GRE Algebra Guide for Nepali Students

GRE Algebra Guide for Nepali Students explains expressions, exponents, factoring, equations, inequalities, functions, coordinate geometry, word-problem modelling and efficient practice. Use this guide to turn familiar school mathematics into accurate GRE decisions, not just longer calculations.

Information checked on 24 July 2026 against the current ETS Quantitative Reasoning overview, Math Review, official strategies and POWERPREP information. Confirm test details with ETS before test day.

Key facts at a glance

Understand the official algebra scope

ETS lists operations with exponents, factoring and simplifying expressions, relations, functions, equations, inequalities, linear and quadratic equations, simultaneous equations and inequalities, word-problem modelling and coordinate geometry. Coordinate topics include graphs, intercepts and slopes of lines.

The Quantitative content is generally no higher than a second high-school algebra course. GRE algebra is less about advanced theory and more about translating information, choosing an efficient representation and respecting restrictions.

Separate expressions from equations

An expression can be simplified or evaluated but does not assert equality. An equation states that two expressions are equal and can be solved under given conditions. Keep this distinction clear when a prompt asks for a value versus an equivalent form.

Combine only like terms. Distribution applies across every term inside parentheses. When substituting a negative number, use parentheses so exponents and signs remain attached to the intended base.

Track restrictions before simplifying

Record denominator restrictions, even if a factor later cancels. Cancelling can produce an equivalent expression only on the original domain. A value that makes the original denominator zero remains excluded.

For square roots in real-number questions, the radicand of an even root must be nonnegative. Restrictions are not an afterthought; they determine which transformations and solutions are valid.

Use exponent rules with matching bases

For the same nonzero base, multiplication adds exponents, division subtracts them and a power raised to a power multiplies exponents. A negative exponent creates a reciprocal, and a zero exponent equals 1 for a nonzero base.

Do not distribute powers over addition or subtraction. Expand a small case to test a suspected identity. Algebra errors often come from applying a correct rule to the wrong structure.

Factor before expanding blindly

Look first for a greatest common factor, then familiar patterns such as a difference of squares or a quadratic trinomial. Factoring can reveal zeros, cancellation and comparison relationships faster than expansion.

Expansion is useful when you need combined coefficients or a standard form. Choose the representation that exposes the question’s target instead of performing both operations automatically.

Solve linear equations cleanly

Preserve equality by performing the same valid operation on both sides. Clear fractions when helpful, distribute carefully, collect variable terms and constants, then isolate the variable.

Classify unusual results. A true statement such as 0 = 0 indicates infinitely many solutions under the original restrictions. A contradiction such as 0 = 5 indicates no solution.

Handle linear inequalities

Solve an inequality much like an equation, but reverse the inequality direction when multiplying or dividing both sides by a negative number. Represent the final solution on a number line or in interval form when useful.

When the sign of an expression is unknown, do not divide by it casually. Split into sign cases or move terms and use a sign chart. Always test a value from the proposed solution set.

Solve absolute-value equations and inequalities

Interpret absolute value as distance. If |x – c| = d with d positive, x lies d units from c and produces two possibilities. If the right side is negative, no real solution exists.

For inequalities, |x – c| d describes values outside that interval. Drawing a number line often prevents reversed endpoints.

Choose a method for simultaneous equations

Use substitution when one variable is already isolated or easy to isolate. Use elimination when coefficients align conveniently. Graphical interpretation can reveal whether two lines intersect once, coincide or remain parallel.

After finding one coordinate, substitute back into an original equation. A pair that satisfies only the transformed work but not both original equations is not a valid solution.

Solve quadratic equations strategically

Put the equation in standard form before factoring. If it factors cleanly, use the zero-product property. Otherwise consider completing the square or the quadratic formula, depending on what the question requires.

Remember that taking a square root while solving may create positive and negative possibilities. Check solutions in the original equation, especially when the problem includes denominators, roots or word-context restrictions.

Understand functions as input-output rules

Function notation f(x) means the output of f at input x; it does not mean f multiplied by x. Substitute the entire input wherever x appears. For f(a + h), use parentheses before simplifying.

Know domain and range, evaluate tables and formulas, and interpret graphs. A vertical-line test identifies whether a graph represents y as a function of x.

Read linear graphs

Slope measures change in y divided by change in x. A positive slope rises left to right, a negative slope falls, zero slope is horizontal and a vertical line has undefined slope. Intercepts occur where the graph crosses an axis.

Use y = mx + b when slope and y-intercept are useful, but also recognise standard form. Parallel nonvertical lines have equal slopes; perpendicular slope relationships require attention to zero and undefined cases.

Interpret equations and inequalities on the coordinate plane

An equation in x and y describes points satisfying an exact relationship. An inequality describes a region, often separated by a boundary line. Test a point to decide which side is included.

A solid boundary indicates inclusion for ≤ or ≥, while a dashed boundary indicates exclusion for . Do not estimate from a sketch when algebra can verify the relationship.

Translate word problems into variables

Define each variable with units before writing equations. Translate one relationship at a time, then check whether the number of independent equations matches the unknowns. Common models include totals, mixtures, rates, work, cost and consecutive numbers.

After solving, interpret the result in context. Reject negative lengths, fractional people or values outside stated ranges when the context forbids them.

Use answer choices as information

When options are numeric, backsolving can be faster than deriving a general formula. Start with a middle choice when the relationship is monotonic, then move according to whether the result is too high or too low.

For variable questions, choose simple values that satisfy all restrictions. One valid counterexample can show that a claimed relationship is not always determined, especially in Quantitative Comparison.

Handle Quantitative Comparison algebra

Simplify the difference between Quantity A and Quantity B when possible. Its sign directly describes the comparison. Factor the difference to expose how variable signs or ranges affect the result.

Do not assume variables are positive, integers or distinct unless stated. Test boundary values and different allowed signs. To choose a fixed relationship, it must hold for every permitted case.

Use the calculator selectively

The on-screen GRE calculator can help with lengthy arithmetic, but it does not choose the equation or detect an invalid domain. Keep symbolic work exact until a decimal is actually useful.

Estimate before entering values and check the output against sign and scale. Calculator keystrokes should support algebraic reasoning, not replace it.

Build an algebra error log

Classify misses as translation, distribution, sign, exponent, factoring, inequality reversal, domain restriction, extraneous solution, graph interpretation or time management. Write the exact line where the reasoning first failed.

Re-solve later from a blank page. Then create a small variation by changing a sign, restriction or coefficient. Transfer to a new case is stronger evidence of learning than remembering the old answer. Compare an alternate valid method when available, because agreement between substitution, factoring or graphical reasoning can expose a hidden sign error before timed habits become fixed.

Practise with official resources

Use the official ETS Quantitative Reasoning overview for current content and question formats. Study definitions, examples and exercises in the official GRE Math Review.

Move from untimed concept work to mixed timed sections. POWERPREP helps you practise current tools, navigation and review decisions. Analyse correct guesses and slow solutions, not only wrong answers.

Follow a seven-step algebra routine

Identify the response required; list restrictions; define variables; translate relationships; choose a representation; solve efficiently; then substitute and interpret. On comparison questions, test whether the result holds for every allowed case.

Write enough steps to protect signs and restrictions, but avoid unnecessary expansion. A short, visible chain of valid reasoning is easier to audit under time pressure.

Connect GRE work with the application

For university planning, documentation and overseas-study guidance, visit MKS Education. For structured GRE preparation and practice support, explore MKS Prep. Check every programme’s current GRE policy directly.

Use a diagnostic to choose algebra priorities, then retest under timed conditions. Coordinate test preparation with application deadlines and score-reporting time.

Frequently asked questions