Core Number

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Sample objectives

What this unit covers

• Types of number: Recognize and utilize different types of numbers, including natural numbers, integers (both positive and negative, including zero), prime numbers, square numbers, cube numbers, rational and irrational numbers, and their reciprocals. Example tasks include converting numbers to words (e.g., six billion to 6,000,000,000), expressing 72 as a product of its prime factors, finding the highest common factor (HCF) of two numbers, and determining the lowest common multiple (LCM) of two numbers.
• Sets: Understand and apply the terminology and symbols related to sets, including the use of Venn diagrams for two sets. Be familiar with the following set notations: • n(A) represents the number of elements in set A • A' denotes the complement of set A • The universal set is indicated by ′ • A ∪ B signifies the union of sets A and B • A ∩ B indicates the intersection of sets A and B. For example, sets can be defined as follows: A = {x: x is a natural number}, B = {a, b, c, …}, C = {x: a < x < b}.
• Powers and roots Notes an⩽d ex⩽amples: Perform calculations involving powers and roots. This includes recalling the squares and their corresponding roots for numbers 1 to 15, as well as the cubes and their corresponding roots for the numbers 1, 2, 3, 4, 5, and 10. For example, find the square root of 169, write down the value of 52, and work out the cube root of 8, along with other powers and roots of numbers.
• Fractions, decimals and percentages: Understand and use the terms and symbols related to fractions, decimals, and percentages in suitable contexts. This includes writing fractions in their simplest form, recognizing proper and improper fractions, mixed numbers, decimals, and percentages. Be able to identify equivalent forms and convert between them, but do not need to convert recurring decimals to fractions or the other way around.
• Ordering: Arrange values in ascending or descending order and show understanding of the symbols for equality, inequality, greater than, less than, greater than or equal to, and less than or equal to.
• The four operations: Perform calculations using the four basic operations with various types of numbers, including integers, fractions, and decimals. This includes handling negative numbers, improper fractions, mixed numbers, and applying the correct order of operations with brackets. Additionally, apply these operations to real-life scenarios, such as changes in temperature.
• Indices I: Comprehend and apply the concept of indices, including positive numbers, zero, and negative integers. Additionally, understand and utilize the rules governing indices, such as calculating values for expressions like 2 × 2, (2^3), and 2 ÷ 2.
• Standard form: Understand and use standard form expressed as A × 10^n, where n is any integer and A is a number between 1 and 10. Be able to convert numbers to and from standard form, and perform calculations involving numbers in standard form. Note that core candidates will only perform calculations in standard form on Paper 3.
• Estimation: 1. Round numbers to a specified level of precision, including decimal places and significant figures. 2. Make estimates for calculations involving numbers, quantities, and measurements, such as rounding 5764 to the nearest thousand or estimating the value of 41.3 by rounding to 1 significant figure. 3. Round results to an appropriate level of accuracy based on the context of the problem.
• Limits of accuracy: Identify the upper and lower limits for values that have been rounded to a certain degree of accuracy, such as determining the upper limit for a length rounded to the nearest metre. Candidates do not need to calculate the limits for results derived from rounded data.
• Ratio and proportion: Understand and apply the concepts of ratio and proportion to: simplify ratios, such as converting 20 : 30 : 40 to its simplest form of 2 : 3 : 4; divide a quantity according to a specified ratio; and utilize proportional reasoning in various contexts, including modifying recipes, interpreting map scales, and identifying the best value in a situation.
• Rates: 1. Utilize standard measures of rate, such as calculating: • hourly wages • currency exchange rates • rates of flow • fuel efficiency. 2. Use additional measures of rate, including calculations for: • pressure • density • population density. The necessary formulas will be provided in the question. 3. Address problems related to average speed, requiring knowledge of the speed/distance/time formula. For example, if a cyclist covers 45 km in 3 hours and 45 minutes, determine their average speed. Notation examples include m/s (metres per second) and g/cm³ (grams per cubic centimetre).
• Percentages: 1 Find a specific percentage of a number. 2 Show how one number relates to another as a percentage. 3 Determine the increase or decrease in percentage. 4 Perform calculations involving simple and compound interest without provided formulas. Percentage calculations may involve: • deposits • discounts • profit and loss (expressed as either a value or a percentage) • earnings • percentages exceeding 100%.
• Using a calculator: Utilize a calculator effectively by avoiding rounding intermediate values and only rounding the final result. Input values correctly into the calculator, such as converting 2 hours 30 minutes to 2.5 hours or 2° 30’ 0’’. Understand the calculator's display, interpreting 4.8 as $4.80 in monetary terms and 3.25 as 3 hours 15 minutes in time.
• Time: 1 Perform calculations involving time units such as seconds, minutes, hours, days, weeks, months, and years, including understanding the relationships between these units. 2 Convert times between the 24-hour clock and the 12-hour clock, for instance, recognizing that 3:15 a.m. is represented as 03:15 and 3:15 p.m. as 15:15. 3 Interpret clocks and timetables, including solving problems related to time zones, local times, and differences in time.
• Money: Perform calculations involving money and convert amounts between different currencies.