all Flashcards
1
Q
What is the equation represented by ‘3x + 8 = 38’?
A
3x + 8 = 38
2
Q
How can ‘five is three more than a number’ be expressed algebraically?
A
5 = x + 3
3
Q
What is the quotient of 3 and x?
A
3/x
4
Q
What does ‘38 is 8 more than 3 times a number’ imply?
A
38 = 3x + 8
5
Q
What is the quotient of x and 3?
A
x/3
6
Q
How is ‘ten times x’ expressed?
A
10x
7
Q
What is the expression for ‘ten percent of x’?
A
0.10x
8
Q
Translate ‘twice a number’ into an algebraic expression.
A
2x
9
Q
How is ‘the difference between 3 and x’ expressed?
A
3 - x
10
Q
What is the expression for ‘a number decreased by 7’?
A
x - 7
11
Q
How is ‘s less than 10’ represented algebraically?
A
10 - s
12
Q
Translate ‘a number increased by 13’ into an algebraic expression.
A
x + 13
13
Q
What does ‘a number added to 5’ yield in algebraic form?
A
x + 5
14
Q
What are some words often used in math problems to indicate operations?
A
- Equal
- Is less than
- Is greater than
- Diminished
- Take away
- Reduce
- Decreased by
- Subtract
- Minus
15
Q
What is the equation form for ‘X multiplied by P1.00 per glass = P20.00’?
A
(X) x (P1.00 per glass) = (P20.00)
16
Q
How can the number of glasses sold be represented?
A
X
17
Q
True or False: Algebraic equations are created to enable the determination of some quantity.
A
True
18
Q
What are some key topics included in the Quantitative Reasoning section of the UPCAT?
A
- Linear Expressions
- Equations of Lines
- Systems of Equations
- Inequalities
- Functions
- Statistics
19
Q
What basic mathematical concepts are essential for the UPCAT?
A
- Understanding of elementary mathematical concepts
- Ability to reason quantitatively
- Basic mathematical skills
20
Q
Fill in the blank: ‘The _______ of x and 3 is expressed as x/3’.
A
quotient
21
Q
What is the expression for ‘ten more than x’?
A
x + 10
22
Q
What does ‘is greater than’ indicate in mathematical terms?
A
greater than symbol (>)
23
Q
What is the expression for ‘the product of x and 3’?
A
3x
24
Q
What is an algebraic equation?
A
An equation that includes algebraic expressions and contains an equal sign.
25
Define numerical expression.
An expression involving arithmetic operations such as addition, subtraction, multiplication, and division.
26
What are factors in arithmetic?
Numbers that are multiplied together.
27
What do the symbols >, <, ≥, and ≤ represent?
Greater than, less than, greater than or equal to, and less than or equal to, respectively.
28
What is the distributive property?
A property that allows multiplication of a term by each term within parentheses.
29
Identify the first term in the expression 3(3x-2)+2x.
3(3x-2)
30
If (3x-2) is grouped inside parentheses, how is it considered?
As one term.
31
What is a variable?
A letter that represents one or more numbers.
32
What is a coefficient?
A constant multiplied by a variable.
33
In the expression -4x, what is the coefficient?
-4
34
Fill in the blank: A _______ is a known quantity represented by a number or letter.
constant
35
What does the term 'term' refer to in an expression?
Numbers and variables that are combined by addition or subtraction.
36
True or False: The sign of a term is determined by the + or - sign preceding it.
True
37
What are the letters at the beginning of the alphabet generally used to represent?
Constants
38
What is the result of the expression 5x + 10 = 12x?
The sum of 5x and 10 is equal to the product of x and 12.
39
The sum of two consecutive integers can be expressed as _______.
(x) + (x + 1)
40
What does the equation 7 > x represent?
Seven is greater than x.
41
What is the product of two times a number equal to if it is 10?
The number is 5.
42
What is the equation for ten subtracted from 10 times a number?
10x - 10 = x + 5
43
Fill in the blank: If variables are present in a numerical expression, it is called an _______.
algebraic expression
44
What is the sum of 5 and the cube of a number represented as?
5 + n^3
45
The square of a number doubled less _______ results in 11.
5
46
What is the equation for five times the difference of a number and 4?
5(x - 4)
47
48
49
What are polynomials?
Algebraic expressions with each variable having a positive integer exponent
## Footnote
Examples include expressions like 2x² + 3x + 1.
50
Define linear equations.
Equations in which the variables do not have any exponents other than 1
## Footnote
Example: 2x + 1 = 5.
51
What is the standard form of a linear equation?
Ax + By = C, where A, B, and C are constants, and x and y are variables
## Footnote
Another form is y = mx + b, where m is the slope and b is the y-intercept.
52
What characterizes nonlinear equations?
Equations in which the variables have exponents with their highest degree greater than 1
## Footnote
Example: 2x² + 1 = 5.
53
What is the formula for distance traveled?
Distance Traveled = (Rate)(Time)
## Footnote
This is used to solve problems involving motion.
54
Calculate the distance traveled by a car that goes 60 miles/hour for 2 hours.
120 miles
## Footnote
(60 miles/hour) * (2 hours) = 120 miles.
55
How far does a car travel if it goes 30 miles/hour for 2 hours?
60 miles
## Footnote
(30 miles/hour) * (2 hours) = 60 miles.
56
What is the total distance traveled by a car in 4 hours, if it travels at 60 miles/hour for 2 hours and 30 miles/hour for 2 hours?
180 miles
## Footnote
120 miles + 60 miles = 180 miles.
57
What is the general formula for solving work problems?
1/n + 1/m = 1/h
## Footnote
Where n and m are the hours taken by two persons or machines working alone, and h is the hours when they work together.
58
If Mary can plant 1,000 bulbs in 4 hours, what is her rate?
250 bulbs per hour
## Footnote
Rate = 1000 bulbs / 4 hours.
59
If Ned can plant 1,000 bulbs in 6 hours, what is his rate?
166.67 bulbs per hour
## Footnote
Rate = 1000 bulbs / 6 hours.
60
How long will it take Mary and Ned to plant 1,000 bulbs together?
Approximately 2.4 hours
## Footnote
Combined rate = 250 + 166.67 = 416.67 bulbs per hour; then 1000 / 416.67.
61
What are 'odd days'?
The number of days more than the complete weeks in a given period
## Footnote
Used to determine the day of the week for a specific date.
62
What defines a leap year?
A year divisible by 4, except for end-of-century years not divisible by 400
## Footnote
Example: 2000 is a leap year, but 1900 is not.
63
What is an ordinary year?
A year that is not a leap year, having 365 days
## Footnote
Examples include the years 2001, 2002, 2003, and 2005.
64
How many odd days are in 1 ordinary year?
1 odd day
## Footnote
Since 365 days = 52 weeks + 1 day.
65
What are polynomials?
Algebraic expressions with each variable having a positive integer exponent
## Footnote
Examples include expressions like 2x² + 3x + 1.
66
Define linear equations.
Equations in which the variables do not have any exponents other than 1
## Footnote
Example: 2x + 1 = 5.
67
What is the standard form of a linear equation?
Ax + By = C, where A, B, and C are constants, and x and y are variables
## Footnote
Another form is y = mx + b, where m is the slope and b is the y-intercept.
68
What characterizes nonlinear equations?
Equations in which the variables have exponents with their highest degree greater than 1
## Footnote
Example: 2x² + 1 = 5.
69
What is the formula for distance traveled?
Distance Traveled = (Rate)(Time)
## Footnote
This is used to solve problems involving motion.
70
Calculate the distance traveled by a car that goes 60 miles/hour for 2 hours.
120 miles
## Footnote
(60 miles/hour) * (2 hours) = 120 miles.
71
How far does a car travel if it goes 30 miles/hour for 2 hours?
60 miles
## Footnote
(30 miles/hour) * (2 hours) = 60 miles.
72
What is the total distance traveled by a car in 4 hours, if it travels at 60 miles/hour for 2 hours and 30 miles/hour for 2 hours?
180 miles
## Footnote
120 miles + 60 miles = 180 miles.
73
What is the general formula for solving work problems?
1/n + 1/m = 1/h
## Footnote
Where n and m are the hours taken by two persons or machines working alone, and h is the hours when they work together.
74
If Mary can plant 1,000 bulbs in 4 hours, what is her rate?
250 bulbs per hour
## Footnote
Rate = 1000 bulbs / 4 hours.
75
If Ned can plant 1,000 bulbs in 6 hours, what is his rate?
166.67 bulbs per hour
## Footnote
Rate = 1000 bulbs / 6 hours.
76
How long will it take Mary and Ned to plant 1,000 bulbs together?
Approximately 2.4 hours
## Footnote
Combined rate = 250 + 166.67 = 416.67 bulbs per hour; then 1000 / 416.67.
77
What are 'odd days'?
The number of days more than the complete weeks in a given period
## Footnote
Used to determine the day of the week for a specific date.
78
What defines a leap year?
A year divisible by 4, except for end-of-century years not divisible by 400
## Footnote
Example: 2000 is a leap year, but 1900 is not.
79
What is an ordinary year?
A year that is not a leap year, having 365 days
## Footnote
Examples include the years 2001, 2002, 2003, and 2005.
80
How many odd days are in 1 ordinary year?
1 odd day
## Footnote
Since 365 days = 52 weeks + 1 day.
