A student entering a Punggol secondary school through Posting Group 2 (PG2) can learn G2 Mathematics indices by understanding the difference between a base and its exponent, why the laws of indices work, how negative and fractional powers are interpreted and when standard form makes very large or very small quantities easier to read. PG2 is an admission grouping under Full Subject-Based Banding, not automatically the level of every subject. A strong student checks each transformation against its mathematical meaning rather than treating exponent rules as a collection of shortcuts.

MOE’s G2 Mathematics syllabus includes work on positive, negative, zero and fractional indices, laws of indices and standard form as part of the secondary course, with particular advanced outcomes in the Secondary 3–4 sequence. The 2027 SEC G2 Mathematics K210 syllabus is for candidates graduating in 2027, not pupils starting Secondary 1 that year. Parents at Edgefield, Greendale, Punggol Secondary and Yusof Ishak Secondary should follow the current school topic list and use the examples here only when appropriate. This guide moves from repeated multiplication to precise exponent rules, scientific notation, calculator notation and error correction, using fictional data rather than made-up local measurements.

• PG2 vs G2: school admission grouping does not set all individual subject levels.
• Base and exponent: in 3⁴, the base is 3 and the exponent 4; the value is 81.
• Product: for the same nonzero base when defined, multiplying powers adds exponents.
• Quotient: dividing powers with the same nonzero base subtracts exponents.
• Power of a power: multiply the exponents in (aᵐ)ⁿ where the expression is defined.
• Zero and negative: a⁰ = 1 and a⁻ⁿ = 1/aⁿ for nonzero a in the relevant domain.
• Fractional: positive real roots can be expressed through fractional powers under appropriate conditions.
• Standard form: A × 10ⁿ, where 1 ≤ |A| < 10 and n is an integer for a nonzero number.
• Next step: explain one exponent law, verify it numerically and use it on a fresh question.

Definition lock: PG2 does not prescribe the exact indices lesson

Posting Group 2 is the admission route; G2 Mathematics is the curriculum level of a particular subject. A PG2-entry student may have a different subject-level offer in Mathematics, and even students taking G2 Mathematics can reach topics in a different school sequence. Indices are mathematical notation, not a separate posting pathway. The first responsible parent action is to read the child’s actual term notes and identify whether the class is currently learning basic square powers, integer indices or more advanced fractional powers.

A careful tutor diagnoses the missing prerequisite. A teenager who cannot multiply negative numbers accurately will struggle with some exponent expressions even if they remember a rule. Another may calculate powers correctly but misunderstand the meaning of a negative exponent. The teaching should address those specific gaps rather than force the whole Secondary 3–4 syllabus into the first week of Secondary 1. Clear progression makes advanced Mathematics more accessible.

What an index actually represents

In 3⁴, the number 3 is the base and 4 is the exponent or index. The expression means 3 × 3 × 3 × 3, which equals 81. The exponent counts repeated factors in this positive-integer example; it does not mean multiplying the base by the exponent. A learner who answers 12 has confused 3⁴ with 3 × 4. The notation is compact because it records an algebraic structure, not merely a large number.

Ask the pupil to expand 2⁵ as a product before calculating. Then compare with 5². The values are 32 and 25 respectively, so exchanging base and exponent generally changes the result. Once the meaning is secure, use letters such as x³ to represent x × x × x. The child can now see that exponent notation is a language for repeated multiplication.

Squares and cubes appear throughout secondary school

The second power is called the square of a number, and the third power is its cube. A square of side 5 cm has area 5² = 25 cm². A cube of edge 5 cm has volume 5³ = 125 cm³. These are not arbitrary nicknames: the units show why two or three independent length dimensions produce squared or cubed quantities. However, squaring a number in algebra does not automatically mean a particular geometric square is physically present.

Parents can use geometric models to explain the pattern without insisting that every power has a simple everyday shape. Once the student can explain 5² and 5³, the same notation applies to other bases, including variables and fractions. Ask the learner to connect the numerical calculation with its relevant context, not just pronounce the exponent correctly.

Brackets decide whether the negative sign is part of the base

The expressions (−3)² and −3² are different under conventional mathematical precedence. In (−3)², the base is −3, so the value is (−3) × (−3) = 9. In −3² without brackets, the exponent applies to 3 before the leading negative, so the value is −9. A student may miss this difference by applying the vague slogan ‘a square is always positive’.

Ask the teenager to expand each expression explicitly and compare results. The sign of a squared real number is nonnegative, but a negative sign outside the square can still make the whole expression negative. The same distinction matters in algebraic substitution. Brackets are part of mathematical meaning, not decoration added for neatness.

A negative base and a negative exponent are not the same

Compare (−2)³ with 2⁻³. The first is a negative base raised to a positive third power, giving −8. The second has a positive base raised to a negative exponent and equals 1/8. If the student treats every superscript minus as part of the base, the results will be wrong. The location of the sign determines which mathematical operation is being described.

Ask the child to identify the base and exponent separately before calculating. Then present another example with a negative base and negative exponent, such as (−2)⁻³ = −1/8. The sign and reciprocal rules both apply, but to different parts of the expression. Clear notation prevents mistakes that later propagate through equations.

The product rule comes from collecting equal factors

For a common base a, the law aᵐ × aⁿ = aᵐ⁺ⁿ applies where the expressions are defined. The simplest explanation uses positive integers: 2³ × 2² means five factors of two, yielding 2⁵ = 32. The exponent counts the total number of factors because multiplication of powers with the same base combines repeated copies of that base.

A frequent error is to write 2³ × 3² = 6⁵. The bases differ, so the common-base rule cannot simply be applied. Ask the learner to compute both sides numerically and compare. Another mistake is adding the exponents when the operation between the powers is addition rather than multiplication. The law belongs to a precise algebraic structure, not to every expression with superscripts.

The quotient rule uses cancellation of factors

For nonzero a, aᵐ ÷ aⁿ = aᵐ⁻ⁿ where the expressions are defined. Consider 5⁴ ÷ 5². The numerator contains four factors of five, and two cancel against the denominator, leaving 5² = 25. This explains why the exponents are subtracted. The restriction a ≠ 0 is important because division by zero is not defined.

A pupil may reverse the subtraction and write 5²⁻⁴, obtaining an unnecessary reciprocal. Ask which power appears on top and which appears below. Then use an example with the denominator’s exponent larger to introduce a negative result for the exponent rather than inventing an unrelated rule. Algebraic laws make sense when they preserve the value of the original expression.

Negative exponents describe reciprocals

For nonzero a, a⁻ⁿ = 1/aⁿ in the familiar integer-exponent setting. Thus 10⁻³ = 1/1000 = 0.001. The minus sign in the exponent does not make the value negative. For positive base 10, the answer remains positive. A student who claims 10⁻³ = −1000 has confused the sign of an exponent with the sign of the numerical value.

Ask the learner to extend the quotient law: 10² ÷ 10⁵ = 10⁻³, yet the numerical quotient is 100/100000 = 0.001. The two representations agree. This makes the reciprocal meaningful. The child should also learn that zero cannot be the base of a negative exponent in the standard real-number setting because it would require division by zero.

Zero exponents are a consistent extension

For nonzero a, a⁰ = 1. This follows from dividing a power by itself: a³ ÷ a³ = 1, and the quotient rule gives a³⁻³ = a⁰. Both expressions must represent the same value. Students may incorrectly state that anything to the power of zero becomes zero because they confuse multiplying by zero with an exponent of zero.

Ask the student to check a few nonzero bases, including fractions and negative numbers in valid contexts. Do not extend the rule uncritically to 0⁰; that expression is treated differently in different mathematical settings and is not covered by the simple nonzero-base law. A responsible lower-secondary explanation states the domain restriction and uses it consistently.

A power raised to another power multiplies exponents

The power-of-a-power law (aᵐ)ⁿ = aᵐⁿ is understood first through grouping repeated products. For (2³)², multiply two copies of 2³: 2³ × 2³ = 2⁶ = 64. The exponents multiply because the group of three factors appears twice. They are not added as 3 + 2, which would produce 2⁵ = 32.

Ask the child to compare expanding the grouped expression with applying the law. Both methods should agree. Then substitute a different base or variable to check transfer. Domain conditions become more important when fractional exponents are introduced, so do not present the symbolic rule as permission to ignore all real-number restrictions.

Powers of products distribute appropriately

For integer exponents, (ab)ⁿ = aⁿbⁿ under the relevant ordinary conditions. Consider (2 × 3)³ = 6³ = 216. Separately, 2³ × 3³ = 8 × 27 = 216. The result follows because each repeated group contains both factors. This law can simplify expressions with coefficients and variables.

But the same pattern does not generally work with addition: (a + b)² is not equal to a² + b². For a = 2 and b = 3, the left side is 25 while the right side is 13. A child who treats a bracket as a licence to distribute an exponent across a sum needs a correction about algebraic structure, not more memorised index rules.

Powers of fractions apply to numerator and denominator

When the denominator is nonzero, (a/b)ⁿ = aⁿ/bⁿ for familiar integer exponents and relevant domain conditions. For example, (2/3)² = 4/9. A student who squares only the numerator and writes 4/3 has changed the value. The same principle can be shown through multiplying two copies of 2/3.

Ask the child to estimate before calculating: the square of a positive proper fraction between zero and one is smaller than the original fraction. Since 4/9 is below 2/3, the result is plausible. Estimation becomes a useful independent check. If the child obtains a value above one, inspect the treatment of the denominator.

Fractional powers and roots must be tied together

For a nonnegative real number a, a¹ᐟ² represents the principal square root of a. Therefore 25¹ᐟ² = 5. Likewise 8¹ᐟ³ = 2, the real cube root of eight. Fractional exponents extend the index language so powers and roots can be expressed in one notation. But real-domain restrictions matter, especially for even roots of negative numbers.

A common confusion is that 25¹ᐟ² means 25 divided by two, giving 12.5. That is incorrect. Ask which number squared gives 25, then connect the answer to the fractional power. The root is a mathematical operation, not a disguised division by the exponent denominator.

The principal square root has one designated nonnegative value

The symbol √25 denotes the principal nonnegative square root, which is 5. By contrast, the equation x² = 25 has two real solutions, x = 5 and x = −5. Students often write ±5 after every square-root symbol without distinguishing an operation from solving an equation. The two tasks are related but not identical.

Ask the teenager whether the question asks for the value of an expression or all solutions to a condition. Then verify by squaring candidate solutions when solving an equation. Precise notation protects against recurring errors in indices, coordinate geometry and algebra. The aim is understanding what each symbol asks the student to do.

Fractional exponents combine roots and powers

For positive real a, aᵐᐟⁿ can be interpreted as the nth root of a raised to the mth power in an appropriate order. For example, 16³ᐟ⁴ = (16¹ᐟ⁴)³ = 2³ = 8. A student might mistakenly multiply 16 by three-quarters or divide the exponent’s numerator and denominator independently. The fractional exponent is one operation involving powers and roots.

Ask the learner to check the result in stages. First identify the relevant root, then apply the power. Use simple perfect powers for the first examples so the arithmetic does not obscure the concept. Introduce more complicated cases only when the current school syllabus calls for them.

Not every exponent expression is a real number

In the usual real-number setting, an even root of a negative number is not defined as a real number. For instance, (−16)¹ᐟ² does not have a real value. An odd root can behave differently: the real cube root of −8 is −2. Students may try to apply the same manipulation across all negative bases without checking whether the expression exists in the specified domain.

At the appropriate course level, teach the restriction explicitly. If a problem gives a positive base, the difficulty may not arise. But the student should not believe the index laws override all domain constraints. Mathematical correctness includes knowing when a result is not defined in the system being studied.

Addition of powers is not the product law

The expression 2³ + 2⁴ equals 8 + 16 = 24, not 2⁷ = 128. Adding exponents is valid for multiplication of powers with the same base, not for addition of their numerical values. A student who sees a superscript in every term may apply the wrong law by visual habit. The operator between the terms is crucial.

Ask the learner to circle the addition, multiplication or division sign before choosing a rule. In algebra, 3x² + 5x² can be combined as 8x² because they are like terms, but that is a different principle from multiplying powers to add exponents. Naming the operation and the reason prevents one shortcut from being misused everywhere.

Coefficients and exponents play different roles

In 4x³, the coefficient is 4 while the exponent belongs to x. The expression means four copies of x cubed, not (4x)³ unless brackets explicitly say so. The second expression expands to 64x³. A learner who ignores the placement of the brackets may multiply the coefficient by the exponent and obtain another incorrect form.

Use x = 2 to check: 4x³ = 4 × 8 = 32, while (4x)³ = 8³ = 512. The numerical contrast makes the difference obvious. This is an important transition from number powers to algebraic manipulation. A well-written expression tells the reader precisely which quantity is raised to a power.

Simplifying algebraic powers needs consistent bases

Consider 3x² × 2x³. Multiply the numerical coefficients to get six, and combine the common x factors to obtain x⁵. The result is 6x⁵. A student may incorrectly write 5x⁶ by adding coefficients and multiplying exponents. The operation should be separated into the coefficient calculation and the common-base index law.

Ask the teenager to expand one copy if necessary: three copies of x × x multiplied by two copies of x × x × x produce six copies of x⁵. The explanation establishes which quantities combine and how. A changed example involving two different letters can show whether the child respects separate bases. Algebra rewards precise grouping rather than one universal sign trick.

Standard form keeps a coefficient within a fixed range

Standard form, often called scientific notation, writes a nonzero quantity as A × 10ⁿ, where the magnitude of A is at least one and less than ten, and n is an integer. For example, 54,000 is 5.4 × 10⁴. Writing 54 × 10³ represents the same number but does not satisfy the standard coefficient range. Both numerical value and notation requirement matter.

Ask the pupil to read the coefficient aloud and verify the exponent through multiplication by a power of ten. The notation is useful because it makes a number’s scale visible. It is particularly valuable for quantities much larger or smaller than one, but it can also be used for ordinary numbers in a valid exercise.

Positive powers of ten make large numbers manageable

The number 7,200,000 can be written as 7.2 × 10⁶. Multiplying 7.2 by one million produces the original value. A student may count zeros incorrectly because the decimal point is shifted by the wrong number of places. The exponent records the scale factor, not a count of all digits in the coefficient and number together.

Ask the learner to reconstruct the number from the notation and compare. If the result has ten times the expected size, inspect the exponent. Estimation can support the check: a value around seven million should not become seventy million. Writing both representations and moving between them builds more reliable understanding than using a calculator key without context.

Negative powers of ten represent small positive values

The number 0.00042 equals 4.2 × 10⁻⁴. It is positive even though the exponent is negative. The factor 10⁻⁴ means one ten-thousandth, so multiplying by 4.2 yields 0.00042. A teenager who treats the exponent minus sign as a negative-value sign might incorrectly answer −4,200 or −0.00042.

Ask the child whether the original number is positive and less than one. Then select a form whose coefficient lies between one and ten and whose power of ten reduces the scale appropriately. Back-converting is an effective check. A small positive number can have a negative index without being negative itself.

Zero is a special case for ordinary standard form

The usual nonzero standard-form convention requires 1 ≤ |A| < 10, so zero does not fit it with a nonzero coefficient. In practice, zero may be written simply as 0 or sometimes 0 × 10ⁿ in other contexts, but that is not normalised scientific notation under the stated strict coefficient condition. The child should follow the exact requirement of the question and teacher.

This distinction matters because algebraic notation has conventions as well as numerical values. A student who understands the purpose of the coefficient range will not insist that every number, including zero, must be forced into one normalised pattern. Reading the definition carefully is part of solving the task correctly.

Calculator E notation must be interpreted carefully

Some scientific calculators display a large value as 5.4E6, meaning 5.4 × 10⁶. That notation is a compact way to express an exponent of ten; it is not the letter e from algebra inserted as an ordinary multiplier. Different calculator models use different keys or display styles, so refer to the actual school-approved device instructions.

A student should be able to translate a calculator display into ordinary standard form on paper and check the coefficient range. If a calculator outputs a rounded approximation, the number of significant digits shown may not preserve the exact value from the original task. Understanding the display is more important than learning which button to press by memory.

Multiplication in standard form combines scales

Consider (3 × 10⁴)(2 × 10³). Multiply coefficients to obtain six and add exponents of the common base ten, giving 6 × 10⁷. This follows from the product rule and ordinary multiplication. The calculation is easier to organise because the coefficient and scale are handled separately.

If the coefficient product exceeds the standard-form range, normalise it. For example, (6 × 10⁴)(4 × 10²) = 24 × 10⁶ = 2.4 × 10⁷. A student who stops at 24 × 10⁶ may have computed the correct value but not the requested normalised representation. Show why shifting the coefficient one place changes the exponent in the opposite compensating direction.

Division in standard form uses the quotient law

For (8 × 10⁶)/(2 × 10²), divide the coefficients to get four and subtract the exponents to obtain 4 × 10⁴. The result is 40,000. The denominator is nonzero, as required for division. A teenager who adds the exponents when dividing will produce a value many orders of magnitude too large.

Ask the learner to estimate first: eight million divided by two hundred should be about forty thousand. That sense of magnitude catches incorrect powers. Then compare the standard-form result with ordinary division. Different representations provide an independent verification and make index laws practical rather than abstract.

Addition in standard form needs compatible scales

Unlike multiplication, adding two standard-form quantities generally requires expressing them with a common power of ten or converting carefully. For example, 3 × 10⁴ + 2 × 10³ equals 30,000 + 2,000 = 32,000 = 3.2 × 10⁴. Simply adding coefficients and exponents to produce 5 × 10⁷ is incorrect.

Ask why different powers of ten behave like different place values. Converting both quantities to the same scale allows meaningful addition. A child should recognise that 30,000 and 2,000 are not equal-sized units. The skill connects standard form with place value rather than relying on an unexamined formula.

Significant figures and standard form are related but separate

Standard form makes the scale explicit, while significant figures communicate numerical precision under a given convention. The value 5.40 × 10⁴ is numerically 54,000 and commonly conveys three significant digits when used as a measured quantity. Writing 5.4 × 10⁴ expresses the same numerical value but may imply a different level of stated precision. The original question’s context matters.

A student should not treat extra zeros as decorations when a measurement is being reported. If the task asks for two significant figures, round appropriately and preserve the scale. If it asks only for exact algebraic conversion, do not invent a measurement uncertainty. Precision and notation serve different purposes and should be taught separately.

A fictional Punggol technology context

Imagine a made-up engineering worksheet describing a sensor measuring 0.0000062 units of a specified quantity. The student converts this to 6.2 × 10⁻⁶ units and explains the negative exponent. This is a fictional number, not a real Punggol Digital District sensor reading or verified scientific measurement. Its value lies in providing a reason to use standard form for a small quantity.

Ask the child to back-convert, check the sign and state the unit supplied by the scenario. Do not insert an invented micro-unit or claim a real instrument achieved that reading. A well-labelled hypothetical problem can teach the same Mathematics without manufacturing technical facts about local facilities.

A fictional large-number comparison

Imagine a worksheet describing two invented data-file sizes of 3 × 10⁶ and 7 × 10⁵ bytes. The first is three million bytes, the second is seven hundred thousand bytes. Their sum is 3.7 × 10⁶ bytes. The problem is about powers and place value rather than any real school’s storage system or device policy.

Ask the student to explain which number is larger before doing addition. The exponent gives a strong clue but the coefficient also matters, especially when the exponents are equal. A correct comparison and sum show that the learner understands magnitude. A fresh example with a coefficient product above ten can test normalisation independently.

A fictional student misuses the product law

Imagine a fictional PG2 entrant, Mira, who simplifies x² + x³ as x⁵. Her teacher asks which operation lies between the terms and contrasts it with x² × x³. Mira learns that the index product law applies to multiplication, not addition. She then checks both expressions at x = 2: 4 + 8 = 12, while 4 × 8 = 32. The numerical test exposes the original mistake.

This invented example is not a testimonial. The important repair is recognising the algebraic structure, not memorising a different answer for one worksheet. The next question should change the variables and exponents to confirm transfer. A child who explains the rule in an unfamiliar setting has learned more than one who copies the corrected line.

Another fictional student reverses a negative exponent

Imagine a learner, Daniel, who writes 10⁻² = −100 because the superscript carries a minus sign. His tutor asks him to express the power as a reciprocal of 10². Daniel obtains 1/100, a positive number smaller than one, and connects it to 0.01. He then converts a new small positive value into standard form without hints.

The teaching success lies in understanding sign and magnitude independently. Many children confuse a negative number with a negative power; a clear contrast can repair the misconception quickly. The story is fictional, and no particular improvement timeline or examination grade is promised. A responsible tutor looks for the first incorrect interpretation and teaches the missing principle.

A six-stage study routine rather than endless worksheets

Begin with repeated multiplication and the meanings of base and exponent. Next, explore the product and quotient laws through expanded factors. Then compare zero and negative powers, checking domain restrictions. After that, introduce fractional powers and roots only when the actual syllabus requires them. Move to standard-form conversions, then finish with mixed operations and one word problem that requires numerical interpretation.

Keep the practice suited to the child’s current class, homework, CCA and rest. A family can revisit an earlier concept after a gap to strengthen retrieval. Do not demand full coverage of upper-secondary indices from a new Secondary 1 pupil whose fractions are still unstable. A short independent explanation of a changed example is a stronger indicator than a large stack of completed mechanical drills.

How to diagnose an indices error

When a student gives a wrong result, ask whether the problem concerns base identification, arithmetic, an exponent law, brackets, sign, or standard-form normalisation. These are not interchangeable. The expression x² × x³ may be simplified correctly even while its numerical evaluation is wrong because the child substituted a negative value incorrectly. Find the earliest invalid step before prescribing another exercise.

A useful error log records the original expression, the false assumption and the corrected principle. The student then solves a different example and explains why the law applies. If a misconception returns, use a simpler representation, such as expanded factors or a fraction. The purpose is durable transfer, not simply covering a chapter.

Checking answers through estimates and inverse operations

Estimation can reveal an impossible scale: 4 × 10⁸ is four hundred million, not forty thousand. Reciprocal checks can verify negative exponents, while numerical substitution can test algebraic identities for selected valid values. A numerical check is useful evidence of a particular error but does not replace a general algebraic proof; two different expressions can coincide at one test value by chance.

Teach the learner to combine checks appropriately. Does the result have the right sign, approximate magnitude and mathematical structure? Does the coefficient meet the standard-form range? Are all denominators nonzero? Asking these questions encourages the student to monitor work independently, a foundational goal of small-group tutorial feedback.

What parents should not claim about the national examination

The 2027 K210 SEC syllabus applies to candidates graduating in that year. A pupil beginning Secondary 1 in 2027 belongs to a later cohort, and the syllabus may be updated before their examination. Parents should not impose every current graduating topic on the first-year timetable or promise that mastering one chapter guarantees promotion between subject levels. School decisions follow the relevant criteria and evidence of learning.

The useful long-term principle remains: powers represent relationships, index laws preserve values under suitable conditions, and standard form communicates magnitude efficiently. A child who understands those ideas deeply is better prepared for later algebra and scientific calculation. Correct cohort information protects families from unnecessary pressure and misleading claims.

Sources and Your Next Step

MOE’s G2 and G3 Mathematics Syllabuses specify indices, laws and standard form in the relevant secondary sequence, while SEAB’s 2027 G2 syllabus index identifies Mathematics K210 for its graduating candidates. The immutable Clementi tutorial reference demonstrates the value of identifying the first unstable reasoning step before increasing question difficulty.

For number foundations see the PG2 negative numbers, fractions and estimation guide. For algebraic modelling rather than exponent laws, use the separate Algebra Word Problems guide. Your next step is to choose one school-appropriate index question, ask the child to state the operation before selecting a rule and then verify the result using expanded factors or a numeric check.

Frequently asked questions about PG2 G2 Mathematics indices and standard form

Is PG2 the same as taking every subject at G2?

No. PG2 is the admission group, and subject levels are individually offered under Full SBB.

What does 3⁴ mean?

Four repeated factors of three, giving 81, not 3 multiplied by 4.

When can exponents be added?

When multiplying powers with the same base under the appropriate index-law conditions.

Is x² + x³ equal to x⁵?

No. That law applies to multiplication, not addition.

Why is 10⁻³ positive?

A negative exponent represents a reciprocal: one divided by 10³.

What is a⁰ for nonzero a?

One, consistent with the quotient law.

Why is (−3)² different from −3²?

Brackets determine whether the negative sign belongs to the squared base.

What does 25¹ᐟ² represent?

The principal square root, which is 5.

How do I write 0.00042 in standard form?

4.2 × 10⁻⁴.

Does the 2027 SEC K210 syllabus dictate a 2027 Secondary 1 pupil’s timetable?

No. It applies to that year’s graduating candidates; follow the student’s current school sequence.

Editorial note: Published 1 November 2026. All numerical technology and student scenarios are illustrative, not live Punggol measurements. Upper-secondary index content should be taught only when appropriate to the actual class. The 2027 K210 SEC examination applies to that year’s graduating cohort.