Sec 1 G1 Maths Tutor Bukit Timah | 75 Vocabulary Terms

Secondary 1 G1 Mathematics Tutor Bukit Timah | G1 Maths Vocabulary: 75 Terms with Examples. Did you know? A student can calculate accurately yet lose the direction of an entire question because a word such as ‘whole’, ‘difference’, ‘height’ or ‘frequency’ was interpreted incorrectly. Mathematical vocabulary helps a learner read the problem before choosing a method.

This guide is a reader-friendly glossary for parents and Secondary 1 G1 students under Singapore’s Full Subject-Based Banding. The seventy-five entries pair a plain-language meaning with a worked example, one tempting mistake and a fresh question. Terms that support G1 foundations are distinguished from the more advanced procedure-heavy content of later subject-level courses.

For quick information pickup, search for the term you need or follow the category index. Read the definition, try the example, then cover the answer to the independent check. The purpose is not to memorise seventy-five definitions in one sitting, but to return to the word that is causing trouble in real marked schoolwork.

Numbers and directed calculations: words 1–17

This section concerns numbers and directed calculations. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

1. Integer

Meaning. A whole number that may be positive, negative or zero, without a fractional part.

Worked G1 example. −4, 0 and 9 are integers. The decimal 2.5 is not an integer because it lies between two whole-number positions.

Watch for this error. Do not treat integer as simply another word for positive whole number; the negative positions also count.

Your turn. Name an integer smaller than −2 and explain where it lies on a number line.

2. Positive number

Meaning. A number greater than zero. The plus sign may be written or left implicit, but its position relative to zero does not change.

Worked G1 example. The number +6 and the number 6 have the same value. On the number line each lies six units to the right of zero.

Watch for this error. Positive does not mean ‘contains a plus operation’. It describes a value’s sign.

Your turn. Is 0 positive? No; it is neither positive nor negative.

3. Negative number

Meaning. A number less than zero; it appears to the left of zero on the number line.

Worked G1 example. If a fictional temperature moves from −3 to −1, it has risen by two units even though both recorded values are negative.

Watch for this error. Do not assume a larger printed digit means a larger negative value: −7 is less than −2.

Your turn. Which value is greater, −4 or −9? Explain using positions.

4. Zero

Meaning. The quantity representing neither a positive nor a negative value, and the origin of the number line.

Worked G1 example. Adding zero to 8 gives 8; subtracting a number from itself gives zero, as in 6 − 6 = 0.

Watch for this error. Zero is not a positive integer. Division by zero is not defined, although zero divided by nonzero five is zero.

Your turn. Evaluate 0 ÷ 5 and explain why 5 ÷ 0 is not an ordinary calculation.

5. Number line

Meaning. A visual arrangement of numerical values in increasing order from left to right, useful for signed values and fractions.

Worked G1 example. Start at −5, add 7 and move seven units right to reach 2. The physical direction reflects the mathematical operation.

Watch for this error. Do not change the direction convention just because both quantities are negative.

Your turn. Sketch −3, 0 and 2 in their correct left-to-right order.

6. Opposite numbers

Meaning. Two numbers equally distant from zero but on different sides; their sum is zero.

Worked G1 example. The opposite of 5 is −5. Adding 5 and −5 gives 0. Zero is its own opposite.

Watch for this error. The opposite of a value is not its reciprocal. The opposite of 2 is −2, not one half.

Your turn. What is the opposite of −7? Answer +7, because the signs reverse while distance remains seven.

7. Ascending order

Meaning. An arrangement from the smallest numerical value to the largest.

Worked G1 example. The correct ascending order of 0, −3, 4 and −1 is −3, −1, 0, 4. Read the number line from left to right.

Watch for this error. Do not arrange negative numbers by digit size alone; −3 is smaller than −1.

Your turn. Put 2, −5, −2 and 0 in ascending order before checking.

8. Inequality symbol

Meaning. A sign expressing less than, greater than, less than or equal to, or greater than or equal to.

Worked G1 example. The sentence −2 > −7 is true. The sentence 5 ≥ 5 is also true because equality is allowed.

Watch for this error. The extra horizontal line in ≥ or ≤ changes whether equal values satisfy the comparison.

Your turn. Is 6 < 6 true? No. Is 6 ≤ 6 true? Yes.

9. Addition

Meaning. An operation for combining quantities or moving by a signed change.

Worked G1 example. −6 + 9 = 3. On a number line, the first number gives the starting point and the positive addition gives a move to the right.

Watch for this error. Do not automatically add magnitudes and attach a negative sign when a positive and negative number are combined.

Your turn. Predict whether −8 + 3 lies left or right of −8, then calculate −5.

10. Subtraction

Meaning. An operation finding a difference or removing a quantity, which may itself be negative.

Worked G1 example. 7 − (−3) = 10: subtracting negative three is equivalent to adding three. This differs from 7 − 3 = 4.

Watch for this error. A minus sign before brackets and a minus sign on a number have different roles; do not cancel marks by appearance.

Your turn. Explain why −2 − 5 is −7 rather than +3.

11. Multiplication

Meaning. An operation combining equal groups or repeated factors. Signed multiplication also follows sign rules.

Worked G1 example. Three groups of four give 3 × 4 = 12. Two negative factors multiply to a positive value: (−3) × (−4) = 12.

Watch for this error. Multiplication does not always increase magnitude; multiplying 0.5 by 0.5 gives 0.25.

Your turn. Estimate whether 0.8 × 0.2 should exceed one; it should not.

12. Division

Meaning. An operation asking how many equal groups of a given size fit in a quantity, or splitting into equal shares.

Worked G1 example. 1.2 ÷ 0.3 = 4 because four groups of 0.3 make 1.2. Also (−18) ÷ 3 = −6.

Watch for this error. Dividing by a positive fraction less than one may make an answer larger; division does not always shrink.

Your turn. How many halves are in three wholes? Answer six.

13. Factor

Meaning. A positive whole number that divides another whole number exactly without a remainder in basic factor questions.

Worked G1 example. Three is a factor of 21 because 3 × 7 = 21. Factor pairs of 12 include 1 × 12, 2 × 6 and 3 × 4.

Watch for this error. Do not interchange the sentence ‘3 is a factor of 21′ with ’21 is a factor of 3’.

Your turn. List the positive factors of 10: 1, 2, 5 and 10.

14. Multiple

Meaning. A quantity obtained by multiplying a starting number by a whole-number multiplier.

Worked G1 example. The positive multiples of four begin 4, 8, 12, 16 and 20. Sixteen is a multiple of four because 4 × 4 = 16.

Watch for this error. Multiples travel through a times table; they are not the same list as a number’s factors.

Your turn. Is 18 a multiple of six? Yes, because six times three is eighteen.

15. Prime number

Meaning. A whole number greater than one that has exactly two distinct positive factors, one and itself.

Worked G1 example. Thirteen is prime because its positive factors are 1 and 13. Two is the only even prime.

Watch for this error. One is not prime; it has only one positive factor. Odd numbers such as nine need not be prime.

Your turn. Explain why 15 is composite using the factor pair 3 × 5.

16. Composite number

Meaning. A whole number greater than one with more than two positive factors.

Worked G1 example. Twelve is composite because, besides 1 and 12, it has factors such as 2, 3, 4 and 6.

Watch for this error. Do not classify 1 as composite. The definitions exclude it from both prime and composite categories.

Your turn. Is 21 composite? Yes: 3 × 7 = 21.

17. Estimate

Meaning. A sensible approximate value used to predict scale and check whether an exact calculation is plausible.

Worked G1 example. 19.8 × 4.9 is near 20 × 5 = 100. The exact result 97.02 is believable; 970.2 would deserve a check.

Watch for this error. Estimating is not random rounding. Choose easy nearby values and use the result to inspect scale.

Your turn. Estimate 29.8 × 3.1 as about 90, then check a calculator result.

Fractions, decimals and precision: words 18–27

This section concerns fractions, decimals and precision. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

18. Numerator

Meaning. The number above a fraction bar; it counts the selected parts of a whole divided into equal-sized pieces.

Worked G1 example. In 3/8, the numerator is three. Three eighths means three parts, each of size one eighth of the same whole.

Watch for this error. The numerator alone is not the fraction’s value; the denominator determines how large each part is.

Your turn. Identify the numerator of 5/12 and explain what five is counting.

19. Denominator

Meaning. The number below a fraction bar; it describes how many equal parts make one whole in basic fraction representation.

Worked G1 example. In 3/8, the denominator is eight. An eighth is smaller than a fourth when both refer to the same whole.

Watch for this error. Do not add denominators during fraction addition. First express parts in a common-sized unit.

Your turn. Why is 1/8 less than 1/4? Explain using equally sized paper strips.

20. Equivalent fractions

Meaning. Different numerator-denominator pairs representing exactly the same rational value.

Worked G1 example. One half equals two quarters and four eighths: 1/2 = 2/4 = 4/8. Both numerator and denominator are scaled equally.

Watch for this error. Multiplying only the numerator changes the fraction, except in special trivial circumstances.

Your turn. Write 3/4 with denominator twelve: 9/12.

21. Common denominator

Meaning. A shared denominator used to express fraction pieces in equal-sized units before addition or subtraction.

Worked G1 example. 1/2 + 1/4 becomes 2/4 + 1/4 = 3/4. The shared denominator lets the numerators count the same-sized parts.

Watch for this error. The denominator of the sum is not the sum of the original denominators.

Your turn. Calculate 2/3 − 1/6: 4/6 − 1/6 = 1/2.

22. Mixed number

Meaning. A whole-number part together with a fractional part, representing one quantity.

Worked G1 example. One and a half is 1 1/2, equivalent to 3/2 or 1.5. It lies between one and two on the number line.

Watch for this error. Do not read 1 1/2 as multiplication of one and one half in ordinary mixed-number notation.

Your turn. Convert 2 1/4 to a decimal: 2.25.

23. Decimal

Meaning. A place-value representation using digits after a decimal point for fractions of one whole.

Worked G1 example. 0.375 represents three tenths, seven hundredths and five thousandths, and equals 3/8.

Watch for this error. More digits do not automatically mean a larger number. 0.7 is greater than 0.65.

Your turn. Which is greater, 0.6 or 0.58? Answer 0.6 because 0.60 > 0.58.

24. Place value

Meaning. The contribution of a digit determined by its position in a number.

Worked G1 example. In 0.305, three represents three tenths, zero represents no hundredths, and five represents five thousandths.

Watch for this error. A zero can locate other digits without representing an added value at its own place.

Your turn. Explain why 0.07 means seven hundredths, not seven tenths.

25. Rounding

Meaning. Replacing a number with a nearby value at a requested precision, often for communication or estimation.

Worked G1 example. 18.76 to one decimal place becomes 18.8 because the hundredths digit is six and rounds the tenths up.

Watch for this error. Do not round intermediate values repeatedly when the question asks for a rounded final answer.

Your turn. Round 4.346 to two decimal places: 4.35.

26. Significant figure

Meaning. A digit that contributes to the stated precision, counted from the first nonzero digit in standard school examples.

Worked G1 example. 0.04873 to two significant figures is 0.049. The leading zeros locate the value but are not counted as significant digits.

Watch for this error. Significant figures are not the same instruction as decimal places. Compare 0.05 to two decimal places with 0.049 to two significant figures.

Your turn. Round 0.006284 to two significant figures: 0.0063.

27. Reciprocal

Meaning. A nonzero quantity that gives one when multiplied by the original value, useful when dividing fractions.

Worked G1 example. The reciprocal of 2/3 is 3/2, because (2/3) × (3/2) = 1. Thus 1 ÷ (2/3) equals 3/2.

Watch for this error. Reciprocal does not mean changing the sign. The opposite of 2 is −2; its reciprocal is 1/2.

Your turn. What is the reciprocal of 5? One fifth, since 5 × 1/5 = 1.

Ratio and percentage relationships: words 28–39

This section concerns ratio and percentage relationships. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

28. Ratio

Meaning. A comparison between quantities expressed in terms of their relative parts.

Worked G1 example. In red : blue = 2 : 3, two red parts correspond to three blue parts. The quantities might be 12 and 18.

Watch for this error. A ratio’s numbers are not necessarily literal counts. Both quantities can be scaled by the same factor.

Your turn. Simplify 10 : 15 to 2 : 3.

29. Ratio part

Meaning. One equal proportional unit that a ratio describes, not necessarily one physical object.

Worked G1 example. For 2 : 3 with a total of 25 counters, there are five parts; one part represents five counters.

Watch for this error. A ratio with five parts does not mean the problem contains exactly five objects.

Your turn. Share 35 in the ratio 2 : 5: one part is five, giving 10 and 25.

30. Equivalent ratio

Meaning. Another ratio with every entry multiplied or divided by the same nonzero factor.

Worked G1 example. 2 : 3, 4 : 6 and 10 : 15 compare quantities in the same proportion.

Watch for this error. Adding the same number to both terms does not generally preserve the ratio.

Your turn. Are 3 : 4 and 6 : 8 equivalent? Yes.

31. Simplest ratio

Meaning. An equivalent ratio written with whole-number entries having no common factor greater than one.

Worked G1 example. 12 : 18 simplifies to 2 : 3 by dividing both entries by six. Decimal ratios can first be scaled to whole numbers.

Watch for this error. Do not simplify just one entry. Every part must be changed using the same multiplier or divisor.

Your turn. Simplify 0.5 : 1.5 to 1 : 3.

32. Known share

Meaning. A part of a ratio question whose amount is given, instead of the full total.

Worked G1 example. If red : blue = 2 : 3 and red has 14 counters, two parts represent 14, so blue has 21.

Watch for this error. Dividing 14 by five would misuse the total ratio parts when the known count is red only.

Your turn. If A : B = 3 : 5 and A = 12, find B = 20.

33. Part-to-whole fraction

Meaning. A fraction with a particular part in the numerator and the entire relevant collection in the denominator.

Worked G1 example. In a 2 : 3 two-group ratio, the first group is 2/5 of the combined total, not 2/3.

Watch for this error. A ratio comparing first to second is different from a fraction comparing first to both together.

Your turn. In A : B : C = 1 : 2 : 3, what fraction belongs to C? One half.

34. Percentage

Meaning. A comparison expressed per hundred, useful for parts, rates of change and proportions.

Worked G1 example. 25% equals 25/100 = 1/4 = 0.25. Thus 25% of 80 is twenty.

Watch for this error. Percentages are not always below 100; 125% represents one and one quarter wholes.

Your turn. Convert 0.6 to a percentage: 60%.

35. Reference whole

Meaning. The quantity treated as 100% in a percentage calculation or comparison.

Worked G1 example. If 75% of a quantity is 30, the whole is 30 ÷ 0.75 = 40. The 30 is only a part.

Watch for this error. A child who divides or multiplies using the wrong base may perform flawless arithmetic but answer the wrong question.

Your turn. Find the whole if 60% equals 18: it is 30.

36. Percentage part

Meaning. A portion of a reference whole described as a percentage of that whole.

Worked G1 example. Twenty per cent of 60 is 12. The whole is sixty; the part being described is twelve.

Watch for this error. Do not mistake the percentage part for the new total after a decrease unless the question says so.

Your turn. If a discount is 20% of $50, how much is discounted? $10.

37. Percentage increase

Meaning. The change upward compared with the starting quantity, expressed as a percentage of that starting base.

Worked G1 example. A rise from 40 to 50 is an increase of 10/40 = 25%. The starting 40 is the reference.

Watch for this error. A 25% increase is not the same as a new quantity equal to 25% of the original.

Your turn. Increase 80 by 25%: the new value is 100.

38. Percentage decrease

Meaning. The change downward compared with the starting quantity, expressed as a percentage of the starting base.

Worked G1 example. A reduction from 50 to 40 is a decrease of 10/50 = 20%. It is not a 25% decrease merely because the reverse rise is 25%.

Watch for this error. A rise of 20% and a fall of 20% do not cancel unless the bases happen to be specially adjusted.

Your turn. Decrease 60 by 15%: the new value is 51.

39. Percentage above 100%

Meaning. A comparison larger than the reference whole, such as 120% of the original quantity.

Worked G1 example. 120% of 50 equals 60. The final amount is twenty per cent more than the starting quantity.

Watch for this error. A 120% increase instead adds 120% of the starting amount, leaving 220% of that amount.

Your turn. How much is 150% of 40? Sixty.

Algebraic symbols, patterns and formulae: words 40–50

This section concerns algebraic symbols, patterns and formulae. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

40. Variable

Meaning. A letter used to stand for a number or quantity that may change or whose value is specified.

Worked G1 example. If x is the number of notebooks and each costs $3, the variable total is 3x dollars.

Watch for this error. Do not treat x as a decoration or an instruction to add. Define what quantity the letter represents.

Your turn. If x = 4, evaluate 3x: 12.

41. Coefficient

Meaning. The numerical multiplier of a variable in a term such as 5y.

Worked G1 example. In 5y, the coefficient is five; when y = 2, the term has value ten.

Watch for this error. A coefficient is not the same as a constant added after the variable term.

Your turn. What is the coefficient of 7x? Seven.

42. Constant

Meaning. A fixed numerical value that does not depend on the variable in a given expression.

Worked G1 example. For 4n + 3, the constant term is three; it can model a one-time fee added to a repeated item cost.

Watch for this error. Do not multiply a one-off charge by n when translating a story into an expression.

Your turn. If a fictional order costs 2n + 5, which amount is fixed? Five.

43. Algebraic expression

Meaning. A collection of numbers, variables and operations that represents a value without necessarily declaring an equality.

Worked G1 example. 3x + 5 is an expression. It can be evaluated for any chosen x; it is not by itself an equation such as 3x + 5 = 17.

Watch for this error. Do not invent an equals sign if the question asks only for an expression.

Your turn. Write ‘two more than three times y’ as 3y + 2.

44. Adjacent multiplication notation

Meaning. The convention that a number and letter placed together mean multiplication without writing the × sign.

Worked G1 example. 3y means 3 × y, or y + y + y. At y = 4, it equals 12.

Watch for this error. 3y is not the number thirty followed by y and it is not 3 + y.

Your turn. Evaluate 5m when m = 2: ten.

45. Bracket

Meaning. A grouping symbol that identifies which terms belong together for an operation.

Worked G1 example. 3(x + 2) means three copies of x + 2. At x = 4 it evaluates to 18.

Watch for this error. 3(x + 2) is not the same as 3x + 2, which would give 14 at x = 4.

Your turn. Evaluate 2(y + 5) when y = −2: six.

46. Substitution

Meaning. Replacing a variable with its given numerical value, while preserving the expression’s operations and grouping.

Worked G1 example. If x = −3, then 2x + 5 becomes 2(−3) + 5 = −1.

Watch for this error. Dropping brackets around a substituted negative value can change the intended calculation.

Your turn. With a = −2, evaluate a²: four.

47. Formula

Meaning. A stated relationship between quantities using symbols that can be evaluated for specified values.

Worked G1 example. The perimeter of a rectangle is P = 2(l + w). If l = 5 and w = 3, the perimeter is 16.

Watch for this error. A formula must be read with its variable meanings and units; not every printed number can be substituted arbitrarily.

Your turn. Calculate 2(l + w) for l = 6 and w = 4: twenty.

48. Sequence

Meaning. An ordered list of values following a stated or inferred pattern.

Worked G1 example. 3, 5, 7, 9 increases by two each step. Identifying the pattern can help predict the next value, 11.

Watch for this error. Guessing one next number does not automatically prove a rule holds for every position.

Your turn. What follows 4, 7, 10, 13 in a constant-step pattern? Sixteen.

49. Nth-term expression

Meaning. A rule that gives a sequence’s value from the position n, beginning at a specified index.

Worked G1 example. For 2n + 1 with n = 1, the first term is three and the fifth is eleven.

Watch for this error. n usually names the position, not the preceding term’s value.

Your turn. Evaluate n + 3 at n = 7: ten.

50. Fraction bar grouping

Meaning. A horizontal fraction line indicating that the whole written numerator is divided by the whole written denominator.

Worked G1 example. (3 + y)/5 at y = 7 equals two; 3 + y/5 at y = 7 equals 4.4.

Watch for this error. Ignoring the grouping can change the expression even when the numbers are copied correctly.

Your turn. Evaluate (4 + x)/3 when x = 2: two.

Angles, lines and symmetry: words 51–60

This section concerns angles, lines and symmetry. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

51. Acute angle

Meaning. An angle greater than zero but less than ninety degrees in the usual school classification.

Worked G1 example. An angle measuring 35° is acute. It takes less than a quarter-turn from one ray to the other.

Watch for this error. A diagram that looks narrow is not proof of an exact measure; use the labelled information.

Your turn. Is 90° acute? No; it is a right angle.

52. Right angle

Meaning. An angle of exactly ninety degrees, often indicated by a small square at its vertex.

Worked G1 example. A perpendicular height meets its chosen base at a right angle; the 90° condition determines the correct height.

Watch for this error. A line drawn nearly vertical is not automatically perpendicular without a stated condition or accurate construction.

Your turn. How many right angles make a full turn? Four.

53. Obtuse angle

Meaning. An angle larger than ninety degrees but smaller than one hundred and eighty degrees.

Worked G1 example. A 120° angle is obtuse. Its supplement on a straight line is 60°.

Watch for this error. Obtuse is not the same as reflex; a reflex angle exceeds 180°.

Your turn. Classify 135°: obtuse.

54. Reflex angle

Meaning. An angle greater than 180° but less than 360°, measured through the larger region between two rays.

Worked G1 example. If the smaller angle between two rays is 75°, the reflex region measures 360° − 75° = 285°.

Watch for this error. A full 360° turn is not called a reflex angle under the standard strict definition.

Your turn. Find the reflex partner to 68°: 292°.

55. Vertically opposite angles

Meaning. The equal pairs of angles directly opposite each other where two straight lines intersect.

Worked G1 example. When one angle at a crossing is 57°, its opposite angle is also 57°; adjacent angles are 123° each.

Watch for this error. Directly opposite is not the same as immediately adjacent. Identify the lines and shared vertex.

Your turn. If one crossing angle is 82°, what is its vertically opposite partner? 82°.

56. Straight-line angle sum

Meaning. The rule that adjacent angles filling a straight angle add to 180°.

Worked G1 example. If one adjacent angle is 74°, the other must be 106° because 74 + 106 = 180.

Watch for this error. Do not apply the 360° around-a-point rule to a single straight-angle region.

Your turn. Find x if 48° and x form a straight line: 132°.

57. Angles around a point

Meaning. The rule that a complete turn at one vertex totals 360°.

Worked G1 example. If three non-overlapping angles around a point are 120°, 95° and x, then x = 145°.

Watch for this error. Angles inside just a straight line total 180°, not 360°, even if both share a point.

Your turn. Find x in 80° + 110° + x = 360°: 170°.

58. Transversal and parallel lines

Meaning. A transversal crosses two or more lines; when the crossed lines are parallel, specific angle relationships follow.

Worked G1 example. On marked parallel lines, corresponding and alternate interior angles are equal, and same-side interior angles sum to 180°.

Watch for this error. Do not infer parallelism solely because two drawn lines seem almost parallel.

Your turn. If one same-side interior angle is 73°, the other is 107°.

59. Line of symmetry

Meaning. A mirror line across which a figure matches itself under reflection.

Worked G1 example. A square has four lines of symmetry, whereas a non-square rectangle has two.

Watch for this error. A diagonal of a non-square rectangle is not a symmetry line even though it joins opposite corners.

Your turn. How many lines of symmetry does an equilateral triangle have? Three.

60. Rotational symmetry

Meaning. A figure’s matching orientation after turns about a fixed centre; the order counts matches during a full turn.

Worked G1 example. A square has rotational order four; a non-square rectangle has order two.

Watch for this error. Do not assume the number of corners equals the rotational order for every shape.

Your turn. What is the order of a generic scalene triangle? One.

Measurement and mensuration: words 61–69

This section concerns measurement and mensuration. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

61. Perimeter

Meaning. The complete distance around the outside boundary of a plane figure.

Worked G1 example. A 7 cm by 3 cm rectangle has perimeter 2(7 + 3) = 20 cm.

Watch for this error. Perimeter is measured in length units, not square centimetres. Remember every outside edge.

Your turn. Find the perimeter of a square of side 4 cm: 16 cm.

62. Area

Meaning. The measure of a two-dimensional region, expressed in square units.

Worked G1 example. An 8 cm by 5 cm rectangle covers 8 × 5 = 40 cm².

Watch for this error. Area is not the same as distance around. A length result in cm cannot be used as cm².

Your turn. Find the area of a 6 cm by 4 cm rectangle: 24 cm².

63. Perpendicular height

Meaning. The shortest distance at a right angle from a chosen base to the relevant parallel line or opposite vertex.

Worked G1 example. A triangle with base 10 cm and perpendicular height 6 cm has area 30 cm².

Watch for this error. A sloping side is not automatically the correct height even if its length is shown.

Your turn. In a parallelogram with base 8 and height 3, area is 24 square units.

64. Triangle area

Meaning. Half the product of a triangle’s base and its corresponding perpendicular height.

Worked G1 example. Base 8 cm and height 5 cm give area 1/2 × 8 × 5 = 20 cm².

Watch for this error. Forgetting the half doubles the answer; using a non-perpendicular side may make the input invalid.

Your turn. What area has base 7 and perpendicular height 4? 14 square units.

65. Parallelogram

Meaning. A quadrilateral with both pairs of opposite sides parallel, whose area is base times perpendicular height.

Worked G1 example. A parallelogram with base 9 cm and perpendicular height 4 cm has area 36 cm².

Watch for this error. Area does not use a sloping edge in place of height unless it is actually perpendicular.

Your turn. Find area when base 6 and perpendicular height 5: 30 square units.

66. Trapezium

Meaning. A quadrilateral with a pair of parallel opposite sides; its area can be found using their average length times perpendicular height.

Worked G1 example. Parallel sides 6 cm and 10 cm with height 5 cm give area (6 + 10) × 5 ÷ 2 = 40 cm².

Watch for this error. Do not substitute a non-parallel sloping edge for one of the parallel side lengths.

Your turn. Find area for parallel sides 4 and 8 with height 3: 18 square units.

67. Radius

Meaning. A straight segment joining the centre of a circle to its boundary; half the diameter.

Worked G1 example. A circle with radius 4 cm has diameter 8 cm. Its circumference is 8π cm.

Watch for this error. Using the diameter in a formula requiring radius doubles the input and can multiply an area by four.

Your turn. If diameter is 12 cm, radius is 6 cm.

68. Circumference

Meaning. The distance around a circle, given by 2πr or πd.

Worked G1 example. A circle with radius 3 cm has circumference 6π cm, a length.

Watch for this error. Circumference is not an area and must not be reported in cm².

Your turn. If diameter is 10 cm, circumference is 10π cm.

69. Volume and surface area

Meaning. Two different measurements of a solid: interior three-dimensional space and total exposed outside-face area.

Worked G1 example. A cube of side 2 cm has volume 8 cm³ but surface area 6 × 4 = 24 cm².

Watch for this error. A cut-out reduces volume but may create new exposed faces, so surface area needs separate reasoning.

Your turn. For a cube of side 3 cm, volume is 27 cm³ and surface area 54 cm².

Data and statistical representations: words 70–75

This section concerns data and statistical representations. A useful reading habit is to say what each quantity represents before calculating, then verify the example by predicting its sign, relative size or unit. Keep the definitions attached to actual questions rather than copying a glossary without understanding.

70. Frequency

Meaning. The number of times a value or category occurs in a set of observations.

Worked G1 example. For responses A, B, A, A, B, the frequency of A is three and the frequency of B is two.

Watch for this error. Frequency counts observations, not the sum of all numbers in a category unless specifically requested.

Your turn. What is the frequency of 2 in 2, 1, 2, 3, 2? Three.

71. Frequency table

Meaning. A structured set of categories or values with their counted frequencies.

Worked G1 example. A table listing A: 4, B: 3 and C: 2 describes nine observations if every observation belongs to exactly one category.

Watch for this error. Always check that the frequencies total the actual number of valid responses.

Your turn. If counts are 5, 2 and 3, how many observations are recorded? Ten.

72. Bar graph

Meaning. A chart using bars to compare numerical counts or measures across separate categories.

Worked G1 example. Bars of heights 8 and 5 show the first category exceeds the second by three units.

Watch for this error. The axis scale matters. Counting printed grid marks instead of reading the labels can give the wrong values.

Your turn. Which has the greater count, a bar at 6 or one at 9? The latter, by three.

73. Pictogram

Meaning. A data display that represents category counts with pictures whose value is explained by a key.

Worked G1 example. If one book icon represents four books, two and a half icons represent ten books.

Watch for this error. A half-icon means half the key value, not automatically half of a real item.

Your turn. With a key of six objects per icon, what does half an icon mean? Three objects.

74. Line graph

Meaning. A plot connecting recorded values, often to show how the same measure changes over an ordered scale such as time.

Worked G1 example. Readings 22, 24, 23 and 27 show changes of +2, −1 and +4; the highest value is 27.

Watch for this error. The largest value is not necessarily the largest increase. Read tick intervals before inferring magnitude.

Your turn. Which consecutive rise is bigger, 22 to 24 or 23 to 27? The second.

75. Pie chart

Meaning. A circular display showing categories as portions of a complete whole, usually one hundred per cent.

Worked G1 example. If 8 of 20 students choose one category, its pie-chart share is 40% of the circle.

Watch for this error. Pie charts can hide small differences between categories; a table may be easier for exact values.

Your turn. If one category is one quarter of the whole, what percentage is that? 25%.

How parents can teach mathematical language without a second textbook

Practice 1: Read the word in its original sentence

A glossary can tell you what a variable or a ratio means, but the learner still has to find which quantity the term describes in the real question. Ask the child to underline a relationship word, circle the known amount, and point to the associated diagram, table or expression.

A useful family check is to finish with the pupil explaining the word in a complete mathematical sentence, not merely saying the short definition. They should identify the quantity, perform one small calculation if relevant, and explain why a similar-looking alternative would not answer the question.

Practice 2: Use one counterexample

A correct definition becomes more dependable when the pupil can reject a tempting wrong example. For instance, ‘every odd number is prime’ fails at nine; ‘every triangle height is vertical on the page’ fails when the drawing is rotated. Explain why the condition does not hold.

Practice 3: Switch representation once

Translate a percentage into a fraction, a signed subtraction into a number line, a ratio into equal boxes or an algebraic expression into a small story. If the original word keeps the same meaning through the representation, it is becoming useful mathematical language.

Practice 4: Retest without the model answer

After a short break, change one number or word and ask the learner to explain the new question. If they can only succeed after the parent names the operation, the concept still needs an independent start. Record the required prompt rather than declaring the whole topic mastered.

Practice 5: Keep a term-to-example notebook

A practical notebook entry contains the term, the pupil’s own explanation, a short correct example and one common wrong reading. This is more useful than a long copied definition because it can be revisited against the child’s marked question.

Practice 6: Keep the G1 scope honest

When checking online resources, distinguish the Ministry of Education’s G1 Secondary One syllabus from G2, G3 and later Secondary Two requirements. Extra material can be helpful when suitable, but it should not be described as mandatory current work merely because it uses familiar chapter names.

Frequently asked questions

Must a Secondary 1 G1 student memorise all seventy-five terms at once?

No. Treat this as a reference to consult when a word prevents the learner from starting a school question. A handful of meaningful examples, used repeatedly in different situations, are more useful than a rushed recitation.

A simple follow-up is to connect this answer to one marked question from the learner’s current school chapter. Have the student name the quantities, draw or describe a suitable representation, and test the explanation with changed values rather than simply repeating the same words.

Are these all exact official chapter names?

No. Some entries are helpful mathematical vocabulary and intermediate ideas within a topic, rather than separately named examination chapters. Use the official G1 syllabus and the student’s actual school sequence to decide immediate priorities.

Why include factors if prime factorisation is excluded?

Understanding a factor helps explain what makes a whole number prime. The MOE G1 Secondary One syllabus explicitly excludes prime factorisation from the prime-number topic; an introductory factor example is not a requirement to teach the full tree method.

Can I teach the same term with a bar model or a number line?

Yes. Diagrams are valuable when they preserve the correct relationship. Use them to support reasoning and explanation, then practise reading the symbols without a compulsory illustration.

What is the difference between a ratio and a fraction?

A ratio such as 2:3 compares two parts. A fraction such as 2/5 can compare the first part with the combined total of both groups. The denominator depends on the reference named in the question.

Why do formulae sometimes include brackets or fraction bars?

The grouping tells you which full expression belongs to a multiplication or division. Ignoring those boundaries can change the mathematical statement while leaving almost all of the same symbols visible.

Do all statistical graphs require the same kind of scale?

No. A bar graph may compare discrete categories; a line graph may track a value over time; a pie chart describes parts of one whole; a pictogram uses a key. Every display still needs labels and truthful interpretation.

Are errors in maths vocabulary always English-language problems?

Not necessarily. A pupil might know the ordinary word ‘difference’ but not recognise which quantities to subtract, or understand ‘height’ in daily life but not its perpendicular geometric meaning. Check the mathematics as well as the wording.

Does this replace the school’s worksheet or teacher’s instructions?

No. It is a reference for interpreting the current G1 material. Follow school chapter timing, permitted calculator instructions, precision requirements and teaching guidance.

How can a tutor use these definitions?

The tutor can ask the learner to read a term, explain it in context, give a numerical example and reject a mistaken alternative. This quickly shows whether the difficulty concerns notation, reasoning or arithmetic.

What does the published eduKateSG tutorial model offer?

The immutable Secondary 1 Mathematics reference describes premium small groups of three near Sixth Avenue MRT, 1.5-hour weekly lessons, focused practice and guided correction. Confirm present availability directly.

How do I know my child has learned a term?

Ask them to explain it correctly without looking, use it in an unfamiliar question and give a reasoned check. One copied definition immediately after a lesson is weak evidence of retention.

Original tutorial reference and continued reading

For definitive subject scope, consult the official Ministry of Education G1 Mathematics syllabus. For the existing small-group tuition programme, see the immutable eduKateSG Secondary 1 Mathematics tutorial reference. The original is unchanged. For current class fit near Sixth Avenue MRT, enquire with eduKate Singapore.

A mathematical word becomes useful when a student can explain it through a new question.