Math Unit 2 - Number Operations and Concepts

Unit 2 - Number

• Integers: Adding, subtracting, multiplying, and dividing integers, including negative numbers.
• BIDMAS/BODMAS: Following the correct order of operations.
• Squares, Cubes, and Roots: Finding squares, cubes, and roots of numbers.
• HCF and LCM: Finding the highest common factor and lowest common multiple of numbers.
• Prime Factorization: Expressing numbers as a product of their prime factors.
• Decimals: Multiplying and dividing decimal numbers by integers and decimals.
• Rounding and Significant Figures: Rounding decimals to a given number of decimal places or significant figures.
• Approximation: Estimating answers to complex calculations.
• Fractions: Adding, subtracting, multiplying, and dividing fractions and mixed numbers.
• Fraction-Decimal-Percentage Conversion: Converting between fractions, decimals, and percentages.
• Recurring Decimals: Converting recurring decimals to fractions.
• Percentages: Calculating percentages of amounts, percentage increase/decrease, profit/loss, multipliers, and simple/compound interest and depreciation. Calculating reverse percentages.
• Ratio: Simplifying ratios and dividing quantities according to ratios. Solving problems using ratio (such as recipes, best buy, exchange rates).
• Proportion: Solving problems relating to direct and inverse proportions. Using graphs to represent direct and inverse proportions, including finding the constant of proportionality.
• Standard Form: Writing numbers in standard form (scientific notation).
• Indices: Working with exponents, including calculations with indices.
• Calculator Use: Using a calculator to perform calculations, including square roots, and working with standard form.
• Error Intervals / Bounds: Calculating lower and upper bounds, considering significant figures in calculations.
• Maps: Calculating real-world distances using a map scale.
• Exchange Rates: Comparing exchange rates for currency conversions.

Long Multiplication and Division

• Long Multiplication: Calculating the product of two larger numbers without a calculator. (e.g., 58 × 46)
• Long Division: Calculating the quotient of two larger numbers without a calculator. (e.g., A company has envelopes and needs to fill boxes, calculate how many are left over.)

Multiplying and Dividing Decimals

• Multiplying Decimals: Performing multiplication with decimals (e.g., 71.2 × 0.4).
• Dividing Decimals: Performing division with decimals (e.g., 71.2 ÷ 0.4).
• Example Calculation: 37.1 × 9.3.

Product of Prime Factors and HCF/LCM

• Prime Factorization: Expressing numbers as products of their prime factors. (e.g., Express 108 as a product of prime factors).
• HCF: Calculating the highest common factor of two numbers (e.g., Find the HCF of 108 and 72).

Rounding and Estimation

• Rounding: Rounding numbers to a specified number of significant figures. (e.g., Write 193.28 correct to one significant figure).
• Estimation: Estimating calculations to approximate the answer. (e.g., estimate the value of 18.3 + 62.8 / 0.13).

Fractions

• Fractions: Adding and subtracting and multiplying fractions. Give the answers as mixed numbers (e.g., 1 4/7 + 1/4)

Reciprocal

• Reciprocal: Finding the reciprocal of a number. (What is the reciprocal of 4?)

FDP

• Decimals to Fractions: Converting decimals to fractions. (e.g., Write 0.124 as a fraction).

Recurring Decimals

• Ordering Decimals: Ordering recurring decimals from smallest to largest (e.g., 0.705, 0.705, 0.705, 0.705).

Use of a Calculator

• Calculator Use: Using a calculator to evaluate expressions.
• Rounding: Rounding calculator answers to a specified number of decimal places. (e.g., √12.36−5.12 / 2.97).

Simple/Compound Interest

• Simple Interest: Calculating simple interest for a given principal, interest rate, and time period (e.g., Nina's investment).
• Compound Interest: Calculating compound interest for a given principal, interest rate, and time period (e.g., Fiona's investment).

Depreciation

• Depreciation: Calculating the depreciated value of an item over time (e.g., the car Greg bought).

Repeated Percentage Change

• Percentage Changes: Demonstrating and calculating repeated percentage changes over multiple years (e.g., Alex's investment in different banks).

Percentage Change

• Percentage Decrease: Calculating the percentage change when a quantity changes from one amount to another. (e.g., Peter's weight).

Reverse Percentages

• Reverse Percentages: Solving problems to calculate a starting amount that was decreased by a certain percentage. (e.g., the sale price of the TV is reduced by 20% and the sale price is £660).

Ratio - Simplifying, Writing as a Fraction, and Sharing

• Simplifying Ratios: Reducing a ratio to its simplest form (e.g., simplify 25:35).
• Sharing in a Ratio: Dividing a quantity into parts in a given ratio (e.g., dividing £700 in the ratio 5:3:2).

Ratio - Exchange Rates and Maps

• Exchange Rates: Calculating the value of a currency in another (e.g., £1 = €1.15).
• Maps: Calculating real-world distances using map scales (e.g., A map scale of 1:50000 and a map distance of 10cm).

Direct and Inverse Proportion

• Proportionality Relationships: Identifying different relationships of proportionality between variables in graphs (e.g., graphs representing A-D).
• Direct vs Inverse Proportion: Determining whether a relationship is directly or inversely proportional or proportional to the square of a variable.
• Solving Problems: Applying the concepts to solve problems involving proportion/inverse-proportion. (Finding a/b) (where a/b = k for example)

Standard Form

• Standard Form: Expressing numbers in scientific notation (e.g., write 0.21 × 106 in standard form).
• Calculations in Standard Form: Performing calculations involving numbers in standard form (e.g., calculate (8.694 × 102) ÷ (6.21 × 10-3)).

Indices

• Indices: Calculating the value of expressions involving exponents. (2⁹ × 2^-2 / 2⁴).

Error Intervals / Bounds

• Error Intervals: Determining an appropriate interval (e.g., given a value rounded to the nearest ten, what is the range of potential values?).
• Significant Figures: Using the concept of significant figures in calculations for bounds.
• Bounds: Finding the lower and upper bounds of a number or of calculated values given that one or more quantities or measurements contain an error margin.

Recipes

• Scaling Recipes: Using ratios to scale recipes up or down (given the number of ingredients that can make 12 shortcakes, finding how many shortcakes can be made with new ingredients).

This quiz covers fundamental concepts in mathematics related to numbers. It includes topics such as integers, operations following BIDMAS/BODMAS, and working with decimals, fractions, and percentages. Test your skills on finding HCF, LCM, prime factorization, and more!