Pre-Calculus

Mourning Sr. High Pre‐Calculus Summer Assignment Directions: 1. Show all of your work. 2. Write the final answer on the line provided. 3. If you need help, use Khan Academy, www.purplemath.com, or google. This assignment will be collected for a grade the first week of school. ATM Pre-Calculus Summer Assignment- Solving Equations
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
First, write the value or values of the variable that make a denominator zero. Then solve the equation.
15
30
+ 5 = 1)
1)
x - 7
x - 7
2)
7
3
6
+ = x + 1 x - 1 (x + 1)(x - 1)
2)
Solve the rational equation.
m + 8
8
m - 8
3)
- = m 2 - 5m + 4 m 2 - 2m + 1 m 2 - 5m + 4
3)
Solve the problem.
4) The formula C = 21,000 + 260x
models the average cost per unit, C, for Electrostuff to
x
4)
manufacture x units of Electrogadget IV. How many units must the company produce to
have an average cost per unit of $460?
Solve the radical equation, and check all proposed solutions.
5) x - 9 = 4x + 9
1
5)
6)
5x - 4 = 4
6)
7) x - 3x - 2 = 4
7)
Solve the problem.
8) For a culture of 90,000 bacteria of a certain strain, the number of bacteria N that will
survive x hours is modeled by the formula N = 9000 100 - x. After how many hours will
54,000 bacteria survive?
Find the zeros of the polynomial function.
9) f(x) = x3 + x2 - 30x
8)
9)
10) f(x) = x3 + 4x2 - 4x - 16
10)
Solve the exponential equation. Express the solution set in terms of natural logarithms.
11) 3 8x = 2.1
12) e2x = 7
11)
12)
2
13) e x + 5 = 3
13)
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
14) e5x = 2
14)
15) 2ex = 19
15)
Solve the problem.
16) The manager of a bulk foods establishment sells a trail mix for $9 per pound and premium
cashews for $13 per pound. The manager wishes to make 200 pounds of a
trail mix-cashew mixture that will sell for $10 per pound. How many pounds of each
should be used?
16)
17) The sum of two numbers is -7. If one number is subtracted from the other, their difference
is -3. Find the numbers.
17)
18) Ellen wishes to mix candy worth $1.00 per pound with candy worth $2.95 per pound to
form 26 pounds of a mixture worth $1.60 per pound. How many pounds of the more
expensive candy should she use?
18)
3
Solve the system by the substitution method.
19) -4x - y = -1
y = x2 + 4
19)
20) x2 + y2 = 5
x + y = 3
20)
Solve the system of equations.
21) x + y + z = 9
x - y + 3z = 13
4x + y + z = 18
21)
22) x - y + 2z = -13
2x
+ z = -5
x + 2y + z = 1
22)
4
ATM Pre-Calculus Summer Assignment- Complex Numbers
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Add or subtract as indicated and write the result in standard form.
1) 4i - (-9 - i)
1)
2) -6 - (- 4 - 4i) - (- 1 - 6i)
2)
3) 9i + (-8 - i)
3)
Find the product and write the result in standard form.
4) (8 - 3i)(-2 - 3i)
4)
5) (8 - 4i)2
5)
Divide and express the result in standard form.
4
6)
4 + i
7)
6)
4 + 3i
3 - 4i
7)
1
Solve the quadratic equation using the quadratic formula. Express the solution in standard form.
8) x2 + x + 1 = 0
9) 7x2 = 5x - 3
8)
9)
10) x2 + 6x + 25 = 0
10)
2
ATM Pre-Calculus Summer Assignment- Polynomial Functions
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Perform the indicated operations.
1) (9x4 y2 - 8x2 y2 + 12xy) + (4x4 y2 - 11x2 y2 + 5xy)
1)
2) (7x4 + 9xy - y3 ) - (x4 + 3xy + 9y3 )
2)
Factor by grouping. Assume any variable exponents represent whole numbers.
3) x3 - 4x2 - 2x + 8
3)
4) x3 + 8x - 5x2 - 40
4)
5) 5x3 - 10x2 + 8x - 16
5)
Factor using the formula for the sum or difference of two cubes.
6) x3 - 8
7) 64x3 - 1
6)
7)
1
Factor completely, or state that the polynomial is prime.
8) x3 - 4x2 - 9x + 36
8)
9) x3 - 64x
9)
10) x2 y - 16y + 96 - 6x2
10)
Solve the problem.
11) A department store is having a clearance sale. The price on a television is reduced by 38%.
That sale price is then reduced by another 38%. If x is the televisionʹs original price, the
sale price can be represented by (x - 0.38x) - 0.38(x - 0.38x). With these two reductions, at
what percentage of the original price is the television being sold? Use the factored,
simplified form of the expression to answer the question.
12) Write an expression for the area of the shaded region and express it in factored form.
8
y
8
y
2
11)
12)
13) Write an expression for the area of the shaded region and express it in factored form.
7y
7y
x
x
7y
x
7y
3
13)
ATM Pre-Calculus Summer Assignment- Rational Functions
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational
expression.
3x + 2
1)
1)
6x2 + 19x + 10
2)
x2 + 9x + 20
x2 + 13x + 40
2)
3)
3x2 - 33x + 54
x - 9
3)
Provide an appropriate response.
4) The rational expression 120x
describes the cost, in millions of dollars, to inoculate x
100-x
percent of the current population of cattle against a particular virus. Choose which of the
following statements are true with regard to this mathematical model.
I. The expression will be undefined when x = 100.
II. The cost of inoculating 70 percent of cattle is 100 million dollars more than the cost of
inoculating 60 percent of cattle.
III. This expression will calculate inoculation costs for any population of cattle, no matter
what the size.
1
4)
Multiply or divide as indicated.
x2 + 6x
x2 + 13x + 36
· 5)
2
2
x + 15x + 54 x - 2x - 24
5)
6)
x2 - 15x + 44
x2 - 8x + 7
· x2 - 13x + 42 x2 - 16x + 55
6)
7)
x2 - 8x + 16 3x - 12
÷ 9x - 36
27
7)
8)
x2 - 8x + 16 5x - 20
÷ 12x - 48
60
8)
Add or subtract as indicated.
7
3
9) + x x - 6
9)
2
10)
4
2
- x + 3 x - 3
10)
11)
x
3
- 2
2
x - 16 x + 5x + 4
11)
Solve the problem.
12) Express the perimeter of the rectangle as a single rational expression.
12)
7
x - 9
3
x
Simplify the complex rational expression.
10
+ 1
x
13)
10
- 1
x
13)
3
x
+ 1
x - 6
14)
15)
27
+ 1
x2 - 36
25y2 - 64x2
xy
14)
15)
5 8
- x y
4