Test Exam - Module 2: Algebraic Reasoning & Integers & Rational Numbers
The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell m muffins at $0.45 apiece and n bags of carrot sticks at $0.40 apiece, the total number of dollars raised will be T = 0.45m + 0.40n. How many dollars will they raise if they sell 140 muffins and 100 bags of carrot sticks?
$103.00
Utako earns money by caring for horses while people are on vacation. Utako earns $10 per week per pet. Evaluate the expression (2 + 6 × 3) × 10 to find out how much Utako earned for the month of July.
$200
Pablo earns money by caring for turtles while people are on vacation. Pablo earns $25 per week per pet. Evaluate the expression (4 + 2 × 3) × 25 to find out how much Pablo earned for the month of July.
$250
Annie paid a basic fee of $15 per month plus $3 for each extra DVD taken from the library beyond her basic plan. Simplify the expression 15 + 7 (3) to find how much Annie paid for a month with 7 DVDs beyond the basic plan.
$36
The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be T = 0.35x + 0.15y. How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?
$91.50
Which of the following illustrates the Associative Property of Addition? = (12+8)+5=12+(8+5) = 12+(8+5), 3+1=1+33+1=1+3, 7+5=7+57+5=7+5, or None of these
(12+8)+5 = 12+(8+5)
Which of the following illustrates the Commutative Property of Addition? None of these, (10+8)+5=10+(8+5)(10+8)+5=10+(8+5), 3+(1+6)=3+(1+6)3+(1+6)=3+(1+6), or 1+3=3+1
1 + 3 = 3 + 1
Write the number 100 using an exponent and base 10.
10 to the 2nd power
Evaluate the expression for the given values of the variables. 2n − 2m for n = 10 and m = 4
12
A planet has an approximate diameter of 1.38 × 10 to the 4th power km. Which is equal to that distance?
13,800 km
Identify the value of 11 to the 3rd power.
1331
Make a table that shows the number of arrows in the figure. Then tell how many arrows are in the 7th figure of the pattern. figure 1 = ⬅️➡️ figure 2 = ⬅️➡️⬅️➡️ figure 3 = ⬅️➡️⬅️➡️⬅️➡️
14
A grocery clerk changes the display of oranges regularly. If the pattern indicated below is continued, determine the number of oranges that will be displayed on the 5th figure. Use a table to find the pattern. figure 1 = figure 2 = figure 3 =
15
Yuan read 15 books from the library each month for y months in a row. Write an expression to show how many books Yuan read in all. Then evaluate the expression for y = 9. = 15 − y; 24 books, 15/y; 135 books, 15 + y; 24 books, or 15y; 135 books
15y; 135 books
Evaluate 4z - 4 for z = 5.
16
Make a table that shows the number of arrows in the figure. Then tell how many arrows are in the 8th figure of the pattern. figure 1 = ⬅️➡️ figure 2 = ⬅️➡️⬅️➡️ figure 3 = ⬅️➡️⬅️➡️⬅️➡️
16
Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day? Category Sunlight Intensity = Dim 2, Illuminated 3, Radiant 4, & Dazzling 5
16 times brighter
Which shows 1.69 × 10 to the 7th power in standard notation?
16,900,000
Make a table that shows the number of arrows in the figure. Then tell how many arrows are in the 9th figure of the pattern. figure = ➡️⬅️ figure 2 = ➡️⬅️ ➡️⬅️ figure 3 =➡️⬅️➡️⬅️➡️⬅️
18
Multiply 182 ⋅ 10 to the 2nd power.
18,200
Simplify the expression = (36 − 6) ÷ 15.
2
Which of the following is an example of the Additive Identity Property? = None of these, 6⋅1=66·1=6, 2+0=22+0=2, −6+6=0-6+6=0, or 2+1=3
2 + 0 = 2
Multiply. 2.931 ⋅ 10 to the 3rd power
2,931
Write the number 2,068 in scientific notation.
2.068 × 10 to the 3rd power
Make a table that shows the number of blue triangles in the figure. Then tell how many blue triangles are in the 7th figure of the pattern. figure 1 = 🔼🔼🔼 figure 2 = 🔼🔼🔼🔼🔼🔼 figure 3 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼 figure 4 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼
21
Identify an expression for the perimeter of the given figure. = 8x + y, 3x + 7y, 8x + y, or 3x + 7y. = 5x − 6y, 22x + 16y, (3x + y)(3x + 7y), or 11x + 8y
22x + 16y
Evaluate the expression for the given value of the variable. 10y − 7 for y = 3
23
Find the missing terms in the sequence. 2, 3, 5, 8, 12, 17, __, 30, 38, __, 57
23, 47
Express in standard notation.2.44 ×; 10 to the 2nd power.
244
Make a table that shows the number of blue triangles in the figure. Then tell how many blue triangles are in the 9th figure of the pattern. figure 1 = 🔼🔼🔼 figure 2 = 🔼🔼🔼🔼🔼🔼 figure 3 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼 figure 4 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼
27
Evaluate the expression for the given values of the variables. 2y + 5z for y = 9 and z = 2
28
Evaluate p - 4 for p = 33.
29
The height of Mount Everest is about 2.9 × 10 to the 4th power feet from sea level. Which of the following represents this number in standard form?
29,000
Evaluate 45/x + 7y for x = 5 and y = 3
30
Make a table that shows the number of blue triangles in the figure. Then tell how many blue triangles are in the 10th figure of the pattern. figure 1 = 🔼🔼🔼 figure 2 = 🔼🔼🔼🔼🔼🔼 figure 3 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼 figure 4 = 🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼🔼
30
Which shows 3.14 × 10 to the 4th power in standard notation?
31,400
Find the product. 33.2 × 10 to the 4th power.
332,000
Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 7 times brighter than the next lower category. For example, a day that is dazzling is 7 times brighter than a day that is radiant. How many times brighter is a dazzling day than a dim day? Category Sunlight Intensity = Dim 2, Illuminated 3, Radiant 4, & Dazzling 5
343 times brighter
Simplify the expression = 3 ∙ 16 − 12.
36
Simplify the expression = 32 − 6 ÷ 6 × 3 + 7.
36
Simplify the expression [(2 + 2 × 3) − 2] to the 2nd power.
36
The expression 12n gives the number of months in n years. Evaluate 12n for n = 3. How many months are in 3 years?
36 months
Evaluate 39/x + 5y for x = 3 and y = 5
38
What is the exponent used when 23,200 is written in scientific notation?
4
Which of the following represents 64 written with an exponent using base 4?
4 to the 3rd power
Evaluate r + 6 for r = 36.
42
A grocery clerk changes the display of oranges regularly. If the pattern indicated below is continued, determine the number of oranges that will be displayed on the 9th figure. Use a table to find the pattern. figure 1 = 🔵 figure 2 = 🔵🔵🔵 figure 3 = 🔵🔵🔵🔵🔵🔵
45
Evaluate 6x + 5y for x = 5 and y = 3.
45
Evaluate ax − (b ∙ c) ÷ d for a = 7, b = 2, c = 4, d = 2, and x = 2.
45
Simplify the expression = 45 + 16 × 2 ÷ 4 − 6.
47
Which of the following represents 562,000 in scientific notation?
5.62 × 10 to the 5th power
Scientists have different estimates for the number of grains of sand in the world. One estimate is that there are 57,900,000,000,000,000,000,000 grains of sand in the world. Write this number in scientific notation.
5.79 × 10 to the 22nd power
Evaluate 9y − 4 for y = 6.
50
Find the missing terms in the sequence. 2, 5, 10, 17, 26, 37, __, 65, 82, __, 122
50, 101
Evaluate y + 19 for y = 34.
53
Find the missing terms in the sequence. 5, 8, 13, 20, 29, 40, __, 68, 85, __, 125
53, 104
Evaluate ax − (b ∙ c) ÷ d for a = 8, b = 10, c = 2, d = 2, and x = 2.
54
Evaluate the expression for the given value of the variable. 7z + 7 for z = 7
56
What is the exponent used when 5,450,000 is written in scientific notation?
6
Identify the algebraic expression for the given word phrase. 6 times the sum of r and 9. = r (6 + 9), 6 (r + 9), 6r + 9, or 6 + r + 9
6 (r + 9)
Evaluate the expression for the given value of the variable. 8y + 4 for y = 7
60
Find the value of 4 to the 3rd power.
64
A comet is about 6.64 × 10 to the 7th power miles from Earth. Write this number in standard form.
66,400,000 miles
Which shows the following phrase as an algebraic expression where e is the cost of an eraser and p is the cost of a pencil? the sum of the costs of 6 erasers of equal value and 3 pencils of equal value = 6e - 3p, none of these, 6e + 3p, 3e - 6p, or 3e + 6p
6e + 3p
Which expression demonstrates how the Distributive Property could be used to find the product of 7 and 92?
7 (90) + 7 (2)
Which of the following is an example of the Multiplicative Identity Property? = 7 ⋅ 1 = 7, 10 + 0 = 10, None of these, −7 + 7 = 0, or 7 ⋅ 0 = 0
7 ⋅ 1 = 7
Find the product 7,246 × 10 to the 3rd power.
7,246,000
Simplify the expression = 70 + 25 ÷ 5.
75
Use the Distributive Property to find 9 (86).
774
Which of the following is an algebraic expression that represents the phrase "the sum of 7 times a number and 25″? = 7 + 25n, 7n + 25n, 7 (n + 25), or 7n + 25
7n + 25
Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 2 times brighter than the next lower category. For example, a day that is dazzling is 2 times brighter than a day that is radiant. How many times brighter is a dazzling day than a dim day? Category Sunlight Intensity = Dim 2, Illuminated 3, Radiant 4, & Dazzling 5
8 times brighter
Which of the following represents 512 written with an exponent using base 8?
8 to the 3rd power
Which shows 8.27 × 10 to the 9th power in standard notation?
8,270,000,000
Find the value of 3 to the 4th power.
81
Express in standard notation. 9.56 × 10 to the 6th power.
9,560,000
Identify a possible pattern. Use the pattern to identify the next three numbers.3, 8, 13, ...
Add 5; 18, 23, 28
Make a table that shows the number of squares in each figure. Then, make a conjecture about the number of squares in the fifth figure of the pattern. Use drawings to justify your answer. figure 1 = figure 2 = figure 3 =
Figure 5 has 15 squares.
Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa's age and her sister's age? = (x + 4) − x, x − (x − 4), None of these, or (x − 4) − x
None of these
A sample from the Sahara Desert contains 2.371 × 10 to the 6th power grains of sand. A sample from the Chihuahuan Desert has 8.171 × 10 to the 5th power grains of sand. Which sample has more grains of sand?
Sahara Desert
Identify a possible pattern. Use the pattern to identify the next three numbers.30, 27, 24, ...
Subtract 3; 21, 18, 15
What property is illustrated by the fact that 44(23⋅30)=(44⋅23)⋅3044(23·30)=(44·23)·30?
The Associative Property of Multiplication
What property is illustrated by the fact that 49 ⋅ 32 = 32 ⋅ 49?
The Commutative Property of Multiplication
What property is illustrated by the fact that 33 (92 + 55) = 33 ⋅ 92 + 33 ⋅ 55?
The Distributive Property
Identify a possible pattern. Use the pattern to write the next three numbers.124, 113, 102, ...
The pattern is to subtract 11; 91, 80, 69
Identify a possible pattern. Use the pattern to write the next three numbers.52, 45, 38, ...
The pattern is to subtract 7; 31, 24, 17
Identify the algebraic expression for the given word phrase. 18 less than a number r = r −18, 18 − r, 18 − 18r, or 18r −r
r −18
Which of the following is an algebraic expression that represents the phrase "15 less than a number"? = x − 15, 15x, x + 15, or 15 − x
x − 15
Write an algebraic expression for the word phrase. the quotient of y and 27 = 27 ÷ y, y ÷ 27, y ÷ 27 + y, or y × 27
y ÷ 27
Write the phrase as an algebraic expression. 10 less than a number = z − 10z, z − 10, 10 ÷ z, 10 + z
z − 10
Identify a possible pattern. Use the pattern to identify the next three figures. ➡️ ⬇️ ⬅️ ⬆️
➡️ ⬇️ ⬅️
Identify a possible pattern. Use the pattern to identify the next three figures. ⬆️ ➡️ ⬇️ ⬅️ ⬆️
➡️ ⬇️ ⬅️
