Admissions Test Preparation · Practice Set 4
ESAT Mathematics Mock Module 4 of 7
27 a full 27-question module, the same length and shape as one sitting of the real test. Mathematics 1 is compulsory for every ESAT candidate. Number, ratio, algebra, geometry, statistics and probability, drawn from across the whole specification. Every question states the specification sub-topic it was written against.
How to use this set
Every question carries a target time, and no question needs a calculator. Attempt each one against the clock with the solution collapsed. If you are still setting up algebra when the target time passes, stop and open the solution: the shortcut is what the question is testing, and the arithmetic is not.
Read the Key Idea before the full breakdown. If the key idea alone lets you redo the question in under a minute, the method has landed and you can move on. If it does not, work the step-by-step breakdown and then return to the question a day later.
The Common Mistake section on each question is the slower route that still reaches the right answer. Under exam conditions that route is usually the difference between finishing the module and running out of time.
Modules in this set
Select a module below to view the questions and their step-by-step worked solutions:
Mathematics
27 questions, 40 minutes in the real test. Mathematics 1 is compulsory for every ESAT candidate. Number, ratio, algebra, geometry, statistics and probability, drawn from across the whole specification. 27 worked solutions.
Shortcut index
Use this as a revision checklist. If you can state the shortcut before opening the question, you already have the mark.
Mathematics
| # | Topic | Shortcut rehearsed |
|---|---|---|
| Q1 | Elimination | Add the equations when one variable's coefficients are opposite |
| Q2 | Factorising a difference of squares | Recognise the pattern rather than trial factors |
| Q3 | Mean from a frequency table | $\sum fx \div \sum f$, never the mean of the values |
| Q4 | Significant figures | Round from the first non-zero digit, and let the carry cascade |
| Q5 | Similar triangles | Find the scale factor once, then apply it to every length |
| Q6 | Volume of a prism | Cross-sectional area times length |
| Q7 | Rearranging formulas | Undo the operations in reverse order |
| Q8 | Repeated percentage increase | Square the multiplier for two identical changes |
| Q9 | Ratios with units | Convert to a common unit before simplifying |
| Q10 | Lowest common multiple in context | Events coincide at the LCM of their intervals |
| Q11 | Independent repeated trials | With replacement, multiply the same probability |
| Q12 | Pythagoras in context | Recognise the triple before computing |
| Q13 | Dividing fractions | Multiply by the reciprocal, cancel before multiplying |
| Q14 | Comparing coefficients | Match the expanded form term by term |
| Q15 | Compound measures | Read the formula straight off the units |
| Q16 | Integer solutions of an inequality | Solve the double inequality, then count carefully at the ends |
| Q17 | Map scales | Multiply by the scale, then convert units once |
| Q18 | Time series trends | Check the differences: a constant difference means a linear trend |
| Q19 | The danger of extrapolation | A line of best fit is only evidence inside the range of the data |
| Q20 | Choosing an average for a purpose | Match the average to the decision being made |
| Q21 | Arc length of a sector | Take the angle's fraction of the whole circumference |
| Q22 | Interpolation within the data | A line of best fit is evidence inside the range and speculation outside it |
| Q23 | Combined proportionality | One constant covers both proportionalities |
| Q24 | Forming an equation from words | Name the unknown, convert each clause, then solve |
| Q25 | Working back from a surface area | Rearrange the formula for the defining length |
| Q26 | Telling an identity from an equation | An identity must hold for every value, not just one |
| Q27 | Finding a constant by comparing coefficients | Match the coefficients of each power on both sides |