Topic 1 - Numbers Flashcards
Number 1 (119 cards)
1
Q
What is the value of √3 * √3?
A
3
2
Q
True or False: √(a*b) = √a * √b for all positive a and b.
A
True
3
Q
Fill in the blank: In standard form, the coefficient must be _____ 10.
A
less than
4
Q
If a = 5 and n = -1, what is a^n?
A
1/5
5
Q
What happens to the upper bound if the precision of a measurement increases?
A
The upper bound increases.
6
Q
Express √18 in its simplest form.
A
3√2
7
Q
Convert 5000 to standard form.
A
5 × 10^3
8
Q
What is the result of (x^3y^2)^2?
A
x^6y^4
9
Q
True or False: a^(-n) = 1/a^n.
A
True
10
Q
True or False: a^m / a^n = a^(m-n)
A
True
11
Q
What is the value of 7 squared?
A
49
12
Q
What is standard form?
A
Standard form is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10.
13
Q
Simplify the expression: 7√2 - 3√2.
A
4√2
14
Q
How do you convert 8 × 10^-2 to a decimal?
A
0.08
15
Q
If a = 4, simplify √(a^2 + 4a).
A
√(32) or 4√2
16
Q
What is the definition of a prime number?
A
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
17
Q
What happens to the exponent when you take the square root of a^n?
A
Divide the exponent by 2.
18
Q
Fill in the blank: To divide numbers in standard form, you divide the _____ and subtract the _____ of 10.
A
coefficients, powers
19
Q
What is the value of 5 factorial (5!)?
A
120
20
Q
Simplify √(72).
A
6√2
21
Q
True or False: A rational number can be expressed as a fraction.
A
True
22
Q
If a car travels 60.5 km with a precision of 0.5 km, what is the lower bound?
A
60.0 km
23
Q
What is the prime factorization of 30?
A
2 × 3 × 5
24
Q
What is the upper bound of 3.6 cm with a precision of 0.1 cm?
A
3.65 cm
25
What is the standard form of 0.00012?
1.2 × 10^-4
26
What is the result of a^m * a^(-m)?
1
27
If a measurement is 14.2 cm ± 0.3 cm, what is the lower bound?
13.9 cm
28
Fill in the blank: The term 'scientific notation' is often used interchangeably with _____ form.
standard
29
If a = 2 and m = 3, what is a^m?
8
30
If a measurement is reported as 9.8 kg ± 0.2 kg, what is the upper bound?
10.0 kg
31
Fill in the blank: The number π (pi) is approximately equal to ___.
3.14
32
True or False: The expression (√a + √b)^2 expands to a + b + 2√ab.
True
33
True or False: Every even number greater than 2 can be expressed as the sum of two prime numbers.
True
34
True or False: The standard form of 800 is 8 × 10^2.
True
35
Convert 0.000007 to standard form.
7 × 10^-6
36
True or False: The square root of 16 is a surd.
False
37
What is the simplified form of √(25/9)?
5/3
38
Fill in the blank: The upper bound is calculated by adding _____ to the measurement.
half the precision
39
What is the value of 3√2 * 2√3?
6√6
40
What is the lower bound of the measurement 2.3 m?
2.25 m
41
Fill in the blank: The upper bound of a value is the maximum possible value, while the _____ is the minimum possible value.
lower bound
42
How do you multiply two numbers in standard form, for example, (2 × 10^3) and (3 × 10^2)?
Multiply the coefficients (2 × 3) and add the powers of 10 (10^3 + 10^2) to get 6 × 10^5.
43
Which number is larger: 3.2 × 10^5 or 2.9 × 10^6?
2.9 × 10^6
44
If a length is measured as 5.2 m with a precision of 0.1 m, what is the upper bound?
5.25 m
45
Fill in the blank: The number 100 can be expressed as 10 to the power of ___.
2
46
What do you do with the exponents when raising a power to a power, such as (a^m)^n?
Multiply the exponents.
47
True or False: The number 0 is an integer.
True
48
True or False: a^m * a^n = a^(m*n).
False
49
Simplify the expression: 2√8 + 3√2.
7√2
50
What is the value of 4√5 * √5?
20
51
What is the standard form of 0.00056?
5.6 × 10^-4
52
What is the result of (x^m)^n?
x^(m*n)
53
Fill in the blank: a^m * b^m = (____)^m.
ab
54
What happens when you multiply (1.5 × 10^3) by (2.0 × 10^4)?
3.0 × 10^7
55
True or False: (a/b)^n = a^n / b^n.
True
56
What is the least common multiple (LCM) of 4 and 5?
20
57
True or False: Upper and lower bounds can be used to determine the accuracy of measurements.
True
58
True or False: The number 1 is a prime number.
False
59
What is the value of (3^2)^3?
729
60
What is the rule for dividing indices with the same base?
Subtract the exponents.
61
What is the sum of √5 and √5?
2√5
62
If a weight is measured as 10.4 kg with a precision of 0.2 kg, what is the lower bound?
10.3 kg
63
Fill in the blank: The number 9.1 × 10^2 represents _____ in standard form.
910
64
True or False: If a^m = a^n, then m = n.
True, if a is not zero.
65
If the height of a building is 25.0 m with a precision of 0.5 m, what is the lower bound?
24.5 m
66
True or False: The lower bound can be greater than the actual measurement.
False
67
Multiple Choice: What is the result of 15 ÷ 3? A) 3 B) 5 C) 7 D) 10
B) 5
68
True or False: You can express any integer in standard form.
True
69
If the length of a pencil is 15.4 cm ± 0.1 cm, what is the upper bound?
15.5 cm
70
Simplify the expression: 5√3 + 2√3.
7√3
71
What is the lower bound of a measurement of 12.5 cm with a precision of 0.5 cm?
12.0 cm
72
What is the difference between 25 and 10?
15
73
True or False: The number 0 is a natural number.
False
74
Which of the following is in standard form? (A) 12 × 10^2 (B) 1.2 × 10^1 (C) 0.5 × 10^3
B
75
What is the result of a^1?
a
76
Multiple Choice: Which of the following is a rational number? A) √2 B) 1/2 C) π D) e
B) 1/2
77
If a number is expressed as 4.5 × 10^6, what is the original number?
4500000
78
Fill in the blank: The first five prime numbers are ___, ___, ___, ___, and ___.
2, 3, 5, 7, 11
79
What happens to the exponent when you raise a fraction to a power, such as (a/b)^n?
Apply the exponent to both the numerator and the denominator.
80
What is 3.0 × 10^4 + 2.0 × 10^4 in standard form?
5.0 × 10^4
81
True or False: √(x^2 + y^2) is always greater than or equal to 0.
True
82
What is the rule for multiplying indices with the same base?
Add the exponents.
83
Fill in the blank: a^m / a^m = ____.
1
84
What is the formula for the square of a product?
(ab)^2 = a^2 * b^2
85
Fill in the blank: (ab)^n = a^____ * b^____.
n, n
86
Fill in the blank: The lower bound is found by subtracting _____ from the measurement.
half the precision
87
Multiple Choice: What is 6 + 2 × 3? A) 24 B) 12 C) 18 D) 12
D) 12
88
True or False: The upper bound is always greater than the actual value.
True
89
What is the power of 10 in the standard form of 0.00089?
-4
90
What is the purpose of knowing upper and lower bounds in measurements?
To understand the range of uncertainty in the measurement.
91
What is the upper bound of a measurement of 6.7 m with a precision of 0.1 m?
6.75 m
92
What is the lower bound of 8.9 m with a precision of 0.2 m?
8.8 m
93
What is the standard form of 0.00000045?
4.5 × 10^-7
94
What is the upper bound of the measurement 4.6 cm?
4.65 cm
95
What is the rule for the exponent of a quotient raised to a power?
Distribute the exponent to the numerator and the denominator.
96
What is the standard form of 123000?
1.23 × 10^5
97
What is the concept of upper and lower bounds primarily used for?
To express the range of possible values for a measurement.
98
True or False: Standard form can be used for very large and very small numbers.
True
99
Fill in the blank: a^m * a^n = a^____.
m+n
100
What is the decimal form of the fraction 3/4?
0.75
101
What is the result of a^m * a^n * a^p?
a^(m+n+p)
102
Fill in the blank: The decimal representation of one half is ___.
0.5
103
What is the result of a^0 where a is not equal to 0?
1
104
What is the greatest common divisor (GCD) of 12 and 16?
4
105
Multiple Choice: Which of the following numbers is a composite number? A) 2 B) 3 C) 4 D) 5
C) 4
106
Which of the following is a surd? A) 4 B) √7 C) 2.5
B) √7
107
Simplify the surd √50.
5√2
108
True or False: The number 0.00034 can be expressed in standard form.
True
109
What is the result of 2 raised to the power of 3?
8
110
True or False: The lower bound can be calculated by subtracting the precision from the measurement.
True
111
What is the product of 7 and 8?
56
112
Convert 7.2 × 10^-3 to a normal number.
0.0072
113
If a box measures 20.3 cm ± 0.4 cm, what is the upper bound?
20.5 cm
114
If a bottle contains 1.5 L ± 0.1 L, what is the lower bound?
1.4 L
115
What is the upper bound of a measurement of 7.8 L with a precision of 0.2 L?
7.9 L
116
Which of the following is not a surd? A) √8 B) √9 C) √18
B) √9
117
What is a surd?
A surd is an irrational number that cannot be expressed as a simple fraction.
118
What is the square root of 81?
9
119
Fill in the blank: The product of two surds is a surd if both are ______.
irrational
