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The study notebook
Make the next attempt count.
Work through an example, test the reasoning, and take one useful habit into your next practice session. These guides are free to read without an account.
Brainliest · Published 5 September 2026 · Original study examples, not official exam questions
01 / Quantitative reasoning
A percentage always needs a starting value
A common mistake is to combine percentage changes as if they were ordinary additions. Before calculating, write down what each percentage is a percentage of. A second change usually applies to a new amount.
Worked example
A backpack costs $80. Its price is reduced by 25%, then the reduced price rises by 25%. What is the final price?
The reduction is 25% of $80: 0.25 × 80 = $20.
The reduced price is $80 − $20 = $60.
The increase is 25% of $60: 0.25 × 60 = $15.
The final price is $60 + $15 = $75.
The changes do not cancel because $20 and $15 are different amounts. A compact check is 80 × 0.75 × 1.25 = 75.
To return from $60 to $80, the price must increase by $20 relative to the new $60 base: 20 ÷ 60 = 1/3, or about 33.3%. In your working, label the base before writing the percentage multiplier. That small step catches many errors before they reach your answer.
Try it: a $50 price rises 10%, then falls 10%. Reveal the answer.
50 × 1.10 = 55, then 55 × 0.90 = $49.50. The increase is $5 and the reduction is $5.50. The final price is 1% below the original, not unchanged.
02 / Reading and reasoning
Separate what a passage says from what seems plausible
For an evidence question, the strongest answer is the one supported by the text. An interesting explanation is not enough. Watch for answers that quietly change a possibility into a certainty, or a comparison into a claim about cause.
After a library extended its weekday opening hours, its monthly visit count rose. During the same period, a nearby library closed for repairs. The report did not record individual visitors’ reasons for attending.
Which conclusion is supported?
A. Longer opening hours caused every additional visit.
B. The visit count rose, but the report cannot isolate the reason.
C. All new visitors previously used the closed library.
B is supported. The increase is explicitly stated. The closure is another relevant change, and visitor motives were not measured. A and C each claim more than the passage establishes. The words “every” and “all” make those claims especially broad.
A practical method is to underline the claim you need to evaluate, find the sentence that supports it, and compare their strength. If an answer adds a cause, motive, quantity, or universal rule that the passage does not supply, treat that addition as a reason to reconsider. This does not mean strong words are always wrong; they need equally strong evidence.
Check your reasoning: does the passage prove the longer hours had no effect?
No. “The effect was not isolated” is different from “there was no effect.” Both claiming a definite effect and claiming no effect would go beyond the evidence given.
03 / Calculation habits
Let the units check your calculation
A correct-looking number can answer the wrong question. Write the units beside every value and keep them through each operation. This helps distinguish a rate from a total and minutes from hours.
Worked example
A pump moves 18 litres in 3 minutes at a constant rate. How much water does it move in 50 seconds?
First find the rate: 18 litres ÷ 3 minutes = 6 litres per minute. Convert the time: 50 seconds ÷ 60 seconds per minute = 5/6 minute. Then multiply: 6 litres per minute × 5/6 minute = 5 litres.
The minute units cancel, leaving litres. As a reasonableness check, 50 seconds is less than one minute, so the answer must be less than 6 litres.
The constant-rate assumption matters. If the flow rate changes, multiplying one average rate by a new time may not be justified. Mark assumptions stated in the question, keep a fraction until the final step when practical, and round only as the instructions require.
Try it: at the same rate, how much moves in 90 seconds?
90 seconds is 1.5 minutes. At 6 litres per minute, the pump moves 9 litres. A common error is to multiply 6 by 90 without converting seconds to minutes.
04 / Practice and review
Turn a mistake into a specific next step
“I need to study more” is hard to act on. After a missed or uncertain question, record the point where your reasoning diverged and one action you can try on a different question. Include correct guesses: getting an answer right without understanding it can hide a gap.
Example: reviewing the backpack problem
What happened
What to do next
I subtracted and added 25 without identifying the base.
Write the current amount before each percentage change.
I assumed opposite percentages cancel.
Check the idea on a new starting amount using multipliers.
A simple 20-minute review session
First 5 minutes: revisit one mistake and explain it in your own words without copying the explanation.
Next 10 minutes: attempt a small set of related questions. Note where you hesitate.
Final 5 minutes: compare your working with available feedback and choose the next topic to review.
This is a study-session suggestion, not an official exam timetable. When preparing for a timed test, first learn the task, then practise under the provider’s actual section rules. A small untimed practice set and a complete timed mock answer different questions about your readiness.
