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AQA GCSE Higher Modular Mathematics – Module 5 Grade Details Grade Details 2-D & 3-D SHAPES D Find angles in triangles & quadrilaterals D Calculate Circumference & Area of Circles C Find interior & exterior angles of polygons D Calculate the Area of a Trapezium B Find angles in circles C Calculate Volume of Prisms & Cylinders A Find angles in circles using the alternate B Calculate Arc Lengths & Sector Areas segment theorem B Calculate Surface Area of A* Use circle theorems to prove geometrical Cylinders/Cones/Spheres results. B Calculate Volume of TRANSFORMATIONS Pyramids/Cones/Spheres D Reflect a 2-D shape in lines x = … & y = … A Calculate Volume & Surface Area of D Rotate a 2-D shape about the origin compound 3-D shapes D Enlarge a 2-D shape by a whole number GEOMETRICAL REASONING scale factor C Use Pythagoras Theorem in right-angle C Translate a 2-D shape by a vector triangles C Reflect a 2-D shape in lines y = x & y = -x C Solve 2-D problems using Pythagoras C Rotate a 2-D shape about any point Theorem C Enlarge a 2-D shape by a fractional scale B Solve 3-D problems using Pythagoras factor Theorem C Enlarge a 2-D shape about any point B Use Trigonometry to find sides and angles B Know the conditions for congruence of 2 in right-angle triangles triangles B Solve problems using Trigonometry B Enlarge a 2-D shape by a negative scale factor A Prove 2 triangles are congruent 1 Grade Details Grade Details CONSTRUCTIONS VECTORS C Construct angle and line bisectors A Solve problems using addition & C Draw & describe the locus on a point from a subtraction of vectors given rule A* Solve complex geometrical problems in C Solve problems using loci terms of vectors B Construct a perpendicular from a point on a ALGEBRA 1 line D Expand a single linear bracket B Construct a perpendicular from a point to a D Substitute numbers into a linear line. expression B Compass construct of an angle of 60o D Factorise simple linear expressions SIMILARITY D Solve linear equations (inc. ones with C Understand why two shapes are similar variable inside a bracket) C Work out unknown sides using scale factors D Solve linear equations with the variable as & ratios a numerator of a fraction B Set up equations to find missing sides in D Solve linear equations with the variable on similar triangles both sides of the equals sign A Solve problems using area and volume scale C Expand & simplify expressions factors C Solve equations using trial & improvement A Solve problems using similar triangles C Rearrange simple formulae A* Use area and volume scale factors to solve B Solve 2 linear simultaneous equations related problems i.e. capacity B Rearrange more complex formulae DIMENSIONS ANALYSIS A Set up and solve simultaneous equations in D Work out a formula for a practical context perimeter/area/volume of simple shapes ALGEBRA 2 C Work out a formula for C Expand a pair of linear brackets (to result perimeter/area/volume of complex shapes in a quadratic expression) C Work out whether an expression/formula is B Factorise a quadratic expression of the dimensionally consistent & whether it form x2 + ax + b represents a length, area or volume 2 Grade Details Grade Details B Solve a quadratic expression of the form x2 A* Use sine & cosine rules to solve more + ax + b = 0 complex problems involving non-right-angled A Factorise a quadratic expression of the triangles form ax2 + bx + c A* Solve 3-D problems using Pythagoras’ A Solve a quadratic expression of the form theorem and trigonometry ax2 + bx + c = 0 by factorisation A* Find two angles 0o to 360o for any given A Solve a quadratic expression of the form value of a trigonometric ratio (positive or ax2 + bx + c = 0 by the quadratic formula negative) A* Solve quadratic equations by Completing A* Solve simple equations where the the Square trigonometric ratio is the subject A* Solve real-life problems that lead to a LINEAR GRAPHS AND EQUATIONS quadratic equation D Draw straight line graphs by plotting points REAL-LIFE GRAPHS C Draw straight-line graphs using the D Draw and read information from a distance- gradient/intercept method time graph B Solve a pair of simultaneous equations from C Calculate the gradient of a straight line and their graphs use it to find speed from a distance-time A Find equations of linear graphs parallel and graph perpendicular to other linear graphs, that B Interpret real-life graphs pass through specific points A Interpret & draw complex real-life graphs OTHER GRAPHS HIGHER TRIGONOMETRY B Plot cubic graphs using a table of values A Solve complex problems using Pythagoras & B Recognise the shapes of the graphs y = x3 Trigonometry and y = 1/x A Use sine & cosine rules to calculate missing A Draw a variety of graphs such as angles/sides in non-right-angled triangles exponential, reciprocal using a table of A Find the area of a triangle using values Area = ½ ab sin C A* Solve equations using the intersection of two graphs 3 Grade Details INEQUALITIES AND REGIONS A* Use trigonometric graphs to solve sine and C Solve inequalities such as 3x + 2 < 5 and cosine problems represent the solution on a number line ALGEBRA 3 B Represent a region that satisfies a linear D Substitute numbers into an nth term rule inequality graphically D Understand how odd and even numbers B Solve more complex linear inequalities interact in addition, subtraction & B Represent a region that simultaneously multiplication problems satisfies more that one linear inequality C Give the nth term of a linear sequence graphically C Give the nth term of a sequence of powers A Translate a problem into an inequality of 2 or 10 TRANSFORMATIONS OF GRAPHS B Find the nth term of a quadratic sequence A* Transform the graph of a given function B Solve linear equations where the subject A* Identify the equation of a function from appears as the numerator its graph, which has been formed by a A Rearrange a formula where the subject transformation on a known function appears twice PROOF A Combine algebraic fractions using the four B Verify results by substituting numbers rules of addition, subtraction, multiplication into them & division B Understand the proofs of simple theorems A* Rearrange more complicated formulae such as exterior angle of a triangle is the where the subject may appear twice or as a sum of the two opposite interior angles power A Show that an algebraic statement is true, A* Solve a quadratic equation obtained from using both sides of the statement to algebraic fractions where the variable justify your answer appears as the denominator A* Prove algebraic and geometric results with A* Simplify algebraic fractions by rigorous and logical mathematical factorisation & cancellation arguments A* Solve a pair of simultaneous equations where one is linear and the other is non- linear 4