Admissions Test Preparation · Practice Set 5
ESAT Mathematics Mock Module 5 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 | Substituting strategic values into an identity | Choose the value of x that kills a term |
| Q2 | Distance from a speed-time graph | Area under a speed-time graph is distance |
| Q3 | Inequalities in two variables | Test the point against each inequality and stop at the first failure |
| Q4 | Congruence criteria | Two sides and a non-included angle prove nothing |
| Q5 | Angle at the centre | The angle at the centre is twice the angle at the circumference |
| Q6 | Scaling and subtracting column vectors | Scale each component, then combine component by component |
| Q7 | Identifying a quadrilateral from its diagonals | Diagonals identify the quadrilateral |
| Q8 | Estimating a calculation | Round each number to one figure, then choose a friendly denominator |
| Q9 | Ordering mixed forms | Put everything into decimals, and remember negatives run backwards |
| Q10 | Mixing two concentrations | Work in the quantity of the ingredient, not in the percentages |
| Q11 | Matching a graph to its equation | Asymptotes name the family before any point is plotted |
| Q12 | Reading a distance-time graph | On a distance-time graph the gradient is speed and a flat section is a stop |
| Q13 | Generating terms from a term-to-term rule | A term-to-term rule is followed, not solved |
| Q14 | Angles on parallel lines | Name the angle fact, then the equation writes itself |
| Q15 | Enlargement with a negative scale factor | A negative scale factor scales and turns through the centre |
| Q16 | Counting edges on a prism | A prism has two copies of its cross-section plus one edge per corner |
| Q17 | Identifying a solid from its views | Each view fixes one dimension; three views fix the solid |
| Q18 | Opposite angles of a cyclic quadrilateral | Opposite angles of a cyclic quadrilateral sum to a straight line |
| Q19 | Estimating an expression with π and a surd | Round π to 3 and every surd to the nearest exact root |
| Q20 | Finding the first term past a threshold | Solve the boundary, then test the integer either side |
| Q21 | Undoing a chain of operations | Reverse the operations in reverse order |
| Q22 | Equivalent forms | Convert everything to decimals and compare |
| Q23 | Map scales | Multiply by the scale, then convert the units once |
| Q24 | One quantity as a fraction of another | Put both into the same unit before writing the fraction |
| Q25 | Translating words into algebra | Read the operations in the order the words impose, not left to right |
| Q26 | Index laws in algebra | The outer power hits every factor, then subtract indices to divide |
| Q27 | Substituting into a formula | Bracket every negative value before you substitute it |