Year 7 Maths - End of Year Revision Guide

Arithmetic Sequences and Linear Algebra

7K1: Finding the nth Term of Arithmetic Sequences - Description: Identification of the rule that describes the relationship between the position of a term in a sequence and its value. - Core Concept: An arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. The formula is typically expressed in the form $an + b$ , where $a$ is the common difference. - Sparx Code: M991.
7K3: Substitution into Expressions and Formulae - Description: The process of replacing variables (letters) or words in mathematical expressions and formulae with specific numerical values, including positive and negative integers, decimals, and fractions. - Mathematical Rule: When substituting a value for a variable, operations such as multiplication (e.g., $3x$ ) and exponentiation (e.g., $x^2$ ) must be performed following the order of operations (BIDMAS/BODMAS). - Sparx Code: M327.
7K11: Simplifying Expressions by Collecting Like Terms - Description: Reducing a mathematical expression to its simplest form by combining terms that have the same variables raised to the same powers. - Process: Only terms with the exact same variable component can be added or subtracted from one another (e.g., $3a + 2a = 5a$ , but $3a + 2b$ remains unchanged). - Sparx Codes: M795, M531.
7D1: Using the nth Term for Positional Calculations - Description: Applying a known $n^{th}$ term formula to determine the value of a term at a specific position in a sequence (e.g., finding the $100^{th}$ term where $n = 100$ ). - Classification: Desirable skill (7D1). - Sparx Code: M166.
7D5: Solving Linear Equations with Unknowns on Both Sides - Description: Solving equations where the variable appears on both the left-hand and right-hand sides (e.g., $5x + 3 = 2x + 12$ ). - Methodology: Involves using inverse operations to move all terms containing the unknown to one side and all constant numerical values to the other. - Classification: Desirable skill (7D5). - Sparx Code: M554.

Number Properties and Basic Arithmetic

7K2: Number Classifications (Primes, Squares, Factors, and Multiples) - Prime Numbers: Numbers greater than $1$ that have exactly two distinct factors: $1$ and the number itself. - Square Numbers: The result of multiplying an integer by itself (e.g., $1, 4, 9, 16, 25, \text{...}$ ). - Factors: Whole numbers that divide exactly into another number without leaving a remainder. - Multiples: Numbers found in the multiplication table of a specific integer. - Sparx Codes: M322, M823.
7K9: Rounding Numbers - Decimal Places (DP): Rounding a number to a specified level of precision based on the digits following the decimal point. - Significant Figures (SF): Rounding a number to a specific number of meaningful digits, starting from the first non-zero digit. - Sparx Codes: M431, M994.
7K16: Real-Life Problem Solving with Four Operations - Scope: Utilizing addition, subtraction, multiplication, and division to solve practical, contextualized word problems.
7K17: Calculating with Time - Core Concepts: Adding and subtracting time durations, converting between units of time (minutes, hours, seconds), and reading digital/analogue clocks. - Sparx Code: M627.

Fractions, Decimals, and Percentages (FDP)

7K4: Fluent Conversions Between FDP - Description: The ability to move interchangeably between fractions, decimals, and percentages (e.g., $\frac{1}{2} = 0.5 = 50\%$ ). - Sparx Code: M264.
7K5: Fractions and Percentages of Amounts - Calculator Methods: Using a scientific calculator to find values (e.g., using the percentage key or multiplying by a decimal equivalent). - Non-Calculator Methods: Finding percentages using benchmarks ( $10\%$ , $5\%$ , $1\%$ ) and fractions by dividing by the denominator and multiplying by the numerator. - Sparx Codes: M695, M437.

Geometry, Angles, and Constructions

7K6: Measuring Angles - Tool Requirement: Proficiency in the use of a protractor to measure the size of angles in degrees ( $^\circ$ ). - Sparx Code: M780.
7K7: Angle Facts in Triangles - Fundamental Principle: The sum of interior angles in any triangle is exactly $180^\circ$ . - Application: Determining the value of a missing angle when two others are known ( $180 - (a + b) = c$ ). - Sparx Codes: M502, M351.
7D2: Accurate Construction of Triangles - Tools: Straight edge, protractor, and compasses. - Specific Construction Methods: - ASA: Angle-Side-Angle. - SAS: Side-Angle-Side. - SSS: Side-Side-Side. - Sparx Codes: M196, M565.
7D3: Forming Equations from Angle Facts - Description: Using geometric properties (such as angles on a straight line or in a triangle) to set up and solve algebraic equations (e.g., $2x + 3x + 40 = 180$ ). - Classification: Desirable skill (7D3). - Sparx Code: M957.

Statistics and Data Representation

7K8: Statistical Diagrams - Pictograms: Representing data using icons where each symbol represents a specific frequency. - Bar Charts: Using rectangular bars with heights/lengths proportional to the values they represent. - Pie Charts: Segmenting a circle into sectors that represent proportions of a whole data set. - Two-Way Tables: Organizing data into rows and columns to show the relationship between two categorical variables. - Sparx Codes: M597, M644, M460, M738, M899.
7K12: Measures of Central Tendency and Spread - Mean: The sum of all values divided by the total number of values ( $\frac{\sum x}{n}$ ). - Median: The middle value when the data set is arranged in numerical order. - Mode: The value that appears most frequently in a data set. - Range: The difference between the maximum and minimum values ( $x_{max} - x_{min}$ ). - Sparx Codes: M940, M934, M841.

Powers, Indices, and Equations

7K10: Simple Index Laws - Focus: Understanding and applying basic rules for exponents (indices). - Sparx Codes: M608, M150.
7D4: Combination of Index Laws - Description: Applying multiple rules of indices simultaneously (e.g., $(a^n)^m = a^{n \times m}$ or $\frac{a^n \times a^m}{a^k}$ ). - Classification: Desirable skill (7D4). - Sparx Code: M120.
7K13: Solving Two-Step Linear Equations - Process: Using two distinct inverse operations to isolate a variable (e.g., to solve $2x + 5 = 15$ , one subtracts $5$ then divides by $2$ ). - Sparx Code: M509.

Mensuration, Perimeter, and Area

7K14: Area and Perimeter of Composite Shapes - Composite Shapes: Shapes constructed from rectangles (rectilinear) and triangles. - Perimeter: The total distance around the boundary of the shape. - Area Formulae: - Rectangle: $\text{Area} = \text{base} \times \text{height}$ . - Triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ . - Sparx Code: M690.

Probability and Inequalities

7K18: Probability Scales - Scale Range: Probability is measured on a scale from $0$ (impossible) to $1$ (certain). - Qualitative Terms: Impossible, unlikely, even chance, likely, certain. - Sparx Code: M655.
7K19: Inequality Symbols - Greater Than: $>$ - Less Than: $<$ - Less Than or Equal To: $\le$ - Greater Than or Equal To: $\ge$ - Sparx Code: M384.
7D6: Representing Inequalities on a Number Line - Notation: Using open circles for $>$ and $<$ (exclusive) and closed/shaded circles for $\le$ and $\ge$ (inclusive). - Classification: Desirable skill (7D6). - Sparx Code: M384.

Coordinates and Transformations

7K20: Plotting Points in Four Quadrants - System: Locating coordinates expressed as $(x, y)$ on a Cartesian plane including positive and negative axes. - Sparx Code: M618.
7D7: Describing Translations with Column Vectors - Column Vector Notation: Represented as $\begin{pmatrix} x \\ y \end{pmatrix}$ , where the top number ( $x$ ) indicates horizontal movement (right if positive, left if negative) and the bottom number ( $y$ ) indicates vertical movement (up if positive, down if negative). - Classification: Desirable skill (7D7). - Sparx Code: M139.

Mathematical Equipment

7K15: Scientific Electronic Calculator Usage - Definition: Proficiency in using a scientific calculator to determine numerical results for complex calculations. - Sparx Code: M757.

Questions & Discussion

Resource Links: The document references several digital resources for revision. - Videos: Links provided for all topics (labeled as "Here"). - Practice Questions: External tasks provided for all topics (labeled as "Here"). - Sparx Maths: Each topic is mapped to a specific Sparx Math code (e.g., M991, M322) for targeted practice.