UCAT PlaybookChapter 3 of 8
The maths is Year 10. The test is the reading and the clock. Plenty of marks go before the first key is pressed, on the question of what to divide by what.
A percentage is always a percentage of something. Point at the row or column that is the of before you divide. Writing the base on the noteboard takes two seconds.
Thousands, per cent, per month, per 100 people. The table’s title and the column headers tell you what the numbers mean. The answers are often the same digits in different units.
Round the numbers and say roughly what the answer should be. If the options are far apart, the estimate is the answer and the calculator never opens. If they are close, the estimate catches a slip.
The on screen calculator is a basic one. It does one sum at a time, so a long chain is easy to lose.
Alt + C opens it, and the number keys work if Num Lock is on. Backspace wipes the whole number, not one digit, and the calculator stops listening when you click back on the question, so click it again before you type.
Do the arithmetic you can do in your head in your head. Halves, tenths and doubling are faster than any calculator. Save the keys for awkward divisions and long multiplications.
With 43 seconds a question, some questions are not worth it. A four step chain with a messy division can take two minutes. Flag it, guess, and come back if time is left. Chapter 5 shows how.
Each one has a name, an example and a fix. The tables are made up for this page.
A fictional gym had 160 members in March and 200 members in April.
By what percentage did membership increase from March to April?
An increase is measured against where it started. The change is 40, and the base is March’s 160, so 40 divided by 160 is 25%. Dividing by 200 gives 20%, the fall you would need to go back down.
FixName the reference quantity before you divide. For an increase, it is the earlier number.
In a fictional school, 80 students take Biology. The number taking Chemistry is 25% more than the number taking Biology.
How many students take Chemistry?
25% of 80 is 20. But the question says 25% more than 80, which is 80 plus 20, so 100. The small word changes the answer by a factor of five.
FixOf means a part. More than means the whole thing plus a part. Circle the word before you work.
A fictional bakery sells 150 loaves a day. 40% are sourdough. Each sourdough loaf uses 0.8 kg of flour.
How much flour goes into the sourdough loaves in a day?
40% of 150 is 60 loaves. That is a step, not the answer, and the options reward stopping there. 60 loaves times 0.8 kg is 48 kg.
FixBefore you click, reread the last five words of the question. Check the unit of your answer matches the unit it asks for.
Five fictional swimmers record these times in seconds: 31, 28, 35, 28, 48.
What is the median time?
The median is the middle value once the list is in order: 28, 28, 31, 35, 48, so 31. The mean is 34, the mode is 28 and the range is 20. All four are in the options.
FixUnderline the statistic word in the question and say what it means before you touch the numbers. Median means sort first.
One table, four questions. Decide the base before the calculator.
A fictional community library records loans in three months. Adult and child loans are separate counts.
march adult renewal rate: 20 %
march child renewal rate: 30 %
march open days: 20 days
The March renewal rates are the shares of loans in each group that were renewals.
What percentage of January loans were child loans?
January had 240 adult loans and 160 child loans, giving 400 loans in total. The child share is 160 / 400 x 100 = 40%. Option B calculates the adult share instead: 240 / 400 x 100 = 60%.
Common trap: of vs more than.
By what percentage did adult loans increase from January to February?
Adult loans rose from 240 in January to 270 in February, an increase of 30 loans. Divide that increase by the original January count: 30 / 240 x 100 = 12.5%. Option E uses the whole February count, 270 / 240 x 100 = 112.5%, rather than the increase.
Common trap: wrong base.
What percentage of all March loans were renewals, when the adult and child renewal rates are applied to their respective loan counts?
Apply the two renewal rates to their own groups: 330 x 0.20 = 66 adult renewals, and 270 x 0.30 = 81 child renewals. That is 147 renewals among 330 + 270 = 600 March loans, giving 147 / 600 x 100 = 24.5%. Option B's 25.0% is an unweighted average of the two rates, despite the different group sizes.
Common trap: chain step missed.
In March, how many loans were recorded per open day, to the nearest whole loan?
March's 330 adult and 270 child loans total 600 loans. Divide by 20 open days: 600 loans / 20 days = 30 loans per open day. Option C omits child loans and gives 330 / 20 = 16.5, which rounds to 17 loans per day.
Common trap: chain step missed.
For every miss, pick which of the 4 above caught you. Never careless. The name.
Wrong baseOne line, in your words, that would have saved you. Keep it on one sheet.
Point at the of before I divide.
On new questions. When it has not caught you three times running, cross it off.
RetiredIn Cutline UCAT this happens on its own: almost every miss gets its trap, the Train tab says Fix wrong base, and the trap retires after three clean, in-time dodges.
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