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College Entrance Test Math
The math that UPCAT, ACET, DCAT and USTET all test, grouped by topic — worked problems across algebra, quadratics, geometry, counting and the shortcut techniques entrance exams reward. Math only; we do not cover the English or Science sections.
No lesson matches that. Try a shorter word — circle, root or mean.
Back-solving from the choices
The answer is already printed on the page. Start at the middle choice and let the direction of the miss kill the rest.
Read the lesson »Plugging in numbers
When the choices are full of letters, pick easy values and turn the whole question into arithmetic — just never 0 or 1.
Read the lesson »Estimating to eliminate
Round hard and compare magnitudes. The sanity rules that kill wrong choices before any calculation happens.
Read the lesson »Spotting the trap answer
The wrong choices are engineered. The one-step-early trap, sign and reciprocal pairs, and the habits that beat them.
Read the lesson »Pacing and when to skip
Seconds per item, three passes through the paper, and the sixty-second rule that stops one question eating three.
Read the lesson »Wording and unit traps
7 h 45 min is not 7.45 hours. Mixed units, squared units, “at least” and “increased to” — the words that decide the answer.
Read the lesson »Sketch it: draw before you solve
Ten seconds of pencil buys minutes of clarity — figures, axes and number lines reveal answers and execute half the choices.
Read the lesson »Integer operations and signs
Rewrite subtraction as adding the opposite, then count the minuses — the rules for + and × are not the same.
Read the lesson »Order of operations
× and ÷ share a rank, so go left to right — and −3² is not the same as (−3)².
Read the lesson »The four operations on fractions
Multiply straight across, flip the second to divide, and find the LCD to add. Mixed numbers converted first.
Read the lesson »Ratio and proportion
2 : 5 is a recipe, not a total. Count the parts, find one part, and learn to tell direct from inverse.
Read the lesson »Fractions, decimals and percents
One number in three costumes. Divide, times 100, and turn a repeating decimal into a fraction with the nines trick.
Read the lesson »Percentage: base, rate and percentage
15% of what is 48? The word “of” marks the base, “is” marks the part.
Read the lesson »Profit, loss, markup and commission
The same ₱120 profit is a 25% markup on cost and a 20% margin on the price. “Percent of what” decides everything.
Read the lesson »Prime factorisation and testing for primes
Divide by primes until you reach 1, then write the exponents. To test 391, only the primes up to √391 matter.
Read the lesson »Divisibility, GCF and LCM
Break both numbers into primes, then take the lowest powers for the GCF and the highest for the LCM.
Read the lesson »How many divisors a number has
Add one to every exponent and multiply — 24 divisors of 360 without listing a single one. An odd answer means a perfect square.
Read the lesson »Rational and irrational numbers
Terminating and repeating decimals are both fractions in disguise. 22/7 is rational; π never will be.
Read the lesson »Scientific notation
One digit before the point and a power of ten. Multiplying adds the powers — but adding needs them to match.
Read the lesson »Significant figures and estimation
Leading zeros never count, trailing ones after a point always do. Then a one-figure estimate catches the decimal-point disasters.
Read the lesson »Consecutive integer problems
n, n+1, n+2 — and both even and odd runs step by two. With an odd count of terms, the average is the middle one.
Read the lesson »Digit problems: place value in algebra
A two-digit number is 10t + u, never tu. Reversing it always changes it by a multiple of 9.
Read the lesson »Clock problems: the angle between the hands
At 3:40 the hour hand is nowhere near the 3. Six degrees a minute, half a degree a minute, and one subtraction.
Read the lesson »Units digit of a large power
The last digit of 7100. Only the last digit matters, and no cycle is ever longer than four.
Read the lesson »Powers of i: four answers, endlessly repeating
Simplify i⁹⁷⁵ with no calculator. The powers loop every four steps, so only the remainder after dividing by 4 matters.
Read the lesson »Operations on complex numbers
Treat i like a letter until you meet i² = −1. FOIL to multiply, and the conjugate to clear a denominator.
Read the lesson »Remainder patterns: find the cycle
The remainder of 2¹⁰ ÷ 3 with no calculator. The remainders loop after two steps, so only the exponent’s position matters.
Read the lesson »LCM and GCF word problems
Bells ringing together again is LCM; cutting into the biggest equal pieces is GCF — the battle is telling which one the story wants.
Read the lesson »Translating verbal phrases
English into algebra, with the two phrases that come out backwards — less than and subtracted from.
Read the lesson »Evaluating expressions
Substitute every letter in brackets, then let the order of operations run. The negatives and the squares are where marks vanish.
Read the lesson »Literal equations
Making a letter the subject uses the same moves as numbers. Clear fractions, unwrap in reverse, and factor when the target repeats.
Read the lesson »Laws of exponents: zero and negative powers
x⁻² is not negative — it is a location. Multiply the powers, subtract when dividing, then move every negative across the bar.
Read the lesson »Radicals and rationalising
Simplify √72, then clear the root off the bottom of a fraction — single roots, and the conjugate trick for two terms.
Read the lesson »Polynomial operations: add, subtract, multiply
Only like terms combine, the minus sign hits every term in the bracket, and multiplying means every term meets every other one.
Read the lesson »Special products: three patterns to know on sight
(2x + 5)² is never just 4x² + 25. Why a square always has a doubled middle, and a difference of squares has none.
Read the lesson »Binomial expansion and Pascal's triangle
1, 4, 6, 4, 1 for a fourth power, one exponent counting down and the other up — and a general term that finds one coefficient alone.
Read the lesson »Factoring trinomials: the AC method
How to factor 3x² − 10x + 3 when the number in front of x² is not 1 — find the pair, split the middle, group, and check by multiplying back out.
Read the lesson »Perfect square trinomials
Root both ends, double the product, compare with the middle. The three-move test, and filling in a missing term.
Read the lesson »Factoring by grouping
Four terms is the signal. Pair them, factor each pair, and a shared bracket appears — flip a sign if they come out reversed.
Read the lesson »Sum and difference of cubes
Two formulas kept straight by one word: SOAP. Unlike a sum of squares, a sum of cubes does factor.
Read the lesson »Remainder and factor theorems
Substitute one number and you know the remainder. Zero means a factor — then synthetic division finishes the job.
Read the lesson »Polynomial long division
Divide, multiply, subtract, bring down — with a 0x placeholder for the missing power, and synthetic division when the divisor is x − c.
Read the lesson »Simplifying rational expressions
You may cancel factors, never terms. Factor both halves, cancel the matching bracket, then say what x can never be.
Read the lesson »Adding and subtracting rational expressions
Factor the denominators, build the LCD from the factors, and bracket the numerator you are subtracting.
Read the lesson »Rational equations and extraneous roots
Write the banned value before you cancel anything. An answer can look perfectly right and still be illegal in the original.
Read the lesson »Linear equations with fractions
Clear the denominators first. Find the LCD, multiply every term by it, cancel — and what is left is ordinary algebra.
Read the lesson »Radical equations
Isolate, square, solve — then check every root, because squaring invents answers that were never there.
Read the lesson »Equations reducible to quadratic
When the middle power is half the first, let u be the smaller piece — then remember that u is not x, and a quartic has four roots.
Read the lesson »Linear inequalities: when the sign flips
−3x + 7 > 22. Dividing by a negative reverses the direction — here is why, on a number line, and how to dodge it entirely.
Read the lesson »Compound inequalities: two boundaries, one x
Solving −2 < 3x + 1 ≤ 10 means working on all three parts at once — then open and closed dots decide the interval.
Read the lesson »Absolute value equations and inequalities
Distance from zero, so everything splits in two. Less than gives one stretch; greater than gives two pieces.
Read the lesson »Systems by substitution
When a letter already sits alone, substitution beats elimination. Keep the brackets, and remember an answer needs both letters.
Read the lesson »Systems of equations: solving by elimination
Two equations, two unknowns. Match the coefficients, add the lines so one letter dies, then substitute back for the other.
Read the lesson »Systems in three variables
Eliminate the same letter twice to get down to two equations, solve those, then climb back for the third.
Read the lesson »Systems of inequalities
Solid line for ≥, dashed for >, shade with a test point — and the overlap is the solution.
Read the lesson »Variation: direct, inverse and finding k
One word decides the formula. Inversely puts x under the bar and fixes the product — find k from the first pair, then use it on the second.
Read the lesson »Absolute value inequalities
|x − a| is a distance: less-thAND traps x between two fences, greatOR throws it outside them.
Read the lesson »Solving quadratics by factoring
Zero on one side, factor, then let each bracket take a turn — and never divide by x, or a root vanishes.
Read the lesson »Solving by extracting square roots
3x² − 75 = 0 needs no formula. Isolate the square, root both sides, and write the ± that carries the second answer.
Read the lesson »The quadratic formula
For 2x² + 3x − 5 = 0. Label a, b and c with their signs, work the discriminant first, then split the ± into two answers.
Read the lesson »Completing the square
Halve b, square it, add it to both sides. Where the quadratic formula comes from, and why the method is named after a picture.
Read the lesson »The discriminant: one number tells you the roots
b² − 4ac for 2x² − 4x + 5. You never solve the equation — the sign of D alone says how many real roots there are.
Read the lesson »Sum and product of roots
Two facts about the answers, read straight off the equation — −b/a and c/a, no solving required.
Read the lesson »The vertex: highest or lowest point
A ball at h = −5t² + 20t. −b/2a gives the time; only substituting back gives the height. Two questions, two numbers.
Read the lesson »Graphing a parabola
Direction, vertex, axis, intercepts — five facts draw the whole curve, and symmetry hands you every second point for free.
Read the lesson »Writing the equation from roots or a graph
Roots give factors, the sum and product give the coefficients, and a graph gives the vertex form — once one more point fixes a.
Read the lesson »Maximum and minimum problems
Constraint, substitute, quadratic, vertex. Fencing, revenue and products — one method behind all three.
Read the lesson »Quadratic inequalities: a stretch, not a point
x² − 4 < 0 does not give x < 2. Factor it, mark the boundaries, and test one number from each of the three zones.
Read the lesson »Age word problems: the Past / Present / Future table
A mother is 4× her daughter’s age, and 7× five years ago. One table keeps every age straight — and shows the trap at the end.
Read the lesson »Catching up: distance, rate and time
A freight train at 40 mph, an express 3 hours behind it at 60 mph. Catching up means the two distances are equal.
Read the lesson »Distance apart: two vehicles, opposite ways
Two cars leave together at 40 and 60 kph in opposite directions. The gap grows from both ends, so the distances add.
Read the lesson »Distance apart: two vehicles, same way
Car A at 75 mph pulls ahead of Car B at 55 mph. Same direction, so the gap is a difference — subtract, don’t add.
Read the lesson »Work problems: working together
Alice paints a fence in 4 hours, Bob in 6. Turn hours into a rate per hour, add the rates, then flip — never average the hours.
Read the lesson »Coin problems: how many coins vs how much money
15 coins worth ₱100. One equation counts the coins, the other weighs them — and the letters must count, not carry value.
Read the lesson »Concentration: the mixing formula
Mixing a 30% solution into 12 L of 70% to land on 45%. Percents never add — litres of the pure stuff do.
Read the lesson »Average speed: total over total
Never average the speeds — total distance over total time, or 2ab/(a + b) for a round trip. The 60-and-40 answer is 48, not 50.
Read the lesson »Boats and currents
Downstream b + c, upstream b − c — add the equations to find the boat, subtract to find the current.
Read the lesson »Two investments
x at one rate, total − x at the other — and the equation lives in the interest, because that is the number the story gives.
Read the lesson »The distance formula
Pythagoras wearing coordinates. Subtract, square, add, root — and the order of the two points never matters.
Read the lesson »The missing endpoint, when you know the midpoint
One end at (−2, 1), the middle at (4, 3). Split the midpoint formula into two tiny equations — one for x, one for y.
Read the lesson »The missing coordinate, when you know the slope
A line of slope 3 through (6, 7) and (x, 1). Drop the numbers into the slope formula and the unknown is just another slot.
Read the lesson »The equation of a line
Slope first, then point-slope, then rearrange into whichever of the four forms the answer choices use.
Read the lesson »Equation of a circle
The distance formula, squared. Watch the flipped bracket signs, and complete both squares to get there from general form.
Read the lesson »Transformations
Translate adds, reflect flips one coordinate, rotate swaps them, dilate multiplies. Only dilation changes the size.
Read the lesson »Parallel and perpendicular slopes
Parallel shares the slope; perpendicular flips the fraction and switches the sign — the product must be −1.
Read the lesson »Area from coordinates: the shoelace method
Cross-multiply down, cross-multiply up, subtract and halve — any polygon's area from its vertex list.
Read the lesson »Reading a line from its graph
b is where it crosses, m is rise over run — two reads off the picture and the equation writes itself.
Read the lesson »Reading a parabola from its graph
Direction, vertex, roots — then one marked point pins down a and the whole equation follows.
Read the lesson »Reading data graphs: bars, lines and averages
Check the scale first, then count gridlines — differences, averages and the steepest climb all follow.
Read the lesson »Reading f(x) from a graph
Up from x to the curve, across to y evaluates f — and f(x) = k is the same trip run backwards, solutions counted with one horizontal line.
Read the lesson »Domain and range from a graph
Domain is the x-shadow, range is the y-shadow — and the lowest point of the curve beats any endpoint.
Read the lesson »The vertical line test
One input, one output: if any vertical line hits the curve twice, it is not a function — one bad line settles it.
Read the lesson »Solving a system from its graph
The crossing point is the solution — read it, check it in both equations, and count solutions on sight.
Read the lesson »Shifts and flips: reading transformed graphs
Inside the bracket moves it sideways — opposite the sign — outside moves it up, and a leading minus flips it.
Read the lesson »Angle pairs
Complementary 90°, supplementary 180°, vertical angles equal — and why adjacent on its own means nothing.
Read the lesson »Angles in a triangle
The three angles total 180°, and an exterior angle equals the two far ones — plus the isosceles ambiguity.
Read the lesson »Triangle inequality and classification
Can 5, 7, 13 be a triangle? The two shorter sides must beat the longest, then the squares say acute, right or obtuse.
Read the lesson »Triangle congruence: SSS, SAS, ASA and the rest
Three matching parts prove two triangles identical — but only the right three. SSA swings two ways, and CPCTC collects everything else afterwards.
Read the lesson »Parallel lines cut by a transversal
Eight angles, but only two sizes. Corresponding, alternate and co-interior pairs — and the shortcut that skips the names.
Read the lesson »Polygon angles and diagonals
Every polygon is a pile of triangles: (n − 2)180 inside, always 360 outside, and n(n − 3)/2 diagonals.
Read the lesson »Parallelograms
Opposite sides and angles equal, consecutive angles supplementary, diagonals bisect — and the rectangle–rhombus–square family.
Read the lesson »Trapezoids and kites
The median is the average of the bases, the area is that average times the height, and a kite's area is half the product of its diagonals.
Read the lesson »Similar triangles
A flagpole and a building casting shadows at the same moment. Two equal angles are enough — and area scales by the square of the ratio.
Read the lesson »The Pythagorean theorem
A 13 m ladder, its foot 5 m out. Add for the hypotenuse, subtract for a leg — plus the triples worth memorising.
Read the lesson »Special right triangles
1 : 1 : √2 and 1 : √3 : 2 — two fixed ratios that replace a calculator.
Read the lesson »Area of triangles and quadrilaterals
Triangle, trapezoid, rhombus and Heron — five formulas and one warning: always the perpendicular height.
Read the lesson »Circles: circumference, area, arc and sector
Two formulas for the whole circle, then θ/360 applied twice — arc from C, sector from A.
Read the lesson »Central and inscribed angles
An angle at the centre equals its arc; one on the rim is half of it. Plus the right angle hiding in every semicircle.
Read the lesson »Chords, tangents and secants
Two chords crossing give equal products. From outside, whole × outside — and a tangent is its own whole and outside.
Read the lesson »Shaded region problems
Almost always one shape minus another. Name both, subtract, and keep π until the very last line.
Read the lesson »Volume and surface area
Base × height, or a third of it if the solid comes to a point — plus what scaling does to each.
Read the lesson »Degrees and radians
π = 180° converts both ways. Then arc length and sector area — two formulas that refuse to work until the angle is in radians.
Read the lesson »SOH-CAH-TOA: picking the right ratio
An angle of elevation of 32° from 40 m away. Tick the side you know and the side you want — only one ratio holds both.
Read the lesson »Exact trig values at 30°, 45° and 60°
Nine values, all read off two triangles — plus the √0 √1 √2 √3 √4 pattern that makes them stick.
Read the lesson »Coterminal and reference angles
Add or subtract full turns to get inside one revolution, measure the acute angle to the x-axis, then let the quadrant set the sign.
Read the lesson »Basic trig identities
Rewrite everything in sines and cosines, then look for sin²θ + cos²θ = 1. Eight identities, all of them from one right triangle.
Read the lesson »The Law of Sines
Pair every side with the angle facing it. For triangles with no right angle — plus the ambiguous case.
Read the lesson »The Law of Cosines
Pythagoras with a correction term. Use it for SAS or SSS, and a negative cosine always means an obtuse angle.
Read the lesson »Medians, altitudes and the centroid
Four special segments told apart — and the centroid cutting every median 2 : 1 from the vertex.
Read the lesson »Similar figures: k, k², k³
Lengths scale by k, areas by k², volumes by k³ — one exponent per dimension, and backwards questions root down to k first.
Read the lesson »Arithmetic sequences and series
Find the 10th term of 2, 5, 8, 11, … without writing all ten. Then total them with the series formula — and see why it is n − 1, not n.
Read the lesson »Arithmetic series
Pair the first term with the last and every pair totals the same. Both sum formulas, plus 1 + 2 + … + 100 in one line.
Read the lesson »Geometric sequences: multiply, don’t add
The 10th term of 3, 6, 12, 24, … — divide to find r, and see why the power is n − 1 rather than n.
Read the lesson »Finite geometric series
Adding a doubling sequence, where pairing fails. The formula, the two negatives that cancel, and where the infinite version comes from.
Read the lesson »Infinite series: endless terms, finite total
8 + 4 + 2 + 1 + … never stops, yet it totals 16. Divide to find r, test that |r| < 1, then a ÷ (1 − r).
Read the lesson »Arithmetic and geometric means
Inserting means is filling in a sequence. Three means make five terms and four gaps — count the gaps, not the blanks.
Read the lesson »Finding the next term in any pattern
Differences, then ratios, then second differences — plus the eight families worth knowing on sight, and the trick of two sequences taking turns.
Read the lesson »Harmonic sequences: flip, solve, flip back
The reciprocals are arithmetic — flip, use the familiar rules, flip back. Plus the harmonic mean, 2ab/(a + b).
Read the lesson »Sigma notation: reading the Σ
Start, stop, recipe: run the index, feed the formula, add — and terms = stop − start + 1, both ends counted.
Read the lesson »Recursive sequences
Each term eats the last: crank carefully with labelled terms, or conjecture the explicit formula and test it.
Read the lesson »The counting principle: one slot at a time
3 × 4 × 2 = 24 meals. Draw a slot per decision, count the options, and learn when “or” means add instead.
Read the lesson »Permutations: arranging things in order
Rearranging UPCAT five ways over. Each letter used shrinks the next slot by one, and that chain is just 5! = 120.
Read the lesson »Repeated letters: when items look identical
MATHEMATICS has 11 letters but three of them come in pairs. Swapping identical letters changes nothing, so divide the overcount out.
Read the lesson »Circular permutations: a round table has no first seat
Seating 5 people round a table is not 5!. Spinning the table reseats nobody, so you divide by n and land on (n − 1)!.
Read the lesson »Combinations: when order does not matter
A committee of 3 from 8. Count the arrangements, work out how many times each group got counted, then divide the duplicates away.
Read the lesson »Sets and Venn diagrams
25 like Math and 8 like both — the 25 already contains the 8. Fill the overlap first, always.
Read the lesson »Sample space: listing outcomes
Count the list before you write it. The 6 × 6 grid for two dice, a fixed order for coins, and why (3, 4) and (4, 3) are two different rolls.
Read the lesson »Probability: “and” versus “or”
Or adds, then subtracts the overlap. And multiplies — and the deck shrinks between draws.
Read the lesson »Independent and dependent events
Does the first draw change the second? Without replacement both the top and bottom of the next fraction move.
Read the lesson »Conditional probability: “given that”
The condition throws people out of the room. Build the two-way table, divide inside one row, and never swap the two conditions around.
Read the lesson »Complementary events and “at least one”
At least one is the signal to work out the opposite. One multiplication instead of four cases, and no double counting.
Read the lesson »Odds versus probability
3 : 7 is not three sevenths. Odds compare the two camps; probability compares one camp to the whole crowd.
Read the lesson »Expected value
The average result over the long run. Value × probability, added, minus what it costs — zero is a fair game.
Read the lesson »Mean, median and mode
All three from one frequency table — and what happens to each when a single zero joins the data.
Read the lesson »Weighted mean
When exams count for half, the plain average is the wrong tool — and you may never average two averages of different-sized groups.
Read the lesson »Quartiles, IQR and box plots
Split the data in half, then split each half again. The 1.5 × IQR fences, and how to read a box plot properly.
Read the lesson »Range, variance and standard deviation
Distances from the mean always total zero, so square them first. Average the squares, then take the root.
Read the lesson »Geometric probability: area odds
A random point's probability is favourable area over total area — and similar shapes square the length ratio first.
Read the lesson »Exactly k successes: binomial probability
One order's probability times C(n, k) orders — and the misses carry their own (1 − p) factors.
Read the lesson »The normal curve: 68–95–99.7
Count the σ steps from the mean and the empirical rule hands you the percent — halved by symmetry for tails.
Read the lesson »Domain and range
Two rules ban everything else — never divide by zero, never even-root a negative. Then read the range off the shape.
Read the lesson »Piecewise functions
One function, two rules. Test the input against the condition, and watch the boundary — it belongs to exactly one piece.
Read the lesson »Function composition
One machine feeding another. The right-hand function runs first, and swapping the order changes the answer.
Read the lesson »Inverse functions: the function that undoes the function
Rewrite f(x) as y, swap x and y, solve and rename. The two graphs come out mirrored in the line y = x.
Read the lesson »Exponential equations
Same base on both sides and the exponents must match. When no common base exists, take logs.
Read the lesson »Exponential growth and decay
Growing 5% a year means multiplying by 1.05, once per year. Half-life is the same formula, counting halvings instead.
Read the lesson »Laws of logarithms
Multiply becomes add, a power becomes a coefficient. Expanding, condensing, change of base — and the laws that do not exist.
Read the lesson »Logarithmic equations: combine, then undo
log₃(x) + log₃(2) = 2. Two logs cannot be undone at once — the product rule squeezes them into one, and the base does the rest.
Read the lesson »Asymptotes of rational functions
Vertical walls at the denominator's uncancelled zeros; the horizontal from comparing degrees. Cancelled zero = hole.
Read the lesson »Limits: what a function approaches
Plug in first — and when 0/0 appears, it is not an answer, it is an instruction to factor and cancel.
Read the lesson »The derivative as slope
A curve has a slope at every point — the derivative is the slope machine, and the tangent line on the graph proves it.
Read the lesson »The power rule
Bring the power down in front, lower it by one — term by term, every polynomial falls in seconds.
Read the lesson »Maxima and minima with derivatives
Peaks and valleys hide where the tangent goes flat — set f′(x) = 0, solve, and let the sign change name each one.
Read the lesson »Antiderivatives: the reverse power rule
Raise the power by one, divide by it, and never lose the + C — then differentiate to check, because integration grades itself.
Read the lesson »Limits at infinity
Only the biggest powers matter: compare the degrees and the end behaviour — and the horizontal asymptote — read off in one glance.
Read the lesson »Area under a curve: the definite integral
Antiderivative at the top limit minus the bottom — one number, the area — then sanity-check it with plain geometry.
Read the lesson »The product and quotient rules
(uv)′ = u′v + uv′ — each factor takes a turn — and quotients follow low d-high minus high d-low, over low squared.
Read the lesson »The chain rule
Outside′ with the inside kept, times inside′ — the forgotten inside factor is THE chain-rule error.
Read the lesson »Continuity: when the pencil never lifts
Value exists, limit exists, they match — or the break is a hole, a jump or an asymptote, each with its own signature.
Read the lesson »The equation of the tangent line
Point from the curve, slope from f′ evaluated at the point, then point-slope form. The slope is a number, always.
Read the lesson »Simple interest
I = PRT, with the rate as a decimal and the time in years. Eight months is two thirds, not eight.
Read the lesson »Compound interest and depreciation
Interest that earns interest. The multiplier (1 + r) raised to the periods — and the same formula run backwards for depreciation.
Read the lesson »Successive discounts: 20% then 10% is not 30%
A ₱500 shirt cut twice lands on ₱360, not ₱350. Multiply what you keep — percents chain, they never add.
Read the lesson »Commission and tax: percents at work
Commission is rate × price; adding 12% VAT is × 1.12 — and removing it means ÷ 1.12, never taking 12% off.
Read the lesson »Installment buying: the real price
Down payment plus every monthly payment, minus the cash price — the finance charge is what paying slowly costs.
Read the lesson »Stuck on one of these?
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