Download Summer Math (Students Expecting to Enter 8th Grade Algebra)

Summer Practice – p.1
Name:
Date:
Summer Math (Students Expecting to Enter 8th Grade Algebra): Show ALL work on separate sheets of
paper to receive credit. This will count as a test grade and must be submitted on the first day of school.
Write a numerical example and an example using variables of each of the following properties:
1) Associative Property of Addition/Multiplication
2) Commutative Property of Addition/Multiplication
3) Identity Property of Multiplication
4) Distributive Property over Addition
Simplify:
5) 7x + 5 – 15 + 6x – 19x
8)
x2 + 3x2 – 8 – 11x2
6) 4(x – 1)
9)
–7(x + 14) – 12x
7) 10x – 3(x – 2) + (–9x)
10)
20x – 17 + 8(–x – 6)
11) 1
5
6 +9
3
8
14)
11 3
−
15 8
17)
8 6
÷
9 7
3
9
20) 1 × 8
4 10
12) 1 5
− 2 ÷1
3 6
15)
13 ⎛ 3 ⎞
+ ⎜ − ⎟
15 ⎝ 10 ⎠
18)
11 ⎛ 4 ⎞
× ⎜ − 3 ⎟
12 ⎝ 5 ⎠
21) −
13) −
2 5
+
5 8
16)
8
6
÷−
11
13
19)
12 4
−
7 3
22) − 9 × 3
23) 20 – 4.578
27) 19.1 + 151
31) 22.5(3.9)
35) 100.2 ÷ 0.03
24) 89 + 15.6
28) (–5.1)(–0.65)
32) (22)(–1.07)
36) 357 ÷ (–0.03)
25) 100 + (–75)
29) –200 + 15
33) –65 ÷ (–5.5)
37) – 40 – 50
26) –82 – (–80)
30) –16 – (+14)
34) (0.0047)(6.6)
38) 5000 ÷ (–150)
Fractions:
7 ⎛ 9 ⎞
÷ ⎜ − ⎟
4 ⎝ 10 ⎠
5
9
Decimals:
Vocabulary:
39) 40) 41) 42) 43) 44) List all prime numbers from 80-120
List all composite numbers from 30-80
List all factors of the numbers: 20, 36, 40, 48, 75, 80, 90, 100, 120
List the first 5 multiples of 6, 9, 11, 12, 15
Write the prime factorization with and without exponents of: 120, 150, 200
1
Identify 10 different “Common FDPs” ; For Example: 100% = 1.0 =
1
Summer Practice – p.2
45) 46) 47) 48) 49) 50) 51) Write a set of natural/counting numbers, whole numbers, and integers
Write all of the perfect squares from 1-15.
Write an example of a linear equation. Identify the slope and y-intercept.
What is the difference between Perimeter, Area, Surface Area, and Volume?
In the expression 5p + 2 – 10p + 11p – 8, identify the number of terms, the coefficients,
and the constants.
What is the Pythagorean Theorem? What is a Pythagorean Triple? Give an example.
Which of the following is considered a rational number?
7
3 .4
a. 50
b. 4%
c. π
d. 6.23
e. 3
f.
8
7
Convert the following:
52) 45% to a decimal and fraction
53) 0.8 to a fraction and percent
11
54) to a percent, an improper fraction, and a decimal
5
12
55) 1.2 to a fraction and percent
56) 80 yards to inches
57) 650 millimeters to meters
58) 95 L to grams
59) 0.0085 and 1620 to scientific notation
Evaluate:
60) 61) 62) 63) a + b
when a = –7 and b = –8
− a + 80 = 144
x + 0.12 = −16.82
− 4 x + 4 < −6
66)
75 + 8 – 33[5 – (4 – 2)]
67)
8 + (−4 − 2)(24 ÷ 4)
− 1 − (−4)(2)
68)
(2)100 – 4(9 + 32)
64) x 8
=
4 9
69)
2a = –5a + 9 – a
65) 1.2
y
=
9
3.6
70)
–6(a + 3) = 12 – a
Simplify using Exponent Rules: Write answers using only positive exponents.
71) a2 · a5
75)
a 12
a 14
72) 6a3 · a4
76) a0
73) 8a11 · 4a7
77) 9a0
74)
78) a-3
a6
a5
Summer Practice – p.3
Ordering: Write the following in order from least to greatest. Consider converting all numbers to
decimals first.
5 7
11 4
,
,– ,
6 10 15 5
79) –
80) –9, – 49 , –
4
, –0.08
5
81)
82)
225 , –
30
, –1.5 , 1.15
2
–0.085, –0.8, –0.058, –0.008
Word Problems:
83) Find the mean, median, mode, and range for the following data:
Average Monthly Texts from Students
Grade
Month
Texts
4
January
50
5
February
150
6
March
125
7
April
200
8
May
500
84) Display the data in #83 using 2 different graphs. For example, histogram.
85) What is 2% of 80 gallons?
86) The legs of a right triangle are 15m and 20m. What is the length of the hypotenuse (the
longest side)?
87) Show which is the better buy: an 8-pack of soda for $6.99 or a 12 pack of soda for $10.99
88) Find the tax of an article of clothing that is priced at $52.00 if purchased in Jacksonville.
89) An umbrella retailing at $25.99 is on sale at 25% off. Find the discount price.
90) A 3.5 ft child casts a shadow that is 6.2 ft. If he is standing next to a tree that is 15.2 ft,
how long is the tree’s shadow?
91) A van travels 80 miles on 4 gallons of gas. At that rate, how much gas will it need to travel
200 miles?
Word Problems:
92) At St. Paul’s, 10% of the students walk or bike home. If there are 300 students at the
school, how many do not walk home?
93) There are 500 children in a cafeteria. If three-fifths of the students brought their lunch from
home, how many brought their lunch from home?
Summer Practice – p.4
94) An elevator starts on the 15th floor then goes down 2 floors, up 9 floors, down 12 floors,
and up 20 floors. What floor does it finally land on?
95) What is the probability that a dice will land on an even number? A number greater than 1?
Translations. Translate the following into an algebraic expression:
96) “Double a number”
101) “Six more than twice a number”
97) “Two less than a number”
102) “10 more than a number squared”
98) “Three-fourths of a number”
103) “The quotient of a and b”
99) 104) “8% of 16 is what number?”
“Twice the difference of a and b”
Geometry/Cartesian Plane:
105) Use a ruler to draw a picture of the following figures: oblique lines, perpendicular lines,
skew lines, supplementary angles, adjacent angles, corresponding angles, concave
polygon, regular pentagon, a diagonal in a polygon, parallelogram, rhombus, chord,
sector, a major arc, and a figure that has been translated.
106) Use the figures below to produce transformations.
A. Translate ABC using
(x, y) à (x – 4, y + 1) and
write the coordinates of its
image.
B. Reflect DEFG across the xaxis and write the
coordinates of its image.
C. Reflect DEFG across the yaxis and write the
coordinates of its image.
D. Dilate ABC by a scale
factor of 4.
E. Dilate ABC by a scale
factor of
.
Summer Practice – p.5
107) Find the Perimeter and Area of a square whose sides are 6 cm.
108) Find the Area of a Trapezoid whose bases are 6 in and 8 in and whose height is 3 in.
109) Find the Circumference of a circle whose radius is 15 m.
110) The angles of a triangle are 63º and 24º degrees. Find the measure of the third angle.
111) Find the Surface Area of a cube whose sides are 15 yd.
112) Plot the following points and describe their location on the Cartesian Plane (i.e.
Quadrant/Axis): (0,0) , (-2, 5) , (-3, -4) , (9, 0) , (7, 2) , (5, -3) , (0, -8)
113) Calculate the slope of a line containing the following points: (5, -6) and (-4, 10)
114) Use a ruler to graph the line 5x – y = 4 on graph paper.