)
a)A rectangle is 9 feet wide and 12 feet long. How long is the diagonal of the rectangle?
b)A 26 foot rope is tied from the top of a pole to a point on the ground 10 feet away from the pole. How tall is the pole?
c)A 25 ft ramp has a horizontal distance of 24 ft. What is the height of the ramp?
Objective #22: Apply the concepts of similarity and congruency of triangles to a contextual (real-world) situation. (Text sections: Geometry supplement 6.7, 6.8)
a)A flag pole casts a 42 ft shadow at the same time a 6 foot woman casts a 4 foot shadow. How tall is the flag pole?
b)The triangle on the right represents the measurements of a triangular plot of land. The triangle on the left is a blueprint of a triangle similar to the lot. How long is the side of the lot that corresponds to the 12 inch side in the drawing?
Blueprint Lot
c)Find the distance across the river. Assume the ratio of d to 25 ft. is the same as the ratio of 40 ft. to 10 ft.