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Alg II/Trig Summer Review
[Due on the first day of school]
Name:__________________________________________
CAREFULLY READ AND FOLLOW ALL INSTRUCTIONS
Algebra II/Trig consists of a great deal of Algebra I material. I often refer to the course as “Algebra I on steroids,” at least
for the first few months. In order to ensure that we are successful at the start of the year, it is important that each student
reviews and refreshes the fundamental components of Algebra I that will be used in Algebra II/Trig. This includes
•
•
•
Simplifying Expressions
Solving Linear Equations
Graphing Lines (standard, slope y-intercept, and
point-slope forms)
•
•
•
Absolute Value (simplifying, solving and graphing)
Inequalities (simplifying, solving and graphing)
Solving systems of equations by graphing, substitution
and elimination
You are to complete this packet and turn it in on the first day of school. It will be scored and entered. There will promptly
be a test on the material in the packet (not on the first day of school, but in the first week).
Feel free to use the internet, textbooks, friends and tutors as guides as you complete the packet. The intention is for you
to review and learn material that will be essential throughout the year, and for you to be successful on the review test at the
beginning of the year.
If you have any questions, you can email Mr. Gilchrist at [email protected] at any time.
Show your work
Box Your Answers
Calculators Allowed
Reduce All Fractions
Evaluate (find the numerical answer by following the order of operations)
1) 18 − 6 + 60 ÷ 3 ⋅ 22
2) -x3 – x2 – x – 4
3) -2x2 + 6x – 3 if x = -6
4)
5)
−6
2
(give solution as a reduced fraction)
÷2
5
3
if x = -4
2 1
1
(give solution as a reduced fraction)
+ −3
3 2
4
6) 3 −
11
(give solution as a reduced fraction)
3
Simplify the following expressions (use the order of operations and the distributive property to eliminate fractions and
combine all like terms).
8) 6x2 – 12x + 4x2 – (3x – 1)
7) 3x – 2(x + 4)
9) 2(x + 3)2 + 4x – 3
[note: (x + 3)2 ≠ x2 + 9 ]
10)
(6x – 2)(3x + 4)
Solve (find the value of x to make the initial equation a true statement). Check your solutions.
2x − 4
=2
3
11) 3x – 6 = 12
12)
2
2
x−4=
3
14) 3x – 2(x + 4) = 6x – 9
15)
3 2
1 x
+ x = − (do you remember how to clear fractions?)
4 3
2 5
17)
x+3 2
=
x
5
16)
3 x
= (hint: this is a proportion)
5 7
13)
18) Solve for y: 6x – 2y = 12
Graph the following equations. Identify which form the equation is in (slope y-intercept, standard, point-slope, or neither).
Make a table of at least 5 inputs and outputs (x-values and y-values). Identify the x- and y-intercepts (these might not be
whole numbers. If they aren’t whole numbers, give them to the nearest tenth or as a reduced fraction).
19) y = 3x – 4
Form:________________
20) y = -x + 2
y
x
x – int:
x – int:
y – int:
y – int:
x
2
3
21) y =
− x+6
x
Form: ______________
y
y
22) y = 7
x
x – int:
y-int:
y – int:
x
y
24) y − 4=
Form: ______________
Form:________________
y
x-int:
23) 5x – 2y = 10
Form:_________________
x
x-int:
x – int:
y-int:
y – int:
y
2
( x + 5)
3
Form:________________
25) x = -6
x
Form: ______________
26) y = -x
x
y
x-int:
x – int:
y-int:
y – int:
Form:________________
y
Solve and Graph the following inequalities. Remember! When you multiply or divide both sides of an inequality by a
negative number, the inequality switches direction (the arrow flips). Check your solutions.
27) x + 3 < 2x – 5
28) 4 – (2x + 5) > 3x + 1
29)
2
x ≤ −12 or x − 5 > 9
3
31) y > -3x + 5
30) -6 < 2x + 10 < 14
32) 2x – 4y < 12
Evaluate the absolute value expressions. (Find a single numerical result)
33) 6 − 2 ( 4 )
34) 6 + 2 −4 − 2a 2
if a = -10
Solve the absolute value equations. (Remember there’s potentially 0, 1 or 2 solutions).
35)
x+7 =
10
12
36) 10 − 3 x − 5 =
37) 2 4 x > 24
Solve the systems of equations. (find the one point that works in both equations. Remember, there could be 0, 1 or infinite
solutions).
38) Solve by Graphing
6x + 4y = -8
y
=
1
x+2
2
39) Solve by Substitution
40) Solve by Elimination
2x + 5y = 31
6x – 4y = 10
4x – y = 7
-9x + 6y = -15