Bishop Walsh School Mathematics Department Year 10 Revision List

Transcription

1 1 Bishop Walsh School Mathematics Department Year 10 Revision List Sets 10W1, 10E1 & 10E2 - Higher Topic Skills Maths Watch Clips ANGLES & SHAPES 1 ANGLES & SHAPES 2 RATIO & PROPORTION ALGEBRA 1 FACTORISE QUADRATICS AREA & PERIMETER 1 CIRCLES VOLUME & SURFACE AREA LINEAR EQUATIONS LINEAR INEQUALITIES FORMULAE (SUBSTITUTION & CHANGING THE SUBJECT) NUMBER 1 STANDARD FORM INDICES SURDS GRAPHS 1 REAL LIFE GRAPHS REVISION PYTHAGORAS THEOREM Properties of triangles & quadrilaterals Angles at a point, on a straight line, in a triangle, quadrilateral etc Corresponding & alternate angles Calculate angles in polygons Use Bearings Write ratios in their simplest form Divide a quantity in a given ratio Solve a ratio problem in a context Simplify algebraic expressions Multiply out brackets Use FOIL rule Understand fractional, negative and zero powers Factorise by taking out common factors Clip 68 Angle Sum of a Triangle (Grade C) Clip 69 Properties of Special Triangles (Grade C) Clip 67 Alternate Angles (Grade C) Clip 36 Triangles, Quadrilaterals & Polygons (Grade E/F/G) Clip 70 Angles of Regular Polygons (Grade D) Clip Bearings ( Grade C) Clip 23 Proportion (Grade E/F/G) Clip 61 Ratio (Grade D) Clip 94 Ratio (Grade C) Clip 62 Proportion Recipe Type Questions (Grade D) Clip 102 Algebraic Simplification (Grade C) Clip 103 Expanding and Simplifying Brackets (Grade C) Clip 104 Factorisation (Grade C) Factorise quadratic expressions Clip 140 Solving Quadratic Equations by Factorising ( B) Clip 141 Difference of two Squares (Grade B) Find the perimeter of a rectangle, triangle, compound shape Clip 33 Perimeter & Area (Grade E/F/G) or other shape. Clip 73 Area of compound shapes (Grade D) Find the area of a rectangle, triangle, parallelogram and Clip 71 Area of a Circle (Grade D) trapezium. Clip 72 Circumference of a Circle (Grade D) Find areas and circumference of circles Find the surface area and volume of cuboids, prisms and cylinders. Find areas and volumes using more complex shapes and solids, including cones, pyramids, spheres, hemispheres, segments of circles and frustums of cones. Use volume and surface area to solve problems. Set up and solve linear equations, including hard ones and with x on both sides. Represent inequalities on the number line. Solve linear inequalities. Substitute numbers into a formula. Use formulae to solve problems. Change the subject of a formula. Factors, multiples & primes Prime factor trees Highest common factor and lowest common multiple Use brackets and BODMAS Convert between ordinary numbers and standard form Use standard form in calculations Use index laws to simplify expressions. (multiplying, dividing and power of a power) Use fractional and negative powers. Use surds and π in exact calculations Simplify expressions involving surds Rationalise a denominator Use coordinates Plot straight line graphs Use y = mx + c Find gradients of parallel and perpendicular lines Draw and interpret straight line graphs for real-life situations Draw and interpret distance-time graphs Clip Surface area of Cuboids (Grade C) Clip 122 Volume of a Prism (Grade C) Clip 178 Segments & Frustrums (Grade A/A*) Clip 177 Cones and Spheres (Grade A/A*) Clip 106 Forming Equations (Grade C) Clip 105 Solving Equations (Grade C) Clip 108 Inequalities (Grade C) Clip 109 Solving Inequalities (Grade C) Clip 107 Changing the Subject of a Formula (Grade C) Clip 66 Substitution (Grade D) Clip 164 Rearranging Difficult Formulae (Grade A/A*) Clip 97 Standard Form (Grade C) Clip 135 Standard Form Calculation(Grade B) Clip 111 Index Notation for Multiplication & Division (C) Clip Fractional and Negative Indices (Grade A/A*) Clip 157 Surds (Grade A/A*) Clip 158 Rationalising the Denominator (Grade A/A*) Clip 78 Find the Mid-Point of a Line (grade D) Clip 143 Understanding y = mx + c (grade B) Clip 166 Gradients of Parallel & Perpendicular Lines ( A/A*) Clip 117 Real Life Graphs (Grade C) Clip 113 Drawing Straight Line Graphs (Grade C) Use Pythagoras theorem in right angled triangles Clip 118 Pythagoras Theorem (Grade C) Clip 119 Pythagoras Line on a Graph Clip 174 Pythagoras in 3D (Grade A/A*)

2 TRIGONOMETRY 1 Understand, recall and use sin, cos and tan in right-angled triangles, and use these to solve problems in 2-D and in 3-D. PROBABILITY Use the probability scale Calculate probabilities, including the probability of successive events, knowing when to x and when to +. Use relative frequency Estimate the number of times an event will occur List all outcomes systematically Use and draw sample space diagrams Draw and use a probability tree diagrams INEQUALITIES & Show the solution set of several inequalities in two REGIONS variables on a graph, by drawing lines and shading regions. GRAPHS 2 Plot graphs of quadratic functions (equations involving x 2 ) Plot graphs of simple cubic functions (equations involving x 3 ), and graphs such as y = 1/x, y = 3 x, y = sin x and y = cos x, x 2 + y 2 = r 2 (circle). Recognise the characteristic shapes of all these functions. ACCURATE DRAWING & SCALE DRAWING DRAWING 3-D SHAPES CONSTRUCTION & LOCI Measure and draw lines angles and make accurate drawings using a ruler and a protractor. Use scale diagrams and bearings. Use 2-D representations of 3-D shapes, including using coordinates, isometric grids, front & side elevations and plan views. Draw nets and show how they fold to make a 3-D solid. Use a ruler and a compass to do standard loci and constructions, e.g. construct triangles, perpendicular bisectors, etc. Clip 147 Trigonometry (Grade B) Clip 175- Trigonometry in 3D (Grade A/A*) Clip 91 Mutually Exclusive Events (Grade D) Clip 182 Probability AND & OR Questions (A/A*) Clip 154 Tree Diagrams (Grade B) Clip 144 Regions (Grade B) CIRCLE GEOMETRY Understand and use circle theorems to calculate angles. Clip 150 Circle Theorems ROUNDING & ESTIMATING Round numbers using decimal places and significant figures Estimate answers to calculations, including use of rounding Clip 116 Drawing Quadratic Graphs (Grade C) Clip 145 Graphs of Cubic and Reciprocal Functions (B) Clip 146 Recognise the Shapes of Functions (Grade B) Clip 170 Graphs of exponential Functions (Grade A/A*) Clip 168 Graphs of Trigonometric Functions (Grade A/A*) Clip Equations of Circle and Loci (Grade A/A*) Clip 79 Measuring & Drawing Angles (Grade D) Clip 39 isometric Drawing (Grade E/F/G) Clip 37 Names of Solids (Grade E/F/G) Clip 34 - Volume of cuboids (Grade E/F/G) Clip 82 Nets (Grade D) Clip 81 Plans & Elevations (Grade D Clip 120 3D Coordinates Clip 127 Bisecting a Line (Grade C) Clip 128 Drawing a Perpendicular to a Line (Grade C) Clip 129 Bisecting an Angle (Grade C) Clip 130 Loci (Grade C) Clip 20 Decimal Places & Significant Places (Grade E/F/G) Clip 14 Estimation (Grade E/F/G) Clip 101 Estimating Answers (Grade C) BOUNDS Calculate the upper and lower bounds of calculations. Clip 125 Upper and Lower Bounds (Grade C) Clip 160 Upper and Lower Bound Difficult Questions (A/A*) COLLECTING & RECORDING DATA QUADRATIC EQUATIONS Use two way tables and lists Design an experiment or survey and use suitable data collection techniques Use random and stratified sampling. Criticise questions for a questionnaire. Solve simple quadratic equations by using the quadratic formula Solve simple quadratic equations by factorisation and completing the square Clip 84 Questionnaires and Data Collection (Grade D) Clip 134 Questionnaires (Grade C) Clip 183 Stratified sampling (Grade A/A*) Clip 161-Solving Quadratics Using the Formula (A/A*) Clip 162-Solving Quadratics by Completing the Square (A/A*) 2

3 3 Bishop Walsh School Mathematics Department Year 10 Revision List Sets 10W2 & 10E3 - Higher Topic Skills Maths Watch Clips ANGLES & SHAPES 1 ANGLES & SHAPES 2 RATIO & PROPORTION ALGEBRA 1 AREA & PERIMETER 1 CIRCLES VOLUME & SURFACE AREA LINEAR EQUATIONS LINEAR INEQUALITIES FORMULAE (SUBSTITUTION & CHANGING THE SUBJECT) NUMBER 1 INDICES STANDARD FORM GRAPHS 1 REAL LIFE GRAPHS PROBABILITY Properties of triangles & quadrilaterals Angles at a point, on a straight line, in a triangle, quadrilateral etc Corresponding & alternate angles Calculate angles in polygons Use Bearings Write ratios in their simplest form Divide a quantity in a given ratio Solve a ratio problem in a context Simplify algebraic expressions Multiply out brackets Use FOIL rule Understand fractional, negative and zero powers Factorise by taking out common factors Find the perimeter of a rectangle, triangle, compound shape or other shape. Find the area of a rectangle, triangle, parallelogram and trapezium. Find areas and circumference of circles Find the surface area and volume of cuboids, prisms and cylinders. Find areas and volumes using more complex shapes and solids, including cones, pyramids, spheres, hemispheres, segments of circles and frustums of cones. Use volume and surface area to solve problems. Set up and solve linear equations, including hard ones and with x on both sides. Represent inequalities on the number line. Solve linear inequalities. Substitute numbers into a formula. Use formulae to solve problems. Change the subject of a formula. Factors, multiples & primes Prime factor trees Highest common factor and lowest common multiple Use brackets and BODMAS Use index laws to simplify expressions. (multiplying, dividing and power of a power) Use fractional and negative powers. Convert between ordinary numbers and standard form Use standard form in calculations Use coordinates Plot straight line graphs Use y = mx + c Find gradients of parallel and perpendicular lines Draw and interpret straight line graphs for real-life situations Draw and interpret distance-time graphs Use the probability scale Calculate probabilities, including the probability of successive events, knowing when to x and when to +. Use relative frequency Estimate the number of times an event will occur List all outcomes systematically Use and draw sample space diagrams Draw and use a probability tree diagrams Clip 68 Angle Sum of a Triangle (Grade C) Clip 69 Properties of Special Triangles (Grade C) Clip 67 Alternate Angles (Grade C) Clip 36 Triangles, Quadrilaterals & Polygons (Grade E/F/G) Clip 70 Angles of Regular Polygons (Grade D) Clip Bearings ( Grade C) Clip 23 Proportion (Grade E/F/G) Clip 61 Ratio (Grade D) Clip 94 Ratio (Grade C) Clip 62 Proportion Recipe Type Questions (Grade D) Clip 102 Algebraic Simplification (Grade C) Clip 103 Expanding and Simplifying Brackets (Grade C) Clip 104 Factorisation (Grade C) Clip 33 Perimeter & Area (Grade E/F/G) Clip 73 Area of compound shapes (Grade D) Clip 71 Area of a Circle (Grade D) Clip 72 Circumference of a Circle (Grade D) Clip Surface area of Cuboids (Grade C) Clip 122 Volume of a Prism (Grade C) Clip 178 Segments & Frustrums (Grade A/A*) Clip 177 Cones and Spheres (Grade A/A*) Clip 106 Forming Equations (Grade C) Clip 105 Solving Equations (Grade C) Clip 108 Inequalities (Grade C) Clip 109 Solving Inequalities (Grade C) Clip 107 Changing the Subject of a Formula (Grade C) Clip 66 Substitution (Grade D) Clip 164 Rearranging Difficult Formulae (Grade A/A*) Clip 111 Index Notation for Multiplication & Division (C) Clip Fractional and Negative Indices (Grade A/A*) Clip 97 Standard Form (Grade C) Clip 135 Standard Form Calculation(Grade B) Clip 78 Find the Mid-Point of a Line (grade D) Clip 143 Understanding y = mx + c (grade B) Clip 166 Gradients of Parallel & Perpendicular Lines ( A/A*) Clip 117 Real Life Graphs (Grade C) Clip 113 Drawing Straight Line Graphs (Grade C) Clip 91 Mutually Exclusive Events (Grade D) Clip 182 Probability AND & OR Questions (A/A*) Clip 154 Tree Diagrams (Grade B)

4 INEQUALITIES & REGIONS Show the solution set of several inequalities in two variables on a graph, by drawing lines and shading regions. GRAPHS 2 Plot graphs of quadratic functions (equations involving x 2 ) Plot graphs of simple cubic functions (equations involving x 3 ), and graphs such as y = 1/x, y = 3 x, y = sin x and y = cos x, x 2 + y 2 = r 2 (circle). Recognise the characteristic shapes of all these functions. ACCURATE DRAWING & SCALE DRAWING DRAWING 3-D SHAPES CONSTRUCTION & LOCI ROUNDING & ESTIMATING Measure and draw lines angles and make accurate drawings using a ruler and a protractor. Use scale diagrams and bearings. Use 2-D representations of 3-D shapes, including using coordinates, isometric grids, front & side elevations and plan views. Draw nets and show how they fold to make a 3-D solid. Use a ruler and a compass to do standard loci and constructions, e.g. construct triangles, perpendicular bisectors, etc. Round numbers using decimal places and significant figures Estimate answers to calculations, including use of rounding Clip 144 Regions (Grade B) Clip 116 Drawing Quadratic Graphs (Grade C) Clip 145 Graphs of Cubic and Reciprocal Functions (B) Clip 146 Recognise the Shapes of Functions (Grade B) Clip 170 Graphs of exponential Functions (Grade A/A*) Clip 168 Graphs of Trigonometric Functions (Grade A/A*) Clip Equations of Circle and Loci (Grade A/A*) Clip 79 Measuring & Drawing Angles (Grade D) Clip 39 isometric Drawing (Grade E/F/G) Clip 37 Names of Solids (Grade E/F/G) Clip 34 - Volume of cuboids (Grade E/F/G) Clip 82 Nets (Grade D) Clip 81 Plans & Elevations (Grade D Clip 120 3D Coordinates Clip 127 Bisecting a Line (Grade C) Clip 128 Drawing a Perpendicular to a Line (Grade C) Clip 129 Bisecting an Angle (Grade C) Clip 130 Loci (Grade C) Clip 20 Decimal Places & Significant Places (Grade E/F/G) Clip 14 Estimation (Grade E/F/G) Clip 101 Estimating Answers (Grade C) BOUNDS Calculate the upper and lower bounds of calculations. Clip 125 Upper and Lower Bounds (Grade C) Clip 160 Upper and Lower Bound Difficult Questions (A/A*) COLLECTING & RECORDING DATA REPRESENTING DATA 1 CUMULATIVE FREQUENCY & BOX PLOTS Use two way tables and lists Design an experiment or survey and use suitable data collection techniques Use random and stratified sampling. Criticise questions for a questionnaire. Draw & interpret bar charts, pie charts, stem & leaf diagrams & frequency polygons. Draw & Interpret cumulative frequency graphs. Find medians, quartiles & IQR. Draw & interpret box plots. Compare distributions using averages & range or IQR Clip 84 Questionnaires and Data Collection (Grade D) Clip 134 Questionnaires (Grade C) Clip 183 Stratified sampling (Grade A/A*) Clip 151 Cumulative Frequency (Grade B) Clip 152 Box Plots (Grade B) 4

5 ANGLES 1 ANGLES 2 RATIO & PROPORTION ALGEBRA 1 5 Bishop Walsh School Mathematics Department Year 10 Revision List Set 10W3 - Foundation Topic Skills Maths Watch Clips TRIAL & IMPROVEMENT AREA & PERIMETER 1 Angles at a point, on a straight line, in a triangle, quadrilateral etc Corresponding & alternate angles Calculate angles in polygons Use Bearings Write ratios in their simplest form Divide a quantity in a given ratio Solve a ratio problem in a context Simplify algebraic expressions Multiply out brackets Factorise by taking out common factors Solve equations using trial & improvement. Find the perimeter of a rectangle, triangle, compound shape or other shape. Find the area of a rectangle, triangle, parallelogram and trapezium. Clip 31 Angles (Grade E/F/G Clip 21 Half-Way Value (Grade E/F/G) Clip 68 Angle Sum of a Triangle (Grade C) Clip 69 Properties of Special Triangles (Grade C) Clip 67 Alternate Angles (Grade C) Clip 70 Angles of Regular Polygons (Grade D) Clip Bearings ( Grade C) Clip 23 Proportion (Grade E/F/G) Clip 61 Ratio (Grade D) Clip 94 Ratio (Grade C) Clip 62 Proportion Recipe Type Questions (Grade D) Clip 102 Algebraic Simplification (Grade C) Clip 103 Expanding and Simplifying Brackets (Grade C) Clip 104 Factorisation (Grade C) Clip 33 Perimeter & Area (Grade E/F/G) Clip 73 Area of compound shapes (Grade D) CIRCLES Find areas and circumference of circles Clip 71 Area of a Circle (Grade D) Clip 72 Circumference of a Circle (Grade D) LINEAR EQUATIONS Set up and solve linear equations. Clip 106 Forming Equations (Grade C) Clip 105 Solving Equations (Grade C) LINEAR INEQUALITIES Represent inequalities on the number line. Solve linear inequalities. Clip 108 Inequalities (Grade C) Clip 109 Solving Inequalities (Grade C) FRACTIONS 1 Equivalent fractions & simplifying fractions Convert between fractions & decimals Order fractions & decimals Clip 47 Equivalent Fractions (Grade D) Clip 48 Simplification of Fractions (Grade D) Clip 58 Change fractions to decimals (Grade D) Clip 98 Recurring Decimals into Fractions (Grade C) Clip 13 Ordering Fractions, Percentages & Decimals ( E/F/G) Clip 49 Ordering Fractions (Grade FRACTIONS 2 Add, subtract, multiply & divide fractions. Clip 56 Addition & Subtraction of Fractions (Grade D) Clip 57 Multiplication & Division of Fractions (Grade D) FRACTIONS 3 Find a fraction of a quantity Express a given number as a fraction of another Clip 8 Fraction of an Amount (Grade E/F/G) Clip 55 Find a fraction of an amount (Grade D) PERCENTAGES GRAPHS 1 REAL LIFE GRAPHS PROBABILITY Convert between fractions, decimals & percentages. Order fractions, decimals & percentages Find a percentage of a quantity Express a given number as a percentage of another Use percentages to solve problems Use coordinates Find the mid-point of a line segment Plot straight line graphs Use y = mx + c Draw and interpret straight line graphs for real-life situations Draw and interpret distance-time graphs Use the probability scale Calculate probabilities Use relative frequency Estimate the number of times an event will occur List all outcomes systematically Use and draw sample space diagrams Clip 10 -Fractions Decimals and percentages (Grade E/F/G) Clip 13 -Ordering Fractions, percentages & decimals ( E/F/G) Clip 51 -Percentage of an amount WITH a Calculator (D) Clip 52-Percentage of an amount WITHOUT a Calculator (D) Clip 53-Change to a percentage WITH a Calculator (Grade D) Clip 54-Change to a percentage WITHOUT a Calculator (D) Clip 92 -Overview of Percentage (Grade C) Clip 93 -Increase/Decrease by a Percentage (Grade C) Clip 28 Coordinates (Grade E/F/G) Clip 78 Find the Mid-Point of a Line (grade D) Clip 27 Line Graphs (Grade E/F/G) Clip 113 Drawing Straight Line Graphs (Grade C) Clip 114- Finding the Equation of a Straight line (Grade C) Clip 43 Conversion Graphs (Grade E/F/G) Clip 117 Real Life Graphs (Grade C) Clip 40 Probability scale (Grade E/F /G) Clip 90 List of Outcomes (Grade D) Clip 91 Mutually Exclusive Events (Grade D) Clip 132 Experimental Probabilities Grade C)

6 GRAPHS 2 Plot graphs of quadratic functions (equations involving x 2 ) Clip 116 Drawing Quadratic Graphs (Grade C) ACCURATE DRAWING DRAWING 3-D SHAPES Measure and draw lines angles and make accurate drawings using a ruler and a protractor. Use 2-D representations of 3-D shapes, including using coordinates, isometric grids, front & side elevations and plan views. Draw nets and show how they fold to make a 3-D solid. Clip 79 Measuring & Drawing Angles (Grade D) Clip 39 isometric Drawing (Grade E/F/G) Clip 37 Names of Solids (Grade E/F/G) Clip 82 Nets (Grade D) Clip 81 Plans & Elevations (Grade D SCALE DRAWING ROUNDING & ESTIMATING COLLECTING & RECORDING DATA Use and interpret maps and scale drawings. Round numbers to nearest 10, 100 Round using decimal places and significant figures Estimate answers to calculations, including use of rounding Use two way tables and lists Design an experiment or survey and use suitable data collection techniques Use random sampling. Criticise questions for a questionnaire. Clip 3 Rounding to nearest 10,100 etc (Grade E/F/G) Clip 20 Decimal Places & Significant Places (Grade E/F/G) Clip 14 Estimation (Grade E/F/G) Clip 101 Estimating Answers (Grade C) Clip 84 Questionnaires and Data Collection (Grade D) Clip 134 Questionnaires (Grade C) 6