How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A firm in perfect competition sells at R10 per unit. Its MC at 100 units is R10. Is this its profit-maximising output?
Before any working — hunt first
Given
Numbers and units already in the sentence: R10 per · 100 units · R10. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Is this its profit-maximising output. Circle that word — that is the missing variable.
Find
We are required to find: Is this its profit-maximising output. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Profit max where MR = MC. Then substitute the given, one line at a time, to get Is this its profit-maximising output.
In other words — as if you have never seen this before
If you have never seen this before: Profit max where MR = MC. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
P=R10; MC=R10.
3. Which method — and why this one?
Profit max where MR=MC.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: R10 per · 100 units · R10. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Is this its profit-maximising output. Circle that word — that is the missing variable. Find: We are required to find: Is this its profit-maximising output. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Profit max where MR = MC. Then substitute the given, one line at a time, to get Is this its profit-maximising output.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
P=R10; MC=R10.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Profit max where MR=MC.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Identify the given
In perfect competition MR = P = R10; MC = MR at 100 units.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
Yes, 100 units maximises profit.
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
Yes, 100 units maximises profit.
Copy onto your answer sheet — in this order
Answer: Yes, 100 units maximises profit.
6. Check it like a marker
Rule MR=MC.
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”