# ECAA Section 1A Guide

Section 1A of the ECAA examines mathematics. Students don't usually have too much trouble with this section, but that doesn't make their preparation any less important. We have included some tips on Section 1A and the syllabus to help you get started with your preparation.

Author: Tom Dyer

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The ECAA is no longer being used for Cambridge Economics. The TMUA is used instead for 2022 Economics Applicants.

ECAA Section 1A tests Maths. Students tend not to struggle too much with this section – but this does not make preparing for it any less important.

Section 1 (A and B) is a 60-minute section with 40 questions so students have just over 2 minutes for each question. Students often lose the most marks by wasting their minimal time on tricky questions. You have an equal amount of time for Section 1A and Section 1B (although you can use the time how you wish, the examiners strongly recommend you spend equal parts on both).

Before we begin, try this practice question (explained answer at the end):

## Starting with the simple tips

Since the time pressure of the exam is quite harsh, students can often disregard this basic tip. Make sure you read the entire question and understand what it is asking of you.

• Use the options

Using the options effectively allows you to pick out key information from the question and quickly disregard some options. This is the beauty of a multiple-choice test and you should use it to your advantage.

• Don’t be afraid to skip and come back to questions

You should do a lot of practice beforehand to ensure you know the timing of the test very well before employing this tip. You can skip questions that will “waste” your time. If a question is difficult and it’s taking you longer than it should do, skip it, make a mental note and come back to it at the end.

• Mental maths

It may be a while since you’ve had to do any significant mental maths, however, it’s worth brushing up on these skills for the ECAA. You cannot use a calculator for any sections of the ECAA so being able to quickly work out figures in your head will save you a lot of time.

## Then Onto The Bulk Of the Specification

The next step is to look at the entire Maths syllabus. This looks like a lot, but once you realise that most of the content in Section 1A is relatively straightforward, it doesn’t seem quite so bad.

Instead of a revision list, consider this specification as more of a checklist to tick off as you read it. Most of these topics will be familiar to you and are unlikely to need much focus. If there are any that you aren’t 100% confident with, brush up on that particular section to ensure you’re prepared for the ECAA.

 M1.1 Use standard units of mass, length, time, money and other measures. Use compound units such as speed, rates of pay, unit pricing, density and pressure, including using decimal quantities where appropriate. M1.2 Change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts.

 M2.1 Order positive and negative integers, decimals and fractions. Understand and use the symbols: = , ≠ , < , > , ≤ , ≥ . M2.2 Apply the four operations (addition, subtraction, multiplication and division) to integers, decimals, simple fractions (proper and improper) and mixed numbers – any of which could be positive and negative. Understand and use place value. M2.3 Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, and prime factorisation (including use of product notation and the unique factorisation theorem). M2.4 Recognise and use relationships between operations, including inverse operations. Use cancellation to simplify calculations and expressions. Understand and use the convention for priority of operations, including brackets, powers, roots and reciprocals. M2.5 Apply systematic listing strategies. (For instance, if there are m ways of doing one task and for each of these tasks there are n ways of doing another task, then the total number of ways the two tasks can be done in order is m× n ways.) M2.6 Use and understand the terms: square, positive and negative square root, cube and cube root. M2.7 Use index laws to simplify numerical expressions, and for multiplication and division of integer, fractional and negative powers. M2.8 Interpret, order and calculate with numbers written in standard index form (standard form); numbers are written in standard form as a × 10n, where 1 ≤ a < 10 and n is an integer. M2.9 Convert between terminating decimals, percentages and fractions. Convert between recurring decimals and their corresponding fractions M2.10 Use fractions, decimals and percentages interchangeably in calculations. Understand equivalent fractions. M2.11 Calculate exactly with fractions, surds and multiples of π. Simplify surd expressions involving squares, e.g. √12 = √4 x 3 = √4√3 = 2√3, and rationalise denominators; for example, candidates could be asked to rationalise expressions such as: 3 / √7, 5 / 3 + 2√5, 7 / 2 – √3, 3 / √5 – √2. M2.12 Calculate with upper and lower bounds, and use in contextual problems. M2.13 Round numbers and measures to an appropriate degree of accuracy, e.g. to a specified number of decimal places or significant figures. Use inequality notation to specify simple error intervals due to truncation or rounding. M2.14 Use approximation to produce estimates of calculations, including expressions involving π or surds.

 M3.1 Understand and use scale factors, scale diagrams and maps. M3.2 Express a quantity as a fraction of another, where the fraction is less than 1 or greater than 1. M3.3 Understand and use ratio notation. M3.4 Divide a given quantity into two (or more) parts in a given part:part ratio. Express the division of a quantity into two parts as a ratio. M3.5 Apply ratio to real contexts and problems, such as those involving conversion, comparison, scaling, mixing and concentrations. Express a multiplicative relationship between two quantities as a ratio or a fraction. M3.6 Understand and use proportion. Relate ratios to fractions and to linear functions. M3.7 Identify and work with fractions in ratio problems. M3.8 Define percentage as ‘number of parts per hundred’. Interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively. Express one quantity as a percentage of another. Compare two quantities using percentages. Work with percentages greater than 100%. Solve problems involving percentage change, including percentage increase/decrease, original value problems and simple interest calculations. M3.9 Understand and use direct and inverse proportion, including algebraic representations. Recognise and interpret graphs that illustrate direct and inverse proportion. Set up, use and interpret equations to solve problems involving direct and inverse proportion (including questions involving integer and fractional powers). Understand that x is inversely proportional to y is equivalent to x is proportional to 1 / y. M3.10 Compare lengths, areas and volumes using ratio notation. Understand and make links to similarity (including trigonometric ratios) and scale factors M3.11 Set up, solve and interpret the answers in growth and decay problems, including compound interest, and work with general iterative processes.

 M6.1 Interpret and construct tables, charts and diagrams, including: a. two-way tables, frequency tables, bar charts, pie charts and pictograms for categorical data b. vertical line charts for ungrouped discrete numerical data c. tables and line graphs for time series data Know the appropriate use of each of these representations. M6.2 Interpret and construct diagrams for grouped discrete data and continuous data: a. histograms with equal and unequal class intervals b. cumulative frequency graphs Know the appropriate use of each of these diagrams. Understand and use the term frequency density. M6.3 Calculate the mean, mode, median and range for ungrouped data. Find the modal class; calculate estimates of the range, mean and median for grouped data, and understand why these are estimates. Describe a population using statistics. Make simple comparisons. Compare data sets using like-for-like summary values. Understand the advantages and disadvantages of summary values. Calculate estimates of mean, median, mode, range, quartiles and interquartile range from graphical representation of grouped data. Use the median and interquartile range to compare distributions. M6.4 Use and interpret scatter graphs of bivariate data. Recognise correlation, and know that it does not indicate causation. Draw estimated lines of best fit. Interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

 M6.1 Analyse the frequency of outcomes of probability experiments using tables and frequency trees. M6.2 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments. Understand that if an experiment is repeated, the outcome may be different. M6.3 Relate relative expected frequencies to theoretical probability, using appropriate language and the ‘0 to 1’ probability scale. M6.4 Apply the property that the probabilities of an exhaustive set of outcomes sum to one. Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one. M6.5 Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams. Candidates are not expected to know formal set theory notation. M6.6 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes, and use these to calculate theoretical probabilities. M6.7 Know when to add or multiply two probabilities, and understand conditional probability. Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams. Understand the use of tree diagrams to represent outcomes of combined events: a. when the probabilities are independent of the previous outcome b. when the probabilities are dependent on the previous outcome.

Whatever your exam board, you should have covered all of these topics at some point during your GCSEs and A-levels.

## How is Section 1 of the ECAA scored?

In Section 1, each correct answer scores 1 mark and is scored on a scale of 1.0 to 9.0. No marks are deducted for incorrect answers. Results for Part A and Part B are reported separately.

Most students score between 3.0-5.0 on Section 1A and the strongest candidates score over 6.0. This is the same with Section 1B but you should aim for 6.5 to stand out from other applicants.

## ECAA Section 1A worked example

Example ECAA Section 1A Question:

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