The purpose of precalculus is to prepare students for calculus, regardless of whether they go on to take it. In preparing for college level math, students must solidify and expand their understanding of previously learned math topics. This summer assignment reviews topics from algebra and geometry that are necessary to be successful in precalculus. Although this assignment will not be collected and graded, you will be given a summative assessment on this material during the second day of class. Remember that you must pass math your senior year to graduate, so if you are a senior and find yourself struggling to complete this assignment, please contact your counselor and switch courses prior to August 1st . This assignment and the solutions will be located on the school website under the information tab 2016 summer school. If you have trouble accessing the assignment contact student services. It is also highly recommended that you use google and youtube to search for the topic you need assistance in. Here are two sites that offer help. http://www.purplemath.com/modules/index.htm http://khanacademy.org
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The purpose of precalculus is to prepare students for calculus, regardless of whether they go on to take it. In preparing for college level math, students must solidify and expand their understanding of previously learned math topics.
This summer assignment reviews topics from algebra and geometry that are necessary to be successful in precalculus. Although this assignment will not be collected and graded, you will be given a summative assessment on this material during the second day of class.
Remember that you must pass math your senior year to graduate, so if you are a senior and find yourself struggling to complete this assignment, please contact your counselor and switch courses prior to August 1st.
This assignment and the solutions will be located on the school website under the information tab 2016 summer school. If you have trouble accessing the assignment contact student services. It is also highly recommended that you use google and youtube to search for the topic you need assistance in. Here are two sites that offer help.
http://www.purplemath.com/modules/index.htmhttp://khanacademy.org
A. FOIL -‐ mul,ply binomials first -‐ outside -‐ inside -‐ last
(x + 2)(x -‐ 1) = (x -‐ 4)(x + 3) =(4x2 -‐ 3)(2x + 7) = (6 -‐ m3)(2 + m) =(3x + y)(m -‐ 5y) = (x + y)(x -‐ y) = (3 -‐ m)(m + m2) = (5 -‐ x)(3 -‐ x) =
B. Factoring -‐ ax2 + bx + c when a = 1 find two numbers that mul,ply to make "c" and add to make "b"
x2 + 14x + 48 = ( )( ) b2 -‐ 8b + 15 = ( )( )p2 + 14p +40 = b2 -‐ 9b + 14 =
when a ≠ 12x2 + 12x -‐ 14 = 4x2 + 8x + 3 =3b2 -‐ 3b -‐ 36 = 5a2 -‐ 23a + 12 =
C. Frac,ons -‐ Adding/Subtrac,ng (get a common denominator)
D. Frac,ons -‐ Mul,plying/Dividing
E. Quadra,c Formula (solve a quadra,c to find the zeros)
x2 -‐ 5x + 4 = 0 x2 -‐ 2x -‐ 24 = 0x2 + 6x = -‐9 x2 -‐ 10 = -‐3x2x2 -‐ x -‐ 6 = 0 -‐ x + 4 = 2x2
F. Solve each equa,on for the given variable
2x + 1 = 5x -‐ 2 7m + 2 = 37x2 + 4 = 29 32w + ½ = 16.52x2 -‐ 98 = 0 -‐ x + 4 = 22 + x
G. Write an equa,on of a line according to the given informa,on
containing (-‐1, -‐4) and parallel to y = 3x + 2
containing (2, -‐4) and parallel to x -‐ 2y = 5
containing (-‐2, 3) and parallel to x = 1
containing (4, 15) and parallel to -‐x + 2/3 y = 6
containing (2, 3) and perpendicular to y = 2x -‐ 1
containing (1, -‐3) and perpendicular to y = -‐ 3
containing (3, 4) and perpendicular to 2x -‐ 3y = -‐6
containing (4, 1) and perpendicular to ½x + y = 3
H.Use the exponent rules to simplify each expression.All answers should be wriben with posi,ve exponents.
(m3)4 = (3c6)2 = (m3)(m4) = (5c6)2(2c) = (5a2)(3a3) = (-‐7cd2)(3c-‐2) =(-‐s3t)(-‐5t4) = (m3n2)(4m2n-‐2) =(3a2b4c)(7a3b3) = (-‐2cd2)2(3c2)3 =a0 = m-‐1 =
I. Find each sum or difference. Express all answers in standard form.
(x2 + 3x + 2) + (3x2 + x -‐ 6) =
(x2 + 3x + 2) -‐ (3x2 + x -‐ 6) =
(3a4 -‐ 2a2 -‐ 1) + (2a3 + 2a2 -‐ 10) =
(3a4 -‐ 2a2 -‐ 1) -‐ (2a3 + 2a2 -‐ 10) =
(-‐ 2a2 -‐ 1) + 2(3b2 -‐ 5) =
(3x + 4xy -‐ 7y) + (-‐x -‐2xy + 4y) =
(-‐5x2 -‐ 2x + 1) -‐ (3x2 + 4x -‐ 2) -‐ (-‐8x2 -‐ 5x -‐ 3) =
Appendix A.2 Polynomials and Factoring
A polynomial is any expressions that can be written:
anxn + an-1xn-1 + ... + a1x + a0
(where n is a nonnegative integer and an ≠ 0)
Standard Form: exponents are in descending order
Degree: highest exponent (all exponents must be +)Addition: combine like terms
Subtraction: change to addition and combine like termsMultiply Binomials: FOIL
Completely Factored:written as a product of its primes
(5x-7)+(2x2+10x) =2x2 + 15x - 7
(10m-3) - (-4m - 2) = 14m - 1
(x3-x2)(x2 + 2) = x5 +2x3 - x4 - 2x2
Steps for Factoring (Grouping-Method)
1.) First, write the equation in Standard Form!
y = ax + bx + c
2.) Next, label a, b, and c.
3.) Multiply a*c
4.) List the factors of a*c
5.) Replace the "b" term with the factor pair of
a*c that adds to get "b".
6.) Group the first two terms together, and the second two terms together
7.) Pull out the GCF
8.) Write the two binomial answers.
2
ax2 + bx + c
fractions
When adding/subtracting find a common denominator
1 + 23 5
55
33
515 + 6
15
1115
fractions
multiply: numerator x numeratordenominator x denominator
2 35 7
= 635
divide: multiply by the reciprocal of the denominator
2 35 7 = 2 7
5 3= 14
15
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