College Bound Math
College Bound Math
Review Packet
(You’re welcome!)
Name: ___________________________________________________________
Review Notes:
Quarter 1 Review!
Major Topics: Solving Equations & Inequalities, Solving Absolute Value Equations & Inequalities, Slope, Writing
Equations of Lines, Systems of Equations (Graphically, Substitution, Elimination), Matrices
Examples:
Solve the following equations or inequalities for the variable (#’s 1 – 8).
1) [pic] 2) [pic]
3) [pic] 4) [pic]
5) [pic] 6) [pic]
7) 3x + 5 ≤ 2x – 4 or 6x + 18 < 11x + 13 8) 9x + 13 < 5x – 3 < 3x + 9
9) Find the slope of the line: 10) Find the slope of the line:
Find the slope of the line that passes through the following points (#’s 11 – 14).
11) (-13, -10) and (-8, -17) 12) (16, 10) and (-17, 7)
13) (15, 11) and (17, 11). 14) (-18, 12) and (-18, -12)
Write the equation of the line given the slope and a point on that line (#’s 15 – 16).
15) m = 4, P(-1, -3) 16) m = [pic], P(-5, -2)
Write the equation of the line that passes through the following points (#’s 17 – 18).
17) (-1, -5) and (0, -2) 18) (3, 7) and (-6, 1)
Solve the following systems of equations graphically (#’s 19 – 20).
19) [pic] 20) [pic]
Solve the following systems of equations algebraically (substitution and elimination) (#’s 21 – 24).
21) [pic] 22) [pic]
23) [pic] 24) [pic]
Perform the following operations with the matrices (#’s 25 – 27).
25) [pic] 26) [pic]
27) [pic]
Find the determinants of the following matrices (#’s 28 – 29).
28) [pic] 29) [pic]
30) What is the inverse of the matrix [pic]?
31) Solve the following system of equations using matrices: [pic]
Quarter 2 Review!
Major Topics: Functions, Inverses of Functions, Composition of Functions, Types of Functions, Transformations,
Add & Subtract Polynomials, Distributive Property, Multiplying Binomials, Factoring, Quadratic
Formula, Multiplying & Dividing Rational Expressions, Rules of Exponents, Exponential Functions
Examples:
Determine whether the following graphs or set of points are functions (#’s 1 – 4).
1) {(-3, 5), (5, -1), (6, -1), (3, 2)} 2) {(0, 4), (4, 2), (2, 1), (4, 1)}
3) 4)
Determine whether the following graphs or set of points are one-to-one functions (#’s 5 – 8).
5) {(0, 3), (1, 5), (-2, 3), (4, 0)} 6) {(1, 2), (2, 3), (3, 4), (4, 5)}
7) 8)
Find the inverse of each function (#’s 9 – 10).
9) [pic] 10) [pic]
Find the composition of the following functions (#’s 11 – 12).
11) [pic] 12) [pic]
[pic] [pic]
Find [pic] Find [pic]
For each function, write an example of an equation and a graph (#’s 13 – 16).
13) Linear 14) Quadratic 15) Absolute Value 16) Exponential
Perform the operation with the following polynomials (#’s 17 – 20).
17) [pic] 18) [pic]subtracted from [pic]
19) [pic] 20) [pic]
Factor completely each of the following polynomials (#’s 21 – 30).
21) [pic] 22) [pic]
23) [pic] 24) [pic]
25) [pic] 26) [pic]
27) [pic] 28) [pic]
29) [pic] 30) [pic]
Use the quadratic formula to solve the following quadratic equations (#’s 31 – 32).
31) [pic] 32) [pic]
Multiply or divide the following rational expressions (#’s 33 – 36).
33) [pic] 34) [pic]
35) [pic] 36) [pic]
Simplify the following expressions using rules of exponents (#’s 37 – 40).
37) [pic] 38) [pic]
39) [pic] 40) [pic]
Use the exponential growth or decay formulas to determine the following (#’s 41 – 43).
41) Matthew bought a new car for $30,000. The car depreciates 10.3% of its value each year. What will the car
be worth in 10 years?
42) Sarah invested $1,200 in a savings account to start saving for college. The account pays 4.5% annual interest.
How much money will be in the account after five years?
43) In order for Kyle’s $5,000 investment to become $7,500 in 10 years, what would his simple interest rate need to be, rounded to the nearest tenth of a percent?
Quarter 3 Review!
Major Topics: Rules of Logarithms, Solving Log Equations, Simple Interest, Compound Interest, Continuous
Interest, APY, Present & Future Values, Loan Tables
Examples:
Evaluate the following logarithms (#’s 1 – 2).
1) [pic] 2) [pic]
Use the properties of logarithms to expand the following (#’s 3 – 6).
3) [pic] 4) [pic]
Use the properties of logarithms to simplify the following (#’s 3 – 6).
5) [pic] 6) [pic]
Solve the following log equations – you may have to use properties (#’s 7 – 10).
7) [pic] 8) [pic]
9) [pic] 10) [pic]
11) How much interest has Marty accrued on $4,500 left in a banking account for seven years at a 3.1% simple interest rate?
12) George wants to know how long it will take for $500 at a 2.7% simple interest rate to double? Round your answer to the nearest year?
13) What is the balance on Meg’s account that offers a 5% interest rate compounded quarterly on $7,800 after nine years? How much interest has Meg accrued on the account?
14) What is the balance on Taliah’s $12,000 account if it offers a 4.3% interest rate compounded continuously at the end of 5 years?
15) What will Robert’s account be worth if he saves $650 monthly for the next three years, in an account that pays 5.1% interest compounded monthly? Of that, how much was money that he invested?
16) Mr. James would like to have $250,000 saved up over the next 20 years. If he finds an account that pays an annual interest rate of 6.8% compounded quarterly, how much of an initial investment, rounded to the nearest hundred dollars, would he have to make?
Using the below loan table, answer the following questions (#’s 17 – 18).
[pic]
17) How much would a monthly payment be for a $20,000 loan for a 48-month lease?
18) How much would a monthly payment be for a $32,000 loan for a 6-year lease?
Quarter 4 Review!
Major Topics: Trig Ratios, Finding Sides & Angles of Right Triangles, Unit Circle, Area of a Triangle, Laws of Sines
& Cosines, Solving Triangles (Forces), Simplifying Radicals, Pythagorean Theorem, Imaginary
Numbers, Adding/Subtracting/Multiplying/Dividing Radicals, Basic Radical Equations, Fractional
Exponents
Examples:
Find the missing sides or angles of the triangles below (#’s 1 – 4).
1) 2)
3) 4)
5)
6) A triangle has two sides that measure 32 inches and 17 inches with an included angle of [pic]. What is the
area of this triangle using the area formula [pic].
Use the Law of Sines to find the missing values in the following triangles (#’s 7 – 8).
7) Find RT 8) Find [pic]
Use the Law of Cosines to find the missing values in the following triangles (#’s 9 – 10).
9) Find RS 10) Find [pic]
11) Forces of 40 pounds and 70 pounds act on a body at an angle measure of [pic]. Find the magnitude of the
resultant of these forces to the nearest hundredth of a pound.
Simplify the following radicals (#’s 12 – 17).
12) [pic] 13) [pic]
14) [pic] 15) [pic]
16) [pic] 17) [pic]
Simplify the following imaginary numbers (#’s 18 – 19).
18) [pic] 19) [pic]
Use the Pythagorean Theorem to find the missing sides of the triangle in simplest radical form (#’s 20 – 21).
20) 21)
Perform the following operations with radicals (#’s 22 – 25).
22) [pic] 23) [pic]
24) [pic] 25) [pic]
Solve each radical equation (#’s 26 – 27).
26) [pic] 27) [pic]
Rewrite each expression (#’s 28 – 31).
28) x2 – 6x + 13 = 0 29) 3x2 + 4 = 6x
30) x(x – 2) = 3(2x – 3) 30) 3x2 + 5x = 28
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