Medical and Mathematical Fundamentals Review

Mathematical Multiplication Short Tricks and Mental Math

Specific patterns in multiplication allow for rapid mental calculation. For two-digit numbers where the tens digit is identical and the units digits sum to exactly $10$, a specific short trick applies. This method splits the answer into a tens part and a ones part.

To calculate $12 \times 18$, identify that the tens digit is $1$ for both and the units digits, $2$ and $8$, sum to $10$. For the tens part of the answer, multiply the tens digit by the next consecutive integer: $1 \times 2 = 2$. For the ones part, multiply the units digits together: $2 \times 8 = 16$. Combining these results gives the final answer of $216$.

Following the same principle for $34 \times 36$, the tens part involves multiplying the tens digit, $3$, by the next integer: $3 \times 4 = 12$. The ones part is found by multiplying the units: $4 \times 6 = 24$, resulting in $1224$. For $56 \times 54$, the calculation is $5 \times 6 = 30$ for the tens part and $6 \times 4 = 24$ for the ones part, yielding $3024$. For $78 \times 72$, calculate $7 \times 8 = 56$ and $8 \times 2 = 16$ to get $5616$. Finally, for $23 \times 27$, multiply $2 \times 3 = 6$ for the tens part and $3 \times 7 = 21$ for the ones part to reach the answer of $621$.

A mental shortcut for calculating percentages involves simplifying the factors. To find $7\%$ of $300$, one can simply multiply the leading non-zero digits: $7 \times 3 = 21$.

Additional multiplication tricks for the number $66$ include standardized products: $66 \times 7 = 462$, $66 \times 6 = 396$, $66 \times 5 = 330$, $66 \times 4 = 264$, and $66 \times 3 = 198$.

Electrocardiogram (ECG) Fundamentals and Interpretation

An Electrocardiogram (ECG) records the electrical activity of the heart. A systematic approach is essential for accurate diagnosis and includes ten specific steps: Rate, Rhythm, P Waves, PR Interval, QRS Complex, QT Interval, QRS Axis, ST Segment, T Waves, and the Overall Interpretation.

Standard ECG paper is calibrated to represent time on the horizontal axis and voltage on the vertical axis. The horizontal axis measures distance where $1\text{ small square} = 1\,mm$ (corresponding to $0.04\text{ seconds}$) and $1\text{ large square} = 5\,mm$ (corresponding to $0.20\text{ seconds}$). Therefore, $5$ large squares equal $1\text{ second}$, and $30$ large squares equal $6\text{ seconds}$. The standard paper speed is $25\,mm/second$. On the vertical axis, $1\text{ small square} = 0.1\,mV$ and $1\text{ large square} = 0.5\,mV$. Standard calibration dictates that $10\,mm$ equals $1\,mV$.

To calculate the heart rate, two methods are primary. For a regular rhythm, the heart rate equals $300 \div \text{number of large squares between two R waves}$. This creates a scale: $1$ large square equals $300\,BPM$, $2$ equals $150\,BPM$, $3$ equals $100\,BPM$, $4$ equals $75\,BPM$, $5$ equals $60\,BPM$, and $6$ equals $50\,BPM$. For an irregular rhythm, count the number of QRS complexes in a $6\text{-second}$ strip (equivalent to $30$ large squares) and multiply that count by $10$. A normal adult resting heart rate is $60-100\,BPM$. Bradycardia is defined as a rate $< 60\,BPM$, while tachycardia is defined as a rate $> 100\,BPM$.

ECG Waveform Morphology and Intervals

Rhythm is determined by checking R-R intervals. Equal R-R intervals indicate a regular rhythm, while variable intervals indicate an irregular rhythm. P waves represent atrial depolarization. A normal P wave has a duration of $< 0.12\text{ seconds}$, is best seen in Lead II, and is typically upright in most leads. In a normal rhythm, every QRS complex is preceded by a P wave. Absent P waves, where no P wave appears before the QRS, can be seen in conditions like Atrial Fibrillation.

The PR interval measures the time from the beginning of the P wave to the beginning of the QRS complex, reflecting atrioventricular conduction time. A normal range is $0.12-0.20\text{ seconds}$, or $3-5$ small squares. A short PR interval is $< 0.12\text{ seconds}$, and a prolonged interval is $> 0.20\text{ seconds}$. Consistency in the PR interval is vital for a normal sinus rhythm.

The QRS complex represents ventricular depolarization and should ideally be narrow, with a duration of $< 0.12\text{ seconds}$. The QT interval measures from the beginning of the QRS complex to the end of the T wave, representing total ventricular depolarization and repolarization. Because the QT interval varies with heart rate, the Corrected QT Interval ($QTc$) is used. A common method for calculation is the Bazett Formula: $QTc = \frac{QT}{\sqrt{RR}}$. A prolonged $QTc$ increases the risk of Torsades de Pointes.

QRS Axis, ST Segment, and T Waves

The QRS axis is determined using Lead I and Lead aVF. If both Lead I and Lead aVF are positive, the axis is normal ($-30^{\circ}$ to $+90^{\circ}$). If Lead I is positive but Lead aVF is negative, Lead II must be checked; if Lead II is positive, it is still a normal axis; if Lead II is negative, it indicates Left Axis Deviation ($-30^{\circ}$ to $-90^{\circ}$). If Lead I is negative and Lead aVF is positive, it signifies Right Axis Deviation ($> +90^{\circ}$). If both Lead I and Lead aVF are negative, it represents an Extreme Axis ($-90^{\circ}$ to $\pm 180^{\circ}$).

The ST segment begins at the end of the QRS complex and lasts until the beginning of the T wave. It is normally isoelectric (on the baseline). ST elevation (above the line) may indicate acute injury such as an ST-Elevation Myocardial Infarction (STEMI), while ST depression (below the line) may indicate ischemia, Digoxin effect, or electrolyte imbalance. The T wave represents ventricular repolarization and should be upright in most leads. T wave inversion or peaking can indicate pathology like ischemia or ventricular strain.

Cardiovascular Pharmacology and Medication Nursing Care

Metoprolol (Lopressor) is a beta-blocker used for hypertension, angina, and heart failure. Nursing considerations include watching for bradycardia and hypotension; the medication should be held if the heart rate is $< 60\,BPM$. It can also mask symptoms of hypoglycemia.

Digoxin (Lanoxin) is a cardiac glycoside used for heart failure and atrial fibrillation. Nurses must watch for toxicity, characterized by vision changes and bradycardia. The drug should be held if the heart rate is $< 60\,BPM$. The therapeutic digoxin level is $0.5-2.0\,ng/mL$. Hypokalemia (low Potassium) increases the risk of digoxin toxicity.

Lisinopril (Prinivil, Zestril) is an ACE inhibitor used for hypertension and heart failure. Key adverse effects to monitor include a persistent dry cough, hyperkalemia, and the life-threatening condition angioedema.

Furosemide (Lasix) is a loop diuretic for heart failure, hypertension, and edema. Monitoring involves checking for hypokalemia and dehydration via Intake and Output (I&O), blood pressure, and daily weights. It is recommended to administer this medication in the morning.

Enoxaparin (Lovenox) is a low molecular weight heparin (LMWH) anticoagulant used for DVT prevention and treatment. It should be injected into the abdomen without expelling the nitrogen air bubble in the pre-filled syringe. Platelets must be monitored due to the risk of Heparin-Induced Thrombocytopenia (HIT).

Warfarin (Coumadin) is an oral anticoagulant for DVT, pulmonary embolism (PE), and atrial fibrillation. The target International Normalized Ratio (INR) is typically $2-3$. Patients should avoid excessive green leafy vegetables (high in Vitamin K). The antidote for warfarin is Vitamin K.

Respiratory, Endocrine, and Pain Management Medications

Albuterol (ProAir, Ventolin) is a beta-2 agonist bronchodilator used for asthma and COPD. Potential side effects include tachycardia and tremors. It should be used before inhaled corticosteroids, and patients should wait $1-2\text{ minutes}$ between puffs.

Levothyroxine (Synthroid) is a thyroid hormone used for hypothyroidism. It requires lifelong therapy and should be taken in the morning on an empty stomach. Signs of overdose include weight loss, anxiety, and tachycardia.

Morphine is an opioid analgesic for moderate to severe pain. Nurses must monitor for respiratory depression, constipation, and pinpoint pupils, which indicate overdose. The antidote is Naloxone (Narcan).

Insulin (Regular, NPH, Lantus) is an antidiabetic used for diabetes mellitus. Hypoglycemia is the primary risk. NPH should be rolled between the hands rather than shaken. Lantus is a long-acting insulin and must never be mixed with other insulins in the same syringe.

Fundamentals of Nursing and Clinical Standards

The "five rights" of medication administration are the right patient, right drug, right dose, right route, and right time. Patient identity must be confirmed using two patient identifiers. The primary method for emergency assessment follows the "ABC" sequence: Airway, Breathing, and Circulation. Measuring oxygen saturation ($SpO_2$) is performed using a pulse oximeter, with normal levels in a healthy adult being $95-100\%$.

Clinical terminology includes tachypnea (rapid breathing), dyspnea (difficulty breathing), tachycardia (fast pulse), and bradycardia (slow pulse). Febrile refers to a patient with a fever, while afebrile means no fever, and hypothermia refers to an abnormally low body temperature. The Glasgow Coma Scale (GCS) assesses the level of consciousness based on three components: eye, verbal, and motor responses, with a maximum score of $15$.

Injection angles are specific to the route: Intradermal injections are given at approximately $5-15^{\circ}$, subcutaneous injections at $45-90^{\circ}$, and intramuscular injections at $90^{\circ}$. For safety, used needles must be disposed of immediately in a sharps container and never recapped. To maintain hygiene and comfort, bed baths are provided, especially for patients at risk of pressure injury due to immobility.

Ethical principles in nursing include Autonomy (respecting a patient's right to make decisions), Non-maleficence (doing no harm), and Beneficence (doing good for the patient). Confidentiality involves protecting private patient information.

Biological Vitals and Digestive System Functions

Normal physiological ranges include:

• Blood Pressure: $120/80\,mmHg$
• Pulse Rate: $60-100/\text{min}$
• Temperature: $36.8-37^{\circ}C$
• Breathing/Respiration Rate: $12-16/\text{min}$
• Hemoglobin: Male $13-17\,g/dl$; Female $12-15\,g/dl$
• Cholesterol: $130-200\,mg/dl$
• Potassium ($K^+$): $3.50-5.00\,mEq/L$
• Sodium ($Na^+$): $135-145\,mg/dl$
• Blood Sugar: $70-115\,mg/dl$
• Minimum Urine Output: Approximately $0.5\,mL/kg/hr$

Digestive glands perform specific chemical breakdowns. Salivary glands produce salivary amylase to convert starch into sugar. Gastric glands produce HCl to create an acidic medium, mucus to protect the inner lining, and pepsin to break down proteins. The liver produces bile juice for the emulsification of fat (stored in the gall bladder). The pancreas secretes pancreatic juice containing trypsin for protein breakdown and lipase for fat breakdown. Finally, intestinal glands facilitate the final conversion of carbohydrates into glucose, proteins into amino acids, and fats into fatty acids plus glycerol. Vitamin K is essential for blood clotting.

Key Cardiology Terminology

Cardiology requires understanding several critical conditions and metrics:

• Hypertension: Persistently high blood pressure ($> 140/90\,mmHg$).
• Hypotension: Abnormally low blood pressure ($< 90/60\,mmHg$).
• Angina Pectoris: Chest pain due to myocardial ischemia.
• Myocardial Infarction (MI): Death of heart muscle due to blockage; often presents with chest pain, increased Troponin levels, and ECG changes.
• Heart Failure: The heart is unable to pump blood effectively.
• Arrhythmia: Irregularity in heart rate or rhythm.
• Atherosclerosis: Plaque buildup in arteries causing narrowing.
• Coronary Artery Disease (CAD): Narrowing or blockage of coronary arteries.
• Congestive Heart Failure (CHF): Fluid accumulation/overload due to heart failure.
• Cardiomyopathy: Disease of the heart muscle affecting function.
• Valvular Heart Disease: Disorder of one or more heart valves, such as Mitral Regurgitation (backflow from LV to LA), Aortic Stenosis (narrowed aortic valve), or Aortic Regurgitation (backflow from aorta to LV).
• Pericarditis/Endocarditis: Inflammation of the pericardial sac or infection of the inner heart lining.
• Venous Thromboembolism (VTE): Includes Deep Vein Thrombosis (DVT), a clot in deep veins usually the leg, and Pulmonary Embolism (PE), where a clot travels to the lungs.
• Ejection Fraction (EF): Percentage of blood pumped out by the ventricles with each contraction.
• Ischemia: Reduced blood flow to the heart muscle.
• Left Ventricular Hypertrophy (LVH): Thickening of the left ventricular muscle.
• Palpitations: Awareness of an abnormal or rapid heartbeat.
• Syncope: Temporary loss of consciousness due to reduced blood flow to the brain.