# Deriving Continuous Compound Interest Formula

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```					                       Scheme of work:KS 4 Higher Tier GCSE (Modular) September 2010- June 2012
Examination board used is: Edexcel, Modular B (2MBO1 www.edexcel.org.uk
The Mathematics Department has paid to join an excellent subscription website:
www.mymaths.co.uk (all students are given the user name and password) and are
encouraged to use this resource. In addition:www.bbc.education.gcsebitesze,is a
good resource. Students sit three written examination papers: Unit 1 (30% of
totalassessment), Unit 2 (30% of total assessment) and Unit 3 (40% of total
assessment)). In Units 1 and 3students can use a calculator, Unit 2 is a non
Calculator examination . Units 1 and 2 have a 1 hour 15 minutes examination, the
Unit 3 examination is 1hour 45 minutes lon.Throughout the course correct use of
notation and mental calculation methods will be used as and when appropriate. All
students must bring with them to all lessons: A calculator in working order, A
pencil, ruler, pair of compasses and a protractor. Some past examination papers
are available via Moodle.

Resources
beginning

Topic(s)

Target
Week

Mon        Unit 2: Non Calculator                                                             D/C/     Tarsia:       Prime
6/9/10      Number and the number system:                                                       B       Factors     (KS 4
Multiplication and Division of whole numbers without a calculator.                          puzzle)
Add, Subtract, Multiply, Divide Decimals Factors and Multiples. Understand
vocabulary of factor (divisor)                                                              Tarsia:Negative
HCF, LCM Prime Numbers and decomposition to Prime Factor form.                              Numbers       (K3
Understand and use negative numbers. Multiply and divide by a negative                      puzzle)
number. Rounding to nearest whole number. Writing a number to a given                       Name the Nines:
number of: decimal places, significant figures.                                             Types of Numbers
Mental Methods: Checking and estimating answers to problems, develop
a range of strategies for mental calculations.
Mon:       Number and the number system:                                                      C/B/     Tarsia:    Indices
13/9/10      Use one calculation to solve another: eg: if 25.3 x 17 = 430.1, what is: 2.53 x    A       (K34 puzzle)
0.17 ? Powers and Roots including positive and negative fractional and                      Name the Nines:
negative powers. Index notation and laws of Indices for multiplication and                  Laws of Indices
division of powers (and algebraic terms). Use of and manipulation of standard               Standards Unit:
index form with and without a calculator Mental Methods: Know that nº = 1,                  N12 Indices
1                       1
n 1 =        , √n = n 0.5 , 5 2 =    etc.
n                       25
Mental Methods: Recall squares from 2x2 to 15x15 and the corresponding
square roots and the cubes of 2,3,4,5,10
Mon:       Algebra: Use correct notation. Distinguish in meaning between terms: “             D/C/     Tarsia:
20/9/10     Equation”, “formula”, “ Identity”, “Expression”. Manipulate algebraic               B       Substitution into a
expressions; collect like terms. Deriving formula from given information.                   formula(KS        4
Substitution into formula- including use of negative numbers (not use of                    puzzle)
fractions- this comes later)
Mon:        Algebra: Expand a single bracket, expand and simplify two linear brackets.         C/B/     Tarsia:Expanding
27/9/10     Factorising; taking out a common factor eg: Factorise fully: 15a³b – 25 ab.         A       brackets/factorisin
Factorise quadratic expressions including use of difference of two squares.                 g quadratics (KS 4
puzzle)

1
Mon:      Algebra: Simplifying algebraic expressions by cancelling and use of laws of         C/B/
4/10/10    indices: eg Simplify fully: 3ab³ x 5a². Generate terms of a sequence using           A
term to term and position to term definitions. Identify which terms cannot be in
a sequence. Find the n th term of an Arithmetic sequence.

Mon:      Measures: Rounding to nearest whole unit. Converting measurements from              D/C    Name the Nines:
11/10/1    one unit to another. Make sensible estimates of a range of measures.                       Maesures:
0       Understand compound measures (Speed). Measure and draw angles (to nearest                  Imperial/ metric
degree) and lines to nearest mm

October test ( 55 mins): Non Calculator on content above.

Geometry: Recall and use angle properties at a point, on a straight line,           D/C/   Name the Nines:
18/10/1    perpendicular lines, vertically opposite angles. Understand the properties of        B     Angle Facts
0          scalene, isosceles, equilateral, right angled triangles. Understand and use angle
properties of: Triangles, Intersecting lines, Parallel lines. Know and use
corresponding and alternate angles. Understand and use angle properties of
Understand proof of: angles in any triangle add up to 180º, exterior angle of a
triangle = sum of interior opposite. Give reasons for angle calculations. Recall
25/10/1    Half Term
0
Mon:      Geometry: : Calculate and use the sums of angles of the interior and exterior       D/C/   Washing line:
1/11/10    angles of polygons. Find the size of each interior and exterior angle, or number     B     Angles in
of sides of a regular polygon. Understand tessellations of regular and irregular           Polygons
polygons. Tessellate combinations of polygons. Explain why some shapes
tessellate and some do not. Recall properties of special types of quadrilaterals:
the Square, Rectangle, Kite, Parallelogram, Trapezium, Rhombus
Mon:      Geometry. :.
8/11/10    Recognise reflection symmetry in 2D shapes. Identify Rotational Symmetry in         C/B/
a 2D shape. Draw or complete diagrams with a given order of rotational               A
symmetry. Know definitions of parts of the circle: Centre, Radius, Chord,
Diameter, Circumference, Tangent, Sector, Segment. Understand and use:
Tangent at any point on a circle is perpendicular to the radius
Tangents from an external point are equal in length.
Find missing angles on diagrams, give reasons for angle calculations using
tangent theorems.

Number and the number system:, Fractions: All four operations, cancelling           D/C/   Tarsia:     Add/
Mon:      down, equivalent fractions, ordering fractions by rewriting them with a              B     Subtract
15/11/10   common denominator Converting fractions to decimals and decimals to                        Fractions (KS 4
fractions in their simplest form. Recurring decimals as exact fractions.                   puzzle)
Recognise that some exact fractions are recurring decimals. Use of unit
fractions as multiplicative inverse (eg x by 1/5 is same as divide by 5).
Understanding of a reciprocal. Use inverse operations.

Mon:     . Number and the number system:                                                     D/C/   Washing Lines: %
22/11/10   Percentages: Understand that “percent” means part of 100.Converting decimals         B     multipliers
and fractions to percentages. Finding x% of Y, express a quantity as a
percentage of another, 15% of Y = 15/100xY. Calculation of percentages in
“real life” problems: VAT, rates of Inflation, Interest Rates, % Profit. Use of a
multiplier (eg £3000 invested for 5 yrs @ 7% ). Reverse percentages.

2
Calculation of percentage increase, percentage decrease. Use of a multiplier to
increase or decrease
Mon:     November test ( 55 mins): Non Calculator on content covered since October             D/C/   Name the Nines: 3
29/11/10   test.                                                                                  B     D shapes
Geometry: Use 2D representations of 3D shapes. Use Isometric grids, draw                     Standards Unit:
nets, understand and draw plans, front and side elevations of simple solids.                 SS6 Representing
Given front and side elevations and plan, draw a 3D sketch. Calculate                        3D shapes
Perimeter and Area of shapes made from Triangles, rectangles and other
shapes. Find area of Trapezium, Parallelogram. Find surface areas of prisms.
Find volume of right prisms and cuboids.
Mon:      Geometry: (complete section above)                                                    B/A/   Tarsia:
6/12/10    Number and the number system: Interpret order and calculate with numbers               A*    Simplifying
in Standard Form. Use surds and π in exact calculations                                      Surds(KS4 puzzle)
(eg: Area of a circle is 25π, Expand and simplify: ( 3 - √3)²
Mon:      Number and the number system: Ratio: use of notation, reduce ratios to                       Tarsia: Ratio
13/12/10   simplest form, links to fractions. Divide a quantity into a given ratio, solve               (KS3 puzzle)
ratio problems.                                                                              Standards Unit:
N6 Proportional
Reasoning
CHRISTMAS
Mon:
20/12/10

Weds:      Unit 1 Work: Statistics: Identify possible sources of bias. Understand sample C/B/           Washing Lines:
5/01/11    size. Design of a questionnaire, Understand Primary and Secondary data.            A         Efficient use of a
Interpret and discuss data. Design and use data collection sheets. Sort, classify            Calculator
and tabulate discrete, continuous, quantitative data. Extract data from lists and
tables. Group discrete and continuous data into class intervals of equal
width.Design and use two way tables. Select and justify a sampling method,
including Random Sampling and Stratified Sampling. Use Stratified Sampling.
Mon:      Statistics: Produce charts and diagrams: Composite Bar charts, Comparative D/C/              Standards Unit:
10/01/11   Bar charts, Pie Charts, Frequency Polygons for grouped data, Scatter graphs,        B        S6
Ordered Stem and Leaf diagrams. Box plots from raw data when given                           Interpreting
quartiles, median.                                                                           Cumulative
Functional Skills: Data Handling Tasks                                                       Frequency
Mon:      Statistics: Produce Grouped Frequency tables for grouped data. Produce            B/A/       Name the Nines:
17/01/11   Cumulative Frequency Graphs. Draw Histograms with unequal class widths.           A*         Handling Data
Use and understand frequency density.                                                        Graphs and
Diagrams
Mon:       Unit 2: Revision of: The straight line, y = mx + c; gradients, parallel and           B/A    Tarsia: y = mx + c
24/01/11   perpendicular lines. Finding the gradient of a straight line passing through two             (KS4 puzzle)
given points. Find the equation of a line given that it is parallel to another line          Standards Unit:
and given a point on the line. Drawing straight line graphs. Defining                        A10 Properties of
coordinates in 3-D. Find the mid point of a line segment.                                    straight line
Mon:       Revision of all Unit 2 Topics
31/01/11
Mon:     Mock Unit 2 exam
7/02/11
Mon:       Revision of all Unit 2 Topics
14/02/11

3
Mon:     Half Term
21/02/11
Mon:     Unit 2 Examination: Tuesday 1st March
28/02/11
Mon:     Unit 1: Statistics: Calculate mean, median mode and modal class, range,            C/B/   Standards Unit:
7/03/11   quartiles and IQ range. Estimate means from grouped frequency data. Use CF          A     S4
curves to find media, quartiles and IQ range. Interpret box plots to find                 Understanding
median, quartiles, range and IQ range.                                                    mean, median,
Use calculators efficiently. Including statistical functions: Σx and Σfx                  mode and range
Mon:      Statistics: Interpret a wide range of graphs and diagrams and draw
14/03/11   conclusions:                                                                       B/A/
Interpret: Composite bar graphs, scatter diagrams, stem and leaf diagrams, box      A*
plots, CF curves, Histograms. Find the median from a Histogram and other
information from a Histogram, eg: number of people in a given interval.
Find greatest and least values from Stem and Leaf diagram.
Functional Skills: Health and Fitness Task
Mon:      Statistics: Look at data to find patterns and exceptions. Compare distributions    B/A/
21/03/11   and make inferences. Explain an isolated point on a scatter graph.                  A*
Appreciate that correlation is a measure of strength of the association
between two variables and that zero correlation does not necessarily imply “
no relationship” but merely “ no linear relationship”. Draw line of best fit by
Mon:       Probability: Understand and use a probability scale. Understand and use           C/B/
28/03/11   estimates of probability from theoretical models or from relative frequency.       A/A*
Identify mutually exclusive events. Draw simple sample space diagrams.
Know that sum of probabilities = 1. Know when to add or multiply two
probabilities. Understand selection with and without replacement.
Use conditional probabilities.
Mon:      Probability: Use tree diagrams to represent outcomes of compound events ( no       B/A/   Tarsia:
4/04/11    more than 3 branches per event). Recognising when events are independent.           A*    Probability(KS4
Understand that if an experiment is repeated the outcome may be different.                puzzle)
Understand that increasing sample size leads to better estimates of outcomes.
Mon:      Easter Holiday
11/04/11
Tues:     Unit 1 Revision of Number and the number system ( this work is in units 1          C/B    Tarsia: Multiply/
26/04/11   and 2): The Operations with whole numbers, fractions and decimals.                        Divide decimals
Understand and use percentages. Convert between fractions, decimals and                   (KS4 puzzle)
percentages. Use percentage, repeated proportional change : Compound                      Name the Nines:
interest, Depreciation. (Calculator application). Find a fraction of a quantity,          Fractions words
find a percentage of a quantity. Use decimals to find quantities. Know angle
properties at a point, measure and draw lines and angles.
Tues.     Unit 1Revision of Number and the number system ( this work is in units 1           C/B
3/05/11    and 2): Use ratios. Multiply and divide numbers using commutative,
associative and distributive laws and factorisation if possible. Use Brackets
and solve word problems. Estimation and rounding numbers ( to a given
number of decimal places and significant figures). Use a calculator efficiently.
Interpret scales, convert units. Make sensible estimates.
Mon:      Unit 1 Revision Algebra: ( This work is in units 1 and 2): Distinguish             C/B/
9/05/11                                                                                        A
between: Equation, Expression, Formula, Identity.All work relating to y
= mx +c. Finding and interpreting gradients. Interpret and analyse
straight lines. Recognise graphs of simple cubic, reciprocal and
exponential functions. Interpret graphs of real life situations.

4
Mon:      Unit 1. Mock
16/05/11
Revision
Mon:     Unit 1 Revision
23/05/11
Mon:       Half Term
30/05/11
Mon:     Unit 1 Examination: Monday 6th June
6/06/11
Mon:     Unit 3: Calculator Unit: Geometry: Use Pythagoras` theorem in 2D and 3D.            C/B/   Name the Nines:
13/6/11   Understand the language of planes and recognise the diagonals of a cuboid.           A     Calculator
Calculate the length of a diagonal of a cuboid.                                            Buttons
Mon:      Geometry: Right angled triangle Trigonometry. Use of the three ratios to solve      C/B/
20/06/11   problems in 2D and 3D. Find the angle between a line and a plane.                    A
Mon:      Geometry: Constructions: Construct: A triangle, An equilateral Triangle,            C/B
27/06/11   Perpendicular Bisector of a given line, The perpendicular from a point to a
line, The perpendicular from a point on a line, Bisect an angle, Construct
angles of 30°, 45°,60°, 90°. Draw parallel lines, Construct a regular hexagon
inside a circle, Draw arcs and circles to a given radius. Constructions involving
Loci
Mon:      Number and the number system: Interpret order and calculate with numbers            C/B/
4/07/11    in standard index form (with and without a calculator).                              A
Calculate the upper and lower bounds of calculations.
Mon:      Activities week?
11/07/11
Mon:      Geometry: Complete Constructions incorporating Loci problems which may              C/B
18/07/11   include shading an area “ nearer than” or “ greater than”
SEPTEMBER Holiday 2011
YEAR 11:
Mon:      Algebra: Collect like terms, simplify expressions, expand brackets.                 C/B/
5/09/11    Factorise expressions including quadratic expressions and the difference of         A/A*
two squares.
Mon:      Algebra: Set up and solve linear equations that contain brackets and an             B/A/   Tarsia: Solve
12/09/11   unknown on each side of the equal sign. Equations may contain fractions.            A*     simple linear
equatuions (KS 4
puzzle)
Washing Lines:
Solving linear
equations – two
unknowns and
brackets.
Also: Solving
linera equations
involving fractions
Mon:       Algebra: Solving simultaneous equations by elimination or substitution.             B/A/   Tarsia: Solve
19/09/11   Interpret solution of linear simultaneous equations as points of intersection on     A*    simultaneous
a graph. Set up and solve a pair of linear simultaneous equations.                         equations (
includes some
inequalities)
equatuions (KS 4
puzzle)
Mon:      Geometry: Transformations: ( Revise y = mc + C first). 2-D transformations:         C/B
26/09/11
2
Translations (Use of a vector       ).Reflections- defining the equation of the
3
mirror line.

5
Mon:      Geometry: Transformations: Rotations (about any point) Enlargements                  C/B/   Name the Nines:
3/10/11    including fractional and negative enlargements.                                       A     Terms used in
Describe and transform 2-D shapes using combined Rotations, Reflections,                    Transformations
Translations or Enlargements.
Mon:      Geometry: Congruence and Similarity. Relate Congruence to shapes that are:           B/A/   Name the Nines:
7/10/11    Translated, Reflected, Rotated. Similar shapes are Enlargements.. Understand          A*    Similarity and
and use: SSS, SAS,ASA, RHS to prove congruence. Prove that two triangles                    Congruence
are similar.
Mon:                                                                                                  Tarsia: Fraction,
14/10/11   Revision of all Unit 3 work to date including: Number and the number                        Decimal revision
system: Revise: Operations with integers, fractions, decimals. Convert between              (KS4 puzzle)
decimals and fractions. Understand a recurring decimal to fraction proof.
Percentages: Compound interest and use of a multiplier. Reverse percentages,
Depreciation, Percentage Profit and Loss. Use of a multiplier for compound
interest. Use a calculator to solve standard form problems.
October Test: ( 55 mins Calculator Assessment).Covering all Unit 3 work
covered to date.
Mon:                                                                                           C/B
21/10/11   Measures: Understand and use Bearings. Use and interpret maps and scale
drawings, read and construct scale drawings, draw lines and shapes to scale.
Estimate lengths. Draw shapes using ruler and protractor. Make accurate scale
drawings.
Mon:                                       Half Term
28/10/11
Mon:     Measures: Find circumference and area of circles. Find perimeters and areas          C/B/
4/11/11   of semi circles and quarter circles. Calculate the lengths of arcs and the area of    A
sectors of circles. Answers in terms of π may be required.
Functional Skills: The Fencing Problem Task
Mon:      Measures: Cylinders: Find surface area and volume. Use volume to solve               B/A/   Tarsia: Volume,
11/11/11   problems. More complex mensuration problems: Finding surface area of                  A*    Area, Length
compound solids made from; cubes, cuboids, cones, pyramids, spheres,                        formula(KS4
hemispheres, cylinders.                                                                     puzzle)
Washing Lines:
Surface Area And
Volume of Cones
and Spheres
Mon:       Measures: find the area of a segment of a circle given the radius and length of      A/A*   Name the Nines:
18/11/11   the chord. Use the effect of enlargement on areas and volumes of shapes and                 Area/ Volume
solids. Know the relationship between Linear, Area and Volume scale factors.                formula.
Name the Nines:
Words used in
Maths questions
Mon:      Algebra: Substituting numbers into a formula (including negative numbers).           B/A/   Tarsia: Change
25/11/11   Revise factorising (including quadratics). Change the subject of a formula (          A*    the subject of a
subject may appear on both sides of the formula, or as a power)                             formula(KS4
Mon:      Algebra: Solving quadratic equations by: Factorising, Use of Formula and             A/A*   Tarsia: Quadratic
2/12/11    completing the square.                                                                      solutions (some
using
formula)(KS4
puzzle)
Mon:      Algebra: Set up and solve problems that lead to a quadratic equation. Solving        A/A*
9/12/11    a quadratic or cubic equation using Trial and Improvement. Solve linear
inequalities. Functional Skills: The Open Box Task

6
Mon:      Algebra: Revise plotting straight lines. Find the solution set of a set of linear   B/A/   Name the Nines:
16/12/11   inequalities by graphical methods. Find the gradient of lines given to points on     A*    Types of Graphs
the line, relate to y = mx + c. Calculate the length of a line segment. Plot               Washing Lines:
graphs of quadratic functions, simple cubic functions, the reciprocal function             y = mx + c
and simple exponential functions. Recognise the shapes of these functions and              Standards Unit:
sketch them. Plot the graph of                                                             A7 Recognising
x² + y² = r². Use graphical methods to solve equations of the form f(x) = 0                Graphs
CHRISTMAS
Mon:                                           Mocks
6/01/12
Mon:     Algebra: Solving pairs of simultaneous equations graphically: Pairs of linear       B/A/
13/01/12   equations; one linear and one quadratic (including solving                           A*
y = mc +c and x² + y² = r²)
Solve a pair of simultaneous equations: one linear and one quadratic
Mon:      Algebra: Direct and Inverse proportion. Set up equations and solve word             A/A*
20/01/12   problems involving direct or inverse proportion. Relate algebraic solutions to
graphical representations of the equations.
Mon:      Measures :Use of the sine and cosine rules to solve 2-D and 3-D problems.           A/A*
27/01/12   Finding angles of elevation and depression. Finding the area of a non right
1
angled triangle using:     absinc
2
Mon:      Algebra: Knowledge of graphs of sine and cosine functions. Select and apply         A/A*
03/02/12   transformations of functions: y =f(x) +a , y = f(ax) , y = f ( x+a),
y = af(x). Terpret and analyse transformations and write functions algebraicly.
Mon:      Geometry: Understand and construct proofs using circle theorems:                    A/A*   Name the Nines:
10/02/12   Angle subtended by an arc, Angle in a semi circle, Angles in same segment,                 Parts of a circle
Opposite angles of a cyclic quadrilateral, Alternate segment theorem,                      Washing Lines:
Perpendicular bi Sector of a chord.                                                        Angles using
Circle Theorems
Mon:      Geometry: Vectors: Use of notation, graphical representation of the sum of          A/A*
17/02/12   two vectors, resultant of two vectors, apply vector methods for simple proofs.
Mon:                                        Half Term ?
24/02/12
Mon:     Number and the number system: Understand Upper and Lower bounds and                 B/A/
02/03/12   solve problems involving bounds. Give a final answer to an appropriate degree        A*
of accuracy. Understand “ reciprocal” as a multiplicative inverse. Find
reciprocals. Efficient use of a calculator. Revise: All Unit 3 work
Mon:      Unit 3 Revision.                                                                           Standards Unit:
9/03/12                                                                                               S7- Developing an
Examination
question
Mon:      Unit 3 Mock and Revision
16/03/12
Mon:     Revision
23/03/12
Mon:     Revision
30/03/12
Mon:                                Easter Holiday(these weeks?)
6/04/12
Mon:     Revision
27/04/12
Tues:    Second Unit 3 Mock
5/05/12
Mon:      Revision
11/05/12
Mon:                                  Examination study leave ?

7
19/05/12

Mon:      Examination study leave
26/05/12

8

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Description: Deriving Continuous Compound Interest Formula document sample