Name __________________________________________________
2016 Summer Packet
Incoming Algebra I Students
*
Please show all work neatly in this packet.
*
No Calculators are to be used.
HELPFUL WEBSITES TO USE:
WWW.KHANACADEMY.COM
WWW.MATHISFUN.COM
http://cs.pcti.tec.nj.us/math/lessons/index.htm
PCTI Mathematics Department Sal F.
Gambino, Supervisor Summer Packet
Grading
• On the first day of school, the teacher will check for completion/effort
of the packet.
• This will be weighted at 50%.
• Teacher will then review the packet with the students.
• Upon completion of the review, the students will be given an
assessment based on the summer packet.
• The assessment will be weighted at 50%.
• The two weighted scores combined will count as one project grade.
• Therefore, the grade for the summer packet will be placed under the
“project” category.
ORDER OF OPERATIONS
*****PEMDAS*****
Evaluate each expression.
1) 5 + 15 ÷ 3 × 42
2) 24 ÷ (5 − 3)
3) 59 − (5 + 62 )
4) 2 [32 ÷ (1 + 7)]
5) (2 ⋅ 2 + 3) 2 − (4 + 3) ⋅ 5
6) 2(b 2 + 5) when b = 4
7)
3
y2 − 4
when y = 7
3y − 6
ADD AND SUBTRACT REAL NUMBERS
1) -63 + 57
2) -21 - (-46)
3) 4.5 + (-10.2)
6) -7 - (-7)
7) -16 + 16
8) −
4
4
+1
5
9
4) 15 + (-8)
5) -9 - 8
9) -11.4 + (3.8)
10) -8 + 17
MULTIPLICATIVE INVERSE OF A NEGATIVE NUMBER
Find the multiplicative inverse ( reciprocal ) of each number.
1) − 17
2) −
1
3
3) −
3
8
4) − 5
2
3
5) − 1
MULTIPLY AND DIVIDE REAL NUMBERS
1 7
÷
4 8
1) − 24 ÷ 3
 8
2) − 1 ÷  − 
 7
1

3) 26 ÷  − 4 
3

4) −
6) − 4(13)
7) 0.5(−10)(−7)
5  1  12 
8) −  −  
6  5  13 
9) − 1.2(−2.45)
5) − 2.5 ÷ −0.05
10) 5(−8.2)
SQUARE OF A NUMBER
Find the square of the 1st 25 positive integers
12 =
62 =
112 =
162 =
212 =
22 =
72 =
122 =
17 2 =
222 =
32 =
82 =
132 =
182 =
232 =
42 =
92 =
142 =
192 =
242 =
52 =
102 =
152 =
202 =
252 =
EVALUATING POWERS
In the power 102 , the base is ______ and the exponent is ______.
3
3
1) 6 =
2)
2
3.2 =
5
3) 2 =
7
4) 1 =
 3
5)  −  =
 5
WRITING EXPRESSIONS, EQUATIONS, AND INEQUALITIES
1) 3 decreased by a number x
2) The quotient of the square of a number m and 3
3) 5 times the sum of 7 and a number y
_____________________________________
_____________________________________
_____________________________________
4) The width of the book is 3 inches less than the length L.
Write an expression for the width of the book.
_____________________________________
5) The sum of twice a number b and 4 is 17.
6) The quotient of a number p and 3 is at most 16.
3
 1
6)  −  =
 4
_____________________________________
_____________________________________
7) The difference of 4 and the quotient of a number w and 3 is equal to 29.
_____________________________________
8) The product of 8 and the quantity 9 less than c is less than 13.
_____________________________________
DISTRIBUTIVE PROPERTY & COMBINING LIKE TERMS
1) 9m + (−16m)
2) 4 p 2 − 8 p 2 − 7
3) 6 − 3 x + 2
4) 2(3a − 5) − 2a
5) − 4(5m + 2 ) − 3m
6) 4 − 3(2 y − 8) − 2 y
7) − 3 y + 2( y 2 + 1) − y 3
8) 5 x − 2( x − 3)
9) 6 + 2(a + 8) + 8
10) Write and simplify an expression for the perimeter of the figure.
1 – 2x
3x – 5
4x +3
COORDINATE PLANE
Plot and label each point on the coordinate plane.
1) A (2, 4)
2) B (0, -3)
3) C (5, 0)
4) D (-1, -2)
5) E (-4, 3)
PERIMETER AND AREA
Find the perimeter and area of each figure. Don't forget to label.
1) Square Perimeter = _______
2) Rectangle Perimeter = _______ 3) Triangle Perimeter = _______
Area = __________
Area = __________
8 yd
15cm
Area = _________
12ft
15 ft
15 yd
9 ft
LINEAR EQUATIONS & INEQUALITIES
Check whether the given number is a solution of the equation or inequality.
1. 5c – 13 = 12 ; 2
2. 21 – 2d < 7 ; 6
3. A family goes to an amusement park. Adult tickets cost $21. Children under 10 years of age pay
$15. Write an algebraic expression for the total cost. Then find the total cost of 4 adult tickets
and 3 children’s tickets.
Approximate (estimate) the square root to the nearest integer.
5.
4. 125
6. – 47
200
7. Order the numbers from least to greatest: – 1.6,
4 , 0, 3.1, – 5 .
Use inverse operations to solve the equation. SHOW ALL WORK/STEPS involved.
m
n
8.
=8
9.
17 = 4x – 7
10. 9 –
= 28
−6
3
11.
16w – 10w + 13 = –5
12.
4h – 13 = 7h + 2
13. The perimeter P of a rectangle is given by the formula P = 2ℓ + 2w where ℓ is the length and w is
the width. Solve the formula for ℓ. Use the rewritten formula to find the length of a rectangle
with a width of 9 inches and a perimeter of 40 inches.
Solve the proportion. Hint: Simplify before you solve.
14.
x 12
=
32
8
15.
12
36
=
3w
63
16.
21 3k − 2
=
15
5
Write the equation so that y is a function of x. Hint: this means “solve for y”
17.
–12x + 3y = 15
18.
5x = –10y + 30
Find the slope of the line that passes through the given points. Hint: use the slope formula
19.
(–7, 3) and (3, 8)
20.
(–2, –9) and (–5, 6)
Identify the slope and y–intercept of the line with the given equation. Hint: y = mx + b
21. y = –
4
x+9
5
22. 4x – 7y = 21
23. 2x –
Graph the equation.
24. y =
1
x–5
4
25. 2x + 5y = 20
1
y=0
5