Did you know? A learner can know exactly how to calculate 3(x + 2) and still lose time because a question says expand rather than evaluate. The two instructions ask for different outputs. Expanding changes the *form* of an expression; evaluating finds its *value* when the necessary numbers are known.
For Secondary 1 G3 Mathematics students in Bukit Timah, recognising command words is an essential part of reading a question. Solve, simplify, evaluate, factorise, estimate, round, explain and justify are not interchangeable. Each tells the pupil what mathematical work must be done and what kind of final answer is expected.
This Secondary 1 G3 Mathematics tutor guide explains the most useful command words with original worked examples, contrasts that reveal common mistakes and a practice diagnostic. It is written for students and parents who want clear answers without turning Mathematics into a dictionary of memorised keywords.
Find a Maths command word
- Quick answer: what the main Mathematics command words mean
- Evaluate: substitute, calculate and keep the meaning
- Simplify: change the form, not the value
- Expand: every term inside the bracket matters
- Factorise: the inverse direction of expansion
- Solve: find the unknown, not just a new form
- Solve versus simplify: a reliable comparison
- Find and calculate: what quantity does the question name?
- State: a direct answer may be enough
- Estimate: the answer should be approximate
- Round: read the requested precision
- Express and convert: change representation, not the amount
- Show that: provide a reasoned demonstration
- Explain, justify and give a reason
- Compare: use the same units and reference quantity
- Interpret: a graph is not just a picture
- Plot, sketch, draw and construct
- Determine: infer a value from the given conditions
- Twenty command-word practice questions
- Answer key: what each instruction requires
- Frequently asked questions
Quick answer: what the main Mathematics command words mean
- Evaluate: find the numerical value of an expression using the supplied values.
- Simplify: rewrite an expression in an equivalent, suitably simpler form.
- Expand: remove multiplication across brackets using the distributive law.
- Factorise: express a sum or expression as a product of factors, where applicable.
- Solve: find the value or set of values that satisfies an equation or comparison.
- Estimate: give a reasonable approximate answer rather than an exact calculation.
- Round: express a value to the requested accuracy or precision.
- Explain or justify: state the mathematical reason that makes a step or conclusion valid.
These descriptions are general guides; the full wording and context determine exactly what is needed. A question may combine several instructions, such as “expand and simplify” or “solve, giving your answer to two decimal places.”
The most useful habit is to underline the command word *before* writing a formula. Then read the requested unit and precision at the end of the question.
One algebra expression, four different questions
Consider the expression 4(x + 2).
If asked to expand, write 4x + 8. The answer is still an algebraic expression.
If asked to evaluate at x = 3, calculate 4(3 + 2) = 20. The answer is a number.
If asked to simplify 4(x + 2) − 2x, expand and collect to obtain 2x + 8.
If asked to solve 4(x + 2) = 20, write the equation, divide by four, then find x = 3.
The same bracket has appeared in all four tasks. A pupil who simply writes “20” whenever they see it may understand substitution but not what the instruction requests.
Evaluate: substitute, calculate and keep the meaning
To evaluate 2x² − 3 when x = −2, substitute the full negative value in brackets: 2(−2)² − 3.
The square of −2 is +4, so the expression becomes 2(4) − 3 = 5.
Writing 2−2² − 3 without clear brackets could change what is squared. The correct substitution shows that the entire negative number is the base.
A tutor should ask the student to name the value supplied for x and to identify the exact expression being evaluated. They are not being asked to solve for x, because the question already gives x.
For more examples of negative substitution, use the algebraic formulae guide.
Simplify: change the form, not the value
Simplify 3x + 2y − x + y.
Combine the x terms: 3x − x = 2x. Combine the y terms: 2y + y = 3y. The simplified result is 2x + 3y.
The values of x and y are not supplied, so you should not invent numerical values or claim the whole result equals five.
A simple test at x = 2 and y = 4 shows the original gives 6 + 8 − 2 + 4 = 16, while the new form gives 4 + 12 = 16. The check catches mistakes, but the valid like-term operation establishes algebraic equivalence in general.
A learner who writes 5xy has combined different variables as though addition meant multiplication. The command “simplify” never grants permission to change the operations.
Expand: every term inside the bracket matters
Expand 5(2x − 3).
Multiply five by 2x to obtain 10x. Multiply five by negative three to obtain −15. The expanded expression is 10x − 15.
Compare −2(x − 4). Its expansion is −2x + 8, since multiplying negative two by negative four gives positive eight.
If the child writes 5(2x − 3) = 10x − 3, the second term was not multiplied. If they write −2x − 8, the sign of the second product was lost.
Ask which exact multiplication was missing. The correction should target the operation, not simply tell the student to be more careful.
Factorise: the inverse direction of expansion
Factorise 12x + 18 by extracting the highest common numerical factor.
The coefficients 12 and 18 share HCF 6. Write 12x = 6(2x) and 18 = 6(3). Then the expression becomes 6(2x + 3).
Check by expanding: 6(2x + 3) = 12x + 18. The value has not changed.
The expression 3(4x + 6) is also mathematically equivalent, but it leaves a shared factor inside. When a question asks for complete factorisation by HCF, extract the greatest factor.
Notice how expand and factorise travel in opposite directions. Both should preserve the expression for every permitted x.
Solve: find the unknown, not just a new form
Solve 3(x − 2) + 5 = 20.
Expand: 3x − 6 + 5 = 20. Simplify: 3x − 1 = 20. Add one to both sides: 3x = 21. Divide by three: x = 7.
Check: 3(7 − 2) + 5 = 15 + 5 = 20.
The final answer is not 3x − 1, because that only simplifies one side of the equation. The instruction “solve” requires identifying a value that makes the original equality true.
In a more complicated equation, there might be no solution or more than one. The original equality determines which values are valid.
Solve versus simplify: a reliable comparison
Question A: “Simplify 2x + 3x − 4.” Answer: 5x − 4.
Question B: “Solve 2x + 3x − 4 = 11.” Combine like terms to get 5x − 4 = 11, then solve 5x = 15, so x = 3.
A student who writes x = 3 for Question A has invented the missing equals sign and comparison value. A pupil who stops at 5x − 4 for Question B has not finished solving.
One pair of questions, differing by only a short phrase and an equals sign, can reveal whether the child reads the actual command.
Find and calculate: what quantity does the question name?
“Find the area of this trapezium” tells you the requested quantity, but you still need to identify the parallel sides and perpendicular height.
Suppose the parallel sides are 10 cm and 16 cm and height is 6 cm. Area = 1/2 × (10 + 16) × 6 = 78 cm².
If the question instead asks to “calculate its perimeter,” you need the actual boundary side lengths. The two parallel sides and perpendicular height alone do not generally determine the lengths of both sloping sides, so the perimeter may be impossible to calculate exactly from the stated information.
This is a powerful reading habit: first identify what is requested, then ask whether sufficient data have been supplied.
State: a direct answer may be enough
“State the value of the gradient of y = 4x + 3” asks for the gradient, which is 4.
A lengthy derivation is not inherently necessary when the property is direct and the question does not request working. The coefficient of x is the gradient in the form y = ax + b.
However, if the question asks to *show how the gradient is obtained from two points*, a calculation such as (y₂ − y₁)/(x₂ − x₁) becomes relevant.
A good tutor teaches flexible presentation: brief for a genuine direct fact, more detailed when the reasoning is the object of the task.
Estimate: the answer should be approximate
Estimate 49.8 × 19.6 ÷ 10.2.
Use nearby convenient values: 50 × 20 ÷ 10 = 100 approximately.
The actual value is about 95.69, but the purpose of an estimation question is to produce a manageable approximation and, where relevant, show which values were rounded.
A pupil who writes only an exact calculator display may have ignored the request to estimate. A student who guesses 100 without any sense of the starting values may not be able to repeat the method with changed numbers.
Explain why your approximation is plausible.
Round: read the requested precision
Round 4.086 to two decimal places. The answer is 4.09, because the third decimal digit is 6 and the hundredths position rounds up.
Round that same number to two significant figures. The answer is 4.1. The first two significant digits are 4 and 0, and the next digit 8 causes the second to round up to 1.
Both answers are correct under their different instructions. They are not interchangeable because they refer to different kinds of accuracy.
For a value such as 9.968 rounded to two significant figures, write 1.0 × 10¹ to show two significant figures clearly.
Express and convert: change representation, not the amount
“Express 3/8 as a percentage.” First divide 3 by 8 to obtain 0.375; then multiply by 100% to get 37.5%.
“Convert 0.75 m² into cm².” One square metre equals 10,000 square centimetres, so the answer is 7500 cm².
The first task changes a fraction into a percentage. The second changes the measurement unit. Both preserve the underlying amount.
A pupil who writes 0.375% for 3/8, or uses a factor of 100 rather than 10,000 for an area conversion, has misunderstood the representation relationship.
The metric conversion guide explains squared and cubed units.
Show that: provide a reasoned demonstration
Suppose the question says “Show that the area of a trapezium with parallel sides 10 cm and 16 cm and perpendicular height 6 cm is 78 cm².”
The numerical result is already stated. The required work is to demonstrate it using a valid formula and substitution: A = 1/2(10 + 16) × 6 = 78 cm².
Simply copying “78 cm²” from the question demonstrates nothing.
Similarly, “show that x = 5 satisfies 2x + 3 = 13” asks for substitution: 2(5) + 3 = 13. It does not ask you to solve an unknown from scratch, although the check relates to the solution process.
A pupil should distinguish a supplied claim from the evidence required to support it.
Explain, justify and give a reason
Consider two co-interior angles between parallel lines, one measuring 112° and another x°.
The calculation 180 − 112 = 68 gives x = 68°. But the reason is that co-interior angles between parallel lines are supplementary.
If the question explicitly says “give a reason,” merely writing the numerical subtraction may not address the requested explanation. Conversely, writing “parallel lines” alone does not identify which particular angle property is being applied.
Good geometry reasoning connects the stated condition, the property and the calculation.
The show-working and mathematical-reasons guide explains how to make this evidence clear without unnecessary lines.
Compare: use the same units and reference quantity
“Compare 0.7 m and 65 cm.” First convert 0.7 m = 70 cm. Therefore 0.7 m is greater than 65 cm by 5 cm.
It would be meaningless to compare the raw digits 0.7 and 65 without considering the measurement units.
Now compare two fictional participation rates. Group A has 15 out of 30 students participating, or 50%. Group B has 18 out of 60 participating, or 30%. Group B has a larger count but a lower participation rate.
A comparison is only meaningful when the student names *which measure* is being compared—count, percentage, total cost or unit price.
Interpret: a graph is not just a picture
A cumulative-distance-time graph rises from 100 m at 2 min to 340 m at 6 min. A straight segment between those points has gradient (340 − 100)/(6 − 2) = 60 m/min.
Interpreting that gradient means saying the cumulative distance increased at a constant 60 metres per minute over the depicted straight segment.
If the vertical axis instead represents speed, the graph’s slope measures speed change per time rather than distance per time. Read axis labels before interpreting the line.
A correct numerical gradient without units or context may still be an incomplete interpretation of what the question asks.
Plot, sketch, draw and construct
“Plot the point (−3, 2)” requires placing it at the correct coordinate position: three units left and two units up from the origin.
“Sketch the graph of y = 2x + 1” generally asks for a shape showing key features such as its increasing straight line and y-intercept, rather than a highly precise graph unless the question says otherwise.
“Draw the graph using a given scale” expects accurate plotted points, axes and labels consistent with that scale.
“Construct a perpendicular bisector using ruler and compasses” expects a geometrically justified construction, including appropriate equal-radius arcs and a line through the midpoint at 90°, when those instruments are specified.
The words describe different expectations for precision and method. They are not simply decorative alternatives to “make a picture.”
Determine: infer a value from the given conditions
“Determine whether three lengths 3 cm, 4 cm and 7 cm can form a nondegenerate triangle.” The two shorter lengths sum to 7 cm, equal to the longest rather than greater.
So no proper triangle can be formed with those lengths. The segments would lie along one straight line in the limiting configuration.
The answer is not just a number. It is a yes-or-no conclusion supported by the relevant condition.
The same command might ask the child to determine a missing angle, a possible integer value or whether a proposed equation has a solution. Read the entire sentence to identify what must be established.
Do not choose a method from one keyword alone
A word problem may contain “total,” “more than” and “difference” in the same paragraph. A learner who simply adds whenever they see “total” could still misunderstand the relationship.
Suppose Aisha has three times Ben’s stickers and together they have 64. One Ben-part and three Aisha-parts make four total parts, so Ben has 64/4 = 16.
But if the same statement says Aisha has 32 *more* stickers than Ben, the difference is two equal parts. One part is 32/2 = 16.
The answers happen to agree in these deliberately linked examples, but the correct starting methods differ. Understanding the story beats memorising isolated keywords.
A combined question can contain several command words
A fictional task says: “Expand and simplify 2(x + 3) − (x − 4), then evaluate the expression when x = 5.”
Expand: 2x + 6 − x + 4.
Simplify: x + 10.
Evaluate: at x = 5, the value is 15.
These are three distinct outputs at three stages of the same question. Stopping after expansion leaves like terms uncombined. Stopping at x + 10 does not fulfil the final evaluation instruction.
The student can check the full original at x = 5: 2(8) − (1) = 15.
A short command-word comparison table
| Command word | Typical output | Example |
|---|---|---|
| Evaluate | A numerical value | 2x + 3 at x = 4 gives 11 |
| Simplify | Equivalent, simpler expression | 3x − x becomes 2x |
| Expand | Expression without the indicated product bracket | 2(x + 4) becomes 2x + 8 |
| Factorise | Product of factors | 6x + 12 becomes 6(x + 2) |
| Solve | Permitted solution values | 3x = 15 gives x = 5 |
| Estimate | Approximate number | 19.9 × 4.8 is about 100 |
| Explain | A valid reason | Co-interior angles sum to 180° |
| Convert | Same quantity in new units or form | 0.5 m² = 5000 cm² |
This is a guide, not a substitute for reading the full question. Some commands can require more than one step or a specified final presentation.
Four errors that reveal a command-word problem
Wrong task: the pupil evaluates an expression that the question asked to simplify, inventing a value for x.
Unfinished task: the pupil expands a bracket but stops even though the instruction was “expand and simplify.”
Wrong form: the pupil gives a decimal when the question specifically requests an exact fraction or a ratio in simplest integer form.
Missing reason: the pupil calculates an angle correctly but omits the requested justification.
These errors differ from ordinary multiplication or subtraction slips. The correction begins by restating the command word and the type of output expected.
Twenty command-word practice questions
For each question, first identify the instruction, then answer it in the required form.
- A. State the gradient of y = 3x + 5.
- B. Evaluate 2x² − 3 when x = −2.
- C. Simplify 3x + 2y − x + y.
- D. Expand 5(2x − 3).
- E. Factorise fully 12x + 18.
- F. Solve 4x + 7 = 31.
- G. Estimate 19.9 × 4.8.
- H. Round 4.086 to two decimal places.
- I. Round 4.086 to two significant figures.
- J. Express 3/8 as a percentage.
- K. Convert 0.75 m² to cm².
- L. Find the area of a trapezium with parallel sides 10 and 16 cm and perpendicular height 6 cm.
- M. Give a reason why two co-interior angles formed by parallel lines sum to 180°.
- N. Determine whether lengths 3, 4 and 7 cm form a nondegenerate triangle.
- O. Compare 0.7 m with 65 cm.
- P. Interpret the gradient of a distance-time line that rises 240 m in 4 minutes.
- Q. Plot the point (−3, 2); say which quadrant contains it.
- R. Solve 2(x − 3) + 4 = 12.
- S. Expand and simplify 2(x + 3) − (x − 4).
- T. Evaluate the simplified expression from S when x = 5.
Answer key: what each instruction requires
A. Gradient 3. The coefficient of x in y = 3x + 5 is three.
B. 2(−2)² − 3 = 8 − 3 = 5.
C. 2x + 3y, collecting only like variable terms.
D. 10x − 15, multiplying both terms by five.
E. 6(2x + 3), the HCF extraction.
F. x = 6, since 4x = 24 after subtracting seven.
G. Approximately 100, using 20 × 5.
H. 4.09, retaining two digits after the decimal point.
I. 4.1, retaining two significant digits.
J. 37.5%, since 3/8 = 0.375.
K. 7500 cm², multiplying by 10,000.
L. 78 cm², using half the sum of the parallel sides times the perpendicular height.
M. They are co-interior angles between parallel lines on the same side of the transversal, so their measures are supplementary.
N. No. The shorter sides sum to 7, not strictly greater than the longest side 7.
O. 0.7 m = 70 cm, which is 5 cm greater than 65 cm.
P. 240/4 = 60 m/min, meaning cumulative distance rises by sixty metres for each minute along that straight segment.
Q. Quadrant II, because x is negative and y is positive.
R. Expand to 2x − 6 + 4 = 12, giving 2x = 14 and x = 7.
S. 2x + 6 − x + 4 = x + 10.
T. At x = 5, x + 10 = 15.
A pupil who knows the calculations but answers a different command should receive a changed question with the same numbers and a different instruction. This isolates reading from arithmetic.
A ten-minute command-word drill
For three minutes, show pairs such as “simplify 2x + 3x” and “solve 2x + 3x = 20.” Ask the child to predict the final form before calculating.
For the next three minutes, compare “expand 3(x + 4)” with “evaluate 3(x + 4) at x = 2.” Explain why one answer contains x and the other does not.
For the final four minutes, mix a geometry “give a reason,” a rate “interpret,” and an exact “express as a percentage” question. The pupil should state in words what a correct answer ought to look like.
Repeat later with changed numbers. If the child can choose the required output without a cue, the command-word understanding is beginning to transfer.
What a parent can ask about a returned paper
Was the question misread before the calculation began, or was the correct task chosen but completed incorrectly? A learner who writes 2x + 8 for a “factorise” question has a command-word problem; one who writes 2(x + 8) for 2x + 8 has a factorisation arithmetic problem.
If a question required a unit or a reason, check whether the final answer included it. If it asked for two significant figures, inspect whether the learner applied decimal-place rules instead.
Don’t rewrite every answer for the child. Ask them to underline the instruction and predict the response format. That small reading habit can repair a surprisingly large number of avoidable mistakes.
A ninety-minute lesson for reading and mathematics together
An effective small-group session can begin with retrieval of six command words. Each student explains one aloud and gives a quick example.
The concept phase then compares nearly identical questions with different commands. Guided practice shows how the same expression changes when the request is to expand, simplify or evaluate.
Independent practice uses unfamiliar questions across number, algebra, geometry and data. The final review identifies whether any error occurred during interpretation, method selection or arithmetic.
In a maximum three-pupil tutorial, the tutor can hear each child’s explanation and correct the first wrong decision, rather than assume all pupils have the same reading or mathematical gap.
What to look for in Secondary 1 G3 support in Bukit Timah
Ask whether a tutor distinguishes weak Mathematics vocabulary from a weak mathematical concept. A child may know what a factor is yet not understand that “factorise” asks for a product expression. Another may interpret the command perfectly but be unable to find the HCF.
The eduKateSG Secondary 1 Mathematics small-group reference describes ninety-minute three-pupil tutorials near Sixth Avenue MRT. The Bukit Timah Secondary 1 G3 tuition overview provides location-specific context. Families should verify lesson suitability and current arrangements.
The MOE G2 and G3 Mathematics syllabus establishes the underlying content; a school’s specific assessment wording and marking scheme determine what is required in that task. This guide teaches language for mathematical reasoning, not unofficial guaranteed marks.
Frequently asked questions
Are simplify and solve the same instruction?
No. Simplify rewrites an expression in an equivalent form; solve finds values satisfying an equation or inequality.
What is the difference between expand and factorise?
Expanding distributes multiplication across bracketed sums. Factorising expresses an appropriate sum as a product of factors. They often reverse one another.
What if a question says “show that”?
The answer may already be supplied. You must demonstrate why it follows from valid steps rather than simply copy the stated result.
Why do estimate and calculate lead to different answers?
Estimation requests a reasonable approximate value. Calculation may request an exact result or a specified numerical precision. Read both the command and accuracy instruction.
Is “state” permission to omit all reasoning in every question?
No. It usually asks for a direct response, but the full wording may add conditions such as a unit or a short justification.
Do geometry questions always need a written reason?
Follow the instruction. If it asks for a reason, name the applicable property. Even when not required, a short reason can help the student check their own method.
What if my child knows English well but misreads Maths words?
Practise pairs of mathematically different commands using the same numerical expression. That isolates interpretation of the mathematical task from general language fluency.
How does this help with school assessments?
It helps the learner choose a valid method and finish in the requested form. Actual marks and marking requirements depend on the school assessment and its scheme.
Other Secondary 1 G3 Mathematics guides
- Showing working and mathematical reasons
- Translating word phrases into algebraic expressions
- Algebraic expressions, like terms and brackets
- Solving multi-step linear equations
- Significant figures and decimal-place rounding
- 2027 G3 topic map and prerequisites
The next time your child reaches for a formula, ask one question first: “What does the question want the answer to look like?” Getting that instruction right makes all the mathematical knowledge that follows much more useful.