comprehenisve UCAT advice from the team at MedEntry UCAT preparation.
Possibly the most confusing questions on the UCAT exam, worded mathematical problems can actually be solved relatively easily if you understand how the question is written and what the words of the question really mean in mathematical terms.
Prior to solving worded mathematical problems on the UCAT exam, it is essential that you are comfortable with translating words into mathematical symbols. Below is a partial list of words and their mathematical equivalents. You should know these by heart before attempting any of the worded mathematical problems as present in the UCAT exam.
Concept |
Symbol |
Words |
Example |
Translation |
equality |
= |
is |
2 plus 2 is 4 |
2 + 2 = 4 |
equals |
x minus 5 equals 2 |
x-5 = 2 |
||
is the same as |
multiplying x by 2 is the same as dividing x by 7 |
2x = x/7 |
||
addition |
+ |
sum |
the sum of y and pi is 20 |
y + pi = 20 |
plus |
x plus y equals 5 |
x + y = 5 |
||
add |
how many marbles must John add to collection P so that he has 13 marbles |
x + P=13 |
||
increase |
a number is increased by 10% |
x + 10%x |
||
more |
the perimeter of the square is 3 more than the area |
P = 3+A |
||
subtraction |
- |
minus |
x minus y |
x-y |
difference |
the difference of x and y is 8 |
lx-yl = 8 |
||
subtracted |
x subtracted from y |
y-x |
||
less than |
the circumference is 5 less than the area |
C = A-5 |
||
multiplication |
x or * or . |
times |
the acceleration is 5 times the velocity |
a = 5v |
product |
the product of two consecutive integers |
x(x+ 1) |
||
of |
x is 125% of y |
x = 125%y |
||
division |
/ |
quotient |
the quotient of x and y is 9 |
x/y = 9 |
divided |
if x is divided by y, the result is 4 |
x / y = 4 |
Although exact steps for solving worded mathematical problems on the UCAT exam cannot be given, the following guidelines will help:
From the example above, we would get by adding the x’s: | 3x-5 = 16 |
Then adding 5 to both sides gives | 3x =21 |
Finally, dividing by 3 gives | x = 7 |
Hence, Jane is 7 years old and Sue is 2x – 5 = 2 * 7 – 5 = 9 years old. |
Motion problems
Virtually all motion problems involve the formula Distance = Rate * Time, or
Work problems
The formula for work problems is Work = Rate * Time, or W = R * T. The amount of work done is usually 1 unit. Hence, the formula becomes 1 = R * T.
Solving this for R gives R = 1/T
Mixture problems
The key to these problems is that the combined total of the concentrations in the two parts must be the same as the whole mixture.
Coin problems
The key to these problems is to keep the quantity of coins distinct from the value of the coins.
Age problems
Typically, in these problems, we start by letting x be a person’s current age and then the person’s age a years ago will be x – a, and the person’s age a years in the future will be x + a.
Interest problems
These problems are based on the formula:
INTEREST = AMOUNT * TIME * RATE
Often, the key to these problems is that the interest earned from one account plus the interest earned from another account equals the total interest earned:
Total Interest = (Interest from first account) + (Interest from second account)
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