Did you know? The cheaper hourly rate can produce the larger bill. G1 Mathematics develops useful numerical reasoning, and a fixed fee changes the whole comparison. Before deciding which quote is cheaper, ask how the total is built.
eduKateSG · G1 Mathematics · Quick learning guide
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1. Understand the subject
G1 Mathematics is Mathematics studied at the G1 subject level. Its 2027 SEC syllabus is K110. The content brings together number and algebra, geometry and measurement, and statistics and probability, with an emphasis on practical application. The official syllabus is linked below.
A quote comparison joins arithmetic with algebra. Arithmetic lets you calculate a bill for a stated duration. Algebra lets you describe how the bill changes when the duration changes. You are looking for a relationship, not merely a number to type into a calculator.
This article uses fictional prices to teach the relationship. They are not quotations from actual businesses or guidance on market prices.
2. Separate the fixed and changing parts
Suppose Service A charges a $24 visit fee plus $18 per hour. Service B charges no visit fee and $30 per hour. Both charge for the exact time used, and neither adds any other charge. These assumptions are part of the problem.
For a two-hour job, A costs $24 + $18 × 2 = $60. B costs $30 × 2 = $60. They tie. For a one-hour job, A costs $42 and B costs $30. The lower hourly rate has not yet made up for A’s visit fee.
Label the quantities before calculating. The visit fee is counted once. The hourly charge is multiplied by the number of hours. Multiplying the entire expression $24 + $18 by the duration would incorrectly charge the visit fee repeatedly.
3. Find the point where they match
Let h be the job duration in hours. Then A’s cost is 24 + 18h dollars and B’s cost is 30h dollars. To find equal costs, solve 24 + 18h = 30h. Subtract 18h from both sides: 24 = 12h. Divide by 12: h = 2.
The $24 fixed fee is balanced by a saving of $12 for each hour. That is why two hours is the matching point. This verbal explanation helps the equation make sense.
Check either side. At three hours, A costs $78 and B costs $90, so A is cheaper by $12. Under the stated assumptions, B is cheaper below two hours, both match at two hours, and A is cheaper above two hours. A matching point is a boundary; it is not a promise about every real invoice.
4. Notice what changes the model
Real conditions can change the result. A minimum charge, billing by each started hour, different included parts or an additional transport fee would require a different calculation. Read the conditions before using the formula.
For example, if charging is by each started hour, a job lasting 1.2 hours may be billed as two hours. You would need to use billed hours, with the provider’s actual rules, rather than automatically substitute 1.2.
For parents, a useful prompt is “Which amount happens once?” For tutors, compare a wrong expression with a correct one and ask the student to explain the difference. For students, write the units beside each quantity. Dollars per hour multiplied by hours gives dollars.
5. Try a fresh comparison
Original practice: Service C charges a $15 setup fee plus $12 per hour. Service D charges $17 per hour without a setup fee. Assume exact-time billing and no other charges. When do the totals match, and which is cheaper for four hours?
Set 15 + 12h = 17h. Subtract 12h to obtain 15 = 5h, so h = 3 hours. At four hours, C costs 15 + 48 = $63. D costs 68 dollars. C is cheaper by $5.
If your equation gives a negative duration here, revisit the signs. C starts more expensive but increases more slowly. A positive matching time fits that story. Use the context to check the calculation rather than treating the answer as an isolated result.
6. Questions and next steps
Does the smallest rate always win? No. Compare the total for the required amount of time, including every applicable fixed charge.
Must every comparison have a positive matching point? No. With different fees and rates, one service might remain cheaper throughout the allowed durations. Check the actual expressions.
What is the next learning step? Make a small table for zero, one, two and three hours, then explain the pattern in words. If the arithmetic is secure but forming the equation is difficult, practise translating one sentence at a time. Use the school’s current topics and confirmed subject level to choose further work.
Sources and further reading
Official reference: SEAB 2027 G1 Mathematics syllabus K110. Check the subject, examination year and candidate category when selecting an examination document. Source checked on 25 October 2026.
Find the other subjects in SEAB’s 2027 G1 school-candidate syllabus list.
For an eduKate example of identifying foundations and sequencing support, read Secondary 1 Mathematics Tutor Clementi. Match any learning support to the student’s actual subject and current work.