WEEK/ DATE

LEARNING OBJECTIVE TOPIC 1

LEARNING OUTCOMES

VALUE

NOTES

WEEK 1 2/1 6/1

PROGRESSIONS 1. Understand and use the concept of arithmetic progression.

WEEK 2 9/1 13/1

WEEK 3 16/1 20/1

2. Understand and use the concept of geometric progressions.

1.1 Identify characteristics of arithmetic progressions. 1.2 Determine whether a given sequence is an arithmetic progression. 1.3 Determine by using formula: a) specific terms in arithmetic progressions: b) the number of terms in arithmetic progressions. 1.4 Find: a) the sum of the first n terms of arithmetic progressions. b) The sum of a specific number of consecutive terms of arithmetic progressions. c) The value of n, given the sum of first n terms of arithmetic progressions. 1.5 Solve problems involving arithmetic progressions. 2.1 Identify characteristics of geometric progressions. 2.2 Determine whether a given sequence is a geometric progression. 2.3 Determine by using formula: c) specific terms in geometric progressions: d) the number of terms in geometric progressions. 2.4 Find: d) the sum of the first n terms of geometric progressions. e) The sum of a specific number of consecutive terms of geometric progressions. f) The value of n, given the sum of first n terms of geometric progressions.

Independent Confident Tidy

Confident Hardworking.

Independent Confident Tidy

WEEK 4 23/1 27/1

2.5 Find: a) the sum of infinity of geometric progressions. b) The first term or common ratio, given the sum to infinity of geometric progressions. 2.6 Solve problems involving geometric progressions. TOPIC 2 1.1 Draw lines of best fit by inspection of given data. 1.2 Write equations for lines of best fit. 1.3 Determine values of variables from: a) lines of best fit b) equations of lines of best fit 2.1 Reduce non-linear relations to linear form. 2.2 Determine values of constants of non-linear relations given: a) lines of best fit. b) data. 2.3 Obtain information from: a) lines of best fit. b) equations of lines of best fit.

Confident Hardworking.

WEEK 5 30/1 3/2

Analytic Careful

LINEAR LAW 1. Understand and use the concept of lines of the best fit. 2. Apply linear law to nonlinear relations.

WEEK 6 6/2 10/2

WEEK 7 13/2 17/2

TOPIC 3 INTERGRATION 1. Understand and use the concept of indefinite integral.

1.1 Determine integrals by reversing differentiation. 1.2 Determine integrals of axn , where a is constant and n is an integer, n -1. 1.3 Determine integrals of algebraic expressions. 1.4 Find constants of integration, c, in indefinite integrals.

WEEK 8 20/2 - 24/2

1.5 Determine equations of curves from functions of gradients. 1.6 Determine by substitution the integrals of expressions of the form ( ax + b )n, where a and b are constants, n is an integer and n -1.2.1 Find definite integrals of algebraic expressions.

Independent Daring to try

WEEK 9 27/2 2/3

2. Understand and use the concept of definite integral.

2.2 Find areas under curves as limit of a sum of areas. 2.3 Determine areas under curves using formula. 2.4 Find volumes of revolutions when region bounded by a curve is rotated completely about the a) x-axis b) y-axis as the limit of a sum of volumes. 2.5 Determine volumes of revolutions using formula. MONTHLY TEST 1

WEEK 10 5/3 9/3 TOPIC 4 WEEK 11 19/3 23/3 VECTOR 1. Understand and use the concept of vector.

1.1 Differentiate between vector and scalar quantities. 1.2 Draw and label directed line segments to represent vectors. 1.3 Determine the magnitude and direction of vectors represented by directed line segments. 1.4 Determine whether two vectors are equal. 1.5 Multiply vectors by scalars. 1.6 Determine whether two vectors are parallel. 2.1 Determine the resultant vector of two parallel vectors. 2.2 Determine the resultant vector of two nonparallel vectors using: a) triangle law b) parallelogram law.

WEEK 12 26/3 30/3

2. Understand and use the concept of addition and subtraction of vectors.

WEEK 13 2/4 6/4

2.3 Determine the resultant vector of three or more vectors using the polygon law. 2.4 Subtract two vectors which are: a) parallel b) non-parallel. 2.5 Represent vectors as a combination of other vectors. 2.6 Solve problems involving addition and subtraction of vectors. 3. Understand and use vectors in the Cartesian plane. 3.1 Express vectors in the form: a) xi + yj x b) ( ) y 3.2 Determine magnitudes of vectors. 3.3 Determine unit vectors in given directions. 3.4 Add two or more vectors. 3.5 Subtract two vectors. 3.6 Multiply vectors by scalars. 3.7 Perform combined operations on vectors. 3.8 Solve problems involving vectors. Independent Daring to try

WEEK 14 9/4 13/4

WEEK 15 16/4 20/6

TOPIC 5 TRIGONOMETRIC FUNCTION 1.Understand the concept of positive and negative angles measured in degrees and radians. 2. Understand and use the six trigonometric functions of any angle.

1.1 Represent in a Cartesian plane, angles greater than 360 or 2 radians for: a) positive angles b) negative angles. 2.1 Define sine, cosine and tangent of any angle in a Cartesian plane. 2.2 Define cotangent, secant and cosecant of any angle in a Cartesian plane. 2.3 Find value of the six trigonometric functions of any angle. 2.4 Solve trigonometric equations.

Analytic

WEEK 16 23/4 27/4

3. Understand and use graphs of sine, cosine and tangent functions.

3.1 Draw and sketch graphs of trigonometric functions: a) y = c + a sin bx, b) y = c + a cos bx c) y = c + a tan bx where a, b and c are constants and b > 0, a 0. 3.2 Determine the number of solutions to a trigonometric equation using sketched graphs. 3.3 Solve trigonometric equations using drawn graphs. 4.1 Prove basic identities: a) sin2 A + cos2 A = 1 b) 1 + tan2 A = sec2 A c) 1 + cot2 A + cosec2 A 4.2 Prove trigonometric identities using basic identities. 4.3 solve trigonometric equations using basic identities. 5.1 Prove trigonometric identities using addition formulae for sin ( A B ), cos ( A B) and tan ( A B). 5.2 Derive double-angle formulae for sin 2A , cos 2A and tan 2A. 5.3 Prove trigonometric identities using addition formulae and/or double-angle formulae. 5.4 Solve trigonometric equations.

Independent Confident Daring to try

WEEK 17 30/4 4/5

4. Understand and use basic identities.

Daring to try

WEEK 18 7/5 11/5

5. Understand and use addition formulae and double-angle formulae

. WEEK 19 14/5 18/5 Mid Term Exam WEEK 20 21/5 25/5 Independent Daring to try

TOPIC 6 WEEK 21 11/6 15/6 PERMUTATION AND COMBINATION 1. Understand and use the concept of permutation. 1.1 Determine the total number of ways to perform successive events using multiplication rule. 1.2 Determine the number of permutations of n different objects. 1.3 Determine the number of permutations of n different object taken r at a time. 1.4 Determine the number of permutations of n different objects for given conditions. 1.5 Determine the number of permutations of n different objects taken r at a time for given condition. 2.1 Determine the number of combinations of r objects chosen from n different objects. 2.2 Determine the number of combinations r objects chosen from n different object for given conditions.

WEEK 22 18/6 22/6

2. Understand and use the concept of combination.

TOPIC 7 WEEK 23 25/6 29/6 PROBABILITY 1. Understand and use the concept of probability 1.1 Describe the sample space of an experiment. 1.2 Determine the number of outcomes of an event. 1.3 Determine the probability of an event. 1.4 Determine the probability of two events: a) A or B occurring. b) A and B occurring

WEEK 24 2/7 6/7

2. Understand and use the concept of probability of mutually exclusive events.

2.1 Determine whether two events are mutually exclusive. 2.2 Determine the probability of two or more events that are mutually exclusive.

3. Understand and use concept of probability of independent events.

3.1 Determine whether two events are independent. 3.2 Determine the probability of two independent events. 3.3 Determine the probability of three independent events. 1.1 List all possible values of a discrete random variable. 1.2 Determine the probability of an event in a binomial distribution. 1.3 Plot binomial distribution graphs. 1.4 Determine mean, variance and standard deviation of a binomial distribution. 1.5 Solve problems involving binomial distributions. 2.1 Describe continuous random variables using set notations. 2.2 Find probability of z-values for standard normal distribution. 2.3 Convert random variable of normal distributions, X, to standardised variable, Z. 2.4 Represent probability of an event using set notation. 2.5 Determine probability of an event. 2.6 Solve problems involving normal distributions. 1.1 Identify direction of displacement of a particle from a fixed point. Brave Daring to try

TOPIC 8 WEEK 25 9/7 13/7 PROBABILITY DISTRIBUTION 1. Understand and use the concept of binomial distribution.

WEEK 26 16/7 20/7

2. Understand and use the concept of normal distribution.

TOPIC 9 WEEK 27 23/7 27/7 MOTION ALONG A STRAIGHT LINE

1. Understand and use the concept of displacement. 2. Understand and use the concept of velocity.

1.2 Determine the total distance travelled by a particle over a time interval using graphical method. 2.1 Determine velocity function of a particle by differentiation. 2.2 Determine instantaneous velocity of a particle. 2.3 Determine displacement of a particle from velocity function by integration. 3.1 Determine acceleration function of a particle by differentiation. 3.2 Determine instantaneous acceleration of a particle. 3.3 Determine instantaneous velocity of a particle from acceleration function by integration. 3.4 Determine displacement of a particle from acceleration function by integration. 3.5 Solve problems involving motion along a straight line.

WEEK 28 30/7 3/8

3. Understand and use the concept of acceleration.

TOPIC 10 WEEK 29 6/8 10/8 LINEAR PROGRAMMING 1. Understand and use the concept of graphs of linear inequalities. 1.1 Identify and shade the region on the graph that satisfies a linear inequality. 1.2 Find the linear inequality that defines a shaded region. 1.3 Shade region on the graph that satisfies several linear inequalities. 1.4 Find linear inequalities that define the shaded region. 2.1 Solve problems related to linear programming by: a) writing linear inequalities and equations describing a situation. b) shading the region of feasible solutions. Confident

WEEK 30 13/8 17/8

2. Understand and use the concept of linear programming.

Daring to try

c) determining and drawing the objective function ax + by = k where a, b and k are constants. d) determining graphically the optimum value of the objective function. WEEK 31 27/8 31/8 WEEK 32 3/9 7/9 WEEK 33 -34 10/9 21/9 WEEK 35-41 24/9 9/11 19/11 19/12 REVISION

SPM TRIAL REVISION

SPM EXAMINATION