Scheme of Work Form 4 (Scheme A)

Transcription

1 Scheme of Work Form 4 (Scheme A) Topic A revision of number work Directed Numbers Content Factors and Multiples Expressing a number as a product of prime factors LCM and HCF Objectives - Core and Paper B The student will be able to.. Understand and use positive and negative numbers in real life contexts. Multiply and divide negative numbers Recognise, understand and use a) Integers b) Factors, multiples, LCM, prime numbers and prime factors Objectives -Paper A The student will be able to.. Find the Highest Common Factor Standard form Expressing numbers in standard form. Write ordinary numbers in standard form and vice-versa. Learn to use the EXP key on the calculator Working with numbers in standard form A revision of number work Changing from standard form to ordinary numbers Working with numbers in standard form Indices Finding the value of numbers in index form Rules of indices Common misconceptions Summary of all the rules Use and interpret positive and negative integral indices including zero. Use the index laws for multiplying and dividing integer power with the same number base. Solve simple exponential equations by inspection e.g. 3 x = 81, 2 x = 1/16 Solving indices by inspection 1

2 Expressions: Expanding and Factorisation Solving linear equations simultaneousl y Addition and subtraction of terms Multiplication and division of terms Expanding brackets Factorisation using a common factor Solve linear equations graphically The Elimination method Equations with different x and y coefficients Alternative Methods Solving by equating equations Solving by substitution Applications of simultaneous equations to real life. Simplify algebraic expressions by collecting, cancelling, and multiplying terms of an expression. Factorise expressions completely by taking out a common factor Multiply a single term over a bracket Use letter symbols to represent unknown quantities in a formula Solve two simultaneous linear equations algebraically. Solve problems leading to the solution of simultaneous linear equations. Solve two simultaneous linear equations graphically Perfect Squares Expand the product of two linear expressions Factorising a difference of two squares Solve two simultaneous linear equations graphically Equations and formulae Subject of a formula One type operation Two type operation Forming formulae Derive a formula and change the subject of the formula Two occurrences of the same unknown Including formulae with fractions, squares and square roots Equations and Formulae Solving linear equations with one variable Simplify algebraic expressions by collecting like terms Add/subtract algebraic fractions with numerical denominators Evaluate algebraic fractions by substitution Simplify algebraic expressions involving square roots Simplifying single algebraic fractions using indices 2

3 2/3 Linear equations involving fractions Solve linear equations in one unknown that involve two or more operations (to include simple use of brackets) Simplifying single algebraic fractions by factorisation Multiplication and division of algebraic fractions Straight line graphs The Quadratic, cubic and reciprocal graph Straight line graphs The equation of a line Types of straight lines The gradient of a line Drawing quadratic graphs Solving equations using quadratic graphs Draw and read values from quadratic graphs Recognise and calculate the significant points of a quadratic graph Pythagoras theorem Converse of Pythagoras theorem Pythagorean triples A summary of the three basic ratios. Finding an angle given two sides. Generate and plot coordinate pairs that satisfy a linear rule. Use straight-line graphs to find the value of one coordinate given the other. Understand, interpret and calculate the gradient of a line from the coordinates of two points on the line. Use straight-line graphs to find the value of one coordinate given the other. Know and understand that parallel lines have equal gradient. Understand the relationship between the equation of a straight line, its gradient and y-intercept. Rearrange linear equations into the form y = mx + c. Plot and interpret graphs of simple linear functions arising from real-life situations. Draw quadratic graphs and identify maxima/minima. Use quadratic graphs to find the value of one coordinate(s) given the other Use Pythagoras theorem to find the side of a right angled triangle given the other two sides Identify Pythagorean triples. Use the converse of Pythagoras theorem. Draw and read values from quadratic graphs Recognise and calculate the significant points of a quadratic graph Solve practical problems involving isosceles triangles and other shapes. Use the trigonometrical ratios to solve problems involving the angles of elevation and depression and bearings. 3

4 Trigonometry Area Finding a side given one angle and a side Applications of trigonometric ratios Bearings Using trigonometry in bearings Working with an outer right angled triangle The triangle Quadrilateral rectangle, square Parallelogram Trapezium Area of composite shapes Understand the tangent function as the ratio between the opposite and the adjacent side of an angle in a right angled triangle. Understand the sine and cosine function as the ratio between pairs of sides of a right angled triangle. Use the tangent ratio to find: the opposite side given an angle and its adjacent side, the adjacent side given an angle and its opposite side, the angle given two sides other than the hypotenuse side. Use the sine and cosine ratios to find the opposite sides given an angle and the hypotenuse, the adjacent side given an angle and the hypotenuse, an angle given the opposite side or the adjacent side and the hypotenuse, the hypotenuse given an angle and the opposite or the adjacent side. Work out the area of a parallelogram and a triangle Work out the area and perimeter of composite shapes Derive and use the formula to find the area of the trapezium by dividing it into two triangles. Use the formula to find the area of a triangle to find the base and height. Bearings: Using trigonometry in bearings. Working with outer right angled triangle. Use algebra to find expressions for the area of simple shapes. 4

5 Arithmetic in a Circle Finding the radius from the circumference and area Finding the circumference from the area Finding the area from the circumference Finding the radius and sector angle from the length of arc Finding the radius and sector angle from sector area Segment of a circle Composite shapes Understand the terms arc, sector and segment of a circle. Use the formula C= d and C= 2 r to find the circumference of a circle and A = r 2 to find the area of a circle. Use formula for the circumference and area to find the radius/diameter. Work out the length of an arc and the area of a sector as fractions of a circle. Work out the area of composite flat shapes by dividing them into simple shapes including circles. Work out the area of segments in a circle. Work out the area of composite shapes by dividing them into simple shapes including circles, sectors and segments. Segment of a circle Volume Finding the volume of solids with uniform cross-section Finding a missing dimension & recasting Water level Convers unit of area and volume Solve problems involving the volume of a prism Use V= Ah to find the volume/area and height of a prism Use appropriate units for area and volume Use the formula V = r 2 h to find the volume, radius or height of a cylinder Solve problems using 1 litre = 1000 cm 3 ; 1m 3 = 1000 litres Convert units of area and volume Percentages Percentage increase and decrease Reverse percentage increase and decrease Percentage change Percentage error Solve problems involving percentage increase and decrease Increase/decrease a quantity using a percentage multiplier Calculate the percentage increase/decrease of a quantity Successive percentage changes Carry out calculations involving reverse percentages. 5

6 Money Simple interest Using simple interest to find rate and time Using the simple interest to find the principal Using compound interest to find the principal, rate and time Appreciation and depreciation Income tax & Repayments Solve problems on personal and household finance (ex. VAT) Revise simple interest Compound interest, appreciation and depreciation Determine by trial and error the number of years by means of a calculator Periodical borrowing and repayment. Ratios The quadratic equation Ratios as comparisons Using ratios to divide quantities Finding unknown quantities in ratios Factorising a difference of two squares The quadratic expression Factorisation using the trinomial method The either/or concept Completing the square A revision of factorization and the meaning of solutions Solve quadratic equations The quadratic formula Use ratio notation in practical situations Recognise the connection between ratios and fractions Reduce ratios to their simplest form Divide a quantity in a given ratio Factorize quadratic expressions involving difference of two squares and trinomials Solve quadratic equations by factorization Solve quadratic equations by completing the square and by using the formula Use quadratic graphs to solve quadratic equations Solve problems leading to quadratic equations Constructions and Loci Constructions Constructing Quadrilaterals Loci Circumscribed circle Inscribed Circle Constructions - Angles of 60, 45, 90, 30 - Bisecting an angle - Parallel lines - Perpendicular bisector of a line segment - Perpendicular from a point to a line Constructing Quadrilaterals Construct drawing and angles Use ruler and compasses only to construct to locus of points which are: - Equidistant from two points - Equidistant from two intersecting straight lines 6

7 Statistics Excel Transformatio ns Discrete variables Mean, median and mode Representing data Continuous variables Grouped data Class boundaries Class boundaries Spreadsheets Translations Reflections Horizontal and vertical mirror lines Rotations Enlargements Enlargements with positive scale factors Enlargements with negative scale factors Describing a translation Describing a reflection Describing a rotation Describing an enlargements Use ruler and compasses only to construct to locus of points which are: - At a fixed distance from a given point - Equidistant from a straight line Circumscribed Circle Inscribed Circle Construct and interpret information tables Understand, compute and interpret the mean, mode, median and range of a set of discrete/continuous and grouped data only. Draw a histogram (frequency diagram) with equal intervals from an un/grouped frequency table. Understand and use a spreadsheet to find the sum for a group of cells Understand and use a spreadsheet to find the mean, mode, median and range for ungrouped data Transform points and shapes using translation, reflection, rotation and enlargements. Translation: Use a given column vector Reflection: Use y = c, x = c, y = x as mirror lines Rotation: Use angles of rotation in multiples of 90 o Enlargements: use positive integers or fractions as scale factor. Recognise that reflections, rotations and translations preserve length and angle so that any figure is congruent to its image under any of these transformations. Recognise that enlargements preserve angles and not length. Solve problems involving the above constructions using intersecting loci and regions Use and interpret different class intervals to draw a frequency chart for the same data. For a grouped frequency distribution (include discrete and continuous data): a) Calculate and an estimate for the mean b) Identify the modal class c) Identify the class interval in which the median lies Use negative scale factors of enlargements Transform 2D shapes by a combination of transformations. Identify and use appropriate language to describe fully the transformation. 7

8 Volume and surface area Volume of a pyramid Finding a missing quantity given the volume The frustum Volume of a sphere Volume of compound shapes Surface area of cylinder Surface area of a cone Surface area of a sphere Derive and use the formulae for the surface area of a cylinder Solve problems involving the volume and surface area of simple compound solid shapes Find the surface area of a sphere Find the surface area of a right circular cone Find the volume of a pyramid, a frustum of a pyramid and a sphere. Find the volume of a right circular cone and a frustum of a right circular cone Solve problems involving the volume and surface area of simple compound solid shapes Rearrange formulae for the surface area and volume of solids to find radius, height and slant height. Sequences Arithmetic sequences The General term of an arithmetic sequence Finding the general term of an arithmetic sequence Using the general term to find a particular term Using the general term to find the position The general term of a quadratic sequence Finding the general term of a quadratic sequence Using the general term of quadratic sequences Extend patterns and sequences of numbers Generate terms of a sequence using term definitions of the sequences Use expressions to describe the nth term of a simple sequence Recognise geometric and number patterns 8

9 Polygons The sum of interior angles of a convex polygon Finding an interior angle of a regular polygon Finding an interior angle of an irregular polygon The sum of exterior angle of a convex polygon Finding an exterior angle of a convex regular polygon Finding an exterior angle of a convex irregular polygon Finding the number of sides of a regular polygon given the exterior angle Finding the number of sides of a regular polygon given the interior angle Understand a proof that the angle sum of a triangle is 180 o Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices Use the angle properties of equilateral, isosceles and right-angled triangles Understand a proof that the angle sum of a quadrilateral is 360 o Understand and use the properties of the square, rectangle, parallelogram, trapezium, rhombus and kite Classify quadrilaterals using their geometric properties Calculate and use the sums of the interior and exterior angles of ir/regular polygons Use a formula, such as (2n 4) right angles or (n 2) 180, for the sum of the interior angles of a polygon with n sides Circle Geometry An angle subtended by an arc, chord or segment Circle facts Angle at centre and angle at circumference Angles in same segment The cyclic quadrilateral Angles in a cyclic quadrilateral Exterior angle of a cyclic quadrilateral Angles in a semicircle Circles and tangents Understand the meaning of terms related to the circle: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment Understand and use the angle properties: - Angle at the centre is twice the angles at the circumference - Angles in the same segment are equal - Angle in a semicircle is a right angle - Angles in opposite segments are supplementary - The exterior of a cyclic quadrilateral is equal to the interior opposite angle Prove that the angle formed by a chord and a tangent at the point of contact is equal to the angle in the alternate segment Circles and tangents Using tangent properties to find unknown angles. Understand the proofs of the angle properties of a circle. Understand the proof of the alternate segment theorem. 9

10 Using tangent properties to find unknown angles Alternate segment theorem Understand the meaning of the term tangent to a circle Angle between the tangent and the radius is right angle. Probability Introduction Finding the probability of an event Probability with two events Possibility Spaces Work out the probability of mutually exclusive events. Work out the probability of in/dependent events occurring Understand and work out the probability of an event Work out the probability of an event by experiment. Work out the probability of an event from a frequency table. Compile a possibility space. Work out the combined probability outcomes of two independent events. Work out the probability of mutually exclusive events. Work out the probability of in/dependent events occurring Compile and use a probability tree. (Tree diagrams write: outcomes - at the end of the branches and probabilities by the sides of the branches. In /dependent and events Using probability trees versus space tables Probability trees Logo Logo Draw any regular polygon using logo and the commands PD, RT, FD, LT, BK, Home. 10