What is the leading coefficient of the polynomial function:     ✏️ Work Requirement:  Show your mathematical thinking clearly by rewriting the function in descending order if needed, copying it, circling the leading coefficient, drawing an arrow to it, and labeling it “leading coefficient.”  

The function has its axis of symmetry at which x-value?      ✏️ Work Requirement:  Show your mathematical thinking by writing the formula for the axis of symmetry and substituting the values of a and b from the function.  

Find the slope of the line that passes through the points and .      ✏️ Work Requirement:  Show your mathematical thinking by writing the slope formula and substituting the coordinates from both points before simplifying.  

Identify the function of the sternocleidomastoid muscle.    

These statements about creatine phosphateare true except:

Diabetes Mellitus Type 1 (Study Outline) For study only—this is not medical advice or a substitute for professional care. 1. Background Definition: Autoimmune destruction of pancreatic β-cells → absolute insulin deficiency. Pathophysiology: T-cell–mediated autoimmune attack on islet cells (especially HLA-DR3/DR4 associations). Leads to complete loss of endogenous insulin production. Onset often in childhood or adolescence but can occur at any age (“LADA” in adults). Epidemiology: Peaks at 4–6 years and 10–14 years. ~5–10% of diabetes cases in the U.S. Increased risk with family history or other autoimmune diseases (thyroiditis, celiac disease). Key Mechanism: Autoantibodies (e.g., anti-GAD65, IA-2, insulin autoantibodies) precede hyperglycemia. 2. History Typical Symptoms (Classic Triad): Polyuria, polydipsia, polyphagia. Weight loss despite normal/increased appetite. Fatigue, blurred vision. Acute Presentation: Diabetic ketoacidosis (DKA): nausea, vomiting, abdominal pain, rapid breathing, fruity breath. Risk Factors/Associations: Family history of autoimmune disease. Viral triggers (e.g., coxsackievirus). Historical Clues: Sudden symptom onset over days to weeks. No history of obesity or metabolic syndrome features. 3. Exam Findings General: Thin or underweight body habitus. Dehydration signs: dry mucous membranes, poor skin turgor. DKA Findings: Kussmaul respirations (deep, labored breathing). Fruity (acetone) odor on breath. Hypotension, tachycardia. Altered mental status in severe cases. Associated Autoimmune Conditions: Goiter (thyroid disease), vitiligo, celiac signs. 4. Making the Diagnosis Key Laboratory Findings: Fasting plasma glucose ≥126 mg/dL on two occasions. Random glucose ≥200 mg/dL with classic symptoms. A1C ≥6.5%. Oral glucose tolerance test (OGTT): 2-hour value ≥200 mg/dL. Autoimmune Markers: Positive GAD65, IA-2, insulin autoantibodies, or ZnT8 confirm autoimmune etiology. Additional Testing: Low or undetectable C-peptide (reflects lack of insulin production). Urine ketones positive in DKA or poor control. Gold Standard: Demonstration of autoimmune β-cell destruction with positive diabetes-associated autoantibodies. Distinguishing from Type 2 DM: Younger, leaner, rapid onset, ketosis-prone, autoimmune antibodies present. 5. Management (Exam Concepts) General Principles: Lifelong exogenous insulin therapy is required. Frequent glucose monitoring (SMBG or CGM). Goal A1C: generally

Pheochromocytoma (Study Outline) For study only—this is not medical advice or a substitute for professional care. 1. Background Definition:A catecholamine-secreting tumor arising from chromaffin cells of the adrenal medulla (or extra-adrenal paraganglia, termed paraganglioma).Secretes epinephrine, norepinephrine, and/or dopamine, leading to episodic or sustained sympathetic overactivity. Pathophysiology: Excess catecholamines → overstimulation of α- and β-adrenergic receptors. Results in vasoconstriction, tachycardia, hyperglycemia, and hypertension. Catecholamine surges may be triggered by stress, surgery, exercise, or certain drugs (e.g., β-blockers before α-blockade). Rule of 10s (Classic Teaching): 10% bilateral 10% extra-adrenal (paragangliomas) 10% malignant 10% in children(Recent data: up to 30–40% associated with germline mutations.) Genetic Associations: MEN 2A/2B (RET mutation) Von Hippel–Lindau (VHL) disease Neurofibromatosis type 1 (NF1) Succinate dehydrogenase (SDH) gene mutations Epidemiology: Rare, accounting for

Hypoparathyroidism (Study Outline) For study only—this is not medical advice or a substitute for professional care. 1. Background Definition:A disorder characterized by deficient secretion or action of parathyroid hormone (PTH), leading to hypocalcemia and hyperphosphatemia. Pathophysiology: ↓ PTH → ↓ bone resorption of calcium, ↓ renal calcium reabsorption, ↓ activation of vitamin D → ↓ intestinal calcium absorption. Simultaneous ↑ renal phosphate reabsorption → hyperphosphatemia. Major Causes: Postsurgical (most common): accidental removal or damage to parathyroid glands during thyroid, parathyroid, or neck surgery. Autoimmune destruction: part of autoimmune polyglandular syndrome type I. Congenital: DiGeorge syndrome (22q11 deletion → absent parathyroids). Infiltrative/metabolic: hemochromatosis, Wilson disease, severe hypomagnesemia (impairs PTH secretion). Idiopathic or genetic PTH resistance: pseudohypoparathyroidism (high PTH, hypocalcemia due to end-organ resistance). Epidemiology: Uncommon; most cases are iatrogenic (post-thyroidectomy). 2. History Symptoms (due to hypocalcemia): Neuromuscular irritability: perioral or fingertip tingling, muscle cramps, carpopedal spasms. Tetany: involuntary muscle contractions, laryngospasm, or seizures in severe cases. Psychiatric: anxiety, irritability, depression. Chronic manifestations: dry skin, brittle nails, coarse hair, cataracts, dental abnormalities. Historical Clues: Recent neck or thyroid surgery. Autoimmune history (e.g., mucocutaneous candidiasis, adrenal insufficiency). Family history of congenital syndromes. 3. Exam Findings Neuromuscular Signs (classic for hypocalcemia): Chvostek sign: facial muscle contraction when tapping facial nerve (cheek). Trousseau sign: carpal spasm after inflation of BP cuff for 3 min. Cardiovascular: Hypotension, prolonged QT interval on ECG. Skin/Hair: Dry, flaky skin; brittle nails; coarse hair. Eyes: Cataracts (chronic hypocalcemia). Dentition: Enamel hypoplasia, defective root formation (pediatric cases). 4. Making the Diagnosis Key Lab Pattern (Primary Hypoparathyroidism): ↓ Serum calcium ↑ Serum phosphate ↓ or inappropriately normal PTH Normal or low magnesium (severe Mg deficiency suppresses PTH). Confirmatory Tests: Serum magnesium: to exclude Mg deficiency. Urinary calcium: may be low. Vitamin D levels: rule out deficiency. ECG: may show prolonged QT interval. If postsurgical: diagnosis is clinical (neck surgery + low calcium + low PTH).If autoimmune/genetic: test for associated antibodies or genetic deletions. Gold Standard: Low PTH with concurrent hypocalcemia and hyperphosphatemia. 5. Management (Exam Concepts) (Conceptual overview only—no dosing or treatment regimens.) Acute Hypocalcemic Crisis (Tetany/Seizure): IV calcium administration under cardiac monitoring. Chronic Management: Oral calcium supplements and activated vitamin D analogs (calcitriol) to maintain normal calcium and phosphate balance. Thiazide diuretics (conceptual) may reduce urinary calcium loss. Recombinant human PTH (rarely used): for refractory chronic cases. Correct hypomagnesemia before calcium replacement. Postsurgical Prevention: Preserve parathyroid glands during thyroidectomy. Prophylactic calcium and vitamin D in high-risk surgical patients. Exam Tips: Low Ca²⁺, high phosphate, low PTH = primary hypoparathyroidism. Low Ca²⁺, high phosphate, high PTH = pseudohypoparathyroidism (PTH resistance). Prolonged QT interval on ECG is a key clue. Most common cause = neck surgery. NBME-Style Practice Question A 46-year-old woman presents with muscle cramps and tingling around her mouth one week after total thyroidectomy. Physical exam shows facial muscle twitching when the facial nerve is tapped. Labs show: Calcium: 7.0 mg/dL (low) Phosphate: 5.8 mg/dL (high) PTH: low Which of the following is the most likely diagnosis? A. Primary hypoparathyroidismB. Secondary hyperparathyroidismC. PseudohypoparathyroidismD. Vitamin D deficiency

Gigantism (Study Outline) For study only—this is not medical advice or a substitute for professional care. 1. Background Definition:Gigantism is excessive growth hormone (GH) secretion before epiphyseal plate closure in children/adolescents, leading to abnormally accelerated linear growth and tall stature.After epiphyseal fusion, the same process manifests as acromegaly. Pathophysiology: GH excess → ↑ hepatic IGF-1, promoting growth of bone, cartilage, and soft tissues. Because epiphyseal plates remain open, longitudinal bone growth increases dramatically. Excess GH/IGF-1 also causes organomegaly, metabolic dysfunction, and pituitary mass effects. Etiology: Pituitary somatotroph adenoma (most common). Rare: ectopic GHRH-producing tumors (pancreatic, bronchial). Genetic syndromes: McCune–Albright, Carney complex, MEN 1. Epidemiology: Very rare; typically presents in adolescence. 2. History Key Presentation: Rapid growth velocity above expected percentiles. Extreme height compared with peers or family norms. Associated Symptoms: Headaches, visual changes (bitemporal hemianopsia) from pituitary mass. Excessive sweating, fatigue, heat intolerance. Joint pain, rapid shoe and clothing size changes. Metabolic: weight gain, insulin resistance, possible diabetes. Reproductive: delayed puberty, menstrual irregularities. Organ/System Effects: Enlargement of hands, feet, facial features (may resemble acromegaly features). Cardiomegaly, sleep apnea. Historical Clues: Growth acceleration charted on pediatric growth curves. Symptoms of pituitary mass (headache, visual deficits). 3. Exam Findings Growth/Anthropometrics: Tall stature with accelerated growth velocity. Arm span often exceeds height. Craniofacial Features: Frontal bossing, prognathism (jaw protrusion), nasal enlargement. Spaced teeth, macroglossia. Musculoskeletal: Large hands/feet, joint laxity or pain. Neurologic: Visual field defects (classically bitemporal hemianopsia). Skin: Oily skin, acne, skin tags. Cardiovascular: Hypertension, signs of cardiomyopathy in advanced cases. 4. Making the Diagnosis Step 1 – Screening: Serum IGF-1: elevated; most reliable initial test (stable marker of GH activity). Step 2 – Confirmatory Testing: Oral glucose tolerance test (OGTT) with GH measurement: Normal response: glucose suppresses GH. Gigantism: GH fails to suppress after glucose load. Step 3 – Identify Source: MRI of the pituitary gland: Detects pituitary adenoma (micro or macroadenoma). If MRI negative → evaluate for ectopic GHRH via serum GHRH level; CT/MRI of chest/abdomen. Additional Labs: Fasting glucose/insulin (insulin resistance). Other pituitary hormones (possible compression effects). Gold Standard: Elevated IGF-1 + failure of GH suppression on OGTT + pituitary adenoma on MRI. 5. Management (Exam Concepts) (Conceptual overview only—no dosing or treatment regimens.) 1. First-Line Therapy Transsphenoidal resection of pituitary adenoma. 2. Medical Therapy Somatostatin analogs (octreotide, lanreotide) — suppress GH secretion. GH receptor antagonist (pegvisomant) — blocks IGF-1 production. Dopamine agonists (cabergoline) — used in some GH/prolactin co-secreting tumors. 3. Radiation Therapy For residual tumor or persistent disease not controlled with surgery/medications. 4. Long-Term Monitoring Serial IGF-1 measurements. Periodic pituitary imaging. Screen for cardiomyopathy, sleep apnea, and metabolic complications.   QUESTION NBME-Style Practice Question A 14-year-old boy is brought to clinic for rapid growth over the past year. His height increased from the 75th to >99th percentile. He reports headaches and needing larger shoes every few months. Exam shows frontal bossing, enlarged hands, and visual field deficits. Labs reveal markedly elevated IGF-1. After an oral glucose load, GH levels remain high. Which of the following is the most appropriate next step to determine the underlying cause? A. Serum GHRH levelB. MRI of the pituitary glandC. Bone age radiographD. Abdominal CT scan  

Vitamin D Deficiency (Study Outline) For study only—this is not medical advice or a substitute for professional care. 1. Background Definition:A condition characterized by inadequate vitamin D levels, resulting in impaired calcium and phosphate absorption, leading to secondary hyperparathyroidism, hypocalcemia, and bone demineralization. Physiology Recap: Vitamin D (cholecalciferol/ergocalciferol) is hydroxylated in the liver → 25-hydroxyvitamin D, then in the kidney → 1,25-dihydroxyvitamin D (calcitriol), the active form. Calcitriol promotes calcium and phosphate absorption in the intestine and reabsorption in the kidney, and stimulates bone mineralization. Pathophysiology: Deficiency → ↓ intestinal calcium absorption → hypocalcemia → compensatory ↑ PTH → secondary hyperparathyroidism. PTH increases bone resorption → osteomalacia (adults) or rickets (children). Causes: Inadequate intake or sunlight exposure (most common). Malabsorption (celiac disease, cystic fibrosis, bariatric surgery). Chronic kidney disease (↓ 1α-hydroxylation). Liver disease (↓ 25-hydroxylation). Medications: anticonvulsants (phenytoin, phenobarbital), glucocorticoids. Exclusive breastfeeding without supplementation in infants. Epidemiology: Common in elderly, limited sun exposure, darker skin pigmentation, and northern latitudes. 2. History Adults (Osteomalacia): Diffuse bone pain and tenderness. Muscle weakness (especially proximal). Fatigue and difficulty walking. Fractures after minimal trauma. Children (Rickets): Delayed growth, bone deformities (bowing of legs, rachitic rosary, frontal bossing). Delayed tooth eruption. Hypotonia and developmental delay (in severe cases). Historical Clues: Minimal sun exposure, low dietary intake, malabsorptive conditions, chronic kidney or liver disease, anticonvulsant use. 3. Exam Findings Adults: Bone tenderness (especially ribs, sternum, long bones). Waddling gait or difficulty rising from chair. Muscle weakness (proximal). Children: Skeletal deformities: Bowed legs (genu varum). Rachitic rosary (costochondral bead-like enlargements). Craniotabes (soft skull). Delayed fontanelle closure. Other: Signs of hypocalcemia in severe cases (Chvostek or Trousseau signs). 4. Making the Diagnosis Laboratory Pattern: Parameter Finding Calcium ↓ or low-normal Phosphate ↓ PTH ↑ (secondary hyperparathyroidism) Alkaline phosphatase ↑ (bone turnover) 25-hydroxyvitamin D (25[OH]D) ↓ (best screening test) Key Diagnostic Points: 25(OH)D < 20 ng/mL = deficiency; 20–30 = insufficiency. 1,25(OH)₂D (calcitriol) is not a good screening test — may be normal or high in early deficiency. X-rays (if bone pain/deformities): Osteopenia, Looser zones (pseudofractures), or bone bowing in children. Bone biopsy (rare): confirms osteoid accumulation (unmineralized bone). Gold Standard: Low 25-hydroxyvitamin D level with corresponding biochemical abnormalities (↑ PTH, ↓ calcium, ↓ phosphate, ↑ ALP). 5. Management (Exam Concepts) (Conceptual overview only—no dosing or treatment regimens.) General Principles: Correct vitamin D deficiency and address calcium intake. Identify and treat underlying causes (malabsorption, CKD, liver disease). Supplementation (Conceptual): Vitamin D2 (ergocalciferol) or D3 (cholecalciferol) replacement. Calcium supplementation to restore balance. Activated vitamin D (calcitriol) in chronic kidney disease (impaired conversion). Lifestyle Measures: Encourage adequate sunlight exposure (10–15 min several times/week). Balanced diet with fortified foods (milk, fish oils, eggs). Monitoring: Recheck calcium, phosphate, ALP, and 25(OH)D levels after therapy. Watch for hypercalcemia during high-dose replacement. NBME-Style Practice Question A 62-year-old woman presents with progressive muscle weakness and diffuse bone pain. She spends most of her time indoors and has a diet low in dairy. Labs show: Calcium: 8.0 mg/dL (low) Phosphate: 2.0 mg/dL (low) Alkaline phosphatase: elevated PTH: elevated 25-hydroxyvitamin D: low Which of the following is the most likely diagnosis? A. Primary hyperparathyroidismB. Osteomalacia due to vitamin D deficiencyC. Paget disease of boneD. Osteoporosis