Notes, summaries, assignments, exams, and exercises for Mathematics for Baccalaureate

Frequency Tables for Data Organization

A frequency table is the easiest way to organize data. To construct a frequency table from the data, essentially we have to count how many times each event occurs among the data. Depending on the type of variable, we can add more or less information to the frequency table.

• Absolute frequency: Count how many times each value appears in the table.
• Relative frequency: Count how many times each value appears in the table, divided by the size of the sample.
• Cumulative absolute frequency: The sum of all previous absolute frequencies (e.g., how many people own 3 cars or less?).
• Cumulative relative frequency: The sum of all previous relative frequencies (e.g., what proportion of people own 3 cars or less?).

Discrete

Points of Polar Coordinates

In the Cartesian plane, a point is located using its distances to the two axes x and y. Another way to represent a point is by specifying the distance from that point to a fixed point and the angle formed between the segment that joins the two points and a fixed line. The fixed point is called the pole and the fixed line is known as the polar axis. This point is represented as , known as a polar coordinate.

In the figure above, r represents the distance between the pole and point P. Angle is considered positive when measured counterclockwise and negative when measured clockwise.

Relation Between Rectangular and Polar Coordinates

If the polar plane is placed over a Cartesian plane so that the pole coincides with the...

VAT Fees Eligible for Deduction

The following fees can be deducted:

• Submission-entry of goods from another taxable person
• Imports of goods
• Intra-Community acquisitions
• Fees relating to cases of reverse charge

Partial Deduction or Pro Rata

This applies when a company performs two types of activities: operations with deduction and operations without deduction.

The consequence is that only a portion or percentage of the taxes charged can be deducted.

What percentage? To determine the coefficient, calculate the following:

(Sum of output-delivery deduction in the year) / (Sum of all delivery-end of the year)

To calculate the deduction, multiply the percentage by the taxes charged.

Dynamics During the Exercise: Provisionally apply the percentage from the previous...

Calculating Mean and Standard Deviation

The marks obtained in a statistics examination are normally distributed. If 15% of students scored ≥ 60 marks and 40% scored < 30 marks, find the mean (μ) and standard deviation (σ).

Given

• P(X ≥ 60) = 0.15
• P(X < 30) = 0.40

We need to find the values of μ and σ.

Step 1: Convert to Z-values

(i) P(X ≥ 60) = 0.15

Since P(X ≥ 60) = 0.15, then P(X < 60) = 0.85. From the standard normal table, P(Z < 1.04) = 0.85. Therefore:

(60 − μ) / σ = 1.04
μ = 60 − 1.04σ (Equation 1)

(ii) P(X < 30) = 0.40

From the standard normal table, P(Z < -0.25) = 0.40. Therefore:

(30 − μ) / σ = -0.25
μ = 30 + 0.25σ (Equation 2)

Step 3: Solve the Equations

Equating (1) and (2):

60 − 1.04σ = 30 + 0.25σ
30

Chapter 1: Margin of Error and Sample Size

• Margin of Error (ME) = (Upper bound - Lower bound) / 2
• Sample size for a proportion type: n = z² × p̂ × (1 - p̂) / ME²
• Standard Deviation = √(pq/n)
• Width = (√n / √new n) × Old width
• Confidence Interval: Helps make correct business decisions by obtaining more information about the population parameter.

Chapter 2: Mean Intervals and T-Tests

• True mean interval for one sample: Use 8:TInterval.
• Critical value of t^*: VARS → InvT(area, df), where df = n - 1 and area = ((1 - confidence level) / 2) + confidence level.
• Sample size for T-test: n = (z × σ / ME)²
• Standard Error of the Mean: SE = s / √n. Alternatively, use 1:T-test to find Sx / √n.
• A t-interval has a larger Margin of Error than a z-interval

Quick revision table for Mathematics and Statistics exams.

Unit I: Integration and Data Presentation

Unit II: Central Tendency and

Financial Reporting & Transaction Analysis

This section presents accounting scenarios focusing on financial statement impact and transaction analysis for various companies.

Problem AP8-8A: Whiskey Industries & Holding Ltd.

Whiskey Industries Ltd. Financial Transactions

Whiskey Industries Ltd., a Nanaimo, British Columbia–based company, has a December 31 year-end. The company's comparative statement of financial position and its statement of income for the most recent fiscal year are presented here, along with some additional information:

• During the year, Whiskey Industries sold, for $500 cash, equipment that had an original cost of $1,000 and a net carrying amount of $200.
• Whiskey Industries borrowed an additional $8,000 by issuing notes

Sample Characteristics: Measures of Location and Variation

Measures of Location

• Average

  The average is a central value, often referred to as a measure of central tendency.

• Mean

  • Also known as the arithmetic mean.
  • Found by dividing the sum of all values by the total number of values.
  • Formula: Mean = (Sum of Quantities) / (Number of Quantities)
  • Example: Find the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
    • Sum of values: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
    • Number of values = 10
    • Mean of values = 55 / 10 = 5.5

• Median

  The median of a set is the middle number when the values are arranged in order from lowest to highest.

• Mode

  • The mode is the value that occurs most frequently in a set of values, also known as the modal value.
  • Example: Find the mode of 1, 2, 2, 3,