# Gareth Evans's Shop

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Secondary Mathematics Resources.

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Secondary Mathematics Resources.

#### Revision Cards for WJEC Mathematics

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A set of revision cards for the WJEC Numeracy and Mathematics specifications. The cards correspond to the 30 workbooks available for free in the author’s TES shop. Instructions for creating the cards: (1) Print the sheets back-to-back (there should be 6 pieces of A4 paper in total). (2) Laminate the sheets (optional). (3) Cut out the individual cards (6 to each piece of A4 paper). (4) Punch a single hole in each corner. (This is easier to do if you have a single hole punch.) (5) Feed a key-ring through the holes.

#### The End of Year 11

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A year 11 unit of work covering the following topics: (1) Surds: Rational and irrational numbers. Surds. Simplifying surds. Expanding with surds. (2) AER, APR. Annual Equivalent Rate (AER). Alternative method of calculating AER. Annual Percentage Rate (APR). (3) Histograms: Frequency density. Drawing a histogram. Interpreting a histogram. Estimating the median from a histogram. Estimating the quartiles from a histogram. Comparing histograms.

#### Measuring Shapes 5

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A year 11 unit of work covering the following topics: (1) 3–D Trigonometry: 2–D Trigonometry (Revision). 3–D Trigonometry. (2) The Sine Rule, The Cosine Rule: The Sine Rule. The Cosine Rule. Sine Rule or Cosine Rule? (3) Area of a Triangle: Calculating the area of a triangle. (4) Trigonometric Graphs: The unit circle. Trigonometric graphs. Solving trigonometric equations. Function transformations.

#### Developing Algebra 4

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A year 11 unit of work covering the following topics: (1) Transformations of Functions: Function notation. Translation. Stretching. Reflection. (2) Pre-Calculus: Tangent to a function. Travel graphs. Displacement, Velocity and Acceleration. The area between a graph and the 𝒙–axis. The Trapezium Rule. (3) Further Changing the Subject: Revision of previous work. Changing the subject where the subject appears more than once. (4) The Quadratic Formula: Solving quadratic equations. Solving problems. (5) Algebraic Fractions: Numerical fractions. Algebraic fractions. Solving equations involving algebraic fractions.

#### Developing Probability

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A year 11 unit of work covering the following topics. (1) Relative Frequency: Revision. Relative Frequency. (2) Combined Events: Independent events. Dependent events. Mutually exclusive events. Venn diagrams. Sample space diagrams and dependent events. (3) Tree Diagrams: Displaying combinations of two or more events. Independent events. Dependent events.

#### Measuring Shapes 4

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A year 11 unit of work covering the following topics. (1) Congruent Shapes: Recognising congruent shapes. Congruent triangles proofs. (2) Angles in Polygons: The interior angles of a polygon. The exterior angles of a polygon. Tessellations. (3) Circle Theorems: Intermediate tier circle theorems. Higher tier circle theorems. (4) Transformations: Translation. Rotation. Reflection. Enlargement. Combinations.

#### Developing Algebra 3

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A year 11 unit of work covering the following topics. (1) Direct and Inverse Proportion: Direct Proportion. Inverse Proportion. More than one Proportion. Proportion Graphs. (2) Proportion Equations: Direct Proportion. Inverse Proportion. Finding Proportion Equations. (3) Quadratic Nth Term Linear Nth Term. The First Difference. Simple Quadratic Sequences. More Complex Quadratic Sequences. (4) Inequalities: Inequality Symbols. Inequalities on a Number Line. Solving Equations. Solving Inequalities. (5) Regions of Graphs: Revising plotting graphs of the form 𝑥 = 𝑎 and 𝑦 = 𝑏. Revising plotting graphs of the form 𝑦 = 𝑚𝑥 + 𝑐. Plotting graphs of the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0. Shading Regions.

#### Accuracy of Measurements

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A year 10 unit of work covering the following topics. (1) Upper and Lower Bounds: Revision of how to round off. Upper and lower bounds. Problem solving (intermediate tier). Problem solving (higher tier). (2) Appropriate Degree of Accuracy: Calculating answers to an appropriate degree of accuracy. (3) Compound Measures: Distance, time and speed. Population, area and population density. Mass, volume and density. Other compound measures.

#### Measuring Solids

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A year 10 unit of work covering the following topics. (1) Solids: Volume and surface area of a cuboid. Volume of a prism. Volume and surface area of a cylinder. Volume of a pyramid. Surface area of a cone. Volume and surface area of a sphere. (2) Dimensions: Length, area and volume. Nonsensical formulae. (3) Composite Solids: Volume of composite solids. Frustum of a cone. Hemisphere. (4) Similar Shapes: Calculating the scale factor. Calculating missing lengths. Similar or not? Similar triangles. Scale factor for length, area and volume. Using similar triangles to calculate the volume of a frustum of a cone. (5) Pythagoras’ Theorem (3-D): Calculating lengths in three-dimensional shapes.

#### Developing Algebra 2

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A year 10 unit of work covering the following topics. (1) Simple Factorising: Reversing Expansion. Simple Factorising.More than one Variable. (2) Factorising Quadratic Expressions: Preparation. Factorising Quadratic Expressions of the form 𝑥² + 𝑎𝑥 + 𝑏. Solving Quadratic Equations through Factorising. Factorising Quadratic Expressions of the form 𝒂𝒙² + 𝒃𝒙 + 𝒄. The Difference of Two Squares. (3) Simultaneous Equations: Multiplying Equations. Subtracting Equations. Multiplying Equations to obtain Equal Coefficients. Solving Linear Equations. Solving Simultaneous Equations. (4) Changing the Subject: Re-arranging formulae. (5) Expression, Equation, Formula, Identity: Recognising expressions, equations, formulae and identities. Proving identities.

#### Fractions, Percentages and Decimals

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A year 10 unit of work covering the following topics: (1) Calculating: Mastering the techniques. Problem solving. (2) Recurring Decimals: Changing fractions to decimals. Terminating and recurring decimals. Changing recurring decimals to fractions. (3) Converting: Converting between fractions, decimals and percentages. Starting with a percentage. Starting with a fraction. Starting with a terminating decimal. Starting with a recurring decimal. (4) Exam Technique: Summary. Assessing written communication. Mark schemes. Timing.

#### Measuring Shapes 3

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A year 10 unit of work covering the following topics. (1) Trigonometry of Right-Angled Triangles. Labelling triangles. Calculating the length of a side. Calculating the size of an angle. (2) Transformations: Enlargement. Positive scale factor. Fractional scale factor. Centre of enlargement. Finding the centre of enlargement. Negative scale factor. (3) Tessellations: Tessellating with triangles. Tessellating with quadrilaterals. (4) Perimeter and Area of Composite Shapes. Composite shapes. Length of an arc and the area of a sector.

#### Powers and Roots

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A year 10 unit of work covering the following topics. (1) Rules of Indices: The index form. Evaluating the index form. The multiplication rule. The division rule. The zeroth index rule. Raising a power to another index. The negative index rule. The reciprocal as a negative index. Unitary fraction index rule. Algebra and rules of indices. The general fraction index rule. (2) Standard Form: Writing numbers 𝑥 ≥ 1 in standard form. Writing numbers 0 &lt; 𝑥 &lt; 1 in standard form. Changing from standard form to an ordinary number. Adding and subtracting in standard form. Almost in standard form. Multiplying and dividing in standard form. (3) Efficient Percentage Changes: Repeated percentage changes. Calculating compound interest efficiently. Fractional changes. Reverse percentages. (4) Graph Plotting: Quadratic graphs. Recognising and sketching graphs of the form 𝑦 = 𝑎𝑥² + 𝑏. Graphical method of solving equations of the form 𝑥² + 𝑎𝑥 + 𝑏 = 0. Other graphs.

#### Data Handling and Statistics 4

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A year 10 unit of work covering the following topics: (1) Questionnaires: Designing questionnaires. Criticising questions. Hypotheses. (2) Sampling: Simple random sampling. Systematic sampling. Stratified sampling. (3) Frequency Polygons: Drawing frequency polygons. Interpreting frequency polygons. (4) Box and Whisker Diagrams: Drawing box and whisker diagrams. The connection between box and whisker diagrams and cumulative frequency diagrams. (5) Comparing Averages: Revising averages. Choosing the most appropriate average. Comparing averages.

#### Movement with Sphero

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A year 9 unit of work on the following topics. (1) Programming Sphero: Working Systematically. Thinking Logically. (2) Travel Graphs: Distance, Time and Speed. Distance-Time Graphs. Speed-Time Graphs. (3) Bearings: Directions of the Compass. Moving on a Plane. Finding Bearings. Locating a Point. (4) Loci: Distance from a Point. Distance from a Line. Perpendicular Bisector. Angle Bisector. Drawing the Perpendicular from a Point to a Line.

#### Straight Line Graphs

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A year 9 unit of work on the following topics: (1) Gradient of a Line: Measuring and finding the gradient of straight lines. (2) Straight Line Graphs: Vertical lines of the form 𝑥 = 𝑎. Horizontal lines of the form 𝑦 = 𝑏. General lines of the form 𝑦 = 𝑚𝑥 + 𝑐. Solving simultaneous equations graphically. (3) The Gradient of Parallel and Perpendicular Lines: The gradient of parallel lines. The gradient of perpendicular lines. (4) Transformations: Reflection: Reflecting shapes in lines of the form 𝑥 = 𝑎 and 𝑦 = 𝑏. Reflecting shapes in lines of the form 𝑦 = 𝑚𝑥 + 𝑐.

#### Working with Money

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A year 9 unit of work containing the following topics. (1) Rounding Off: Significant Figures: Rounding a number off to a specified number of significant figures. Labelling the significant figures of a number. (2) Estimation: Estimating the answer to calculations. (3) Compound Interest: Revising simple interest. The compound interest method of borrowing and investing money. (4) Foreign Money: Exchange rates. Exchanging money. (5) Household Bills: Electricity; gas; water; sewerage and mobile phone bills.

#### Data Handling and Statistics 3

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A year 9 unit of work containing the following topics. (1) The Median: Calculating the median. Calculating the median from a table. Comparing two distributions. (2) The Median Class: Finding the median class or the estimate for the median. (3) The Interquartile Range: Calculating the interquartile range of a set of data. (4) Cumulative Frequency Diagrams: Cumulative frequency tables. Drawing a cumulative frequency diagram. Estimating the median and the interquartile range. (5) Scatter Diagrams: Drawing a scatter diagram. Types of correlation. Line of best fit. (6) Probability as a Fraction Writing the probability of an event as a fraction. The probability that an event will not happen. Sample space diagrams. Expected frequency.

#### Developing Algbera 1

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A year 9 unit of work covering the following topics: (1) Linear Nth Term: Terms of a sequence. Finding the 𝑛th term. Finding the position of a term. (2) Expanding Brackets: Expanding numerical sums. Multiplying algebraic terms. Expanding algebraic expressions. Expanding and simplifying. (3) FOIL: Expanding a double bracket. Expanding and simplifying a double bracket. FOIL with more than one variable. Brackets containing more than two terms. (4) Solving Equations 2: Revision of year 8 work on solving equations. Solving equations containing brackets. Solving equations where a double bracket is equal to zero. Equations containing fractions. Equations containing more than one fraction. (5) Trial and Improvement: Solving equations using trial and improvement (to the nearest unit; to one decimal place; to two decimal places). Using the table mode on a calculator.

#### Measuring Shapes 2

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A year 9 unit of work covering the following topics. (1) Circle Terminology: Parts of a circle. (2) Circumference and Area of a Circle: Finding 𝜋. Calculating the circumference of a circle. Calculating the area of a circle. Finding the radius from the area. (3) Shapes on Isometric Paper: Drawing shapes on isometric paper. (4) Plans and Elevations: Drawing solids from different plans and elevations. (5) Pythagoras’ Theorem (2-D): The hypotenuse of a right-angled triangle. Pythagoras’ Theorem. Pythagorean Triples. Proving whether or not a triangle is right-angled. (6) Scale Drawings: Creating a scale drawing. Interpreting a scale drawing.