PRECALCULUS PRACTICE FINAL
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If you have difficulty with a problem go to the table of content and study the material
under that topic and try the problem again. Another method of learning is if you get
the wrong answer study the solution then retry the problem. Do this until you understand
the problem and your able to obtain the correct answer.
I will be adding additional problems and answers at a
future date
- Find the midpoint of the line segment connecting the
points
(5, -3), ( -2, 4)
answer
- What is the distance between the following points?
(3,
6), (-3,- 5)
answer
- Are the following coordinates a solution to the function f(x) = x^{2}
- x + 3 ?
(-2, 9)
answer
- A rectangular field has an area of 372 m^{2} What is the
perimeter of the field if the
lenght is twice the width?
answer
- Find the slope the following lines and determine if the lines are
parallel, perpendicular or neither.
line one (4, 3), (-2, 5)
line two (2,-3), (-1, 6)
answer
- Find the equation of the line that passes through (3, 2) and has a
slope of 4.
answer
- What is the domain of the following functions.
a. f(x) = 4x/(3x + 2)
b. p(x) = 3x^{2} - 4
answer
- a Graph the function f(x) = x^{2}- 4
b) identify the
interval for which f(x) ≤ 0
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- What is the average rate of change of the following function from
x = 3 to
x = 2
f(x) = -x^{2} + 4
answer
- . Write the following in logarithmic format 4^{3}
= 64.
answer
- Write the following in logarithmic format for e^{7} =
1096.633158
answer
- Write the following in exponential form log 1000 = 3
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- Solve the following equations for x
a) log_{5}
3.5 = x
b)
log (x + 5) = log ( x -2) ─ log ( x + 2)
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- Find the exact answer: log _{5} 5 ^{1.4}
─ log _{5} 5 ^{0.7}
answer
- Express the following in a single logarithm term.
a)
2ln x + 3ln y ─ ln g
b) 4log x - (3 log
y + 2 log z)
answer
- Expand the logarithmic expression ln
(t^{4} / p^{-3} )
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- The following angles are measured in
radians. Without using a calculator identify what quadrant they are in:
a)3π / 4
b) -2π/5
answer
- Express the following in radian measure.
a) 45^{o} b) 120^{0}
c) 107^{0} 30' 10"
answer
- List the six trig functions for a right triangle
with the side opposite = 3 and the adjacent side = 4
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- What is the cot θ if sin θ = 4/5
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- What is the angular speed, # of revolutions and linear speed per second of a point on the rim of a
wheel with a diameter of 14 cm that travels at 9 dm per minute?
answer
- For what values of θ between 0 ≤ θ ≤ 2π is the sine, secant and tangent function not defined?
answer
- What is the sign of the tan θ in quadrants 1, 2 and 4? answer
- What is the period of the tan θ and cos θ ? answer
- What is the reference angle for 120^{0}? answer
- What is the reference angle for 237^{0}? answer
- What is the radian measure of a circle's central angle opposite and arc of 12 dm with a radius of 4.3 cm? answer
- Without a calculator what does sin^{-1}(.5) = answer
- Without using a calculator what does arccos(.5) = answer
- Without a calculator what does cos(sin^{-1}(.5)) = answer
- What does cos(arccos(.5)) = answer
- What is a one to one function? Are any of the six trig functions one to one? answer
- Convert .44879 radians to degree measure answer
- What angle is coterminal with 237^{0} and is between 360^{0} and 720^{0} answer
- What are the turning point of sin x = y from 0 to 2π answer
- What are the zero point of sin x = y from 0 to 2π answer
- You are standing 154 meters from a building. The angle from the ground to the building's top is 67.3 ^{0}
How tall is the building? answer
- Solve for x: 8x - 4 = 3(x + 2) - 6 answer
- Solve for x: 8x^{2} - 4 = 3(x + 2) - 6 answer
- Solve for t: 5t - 4 ≤ 6(t + 2) - 2 answer
- Solve for p: 7p - 2 ≥ 5(p + 2) + 3 answer
- Solve for x: |8x - 4| ≥ 6 answer
- Solve for r: |9.5r - 3| ≤ 4.3 answer
- Solve for x: (8x + 4)^{1/2} = 2x + 1 answer
- A ball is launched from ground level and forms a parabolic path based on the function f(x) = -.2x^{2} + x + 3
- What is the maximum height the ball reaches?
answer
- What is the horizontal distance the ball travels from launch to touch down?
answer
- You are instructed to make an open box from a piece of metal that is 60 cm on each side.
The sides have to be t cm high. What is the function that describes the boxes volume? answer
- You are instructed to make an open box from a piece of cardboard that is 60 cm on each side.
The bottom of the box must have an area of 3,100 sq cm. How high will the sides t be? answer
- The end points of a circle's diameter are (-2, 2),(4,8). What is the equation, in standard form, for this circle?
answer
- The circle's radius is ∜5. The center is at (2, 3) What is the equation, in standard form, for this circle?
answer
- Is 4x⁴ + 3x² + 9y + 3 = 0 symmetrical to the x axis, y axis, origin or all three?
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- Is x⁵ - 3y⁵ - 9 = 0 symmetrical to the x axis, y axis, origin or all three?
answer
- The half life of phosphorus-32 is 14.26 days. How much of the initial amount of 115 mg will be left in 4 days?
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- The half life of krypton-85 is 10.76 years. How much of the initial amount of 210 mg will be left in 3.5 years?
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- How much will you have in 3 years if you deposit $6,000 at 7% compounded weekly?
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- How much will you have in 3 years if you deposit $6,000 at 7% compounded daily?
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- How much will you have in 3 years if you deposit $6,000 at 7% compounded continuously?
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- How much will you have in 5 years if you deposit $6,500 at 5.5% compounded continuously?
answer
- Using parent functions write a functions whose graph will be approximately the same as the one below.
What parent function closes resemble this graph?
answer
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