Notes, summaries, assignments, exams, and exercises for Mathematics for Primary education

Final Exam Cheat Sheet

Machine Rate Problems

Set Difference Calculation

To find the set difference A - B, we identify all elements present in set A but not in set B.

Step-by-Step Subtraction

• Is 1 ∈ B? No. (Keep 1)
• Is 2 ∈ B? No. (Keep 2)
• Is 3 ∈ B? Yes. (Remove 3)
• Is 5 ∈ B? No. (Keep 5)
• Is 7 ∈ B? Yes. (Remove 7)
• Is 8 ∈ B? No. (Keep 8)

The remaining elements from set A are {1, 2, 5, 8}.

Symbolic Logic

In symbolic logic, the word "but" functions like "and," indicating that both conditions occur simultaneously. To write "He is rich but not generous" in symbolic form:

• p: "He is rich"
• q: "He is generous"
• ¬q: "He is not generous"
• ∧: The conjunction operator

Logic Symbol Reference

Logarithm Calculations

To find the value of log 360,...

Core Cash Assets

Petty Cash: A small amount of cash kept on hand for minor business expenses.

Banks: Funds held in bank accounts available to cover payments at any time.

Bank Reconciliation Methods

There are three primary ways to perform bank reconciliation:

1. Adjusting the business accounting records to match the bank statement balance.
2. Adjusting the bank statement balance to match the business accounting records.
3. Using a reconciliation statement to adjust both balances to reach a reconciled figure.

Common Reconciliation Adjustments

• Outstanding Checks: Checks issued by the company that have not yet been cashed by the recipient.
• Bank Errors: Discrepancies caused by the bank, such as incorrect charges or processing another company's check.
• Bank Service Charges:

Vertex Cover ≤ CLIQUE

Suppose G has a clique S with |S| = k. Consider S' = V – S. Then, |S'| = |V| - k. To show S' is a cover, consider any edge (v, w) ∈ E'. Then, (v, w) ∉ E, at least one of v or w is not in S (since S forms a clique), and at least one of v or w is in S'; hence, (v, w) is covered by S'.

Suppose G' has a cover S' with |S'| = |V| - k. Consider S = V – S'. Clearly, |S| = k. To show S is a clique, consider some edge (v, w) ∈ E'. Then, if (v, w) ∈ E', either v ∈ S', w ∈ S', or both. By contrapositive, if v ∉ S' and w ∉ S', then (v, w) ∈ E; thus, S is a clique in G.

Vertex Cover ≤ SET COVER

Given a black box that solves instances of SET-COVER, let G = (V, E) and k be an instance of VERTEX-COVER. Create a SET-...

Ch 12 Anova

Goal/purpose: Evaluate mean difference between 2 or more treatments

• Factor: The IV that designates the groups being compared
• Levels: Individual conditions or values that make up a factor
• Factorial design: A study that combines two or more factors

The Logic:

• Between treatment variance
  • Variability results from general differences between the treatment conditions
  • Variance between treatments measures differences among sample means
• Within treatments variance
  • Variability within each sample
  • Individual scores are not the same within each sample

Notations:
k= # of treatment condition
T= sum of squares for each treatment
G= grand total of all scores in study
N= total number of scores
kn= when all samples are same size
n1,n2= # of scores in each treatment

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Personal Finance Math and Interest Calculations

Interest and Yield Calculations

1. Simple Interest: Katie invests $2,300 in an account that pays 7% simple interest annually. Find the future value of the account after 9 years. Round your answer to the nearest cent.
2. Monthly Compounding: Suppose you invest $1,900 at a fixed rate of 5% per year, compounded monthly. Find the future value of the account after 6 years. Round your answer to the nearest cent.
3. Continuous Compounding: Suppose you instead invest your $1,900 in an account that earns 6% interest compounded continuously. What is the total amount of your investment after 7 years? Round your answer to the nearest cent.
4. Effective Annual Yield: Find the effective annual yield to the nearest hundredth

Decision Making and Problem Solving

Defining the Process

Problem Solving: Identifying the difference between the actual and desired state of affairs, and taking action to resolve the difference.

Decision Making: Defining the problem, identifying alternatives, determining criteria, evaluating alternatives, and choosing an alternative.

Types of Decision Problems

Single-Criterion Decision Problem: Finding the best solution based on one criterion.

Multicriteria Decision Problem: Finding the best solution considering multiple criteria.

Key Concepts in Decision Making

Decision: The selected alternative.

Model: A representation of a real object or situation.

• Iconic Model: A physical replica of a real object.
• Analog Model: A physical representation, but doesn'