Sec 2 G1 Maths Tutor Bukit Timah

Did you know? In Mathematics, simplify, solve and evaluate can use the same algebraic symbols but ask for different kinds of answers. A student might understand every operation and still lose marks by completing the wrong task. That is why reading the first verb matters just as much as reading the numbers.

Quick answer: read the command before the numbers

Before calculating, circle the instruction word: simplify, evaluate, solve, expand, form, estimate, interpret, explain, construct, compare or another verb. Then ask what kind of response the examiner is requesting—a numerical value, algebraic expression, equation, diagram, estimate, comparison or explanation. A correct-looking calculation does not complete a question if it returns the wrong kind of result.

This is a conversational guide for parents and tutors working with Secondary 2 G1 Mathematics students in Bukit Timah. It is not a dictionary of official marking verbs for every school. Questions differ by context, and some have two instructions. Always read the entire sentence and follow the teacher-issued topic list for the student’s current G1 subject level.

A practical quick-reference dictionary

Simplify: write an equivalent expression in a simpler form; do not invent a value for the unknown.
Evaluate: substitute given values or calculate the numerical value of an expression.
Solve: find the unknown value or values that satisfy the stated equation or condition.
Expand: multiply out bracketed products while keeping equivalence.
Form: translate a described relationship into an equation, expression or other requested model.
Determine/Find: identify the requested result using appropriate working; the type depends on the rest of the question.
State/List/Identify: report the requested fact, outcomes or class clearly.
Explain/Justify/Show that: communicate reasons or an argument, not merely a bare claim.
Plot/Sketch/Construct/Measure: produce or read a geometric or graphical representation as specified.
Estimate/Round/Calculate: distinguish an approximate check, specified output accuracy and exact calculation.

Three useful verb pairs to practise

Simplify is not the same as solve

Consider 3x+5x. To simplify, write 8x. Without an equals sign or a supplied value, no numerical x can be deduced. Now consider 3x+5x=24. This is an equation: combine like terms to obtain 8x=24, then solve x=3. A learner who writes x=8 for the first question is confusing the coefficient with an unknown’s value.

Evaluate may use a given value; solve must find it

Evaluate 2a+5 when a=4: substitute and obtain 13. Solve 2a+5=13: rearrange the equation and obtain a=4. The first task starts with the value of a and produces an output; the second starts with an output and finds the input. Tutors can deliberately reverse pairs like this to test whether a learner understands the role of the variable.

Estimate and calculate have different jobs

Estimate 49.8×3.9: a sensible answer is about 50×4=200. Calculate exactly: 49.8×3.9=194.22. If a question requests a rounded final answer, the rounding instruction may make yet another result appropriate. A learner who automatically rounds every quantity early can lose accuracy even though the underlying formula was correctly selected.

38 original Secondary 2 G1 question-verb clinics

Each example begins with the instruction, then shows the type of answer it requires. Cover the explanation, read the verb aloud and decide what you would write before doing the arithmetic. Use a few cases at a time; the goal is not to memorise 38 phrases, but to recognise a command even when the topic changes.

1. Simplify: what the instruction really asks

Question: Simplify 4x+3x−2.

The right response: Combine like terms: 7x−2. The expression still contains x; no numerical value for x is requested.

Common wrong task: Do not write x=7 or x=2. Simplifying does not automatically make a variable a known number.

Quick self-check: Substitute x=3: 4(3)+3(3)−2=19, matching 7(3)−2.

2. Evaluate: what the instruction really asks

Question: Evaluate 4x+3 when x=2.

The right response: Replace the symbol with its given value: 4(2)+3=11. This is a numerical output.

Common wrong task: Do not report 7x or collect unlike terms; the task asks for a value after substitution.

Quick self-check: Check that 4×2 is eight and the additional three is eleven.

3. Solve: what the instruction really asks

Question: Solve 4x+3=19.

The right response: Maintain equality: 4x=16, so x=4. The object to report is the unknown’s value.

Common wrong task: Do not stop at 4x=16, which is an intermediate equation rather than the value of x.

Quick self-check: Substitute four into the original equation to obtain nineteen.

4. Expand: what the instruction really asks

Question: Expand 3(x+5).

The right response: Distribute the three across the two bracketed terms: 3x+15. The brackets are removed without changing the expression’s value.

Common wrong task: The answer 3x+5 leaves the constant unmultiplied and is not equivalent.

Quick self-check: At x=2, 3(7)=21 and 3(2)+15=21.

5. Simplify after expansion: what the instruction really asks

Question: Simplify 2(x+3)+4x.

The right response: Expand to 2x+6+4x, then collect like terms: 6x+6.

Common wrong task: Stopping at 2x+6+4x has expanded but not fully simplified, which the instruction also requests.

Quick self-check: Test x=1: original and final each give twelve.

6. Write an expression: what the instruction really asks

Question: Write an expression for seven more than twice n.

The right response: Twice n is 2n; seven more gives 2n+7. The task asks for an expression, not a numerical solution.

Common wrong task: Writing 7−2n reverses the relationship; writing n=7 assumes information not supplied.

Quick self-check: Use n=3 to check that twice three plus seven is thirteen.

7. Form an equation: what the instruction really asks

Question: Six more than three times a number equals 24. Form an equation.

The right response: Let x be the number and write 3x+6=24. That completes ‘form’ before a separate instruction to solve.

Common wrong task: Writing a value of x without first showing the equation obscures the required model.

Quick self-check: Check that the words ‘equals 24’ correspond to the equals sign.

8. Form and solve: what the instruction really asks

Question: Form an equation and find the number if three times it plus six is 24.

The right response: Write 3x+6=24, then 3x=18 and x=6. Both tasks must be addressed.

Common wrong task: Only forming the equation leaves the ‘find’ request unanswered.

Quick self-check: Check 3×6+6=24.

9. State: what the instruction really asks

Question: State the number of sides of a hexagon.

The right response: A hexagon has six sides. A short factual answer is appropriate.

Common wrong task: Do not pad a direct factual request with unrelated formula calculations.

Quick self-check: Count six straight boundary segments on a labelled sketch.

10. List: what the instruction really asks

Question: List the even numbers on a fair six-sided die.

The right response: The set is 2, 4, 6. List each relevant outcome once.

Common wrong task: Reporting only the probability 1/2 does not satisfy a request to list outcomes.

Quick self-check: Check all six faces against divisibility by two.

11. Find the probability: what the instruction really asks

Question: A fair die is thrown once. Find P(even).

The right response: Three eligible equally likely outcomes out of six give 3/6=1/2.

Common wrong task: The list {2,4,6} is useful working, but the requested answer is a chance.

Quick self-check: Check the result lies between zero and one.

12. Give a reason: what the instruction really asks

Question: Explain why vertically opposite angles are equal.

The right response: When two straight lines intersect, the vertically opposite angles each supplement the same adjacent angle to 180°, so they are equal.

Common wrong task: Stating ‘because it looks equal’ does not identify a geometric property.

Quick self-check: Draw four angles around a point and show the two straight-line sums.

13. Measure: what the instruction really asks

Question: Measure a drawn line segment AB using a ruler.

The right response: Place the ruler’s zero mark at A and read the length at B, reporting the number with a length unit. The actual answer depends on the printed drawing.

Common wrong task: Inventing a length from the text or starting at the physical edge of a ruler is unsupported.

Quick self-check: Repeat from a different pair of ruler marks to verify the same length.

14. Construct: what the instruction really asks

Question: Construct the perpendicular bisector of AB with compass and ruler.

The right response: Use equal-radius arcs centred at A and B, above and below the segment, then join their intersections. The line crosses AB at its midpoint at 90°.

Common wrong task: A line that merely looks upright is not evidence of a compass construction.

Quick self-check: Check equal half-lengths and a right angle; retain necessary construction arcs.

15. Draw: what the instruction really asks

Question: Draw a triangle with a right angle at B.

The right response: Draw three vertices A, B, C, with BA perpendicular to BC and mark the 90° angle at B.

Common wrong task: A right-angle mark at A or C answers a different drawing request.

Quick self-check: Name the side opposite B as hypotenuse AC, regardless of orientation.

16. Sketch: what the instruction really asks

Question: Sketch the graph y=2x+1 using two accurate points.

The right response: At x=0, y=1; at x=1, y=3. Mark (0,1) and (1,3) on labelled axes and draw the straight line.

Common wrong task: A decorative upward line with no scale or checked points may miss the intercept.

Quick self-check: Substitute a third point (2,5) to check the line’s direction and position.

17. Complete the table: what the instruction really asks

Question: For y=3x+2, complete outputs at x=0,1,2.

The right response: The y-values are 2, 5, 8 in the same row order.

Common wrong task: Changing the x values or reading a different table column misrepresents the task.

Quick self-check: Check differences between successive y values are three.

18. Plot: what the instruction really asks

Question: Plot the point P(−2,3).

The right response: Begin at origin, move two units left and three up, then label the point P.

Common wrong task: Moving left and down because a negative sign appears ignores the sign of y.

Quick self-check: Trace horizontally and vertically back to the corresponding axis values.

19. Read from a graph: what the instruction really asks

Question: A labelled straight-line graph passes through (0,2) and (2,8). What y-value should be read at x=1?

The right response: The line has constant gradient three, so at x=1 its y-value is 5.

Common wrong task: Reporting the x-coordinate one or reading a grid square without consulting the scale.

Quick self-check: Check that (1,5) sits halfway between the two given points.

20. Calculate gradient: what the instruction really asks

Question: Find the gradient of a line passing through (1,2) and (3,6).

The right response: Vertical change 4 divided by horizontal change 2 gives 2.

Common wrong task: Reversing the ratio gives 1/2, an answer to a different ratio.

Quick self-check: One extra x-unit changes y by two.

21. Compare: what the instruction really asks

Question: Two hypothetical packs cost $10 for 2 kg and $12 for 3 kg. Compare unit prices.

The right response: Pack A costs $5/kg and Pack B $4/kg; B costs $1 less per kg.

Common wrong task: Comparing ticket totals alone ignores different quantities.

Quick self-check: State the common unit and the actual difference.

22. Explain: what the instruction really asks

Question: Explain why 0.4 is greater than 0.35.

The right response: Rewrite 0.4 as 0.40; forty hundredths exceeds thirty-five hundredths.

Common wrong task: A bare ‘yes’ or greater-than symbol is not the explanation requested.

Quick self-check: Locate both numbers on a number line between 0.3 and 0.5.

23. Show that: what the instruction really asks

Question: Show that a triangle with sides 6,8,10 cm is right-angled.

The right response: Use the converse: 6²+8²=36+64=100=10², so a 90° angle lies opposite the 10-cm side.

Common wrong task: Simply declaring ‘it is a 6–8–10 triple’ skips the justification.

Quick self-check: Name the longest side before comparing squares.

24. Justify: what the instruction really asks

Question: Justify that y=3x is directly proportional to x.

The right response: For nonzero x, y/x=3 is constant, and the relation passes through the origin. This supports direct proportion.

Common wrong task: Claiming every increasing linear relationship is direct proportion ignores nonzero intercepts.

Quick self-check: Contrast with y=3x+2, where the quotient changes with x.

25. Estimate: what the instruction really asks

Question: Estimate 49.8×3.9.

The right response: Use nearby simple factors 50×4≈200; this is an estimate, not the exact product.

Common wrong task: Giving a calculator’s many-digit output fails to demonstrate estimation.

Quick self-check: Exact product 194.22 is reasonably near 200.

26. Calculate exactly: what the instruction really asks

Question: Find 5/6−1/4 exactly.

The right response: Use twelfths: 10/12−3/12=7/12. The fraction is exact.

Common wrong task: Reporting 0.583 without accuracy instruction needlessly discards the exact value.

Quick self-check: Check 7/12≈0.5833 and is smaller than 5/6.

27. Round to decimal places: what the instruction really asks

Question: Round 17.486 to two decimal places.

The right response: Keep hundredths and inspect thousandths six: 17.49.

Common wrong task: Keeping 17.48 by truncation ignores rounding.

Quick self-check: Two digits remain after the decimal point.

28. Round to significant figures: what the instruction really asks

Question: Round 0.00467 to two significant figures.

The right response: The first two significant digits are four and six; seven rounds to 0.0047.

Common wrong task: Counting leading zeros as significant produces a different value.

Quick self-check: The number 0.0047 has two significant digits, four and seven.

29. Interpret: what the instruction really asks

Question: A simple graph shows distance increasing by 12 m in four seconds at constant rate. Interpret the gradient.

The right response: Gradient is 3 m/s, meaning distance increases by three metres per second in that model.

Common wrong task: Reporting gradient as three without units loses the physical interpretation.

Quick self-check: 12 m÷4 s=3 m/s; a positive gradient means distance rises with time.

30. Describe: what the instruction really asks

Question: Describe what happens to y as x increases in y=−2x+5.

The right response: The y-value decreases by two for each increase of one in x.

Common wrong task: ‘It gets negative’ is not always true because y can initially be positive.

Quick self-check: Compare y=5 at x=0 with y=3 at x=1.

31. Determine whether: what the instruction really asks

Question: Determine whether the sequence 3,6,9,12 follows 3n for positions n=1,2,3,4.

The right response: Yes: 3n gives 3,6,9,12 at those positions. Test all displayed terms before making the claim.

Common wrong task: Guessing that it fits merely because multiples of three are present.

Quick self-check: At position five, the proposed rule predicts fifteen.

32. Find the range: what the instruction really asks

Question: For observations 2,4,4,7,9 find their range.

The right response: Largest minus smallest: 9−2=7.

Common wrong task: Reporting seven as the number of observations confuses range and sample size.

Quick self-check: Five observations can have a range of seven.

33. Find the median: what the instruction really asks

Question: For 2,4,4,7,9, find the median.

The right response: The values are sorted; the middle is the third value, 4.

Common wrong task: Dividing the total sum by five calculates a mean instead.

Quick self-check: Changing the largest value from nine to thirty keeps the median at four.

34. Identify the modal class: what the instruction really asks

Question: Histogram frequencies are 2,6,4 for equal-width classes 0–under5, 5–under10, 10–under15. Identify modal class.

The right response: The class 5 to under 10 has highest frequency six.

Common wrong task: Calling 7.5 the exact individual mode invents information not present in grouped data.

Quick self-check: A grouped histogram does not generally reveal the raw individual values.

35. Check your answer: what the instruction really asks

Question: Solve 2x+5=19 and check your answer.

The right response: Subtract five and divide by two: x=7. Substitution yields 2(7)+5=19.

Common wrong task: Stopping at x=7 despite an explicit request to check leaves the task incomplete.

Quick self-check: Explain why a true substituted equality verifies this candidate.

36. Explain units: what the instruction really asks

Question: A rectangle has sides 5 cm and 3 cm. Find its area and state units.

The right response: Area=5×3=15 cm² because length times length gives square centimetres.

Common wrong task: Reporting 15 cm confuses a boundary length with covered surface.

Quick self-check: The perimeter of the same rectangle is 16 cm, not 15.

37. Give an answer to a requested accuracy: what the instruction really asks

Question: Compute √74 cm to three significant figures.

The right response: The square root is about 8.602325; to 3 s.f. give 8.60 cm.

Common wrong task: Reporting 8.6 is two significant figures, not three.

Quick self-check: Because 8.6² is about 73.96, the rounded result is plausible.

38. Complete and explain: what the instruction really asks

Question: A card shows 4,7,10,13,… . Complete the next two values and explain the rule.

The right response: The next terms are 16 and 19; each term rises by three.

Common wrong task: Listing 16,19 without explanation does not meet the second command.

Quick self-check: Check successive differences from the beginning are always three.

How a tutor can teach question-reading without slowing every answer

Step 1: underline the verb and the answer noun

For a percentage question, ‘Find the discount’ and ‘Find the price after discount’ produce different numbers. Underline both the verb and its object. For a graph, ‘plot the points’ is not the same as ‘interpret the gradient’. This quick practice stops the learner from answering the first familiar sub-question instead of the question actually printed.

Step 2: predict the form of the result

Before calculation, ask: will this answer be an algebraic expression, a value for x, a sentence, a probability fraction, a line drawing, centimetres, square centimetres or kilometres per hour? A quick predicted answer form helps catch mismatches. It also makes the unit part of the instruction rather than a detail added reluctantly at the end.

Step 3: change only the verb

Give the same information in two forms. First ‘Simplify 2x+3x’; next ‘Solve 2x+3x=20’. Or first ‘Find the saving on $80 with 25% off’; next ‘Find the final payment’. With numbers held nearly constant, the changed verb becomes the only important difference. The student learns to respond to meaning rather than searching for a familiar number pattern.

Step 4: check whether every command has been satisfied

A question can say ‘Form an equation and solve it’, or ‘Find the answer and explain why it is reasonable’. Treat each instruction as a small requirement. On finishing, return to the printed question and check the list of requested outputs, without assuming a correct numeric answer covers an explanation, diagram or units automatically.

Five short parent–student practice sessions

Day 1: compare simplify, evaluate and solve with one expression and one equation.
Day 2: ask for a percentage saving, then the final payment from identical data.
Day 3: distinguish state, list and explain in probability or geometry.
Day 4: compare sketch, plot, measure and construct using real tools and a labelled diagram.
Day 5: mix six instructions and ask the learner to predict the answer form before completing them.

A parent does not have to know every mathematical formula. Ask ‘What does the verb ask you to do?’, ‘What kind of answer will you return?’, and ‘Have you completed all parts of the instruction?’ The learner should be able to answer those three questions without a model solution. This makes school homework more efficient and encourages confident independent reading.

How a three-pupil tutorial can support this

The unchanged eduKateSG Clementi three-pupil Mathematics programme describes 90-minute tutorials near Sixth Avenue MRT. In an illustrative Secondary 2 G1 lesson, one pupil may confuse simplify and solve, another may confuse estimate and exact calculation, and a third may misread graph instructions. The tutor can give each learner a tailored two-question contrast and check transfer in a mixed set. The programme reference does not confirm current G1 group availability.

How G1 Mathematics fits the examination pathway

Under Full Subject-Based Banding, G1 is a subject level. MOE’s Secondary Two G1 Mathematics content includes algebraic expressions, linear equations, coordinate graphs and other topics where command words are important. SEAB lists K110 for G1 Mathematics in the 2027 graduating SEC (earlier reference 4046). That syllabus is not the timetable for a pupil’s current Secondary 2 school test; use school-specific instructions now and later the correct examination cohort.

Frequently asked questions

If an answer is mathematically correct, can it still miss the instruction?

Yes. A correct discount saving is not the requested final sale price. A correct expression is not necessarily the solution of an equation, and a numerical result is not an explanation when the question asks why.

Do all schools use every verb identically?

Common mathematical conventions are widely shared, but the entire question and school marking instructions determine what is required. This guide is instructional, not an official universal verb glossary.

Does ‘show that’ require a reason?

Typically it asks the pupil to demonstrate the stated result with valid steps or evidence rather than restating it. The required detail depends on the actual problem.

What is the difference between drawing and construction?

A geometric construction follows a specified method and defining properties, often with compass and ruler marks. A sketch usually communicates shape or relationships without the same exact-instrument requirement.

What should the pupil do when two verbs appear?

Complete both requested tasks in a sensible sequence. For example, form an equation first, then solve it, then check if requested.

How can a tutor tell reading trouble from arithmetic trouble?

Ask the learner to predict what kind of answer is needed before computing. If that prediction is wrong, clarify the task; if it is correct but the arithmetic fails, address the calculation separately.

Official curriculum and reader notes

Reader note: These instructional verbs and 38 original examples are not official marking instructions for every school, a reproduced examination paper or a claim of guaranteed results. Confirm a learner’s actual assessment scope, tutoring arrangements and available classes directly.

For a parent–student conversation, bring two questions that use similar numbers but different command words. Enquire with eduKate Singapore about how G1 Mathematics tutors can teach pupils to read and complete each instruction independently.

Secondary 2 G1 Mathematics Tutor Bukit Timah | Understand Mathematics Question Verbs