- Newton's first law
- Inertia: an object stays at rest, or in motion at constant velocity, unless a net force acts on it. (Why riders lurch forward when a car brakes.)
- Newton's second law
- F = ma — net force equals mass times acceleration. For the same force, more mass means less acceleration.
- Newton's third law
- For every action there is an equal and opposite reaction. A rocket pushes gas down; the gas pushes the rocket up.
- The six simple machines
- Lever, wheel and axle, pulley, inclined plane, wedge, and screw. Every complex machine is built from these.
- Mechanical advantage (MA)
- How many times a machine multiplies your input force: MA = output force ÷ input force. MA > 1 multiplies force; MA < 1 multiplies speed/distance.
- First-class lever
- Fulcrum in the middle (effort–fulcrum–load). Examples: seesaw, crowbar, scissors. Can multiply force or distance.
- Second-class lever
- Load in the middle (fulcrum–load–effort). Always multiplies force (MA > 1). Examples: wheelbarrow, bottle opener, nutcracker.
- Third-class lever
- Effort in the middle (fulcrum–effort–load). Always multiplies distance/speed (MA < 1). Examples: tweezers, fishing rod, human forearm.
- Fulcrum
- The fixed pivot point a lever rotates around.
- Law of the lever
- Effort × effort arm = load × load arm. A longer effort arm lets a small force lift a large load.
- Pulley mechanical advantage
- Equals the number of rope segments that support the load. One fixed pulley = MA 1 (changes direction only); two supporting ropes = MA 2.
- Fixed pulley
- A pulley attached to a fixed point. It changes the direction of the force but gives no mechanical advantage (MA = 1).
- Movable pulley
- A pulley that moves with the load. It gives a mechanical advantage of 2 but you must pull twice the rope length.
- Trade-off rule for machines
- A machine never gives free energy: the more it multiplies force, the more distance you must move the input. Work in ≈ work out.
- Inclined plane
- A ramp. It reduces the force needed to raise a load by spreading the work over a longer distance. A longer, gentler ramp needs less force.
- Wedge
- Two inclined planes back to back. It converts a downward force into sideways splitting force. Examples: axe, knife, chisel.
- Screw
- An inclined plane wrapped around a cylinder. Closer threads (finer pitch) give more mechanical advantage.
- Wheel and axle
- A large wheel fixed to a smaller axle. A small force on the large wheel produces a large force at the axle. Examples: doorknob, steering wheel.
- Gear ratio
- Driven gear teeth ÷ driver gear teeth. Meshed gears turn in opposite directions.
- Small gear driving a large gear
- The large (driven) gear turns slower but with more torque. Speed is traded for force.
- Large gear driving a small gear
- The small (driven) gear turns faster but with less torque. Force is traded for speed.
- Torque
- A turning force: torque = force × distance from the pivot. A longer wrench gives more torque for the same push.
- Work (physics)
- Work = force × distance, when the force acts in the direction of motion. Measured in joules. No motion means no work.
- Power
- The rate of doing work: power = work ÷ time. The same job done faster requires more power.
- Kinetic energy
- Energy of motion: KE = ½ × mass × velocity². Doubling speed quadruples kinetic energy.
- Potential energy (gravitational)
- Stored energy of position: PE = mass × gravity × height. Lifting an object higher stores more energy.
- Conservation of energy
- Energy is never created or destroyed, only converted. A falling object trades potential energy for kinetic energy.
- Friction
- A force that opposes motion between surfaces in contact. It always acts opposite to the direction of motion and produces heat.
- Static vs kinetic friction
- Static friction holds a still object in place and is usually larger; kinetic (sliding) friction acts on a moving object and is usually smaller.
- Gravity
- The force that pulls masses together. Near Earth it accelerates falling objects at about 9.8 m/s² regardless of their mass (ignoring air resistance).
- Weight vs mass
- Mass is the amount of matter (constant). Weight is the force of gravity on that mass (weight = mass × gravity) and changes with location.
- Velocity vs speed
- Speed is how fast (magnitude only). Velocity is speed with a direction.
- Acceleration
- The rate of change of velocity. A change in speed OR direction is acceleration. Units: m/s².
- Pressure
- Force per unit area: pressure = force ÷ area. The same force on a smaller area gives higher pressure (why a sharp knife cuts).
- Pascal's principle
- Pressure applied to a confined fluid is transmitted equally in all directions. The basis of hydraulic lifts and brakes.
- Hydraulic advantage
- In a hydraulic system, a small force on a small piston creates a large force on a large piston, in proportion to the piston areas.
- Bernoulli's principle
- In a moving fluid, faster flow means lower pressure. It explains lift on a wing and why fluid speeds up in a narrow pipe.
- Continuity (fluid in a pipe)
- When a pipe narrows, the fluid speeds up; when it widens, the fluid slows down. The flow rate stays the same.
- Buoyancy (Archimedes' principle)
- An object in a fluid is pushed up by a force equal to the weight of the fluid it displaces. It floats if that force ≥ its weight.
- Density
- Mass per unit volume: density = mass ÷ volume. Less-dense objects float on denser fluids.
- Heat conduction
- Transfer of heat through a material by direct contact. Metals are good conductors; wood, air, and plastic are insulators.
- Electrical conductor vs insulator
- Conductors (copper, most metals) let current flow easily; insulators (rubber, glass, wood) resist it.
- Ohm's law
- Voltage = current × resistance (V = I × R). For a fixed voltage, higher resistance means lower current.
- Series circuit
- Components on one path. The same current flows through all; if one breaks, the whole circuit stops.
- Parallel circuit
- Components on separate branches. Each gets the full voltage; if one branch breaks, the others keep working.
- Spring (Hooke's law)
- The force a spring exerts is proportional to how far it is stretched or compressed: F = k × x.
- Center of gravity
- The point where an object's weight is balanced. A lower, more central center of gravity makes an object more stable.
- Momentum
- Mass in motion: momentum = mass × velocity. A heavier or faster object has more momentum and is harder to stop.
- Equilibrium
- A state of balanced forces — no net force and no net torque, so the object stays at rest or moves at constant velocity.
- Tension and compression
- Tension is a pulling force that stretches; compression is a pushing force that squeezes. Cables carry tension; columns carry compression.
- Lever for force vs speed
- Putting effort far from the fulcrum multiplies force; putting it close multiplies speed and distance.
- Pendulum period
- The time for one swing depends on the pendulum's length and gravity — not on the mass of the bob or (for small swings) the size of the swing.
- Thermal expansion
- Most materials expand when heated and contract when cooled. Why bridges and rails have expansion gaps.
- Force
- A push or pull that can change an object's motion or shape. Measured in newtons; it has both size and direction.
- Net force
- The single combined force from all forces acting on an object. A nonzero net force causes acceleration.
- Why a longer ramp is easier
- It trades force for distance: raising a load over a longer, gentler slope needs less force but more travel — the same total work.
- Order of operations (PEMDAS)
- Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
- Percent of a number
- Convert the percent to a decimal and multiply. 35% of 80 = 0.35 × 80 = 28.
- Percent change
- Percent change = (change ÷ original) × 100. Always divide by the starting value, not the new one.
- Converting a fraction to a decimal
- Divide the numerator by the denominator. 7/8 = 7 ÷ 8 = 0.875.
- Converting a percent to a fraction
- Write it over 100 and simplify. 25% = 25/100 = 1/4.
- Simplifying a fraction
- Divide the top and bottom by their greatest common factor. 18/24 = 3/4 (both ÷ 6).
- Adding fractions
- Find a common denominator, add the numerators, keep the denominator, then simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- Multiplying fractions
- Multiply the numerators and the denominators straight across, then simplify. 2/3 × 3/4 = 6/12 = 1/2.
- Dividing fractions
- Multiply by the reciprocal of the second fraction (flip and multiply). 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
- Solving a linear equation
- Isolate the variable using inverse operations. For 3x + 7 = 22: subtract 7 (3x = 15), divide by 3 (x = 5).
- Slope of a line
- Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). It measures steepness; positive rises left to right.
- Slope-intercept form
- y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).
- Solving a proportion
- Cross-multiply: a/b = c/d means a × d = b × c, then solve for the unknown.
- Ratio
- A comparison of two quantities. A 3:2 ratio means 3 parts to 2 parts, for 5 parts total.
- Average (mean)
- Add all the values and divide by how many there are. The average of 14, 18, 22 is 54 ÷ 3 = 18.
- Median
- The middle value of a data set in order. With an even count, average the two middle values.
- Mode
- The value that appears most often in a data set.
- Exponent (power)
- Repeated multiplication. 4² = 4 × 4 = 16; 3³ = 3 × 3 × 3 = 27.
- Multiplying powers of the same base
- Add the exponents: xᵃ × xᵇ = xᵃ⁺ᵇ.
- Dividing powers of the same base
- Subtract the exponents: xᵃ ÷ xᵇ = xᵃ⁻ᵇ.
- Power of a power
- Multiply the exponents: (xᵃ)ᵇ = xᵃᵇ.
- Negative exponent
- A negative exponent means reciprocal: x⁻ⁿ = 1 ÷ xⁿ.
- Square root
- The number that, multiplied by itself, gives the value. √64 = 8 because 8 × 8 = 64.
- Area of a rectangle
- Area = length × width.
- Area of a triangle
- Area = ½ × base × height.
- Area of a circle
- Area = π × radius². Use π ≈ 3.14.
- Circumference of a circle
- Circumference = 2 × π × radius = π × diameter.
- Perimeter
- The total distance around a shape — add the lengths of all sides.
- Volume of a rectangular box
- Volume = length × width × height.
- Pythagorean theorem
- For a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).
- Interior angles of a triangle
- They always add up to 180°.
- Interior angles of a quadrilateral
- They always add up to 360°.
- Supplementary angles
- Two angles that add up to 180° (a straight line).
- Complementary angles
- Two angles that add up to 90° (a right angle).
- Distance, rate, time
- Distance = rate × time. A car at 60 mph for 4 hours travels 240 miles.
- Average speed
- Total distance ÷ total time. 240 miles in 4 hours = 60 mph.
- Probability
- Favorable outcomes ÷ total outcomes, a value from 0 to 1. One head on a coin flip = 1/2.
- Least common multiple (LCM)
- The smallest number both values divide into evenly. LCM of 6 and 8 is 24.
- Greatest common factor (GCF)
- The largest number that divides both values evenly. GCF of 18 and 24 is 6.
- Prime number
- A whole number greater than 1 with exactly two factors: 1 and itself (2, 3, 5, 7, 11, ...).
- Absolute value
- The distance of a number from zero, always non-negative. |−7| = 7.
- Combining like terms
- Add or subtract terms with the same variable. 3x + 5x = 8x; you can't combine 3x and 5.
- Distributive property
- Multiply a term across a sum: a(b + c) = ab + ac. 3(x + 4) = 3x + 12.
- Solving an inequality
- Solve like an equation, but flip the inequality sign when you multiply or divide by a negative number.
- FOIL
- Multiply two binomials: First, Outer, Inner, Last. (x + 2)(x + 3) = x² + 5x + 6.
- Difference of squares
- a² − b² = (a + b)(a − b).
- Converting a decimal to a percent
- Multiply by 100 and add a percent sign. 0.875 = 87.5%.
- Rounding
- Look at the digit to the right of the place you're rounding to: 5 or more rounds up, 4 or less rounds down.
- Scientific notation
- A number written as a value between 1 and 10 times a power of 10. 4,500 = 4.5 × 10³.
- Simple interest
- Interest = principal × rate × time (I = P × r × t).
- Markup and discount
- A 25% markup multiplies the price by 1.25; a 25% discount multiplies it by 0.75.
- Mixed number to improper fraction
- Multiply the whole number by the denominator, add the numerator, keep the denominator. 2 1/3 = 7/3.
- Reciprocal
- The number you multiply by to get 1 — flip a fraction. The reciprocal of 3/4 is 4/3.
- Solving for a variable in a formula
- Use inverse operations to isolate the wanted variable, treating the others as constants.
- Two-step word problem strategy
- Translate words to an equation, solve step by step, then check the answer against the question asked.
- Main idea
- The central point the whole passage supports — broader than any single detail but never beyond what the text says.
- Supporting detail
- A specific fact, example, or statement the passage gives to back up the main idea.
- Inference
- A conclusion the passage implies but does not state outright. The correct inference is the one the text most directly supports.
- OAR reading golden rule
- Answer only from the passage. The correct choice is supported by the text — never by your own outside knowledge or opinion.
- Author's purpose
- Why the author wrote the passage — to inform, persuade, describe, or entertain. Look at tone and word choice.
- Tone
- The author's attitude toward the subject (neutral, critical, enthusiastic, skeptical), revealed by word choice.
- Vocabulary in context
- Choosing the meaning of a word based on how it is used in the sentence — not its most common dictionary definition.
- Drawing a conclusion
- Combining stated facts in the passage to reach a logical end point the text supports.
- Distinguishing fact from opinion
- A fact can be verified; an opinion expresses a belief or judgment (often signaled by words like 'best' or 'should').
- Eliminating wrong answers
- Cross out choices that are too extreme, off-topic, contradicted by the text, or true in the world but not in the passage.
- Extreme-word trap
- Be cautious of answer choices with absolute words like 'always,' 'never,' or 'all' — passages rarely support them.
- Out-of-scope trap
- A choice that brings in information the passage never mentions. If you can't point to support in the text, eliminate it.
- Restatement vs inference
- A restatement repeats what the passage directly says; an inference goes one logical step beyond what is stated.
- Reading actively
- Note the main idea and the structure as you read so you can find support quickly — passages are short, so read for the point.
- Best-supported answer
- When two choices seem possible, pick the one with the most direct textual support, not the most interesting one.
- Topic vs main idea
- The topic is what the passage is about (one phrase); the main idea is the point the passage makes about that topic (a full claim).
- Implied meaning
- What the author suggests without saying directly — read between the lines, but stay anchored to the text.
- Context clues
- Surrounding words and sentences that hint at the meaning of an unfamiliar word or the answer to a question.
- Predicting the answer
- Form your own answer before reading the choices, then match it to the closest option — it guards against trap answers.
- Summarizing a passage
- Capturing the main idea and key support in a sentence or two — a check that you grasped the point.
- Signal words
- Transitions like 'however,' 'therefore,' and 'for example' that show how ideas relate — contrast, cause, or example.
- Cause and effect
- Identifying what made something happen (cause) and the result (effect), often linked by words like 'because' or 'so.'
- Comparing and contrasting
- Finding how two ideas in a passage are alike and how they differ.
- Specific-detail question
- Asks for an exact fact stated in the passage — scan back to the relevant line rather than relying on memory.
- Pacing the reading subtest
- Roughly 20 questions in about 30 minutes — read efficiently, don't reread the whole passage, and don't dwell on one question.
- Effort arm vs load arm
- On a lever, the effort arm is the distance from the fulcrum to the effort; the load arm is from the fulcrum to the load. Longer effort arm = more force advantage.
- Idler gear
- A gear placed between two others that changes the direction of rotation without changing the overall gear ratio.
- Two children on a seesaw
- To balance, the lighter child sits farther from the fulcrum so weight × distance is equal on both sides.
- Heat (thermal energy)
- Energy transferred because of a temperature difference, always flowing from hotter to colder objects.
- Lubrication
- Reduces friction between surfaces, lowering heat and wear and making machines more efficient.
- Why sharp tools cut
- A small edge area concentrates force into high pressure (pressure = force ÷ area).
- Stable vs unstable equilibrium
- Stable: an object returns to position after a small push. Unstable: a small push topples it. A wide base and low center of gravity add stability.
- Terminal velocity
- The constant speed a falling object reaches when air resistance balances gravity, so net force becomes zero.
- Converting units
- Multiply by a conversion factor so unwanted units cancel. 5 feet × 12 in/ft = 60 inches.
- Estimating to check answers
- Round numbers to estimate the result; if your exact answer is far from the estimate, recheck your work.
- Percent greater than 100
- 150% of a number is 1.5 times it. Percents above 100 mean more than the whole.
- Quadratic equation form
- ax² + bx + c = 0. Solve by factoring, completing the square, or the quadratic formula.
- Paraphrasing
- Restating an idea from the passage in your own words while keeping its exact meaning.
- Logical sequence
- The order in which events or steps occur in a passage — watch for time or order signal words (first, then, finally).
- Block and tackle
- A pulley system combining fixed and movable pulleys to multiply force. The mechanical advantage equals the number of supporting rope segments.
- Ideal vs actual mechanical advantage
- Ideal MA assumes no friction; actual MA is always lower because friction wastes some input force as heat.
- Efficiency of a machine
- Useful work output ÷ work input, as a percent. Friction makes real machines less than 100% efficient.
- Compound machine
- Two or more simple machines working together, like scissors (two levers + two wedges) or a bicycle (gears, levers, wheels).
- Crowbar as a lever
- A first-class lever: you push down on one end (effort), the fulcrum is the bend, and the load is lifted at the other end.
- Wheelbarrow as a lever
- A second-class lever: the wheel is the fulcrum, the load sits in the middle, and you lift the handles (effort).
- Human forearm as a lever
- A third-class lever: the elbow is the fulcrum, the biceps applies effort in the middle, and the hand holds the load.
- Screw pitch
- The distance between threads. A smaller pitch (threads closer together) gives a greater mechanical advantage.
- Why oil reduces wear
- It lubricates contacting surfaces, lowering friction so less force is lost to heat and parts last longer.
- Coefficient of friction
- A number describing how much two surfaces resist sliding. Rougher surfaces have a higher coefficient.
- Free fall
- Motion under gravity alone. All objects fall at the same rate (about 9.8 m/s²) when air resistance is ignored.
- Projectile motion
- Horizontal and vertical motion act independently: gravity pulls the object down while it keeps moving forward.
- Inertia depends on mass
- The more mass an object has, the more inertia — and the harder it is to start, stop, or turn it.
- Action–reaction pairs
- Forces always come in pairs that are equal in size and opposite in direction, acting on two different objects.
- Centripetal force
- The inward force that keeps an object moving in a circle, directed toward the center of the curve.
- Lever mechanical advantage
- MA = effort arm length ÷ load arm length. A longer effort arm lets a small effort move a large load.
- Gear train direction
- Two meshed gears turn in opposite directions. An odd number of gears reverses direction; an even number keeps it.
- Speed of gears in mesh
- Meshed gears have the same speed at their teeth, so a smaller gear must spin faster than a larger one.
- Mechanical energy
- The sum of kinetic and potential energy. In an ideal system it stays constant as one converts to the other.
- Work against gravity
- Lifting a load does work equal to weight × height — independent of the path taken to raise it.
- Pulley changes direction
- A single fixed pulley lets you pull down to lift up; it gives no force advantage but is easier to use.
- Hydraulic press
- Uses Pascal's principle: a small force on a small piston produces a large force on a large piston.
- Why airplanes generate lift
- Air moving faster over the curved top of a wing has lower pressure (Bernoulli), and the wing deflects air downward.
- Boyle's law
- At constant temperature, a gas's pressure and volume are inversely related: squeeze the volume and pressure rises.
- Charles's law
- At constant pressure, a gas's volume increases as its temperature rises.
- Atmospheric pressure
- The weight of the air above us pressing down, about 14.7 pounds per square inch at sea level.
- Why heavy objects don't fall faster
- In a vacuum all objects accelerate equally under gravity; air resistance, not weight, makes some fall slower.
- Stable structures
- A wide base and a low center of gravity resist tipping — that's why race cars are low and wide.
- Conduction, convection, radiation
- The three ways heat moves: direct contact (conduction), fluid currents (convection), and waves (radiation).
- Why a flywheel stores energy
- Its rotating mass has rotational inertia, so it keeps spinning and smooths out changes in speed.
- Integer
- A whole number and its negatives, including zero: ..., −2, −1, 0, 1, 2, ... (no fractions or decimals).
- Factor
- A number that divides another evenly. The factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple
- The product of a number and an integer. Multiples of 4 are 4, 8, 12, 16, ...
- Coefficient
- The number multiplying a variable. In 7x, the coefficient is 7.
- Variable
- A letter that stands for an unknown or changing value, like x or y.
- Solving a two-step equation
- Undo addition/subtraction first, then multiplication/division. For 2x − 3 = 7: add 3 (2x = 10), divide by 2 (x = 5).
- Percent increase example
- From 80 to 100: change is 20, so increase is 20 ÷ 80 = 25%.
- Percent decrease example
- From 100 to 80: change is 20, so decrease is 20 ÷ 100 = 20%.
- Cross-multiplication
- To compare or solve fractions, multiply each numerator by the other's denominator. a/b = c/d gives ad = bc.
- Common denominator
- A shared multiple of two denominators, needed to add or subtract fractions.
- Improper fraction
- A fraction whose numerator is at least as large as its denominator, like 7/4.
- Decimal place value
- Digits after the point are tenths, hundredths, thousandths, ... 0.25 is 2 tenths + 5 hundredths.
- Multiplying decimals
- Multiply as whole numbers, then place the decimal point so the answer has as many decimal places as both factors combined.
- Dividing by a decimal
- Move the decimal point in the divisor to make it whole, move it the same in the dividend, then divide.
- Negative times negative
- A negative times a negative is positive; a negative times a positive is negative.
- Squaring a number
- Multiply the number by itself. 9² = 81.
- Cube of a number
- Multiply the number by itself three times. 2³ = 8.
- Perfect square
- A number that is the square of an integer: 1, 4, 9, 16, 25, 36, ...
- Estimating a square root
- Find the perfect squares it falls between. √50 is between √49 (7) and √64 (8), so about 7.1.
- Surface area
- The total area of all the faces of a 3-D shape, measured in square units.
- Volume of a cylinder
- Volume = π × radius² × height.
- Diameter and radius
- The diameter is twice the radius; the radius runs from the center to the edge of a circle.
- Right angle
- An angle of exactly 90°, marked with a small square.
- Acute and obtuse angles
- Acute angles are less than 90°; obtuse angles are between 90° and 180°.
- Parallel vs perpendicular
- Parallel lines never meet (equal slopes); perpendicular lines cross at 90° (slopes are negative reciprocals).
- Solving a system by substitution
- Solve one equation for a variable, plug it into the other, then solve for the remaining variable.
- Range of a data set
- The difference between the largest and smallest values.
- Converting hours and minutes
- 60 minutes = 1 hour. 90 minutes = 1.5 hours; 2.25 hours = 2 hours 15 minutes.
- Work-rate problem
- If one worker finishes in a hours and another in b hours, together they do 1/a + 1/b of the job per hour.
- Mixture problem strategy
- Track the amount of the key ingredient: amount = concentration × total, and set the parts equal to the whole.
- Translating 'of' and 'is'
- In percent word problems, 'of' means multiply and 'is' means equals: 'what is 20% of 50' = 0.20 × 50.
- Checking a solution
- Substitute your answer back into the original equation to confirm both sides are equal.
- Sum of consecutive integers
- Consecutive integers differ by 1: n, n+1, n+2. Their sum is 3n + 3 for three of them.
- Reading for the point
- Since OAR passages are short, read to grasp the author's main claim quickly rather than memorizing every detail.
- Answering from the text only
- If you can't underline support for a choice in the passage, it's wrong — even if it sounds true.
- Detecting bias
- Loaded or emotional language can reveal the author leans toward one side of an issue.
- Primary purpose question
- Asks why the passage as a whole was written — the answer should fit every paragraph, not just one.
- Strengthen vs weaken (logic)
- A strengthening fact supports the author's claim; a weakening fact undermines it.
- Implication vs assumption
- An implication follows from what's said; an assumption is something the author takes for granted without stating.
- Scanning for keywords
- For detail questions, find a distinctive word from the question in the passage and read around it.
- Negative or 'EXCEPT' questions
- Ask which choice is NOT supported — eliminate the three that ARE supported and pick the leftover.
- Topic sentence
- Often the first or last sentence of a paragraph; it usually states that paragraph's main point.
- Synonyms in answer choices
- Correct answers often paraphrase the passage rather than repeat it word for word.
- Pacing tip for reading
- Don't reread the whole passage for each question; locate the relevant lines and move on.
- Inference vs guess
- An inference is firmly supported by the text; a guess adds information the passage never provides.
- Identifying the conclusion
- Look for the claim the rest of the passage is built to support — often signaled by 'therefore' or 'thus.'
- Stay objective
- Don't pick an answer because you personally agree with it; pick the one the passage supports.
- Comparison passages
- When a passage weighs two views, note where they agree and disagree before answering.
