PiCAT cheat sheet

Water boils at 100 °C (212 °F) and freezes at 0 °C (32 °F) at standard atmospheric pressure.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts with the aid of chlorophyll.

Force = mass × acceleration (F = ma); weight = mass × gravitational acceleration (W = mg).

Earth's atmosphere is about 78% nitrogen, 21% oxygen, and 1% argon, carbon dioxide, and other gases.

pH below 7 is acidic, pH 7 is neutral, and pH above 7 is basic (alkaline).

The speed of light in a vacuum is about 3 × 10⁸ meters per second.

Density = mass ÷ volume; an object denser than a fluid sinks in it, and one less dense floats.

Newton's third law: for every action force there is an equal and opposite reaction force.

Average = sum of all values ÷ number of values.

Percent change = (new value − old value) ÷ old value × 100.

Distance = rate × time; rate = distance ÷ time; time = distance ÷ rate.

Part = percent × whole, with the percent converted to a decimal (35% of 80 = 0.35 × 80 = 28).

Simple interest = principal × annual rate × time in years.

Combined work rate = sum of the individual rates; time working together = 1 ÷ combined rate.

To convert units, multiply by a fraction equal to 1 that places the desired unit on top so unwanted units cancel.

Profit = revenue − cost; total cost = unit price × quantity plus any fixed fees.

Prefixes: un-/dis-/non- (not), re- (again), pre- (before), post- (after), sub- (under), inter- (between), anti- (against).

Common roots: -spect- (look), -dict- (say), -ject- (throw), -port- (carry), -cred- (believe), -bene- (good), -mal- (bad).

Suffixes: -tion and -ment form nouns; -ous, -ful, and -ive form adjectives; -ize and -ify form verbs; -ly forms adverbs.

Contrast signals such as but, although, however, and unlike often mean the answer is the opposite of a nearby word.

Definition clues follow dashes, commas, or phrases such as "that is" and "in other words."

A positive connotation suggests approval and a negative connotation suggests disapproval, even when literal meanings are similar.

On antonym questions, eliminate any choice that means the same as the stem word before selecting.

The main idea is the point the whole passage supports; it is broader than any single detail but narrower than the topic alone.

Topic sentences most often appear as the first or last sentence of a paragraph.

Detail questions are answered by locating the exact sentence; the correct choice restates it without adding claims.

A valid inference follows logically from stated details and requires no outside information.

Signal words: first, next, then, finally indicate sequence; because, therefore, as a result indicate cause and effect.

Tone words classify an author's attitude as positive, negative, or neutral (for example critical, admiring, objective).

Eliminate choices that are too broad, too narrow, or absolute (always, never, all) when the passage qualifies its claim.

Triangle area = ½ × base × height; circle area = πr²; circumference = 2πr.

Pythagorean theorem: a² + b² = c², where c is the hypotenuse of a right triangle.

Slope m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form is y = mx + b.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0.

Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1; x⁻ᵃ = 1/xᵃ.

Angles in a triangle sum to 180°, in a quadrilateral to 360°, and on a straight line to 180°.

Volume: rectangular solid V = lwh; cylinder V = πr²h; cube V = s³.

FOIL: (x + a)(x + b) = x² + (a + b)x + ab; (a + b)² = a² + 2ab + b².

Median is the middle value of ordered data; mode is the value that appears most often.

Ohm's law: V = IR, where V is volts, I is amperes, and R is ohms.

Power: P = VI = I²R = V²/R, measured in watts.

Series circuit: R_total = R₁ + R₂ + …; current is the same through every component and voltages add.

Parallel circuit: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is the same across each branch and branch currents add.

Resistor color digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9.

A capacitor (farads) stores charge and opposes changes in voltage; an inductor (henries) opposes changes in current.

A diode conducts in one direction only; a transistor can amplify a signal or act as an electronic switch.

Copper and silver are good conductors, while rubber, glass, and plastic are insulators.

Four-stroke cycle order: intake, compression, power, exhaust.

Most passenger vehicles use a 12-volt battery with the negative terminal connected to the chassis (negative ground).

The alternator recharges the battery and supplies electrical power while the engine runs; the starter cranks the engine.

The cooling system circulates coolant through the engine and radiator, and the thermostat controls flow to regulate temperature.

Engine oil lubricates moving parts, carries away heat, and suspends contaminants; the oil filter traps particles.

Brakes are hydraulic: pedal pressure pressurizes brake fluid, which pushes calipers or wheel cylinders against rotors or drums.

Check tire pressure when tires are cold; pressure is measured in psi and specified on the vehicle placard.

Wear safety glasses for cutting, drilling, and chipping, and keep guards in place on power tools.

Lower sandpaper grit numbers are coarser and remove material fast; higher numbers are finer and produce a smooth finish.

Saw blades with fewer teeth per inch cut faster and rougher; more teeth per inch cut slower and smoother.

Drill a pilot hole smaller than the screw shank to prevent splitting and to guide fasteners near board edges.

Screws hold better than nails in wood and can be removed; nails rely on friction and drive faster.

A combination square checks 90° and 45° angles; calipers measure inside, outside, and depth dimensions precisely.

Cut wood along the grain with a ripsaw and across the grain with a crosscut saw; use a fine-tooth hacksaw for metal.

Lever mechanical advantage = effort arm length ÷ resistance arm length.

A single fixed pulley changes direction only (MA = 1); a single movable pulley has a mechanical advantage of 2.

Inclined plane mechanical advantage = length of the incline ÷ height of the incline.

Gear ratio = teeth on driven gear ÷ teeth on driving gear; a larger driven gear turns slower with greater torque.

Work = force × distance; power = work ÷ time.

Efficiency = (useful output work ÷ total input work) × 100%.

In hydraulics, pressure = force ÷ area and is transmitted equally in all directions (Pascal's principle).

Torque = force × perpendicular distance from the pivot; friction increases with rougher surfaces and greater normal force.

A rotation preserves the shape of a piece; a mirror image cannot be rotated into a match, so reject reflected options.

Identify unique features such as tabs, slots, holes, and notches, then trace where each must connect in the assembled figure.

Anchor on the piece that appears unchanged in the answer choices, then position the remaining pieces relative to it.

Match line lengths and joint angles; a mismatched angle rules out that choice.

Count the pieces: an option showing more or fewer pieces than given is incorrect.

Reject options in which parts overlap or occupy space the original pieces cannot share.

Water boils at 100 °C (212 °F) and freezes at 0 °C (32 °F) at standard atmospheric pressure.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts with the aid of chlorophyll.

Force = mass × acceleration (F = ma); weight = mass × gravitational acceleration (W = mg).

Earth's atmosphere is about 78% nitrogen, 21% oxygen, and 1% argon, carbon dioxide, and other gases.

pH below 7 is acidic, pH 7 is neutral, and pH above 7 is basic (alkaline).

The speed of light in a vacuum is about 3 × 10⁸ meters per second.

Density = mass ÷ volume; an object denser than a fluid sinks in it, and one less dense floats.

Newton's third law: for every action force there is an equal and opposite reaction force.

Average = sum of all values ÷ number of values.

Percent change = (new value − old value) ÷ old value × 100.

Distance = rate × time; rate = distance ÷ time; time = distance ÷ rate.

Part = percent × whole, with the percent converted to a decimal (35% of 80 = 0.35 × 80 = 28).

Simple interest = principal × annual rate × time in years.

Combined work rate = sum of the individual rates; time working together = 1 ÷ combined rate.

To convert units, multiply by a fraction equal to 1 that places the desired unit on top so unwanted units cancel.

Profit = revenue − cost; total cost = unit price × quantity plus any fixed fees.

Prefixes: un-/dis-/non- (not), re- (again), pre- (before), post- (after), sub- (under), inter- (between), anti- (against).

Common roots: -spect- (look), -dict- (say), -ject- (throw), -port- (carry), -cred- (believe), -bene- (good), -mal- (bad).

Suffixes: -tion and -ment form nouns; -ous, -ful, and -ive form adjectives; -ize and -ify form verbs; -ly forms adverbs.

Contrast signals such as but, although, however, and unlike often mean the answer is the opposite of a nearby word.

Definition clues follow dashes, commas, or phrases such as "that is" and "in other words."

A positive connotation suggests approval and a negative connotation suggests disapproval, even when literal meanings are similar.

On antonym questions, eliminate any choice that means the same as the stem word before selecting.

The main idea is the point the whole passage supports; it is broader than any single detail but narrower than the topic alone.

Topic sentences most often appear as the first or last sentence of a paragraph.

Detail questions are answered by locating the exact sentence; the correct choice restates it without adding claims.

A valid inference follows logically from stated details and requires no outside information.

Signal words: first, next, then, finally indicate sequence; because, therefore, as a result indicate cause and effect.

Tone words classify an author's attitude as positive, negative, or neutral (for example critical, admiring, objective).

Eliminate choices that are too broad, too narrow, or absolute (always, never, all) when the passage qualifies its claim.

Triangle area = ½ × base × height; circle area = πr²; circumference = 2πr.

Pythagorean theorem: a² + b² = c², where c is the hypotenuse of a right triangle.

Slope m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form is y = mx + b.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0.

Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1; x⁻ᵃ = 1/xᵃ.

Angles in a triangle sum to 180°, in a quadrilateral to 360°, and on a straight line to 180°.

Volume: rectangular solid V = lwh; cylinder V = πr²h; cube V = s³.

FOIL: (x + a)(x + b) = x² + (a + b)x + ab; (a + b)² = a² + 2ab + b².

Median is the middle value of ordered data; mode is the value that appears most often.

Ohm's law: V = IR, where V is volts, I is amperes, and R is ohms.

Power: P = VI = I²R = V²/R, measured in watts.

Series circuit: R_total = R₁ + R₂ + …; current is the same through every component and voltages add.

Parallel circuit: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is the same across each branch and branch currents add.

Resistor color digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9.

A capacitor (farads) stores charge and opposes changes in voltage; an inductor (henries) opposes changes in current.

A diode conducts in one direction only; a transistor can amplify a signal or act as an electronic switch.

Copper and silver are good conductors, while rubber, glass, and plastic are insulators.

Four-stroke cycle order: intake, compression, power, exhaust.

Most passenger vehicles use a 12-volt battery with the negative terminal connected to the chassis (negative ground).

The alternator recharges the battery and supplies electrical power while the engine runs; the starter cranks the engine.

The cooling system circulates coolant through the engine and radiator, and the thermostat controls flow to regulate temperature.

Engine oil lubricates moving parts, carries away heat, and suspends contaminants; the oil filter traps particles.

Brakes are hydraulic: pedal pressure pressurizes brake fluid, which pushes calipers or wheel cylinders against rotors or drums.

Check tire pressure when tires are cold; pressure is measured in psi and specified on the vehicle placard.

Wear safety glasses for cutting, drilling, and chipping, and keep guards in place on power tools.

Lower sandpaper grit numbers are coarser and remove material fast; higher numbers are finer and produce a smooth finish.

Saw blades with fewer teeth per inch cut faster and rougher; more teeth per inch cut slower and smoother.

Drill a pilot hole smaller than the screw shank to prevent splitting and to guide fasteners near board edges.

Screws hold better than nails in wood and can be removed; nails rely on friction and drive faster.

A combination square checks 90° and 45° angles; calipers measure inside, outside, and depth dimensions precisely.

Cut wood along the grain with a ripsaw and across the grain with a crosscut saw; use a fine-tooth hacksaw for metal.

Lever mechanical advantage = effort arm length ÷ resistance arm length.

A single fixed pulley changes direction only (MA = 1); a single movable pulley has a mechanical advantage of 2.

Inclined plane mechanical advantage = length of the incline ÷ height of the incline.

Gear ratio = teeth on driven gear ÷ teeth on driving gear; a larger driven gear turns slower with greater torque.

Work = force × distance; power = work ÷ time.

Efficiency = (useful output work ÷ total input work) × 100%.

In hydraulics, pressure = force ÷ area and is transmitted equally in all directions (Pascal's principle).

Torque = force × perpendicular distance from the pivot; friction increases with rougher surfaces and greater normal force.

A rotation preserves the shape of a piece; a mirror image cannot be rotated into a match, so reject reflected options.

Identify unique features such as tabs, slots, holes, and notches, then trace where each must connect in the assembled figure.

Anchor on the piece that appears unchanged in the answer choices, then position the remaining pieces relative to it.

Match line lengths and joint angles; a mismatched angle rules out that choice.

Count the pieces: an option showing more or fewer pieces than given is incorrect.

Reject options in which parts overlap or occupy space the original pieces cannot share.

Water boils at 100 °C (212 °F) and freezes at 0 °C (32 °F) at standard atmospheric pressure.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts with the aid of chlorophyll.

Force = mass × acceleration (F = ma); weight = mass × gravitational acceleration (W = mg).

Earth's atmosphere is about 78% nitrogen, 21% oxygen, and 1% argon, carbon dioxide, and other gases.

pH below 7 is acidic, pH 7 is neutral, and pH above 7 is basic (alkaline).

The speed of light in a vacuum is about 3 × 10⁸ meters per second.

Density = mass ÷ volume; an object denser than a fluid sinks in it, and one less dense floats.

Newton's third law: for every action force there is an equal and opposite reaction force.

Average = sum of all values ÷ number of values.

Percent change = (new value − old value) ÷ old value × 100.

Distance = rate × time; rate = distance ÷ time; time = distance ÷ rate.

Part = percent × whole, with the percent converted to a decimal (35% of 80 = 0.35 × 80 = 28).

Simple interest = principal × annual rate × time in years.

Combined work rate = sum of the individual rates; time working together = 1 ÷ combined rate.

To convert units, multiply by a fraction equal to 1 that places the desired unit on top so unwanted units cancel.

Profit = revenue − cost; total cost = unit price × quantity plus any fixed fees.

Prefixes: un-/dis-/non- (not), re- (again), pre- (before), post- (after), sub- (under), inter- (between), anti- (against).

Common roots: -spect- (look), -dict- (say), -ject- (throw), -port- (carry), -cred- (believe), -bene- (good), -mal- (bad).

Suffixes: -tion and -ment form nouns; -ous, -ful, and -ive form adjectives; -ize and -ify form verbs; -ly forms adverbs.

Contrast signals such as but, although, however, and unlike often mean the answer is the opposite of a nearby word.

Definition clues follow dashes, commas, or phrases such as "that is" and "in other words."

A positive connotation suggests approval and a negative connotation suggests disapproval, even when literal meanings are similar.

On antonym questions, eliminate any choice that means the same as the stem word before selecting.

The main idea is the point the whole passage supports; it is broader than any single detail but narrower than the topic alone.

Topic sentences most often appear as the first or last sentence of a paragraph.

Detail questions are answered by locating the exact sentence; the correct choice restates it without adding claims.

A valid inference follows logically from stated details and requires no outside information.

Signal words: first, next, then, finally indicate sequence; because, therefore, as a result indicate cause and effect.

Tone words classify an author's attitude as positive, negative, or neutral (for example critical, admiring, objective).

Eliminate choices that are too broad, too narrow, or absolute (always, never, all) when the passage qualifies its claim.

Triangle area = ½ × base × height; circle area = πr²; circumference = 2πr.

Pythagorean theorem: a² + b² = c², where c is the hypotenuse of a right triangle.

Slope m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form is y = mx + b.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0.

Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1; x⁻ᵃ = 1/xᵃ.

Angles in a triangle sum to 180°, in a quadrilateral to 360°, and on a straight line to 180°.

Volume: rectangular solid V = lwh; cylinder V = πr²h; cube V = s³.

FOIL: (x + a)(x + b) = x² + (a + b)x + ab; (a + b)² = a² + 2ab + b².

Median is the middle value of ordered data; mode is the value that appears most often.

Ohm's law: V = IR, where V is volts, I is amperes, and R is ohms.

Power: P = VI = I²R = V²/R, measured in watts.

Series circuit: R_total = R₁ + R₂ + …; current is the same through every component and voltages add.

Parallel circuit: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is the same across each branch and branch currents add.

Resistor color digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9.

A capacitor (farads) stores charge and opposes changes in voltage; an inductor (henries) opposes changes in current.

A diode conducts in one direction only; a transistor can amplify a signal or act as an electronic switch.

Copper and silver are good conductors, while rubber, glass, and plastic are insulators.

Four-stroke cycle order: intake, compression, power, exhaust.

Most passenger vehicles use a 12-volt battery with the negative terminal connected to the chassis (negative ground).

The alternator recharges the battery and supplies electrical power while the engine runs; the starter cranks the engine.

The cooling system circulates coolant through the engine and radiator, and the thermostat controls flow to regulate temperature.

Engine oil lubricates moving parts, carries away heat, and suspends contaminants; the oil filter traps particles.

Brakes are hydraulic: pedal pressure pressurizes brake fluid, which pushes calipers or wheel cylinders against rotors or drums.

Check tire pressure when tires are cold; pressure is measured in psi and specified on the vehicle placard.

Wear safety glasses for cutting, drilling, and chipping, and keep guards in place on power tools.

Lower sandpaper grit numbers are coarser and remove material fast; higher numbers are finer and produce a smooth finish.

Saw blades with fewer teeth per inch cut faster and rougher; more teeth per inch cut slower and smoother.

Drill a pilot hole smaller than the screw shank to prevent splitting and to guide fasteners near board edges.

Screws hold better than nails in wood and can be removed; nails rely on friction and drive faster.

A combination square checks 90° and 45° angles; calipers measure inside, outside, and depth dimensions precisely.

Cut wood along the grain with a ripsaw and across the grain with a crosscut saw; use a fine-tooth hacksaw for metal.

Lever mechanical advantage = effort arm length ÷ resistance arm length.

A single fixed pulley changes direction only (MA = 1); a single movable pulley has a mechanical advantage of 2.

Inclined plane mechanical advantage = length of the incline ÷ height of the incline.

Gear ratio = teeth on driven gear ÷ teeth on driving gear; a larger driven gear turns slower with greater torque.

Work = force × distance; power = work ÷ time.

Efficiency = (useful output work ÷ total input work) × 100%.

In hydraulics, pressure = force ÷ area and is transmitted equally in all directions (Pascal's principle).

Torque = force × perpendicular distance from the pivot; friction increases with rougher surfaces and greater normal force.

A rotation preserves the shape of a piece; a mirror image cannot be rotated into a match, so reject reflected options.

Identify unique features such as tabs, slots, holes, and notches, then trace where each must connect in the assembled figure.

Anchor on the piece that appears unchanged in the answer choices, then position the remaining pieces relative to it.

Match line lengths and joint angles; a mismatched angle rules out that choice.

Count the pieces: an option showing more or fewer pieces than given is incorrect.

Reject options in which parts overlap or occupy space the original pieces cannot share.