Admissions Test Preparation · Practice Set 6
ESAT Mathematics Mock Module 6 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 | Midpoint across quadrants | Average the x-coordinates and average the y-coordinates |
| Q2 | Reading geometric notation | Matching marks mean matching measurements |
| Q3 | Circle vocabulary | A chord joins two points; a tangent touches at one |
| Q4 | Highest common factor | Take the lowest power of each shared prime |
| Q5 | Dividing powers of the same base | Same base dividing means subtract the indices |
| Q6 | Sharing in a three-part ratio | Total the parts, find one part, then scale |
| Q7 | Percentage increase | The change over the original, never over the new value |
| Q8 | Expanding two brackets | Every term in the first meets every term in the second |
| Q9 | Factorising a quadratic | Two numbers multiplying to c and adding to b |
| Q10 | Simultaneous equations by elimination | Add when the coefficients are equal and opposite |
| Q11 | Solving a quadratic by factorising | Factorise, then set each bracket to zero |
| Q12 | Area of a trapezium | Average the parallel sides, then multiply by the height |
| Q13 | Volume of a cylinder | Cross-sectional area times length |
| Q14 | Arc length of a sector | The angle's fraction of 360 degrees, applied to the circumference |
| Q15 | Choosing the right trigonometric ratio | Label the sides relative to the angle, then pick the ratio that uses the two you have |
| Q16 | Locating the median on a cumulative frequency graph | Read across at half the total frequency |
| Q17 | A possibility space for two dice | Count the favourable cells out of thirty-six |
| Q18 | Mean, median and range | Order the list once, then read every average off it |
| Q19 | Median of an even-sized set | Locate the median by position, then average the two middle values |
| Q20 | Mean from a frequency table | $\bar x = \dfrac{\sum fx}{\sum f}$ — weight every value by how often it occurs |
| Q21 | Estimated mean of grouped data | Use the class midpoint as the value |
| Q22 | Median class from cumulative frequency | Find the median position, then read across the running total |
| Q23 | Interquartile range | Quartiles are positions too, and the IQR ignores the extremes |
| Q24 | Working backwards from a mean | Means become totals, and totals subtract |
| Q25 | Coding a data set | The mean follows the whole transformation; the range ignores the shift |
| Q26 | Identifying an outlier | A value beyond $1.5\times\text{IQR}$ past a quartile is an outlier |
| Q27 | Reading a cumulative frequency total | Subtract running totals to count what lies above a value |