Download Reference Sheet Algebra 1 Summer Packet

Keyport Public Schools
Summer Mathematics Packet for Students Entering
Algebra 1
Name:_________________
Teacher:_______________
Keyport School District
Summer Course Work
Review for Algebra 1
The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
Work with radicals and integer exponents.
Understand the connections between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry
software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.
Statistics and Probability
Investigate patterns of association in bivariate data.
Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Reference Sheet
Algebra 1 Summer Packet
This packet is to be completed WITHOUT the use of a calculator. Show all work for each
question in order to receive full credit.
1. Evaluate the expression 22𝑥 , when 𝑥 = 3
2. Evaluate the expression 𝑦 2 , when 𝑦 = 15
1
2
4
3
3. Evaluate the expression 𝑘 , when 𝑘 =
4. Evaluate the expression 2𝑛 , when 𝑛 = 5
5. Evaluate the expression 32 − 5 + 9 − 3
6. Evaluate the expression 15 ÷ (32 − 6)
7. Evaluate the expression
(1+32 )
5
8.
5
6
+
2
3
9. 2.4(−0.7)
10. −40.5 ÷ (−8.1)
11.
1
9
×
3
4
12. Express 20% percent as a fraction in simplest form.
13. Express 5.2% as a decimal.
14. 18 is what percent of 72?
15. 35 is 50% of what number?
16. What number is 75% of 300?
17. Translate the verbal phrase “the product of five and a number x, minus two” into an
expression.
18. Translate the verbal phrase “the quantity of 5 plus a number, times 4” into an
expression.
19. Translate the verbal phrase “3 less than the product of 4 and a number is seventeen”
into an equation, then solve.
20. Is 4 a solution of the inequality 𝑛2 + 8 > 21?
21. Solve, then graph the following inequality on a number line: 𝑥 − 7 ≤ 10
22. Identify the domain and range of the function below. Remember the domain represents
the x-values, and the range represents the y-values:
Input
2
Output 15
4
20
6
25
8
30
23. Create a table for the function 𝑦 = 𝑥 + 5 , using the values 2, 3, 4, and 5 for the
domain.
x
y
24. Use the table from question 23 to graph the function 𝑦 = 𝑥 + 5 on the coordinate plane
below. Make sure to label the axes.
25. What is the absolute value of −3?
26. What is the absolute value of 3?
27. |4| =
28. |−4| =
29. Identify the property being illustrated. Possible answers are: Commutative, Associative,
Identity, and Distributive.
a. 3(24) = 3(20) + 3(4)
___________________________
b. 4 × 9 = 9 × 4
___________________________
c. (𝑥 + 2) + 5 = 𝑥 + (2 + 5) ___________________________
d. 5 + 0 = 5
___________________________
30. Put a check in each box to indicate if the number belongs to that group.
Number
Real
Numbers
Rational
Numbers
Irrational
Numbers
√23
√25
0.4
-17
8
31. √121 =
32. 172 =
33. Simplify 3(4𝑥 + 5)
34. What is the mean of the numbers 5, -12, 33, 15, and 4?
Integers
Whole
Numbers
35. What is the median of the numbers 4, 7, 4, 6, 4, 13, 13, and 12?
36. What is the mode of the data set in question #35?
37. The two shorter sides of a right triangle have measures of 3 inches and 4 inches
respectively. What is the measure of the hypotenuse? (hint: Use the Pythagorean
Theorem)
38. What is the volume of a rectangular prism with a length of 10 cm, a width of 15cm, and
a height of 3 cm?
39. What is the volume of a cylinder with a height of 10 in and a radius of 4 in? (Use 3.14
for 𝜋)
40. The volume of a cylinder is 3 times larger than a cone with the same height and radius.
What would the volume of a cone be if a cylinder with the same height and radius has a
volume of 180 𝑐𝑚3 ?
41. The area of a square is 81 square centimeters. Suppose the sides of the figure are
doubled. What will be the new area of the similar figure?
42. What is the sum of the measures of the interior angles of a hexagon? Use 180(n-2).
43. Between which two integers does √55 lie on the number line?
44. Solve for x:
5
25
=
𝑥 100
45. Solve for the missing value:
𝑦
18
=
33 99
46. Solve for the missing value:
24
𝑟
=
64 32
47. Tanya needs 12 bottles of juice for every 4 people that show up to her party. How many
bottles of juice will she need if she is expecting 48 people?
48. Solve: 10𝑥 + 2 = 72
49. Solve: −3𝑦 + 18 + 5𝑦 = 38
50. Solve: 2𝑥 − 7 = 5𝑥 − 40