| 1 |
Study Plan |
Self Assessment – Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Functions |
Definition, domain and range |
| Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. |
| 3 |
Functions |
Notation and evaluations |
| Objective: On completion of the lesson the student will be understand different notations for functions. |
| 4 |
Functions |
More on domain and range |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. |
| 5 |
Functions |
Domain and range from graphical representations |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. |
| 6 |
Coordinate Geometry-gradient |
Gradient |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. |
| 7 |
Coordinate Geometry-gradient |
Gradient formula. |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. |
| 8 |
Coordinate Geometry-straight line |
The straight line. |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. |
| 9 |
Coordinate Geometry-slope, etc. |
Lines through the origin. |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. |
| 10 |
Coordinate Geometry-equation of line |
General form of a line and the x and y Intercepts. |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. |
| 11 |
Coordinate Geometry-intercept |
Slope intercept form of a line. |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. |
| 12 |
Coordinate Geometry-point slope |
Point slope form of a line |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. |
| 13 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 14 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 15 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 16 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 17 |
Algebra- formulae |
Equations resulting from substitution into formulae. |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. |
| 18 |
Algebra- formulae |
Changing the subject of the formula. |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. |
| 19 |
Algebra-inequalities |
Solving Inequalities. |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. |
| 20 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 21 |
Simultaneous equns |
Simultaneous equations |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. |
| 22 |
Simultaneous equns |
Elimination method |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. |
| 23 |
Simultaneous equns |
Elimination method part 2 |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. |
| 24 |
Simultaneous equns |
Applications of simultaneous equations |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. |
| 25 |
Simultaneous equations |
Number of solutions (Stage 2) |
| Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same. |
| 26 |
Linear systems |
Optimal solutions (Stage 2) – Vectors |
| Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. |
| 27 |
Linear systems |
Linear systems with matrices (Stage 2) |
| Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. |
| 28 |
Calculus |
Limits |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. |
| 29 |
Calculus=1st prin |
Differentiation from first principles. |
| Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. |
| 30 |
Calculus=1st prin |
Differentiation of y = x to the power of n. |
| Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. |
| 31 |
Calculus-differential, integ |
Meaning of dy over dx – equations of tangents and normals. |
| Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. |
| 32 |
Calculus-differential, integ |
Function of a function rule, product rule, quotient rule. |
| Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. |
| 33 |
Calculus-differential, integ |
Increasing, decreasing and stationary functions. |
| Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. |
| 34 |
Calculus |
First Derivative – turning points and curve sketching |
| Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. |
| 35 |
Calculus-2nd derivative |
The second derivative – concavity. |
| Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. |
| 36 |
Calculus – Curve sketching |
Curve sketching |
| Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. |
| 37 |
Calculus – Maxima minima |
Practical applications of maxima and minima |
| Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. |
| 38 |
Calculus – Integration |
Integration – anti-differentiation, primitive function |
| Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. |
| 39 |
Calculus – Computation area |
Computation of an area |
| Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. |
| 40 |
Calculus – Trapezoidal and Simpson’s rules |
The Trapezium rule and Simpson’s rule |
| Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. |
| 41 |
Logic |
Inductive and deductive reasoning |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. |
| 42 |
Logic |
Definition and use of counter examples |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. |
| 43 |
Logic |
Indirect proofs |
| Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved. |
| 44 |
Logic |
Conditional statements (converse, inverse and contrapositive) (Stage 2) |
| Objective: On completion of the lesson the student will be able to form related conditional statements. |
| 45 |
Geometry |
To identify collinear points, coplanar lines and points in 2 and 3 dimensions |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. |
| 46 |
Geometry – angles |
To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. |
| 47 |
Geometry-constructions |
Angle bisector construction and its properties (Stage 2) |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. |
| 48 |
Geometry-constructions |
Circumcentre and incentre (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. |
| 49 |
Geometry-constructions |
Orthocentre and centroids (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. |
| 50 |
Geometry-quadrilaterals |
Midsegments of Triangles |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. |
| 51 |
Geometry-quadrilaterals |
Classifying Quadrilaterals |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. |
| 52 |
Geometry-quadrilaterals |
Using the Properties of a Parallelogram |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. |
| 53 |
Geometry-quadrilaterals |
Proving a Shape is a Parallelogram |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. |
| 54 |
Geometry-quadrilaterals |
Properties of the Rectangle, Square and Rhombus |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. |
| 55 |
Geometry-quadrilaterals |
Properties of the Trapezium and Kite |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. |
| 56 |
Geometry-quadrilaterals |
The quadrilateral family and coordinate methods in geometry |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. |
| 57 |
Geometry-locus |
Constructions and loci – single condition |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. |
| 58 |
Geometry-locus |
Constructions and loci – multiple conditions |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. |
| 59 |
Exam |
Exam – Unit 3BMAT – Yr11 (Opt 8-9) Yr12 (Opt 7) |
| Objective: Exam |
