1. Number
- Syllabus
- 0580–2028–2029
- Section
- 1
- Level
- Core
Exam analysis
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Recent 5 years
In this section
Topic C1.1
C1.1 Types of number
Objectives in this topic
C1.1.1 Identify and use: • natural numbers • integers (positive, zero and
- Identify and use: • natural numbers • integers (positive, zero and negative) • prime numbers • square numbers • cube numbers • common factors • common multiples • rational and irrational numbers • reciprocals. Example tasks include: • convert between numbers and words, e.g. six billion is
Topic C1.2
C1.2 Sets
Objectives in this topic
C1.2.1 Understand and use set language, notation and Venn diagrams to describe
- Understand and use set language, notation and Venn diagrams to describe sets. Venn diagrams are limited to two sets. The following set notation will be used: • n(A) Number of elements in set A • A′ Complement of set A • Universal set • A ∪ B Union of A and B • A ∩ B Intersection of A and B. Example definition of sets: A = {x: x is a natural number} B = {a, b, c, … } C = {x: a ⩽ x ⩽ b}.
Topic C1.3
C1.3 Powers and roots
Objectives in this topic
C1.3.1 Calculate with the following: • squares • square roots • cubes • cube
- Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers. Includes recall of squares and their corresponding roots from 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, For example, evaluate square and cube roots of familiar perfect powers.
Topic C1.4
C1.4 Fractions, decimals and percentages
Objectives in this topic
C1.4.1 Use the language and notation of the following in appropriate contexts:
- Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.
C1.4.2 Recognise equivalence and convert between these forms
- Recognise equivalence and convert between these forms. Candidates are expected to be able to write fractions in their simplest form. Candidates are not expected to use recurring decimal notation. Candidates are not expected to demonstrate the conversion of a recurring decimal to a fraction and vice versa.
Topic C1.5
C1.5 Ordering
Objectives in this topic
C1.5.1 Order quantities by magnitude and demonstrate familiarity with the
- Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, <, ⩾ and ⩽.
Topic C1.6
C1.6 The four operations
Objectives in this topic
C1.6.1 Use the four operations for calculations with integers, fractions and
- Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets. Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.
Topic C1.7
C1.7 Indices I
Objectives in this topic
C1.7.1 Understand and use indices (positive, zero and negative integers).
- Understand and use indices (positive, zero and negative integers).
C1.7.2 Understand and use the rules of indices
- Understand and use the rules of indices. e.g. find the value of 7 –2. e.g. find the value of 2–3 × 24, (23)2, 23 ÷ 24.
Topic C1.8
C1.8 Standard form
Objectives in this topic
C1.8.1 Use the standard form A × 10n where n is a positive or negative integer
- Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10.
C1.8.2 Convert numbers into and out of standard form.
- Convert numbers into and out of standard form.
C1.8.3 Calculate with values in standard form
- Calculate with values in standard form. Core candidates are expected to calculate with standard form only on Paper 3.
Topic C1.9
C1.9 Estimation
Objectives in this topic
C1.9.1 Round values to a specified degree of accuracy.
- Round values to a specified degree of accuracy.
C1.9.2 Make estimates for calculations involving numbers, quantities and
- Make estimates for calculations involving numbers, quantities and measurements.
C1.9.3 Round answers to a reasonable degree of accuracy in the context of a
- Round answers to a reasonable degree of accuracy in the context of a given problem. Includes decimal places and significant figures. e.g. write 5764 correct to the nearest thousand. For example, estimate a calculation by rounding each value to one significant figure.
Topic C1.10
C1.10 Limits of accuracy
Objectives in this topic
C1.10.1 Give upper and lower bounds for data rounded to a specified accuracy
- Give upper and lower bounds for data rounded to a specified accuracy. e.g. write down the upper bound of a length measured correct to the nearest metre. Candidates are not expected to find the bounds of the results of calculations which have used data rounded to a specified accuracy.
Topic C1.11
C1.11 Ratio and proportion
Objectives in this topic
C1.11.1 Understand and use ratio and proportion to: • give ratios in their
- Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context. e.g. 20: 30: 40 in its simplest form is 2: 3: 4. e.g. adapt recipes; use map scales; determine best value.
Topic C1.12
C1.12 Rates
Objectives in this topic
C1.12.1 Use common measures of rate.
- Use common measures of rate.
C1.12.2 Apply other measures of rate.
- Apply other measures of rate.
C1.12.3 Solve problems involving average speed
- Solve problems involving average speed. e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption. e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45 km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm³ (grams per cubic centimetre).
Topic C1.13
C1.13 Percentages
Objectives in this topic
C1.13.1 Calculate a percentage of a quantity
- Calculate a given percentage of a quantity.
C1.13.2 Express one quantity as a percentage of another
- Express one quantity as a percentage of another.
C1.13.3 Percentage increase and decrease
- Calculate percentage increase or decrease.
C1.13.4 Simple and compound interest
- Calculate with simple and compound interest; formulas are not given. Percentage contexts may include deposits, discounts, profit and loss, earnings and percentages greater than 100%.
Topic C1.14
C1.14 Using a calculator
Objectives in this topic
C1.14.1 Use a calculator efficiently.
- Use a calculator efficiently.
C1.14.2 Enter values appropriately on a calculator.
- Enter values appropriately on a calculator.
C1.14.3 Interpret the calculator display appropriately
- Interpret the calculator display appropriately. e.g. know not to round values within a calculation and to only round the final answer. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.
Topic C1.15
C1.15 Time
Objectives in this topic
C1.15.1 Calculate with time: seconds (s), minutes (min), hours (h), days,
- Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
C1.15.2 Calculate times in terms of the 24-hour and 12-hour clock.
- Calculate times in terms of the 24-hour and 12-hour clock.
C1.15.3 Read clocks and timetables
- Read clocks and timetables. 1 year = 365 days. In the 24-hour clock, for example, 3.15 a.m. will be denoted by 03 15 and 3.15 p.m. by 15 15. Includes problems involving time zones, local times and time differences.
Topic C1.16
C1.16 Money
Objectives in this topic
C1.16.1 Calculate with money.
- Calculate with money.
C1.16.2 Convert from one currency to another.
- Convert from one currency to another.