## YHWH HAMASCHIAC SCHOOL, Christmas Term2021-2022, SS3 MATHEMATICS-THEORY OF LOGARITHM – LESSON 1

Author: Mary Okoh

WEEK                             SCHEME OF WORK   Theory of Logarithms: Laws of Logarithms and application of Logarithmic equations and indices Surds: Rational and Irrational numbers; basic operations with surds and conjugate of binomial surds Application of surds to trigonometrical ratios. Draw the graphs of ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021-2022 SS3 MATHEMATICS THEORY OF LOGARITHM LESSON 2

Author: Mary Okoh

The video above is the explanation of the note in the previous class. Below is the note for your perusal     Evaluation: Evaluate the following logarithms Log48  Log6216  Log80.0625

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-THEORY OF LOGARITHM (CONTD.)-LESSON 3

Author: Mary Okoh

MATEHEMATICS THEORY OF LOGARITHM Basic Laws of Logarithms Log mn = Log m + Log n Log (m/n) = Log m – Log n Log mp  = pLog m Log 1 = 0 Logmm = 1 Log (1/m)n= Log m-n = -nLog m     Change of base Log mn =  Logan Logam Examples: Express ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-THEORY OF LOGARITHM (CONTD.)-LESSON 4

Author: Mary Okoh

MATHEMATICS LAWS OF LOGARITHM APPLICATIONS OF  THE LAWS OF LOGARITHM EXAMPLES Given that log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, evaluate the following   a. log 5   b. log 6 c. log 0.9                                    ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-SURDS-LESSON 5

Author: Mary Okoh

MATHEMATICS ADDITION, SUBTRACTION AND MULTIPLICATION OF SURDS   CONTENTS: Definition of surd Like surds Simplification of surd Addition and subtraction of surd multiplication of surds   DEFINITION OF SURDS A number which can be expressed as a quotient m/n of two integers, (n≠ 0) iscalled a rational number. Any real number which is not rational ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-SURDS-LESSON 6

Author: Mary Okoh

MATHEMATICS SURDS(CONTD.) ADDITION AND SUBTRACTION OF SURDS

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-SURDS-LESSON 7

Author: Mary Okoh

MATHEMATICS MULTIPLICATION OF SURDS

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-SURDS-LESSON 8

Author: Mary Okoh

MATHEMATICS SURDS

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-SURDS-LESSON 9

Author: Mary Okoh

MATHEMATICS SURDS(CONTD.)

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-APPLICATION OF SURDS-LESSON 10

Author: Mary Okoh

MATHEMATICS APPLICATION OF SURDS APPLICATION OF SURDS TO TRIGONOMETRICAL RATIOS   Application of Surds to Trigonometrical Ratios: The following summary shows how to find the sine, cosine and tangent of angles in surd form.   Trigonometric ratios of 300 and 600: An equilateral triangle of side 2 units is used to obtain the values of ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 11

Author: Mary Okoh

MATHEMATICS MATRICES A matrix is an ordered set of numbers listed rectangular form. A matrix is, by definition, a rectangular array of numeric or algebraic quantities which are subject to mathematical operations. Matrices can be defined in terms of their dimensions (number of rows and columns). Let us take a look at a matrix with ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 12

Author: Mary Okoh

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 13

Author: Mary Okoh

MATHEMATICS MATRICES Matrix Addition and Subtraction DEFINITION: Two matrices A and B can be added or subtracted if and only if their dimensions are the same (i.e. both matrices have the same number of rows and columns. Take: Addition Addition and subtraction operations can easily be performed on matrices, provided the matrices have the same dimensions. ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 14

Author: Mary Okoh

MATHEMATICS MATRICES MULTIPLICATION Performing the operation product involves multiplying the cells of a particular rows in the first matrix by the cells of a particular column in the second matrix, adding the products, and storing the result in the cell of the resultant matrix whose coordinates correspond to the row of the first matrix and ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 14B

Author: Mary Okoh

MATHEMATICS MATRICES

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 15

Author: Mary Okoh

MATHEMATICS MATRICES     TRANSPOSE AND INVERSE OF MATRICES, DETERMINANT OF MATRICES, APPLICATION OF DETERMINANTS   TRANSPOSE OF MATRICES DEFINITION: The transpose of a matrix is found by exchanging rows for columns i.e. Matrix A = (aij) and the transpose of A is: AT = (aji) where j is the column number and i is the row ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-TEST

Author: Mary Okoh

MATHEMATICS TEST OBJECTIVE: ANSWER ALL QUESTIONS Simplify the following: a. ½ log 25 1 + log 3   c. log 8 + log 4 Evaluate log 45 – log 9 + log 20 Given that log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, evaluate a. log 42 log 35 (d) 105 ….  Read More

## YHWH HAMASCHIAC SCHOOL CHRISTMAS/FIRST TERM 2021- 2022 SS3 MATHEMATICS-MATRICES-LESSON 16

Author: Mary Okoh

MATHEMATICS MATRIX The Inverse of a Matrix DEFINITION: Assuming we have a square matrix A, which is non-singular (i.e. det(A) does not equal zero), then there exists an n×n matrix A-1 which is called the inverse of A, such that this property holds: AA-1 = A-1A = I, where I is the identity matrix. The inverse of a ….  Read More

## YHWH HAMASCHIAC SCHOOL, SS3 YHWH YESHUA HAMASCHIAC’S DAY #Christmas /First Term 2021- 2022 SESSION- AREA OF CONCENTRATION

Author: Mary Okoh

MATHEMATICS AREA OF CONCENTRATION LOGARITHM SURDS ADDITION OF SURDS SUBTRACTION OF SURDS MULTIPLICATION OF SURDS CONJUGATION OF SURDS RATIONALIZATION OF SURDS APPLICATION OF SURDS MATRICES ADDITION OF MATRIX SUBTRACTION OF MATRIX MULTIPLICATION OF MATRIX INVERSE OF A MATRIX

## YHWH HAMASCHIAC SCHOOL, SS3 YHWH YESHUA HAMASCHIAC’S DAY #Christmas /First Term 2021- 2022 SESSION- Mathematics EXAMINATION

Author: Mary Okoh

YHWH HAMASCHIAC SCHOOL, SS3 YHWH YESHUA HAMASCHIAC’S DAY #Christmas /First Term 2021- 2022 SESSION- EXAMINATION. MATHEMATICS SECTION A: ANSWER ALL QUESTIONS Evaluate log80.0625 a. 3 b. -4 c. -4/3 d. -3/2 Find the value of log749 + log7 (1/7) a. 1 b. 2 c. 3 d. 7  Evaluate log 80625 a. 3 b. -4 c. ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Scheme of Work. 2021/2022 Academic Year.

Author: Mary Okoh

MATHEMATICS SCHEME OF WORK WEEK              TOPICS 1                           Revision 2                          Co-ordinate geometry of straight lines 3                      ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 1, Co-ordinate Geometry. 2021/2022 Academic Year.

Author: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY Distance between two points Using Pythagoras theorem: C2 = a2 + b2 C = √( a2 + b2) /AB/ = √(x2 – x1)2 + (y2 – y1)2 Distance between two points AB is given by /AB/ = √(x2 – x1)2 + (y2 – y1)2   Example: Find the distance between the each ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 2, Co-ordinate Geometry (contd.). 2021/2022 Academic Year.

Author: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY(CONTD.) Mid-point of a line: The mid-point of the line joining two points: Triangle MAN and BMD are congruent, so AM = MD and BD = MN x – x1 = x2 – x                                          y – y1 = y2 – y x + x = x2 + x1                                          y + y = y2 ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 3, Co-ordinate Geometry (contd.). 2021/2022 Academic Year.

Author: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY Gradient and Intercepts of a line Gradient of a line of the form y = mx + c, is the coefficient of x, which is represented by m and c is the intercept on the y axis. Example Find the equation of the line with gradient 4 and y-intercept -7. Solution m ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 5B, Co-ordinate Geometry (contd.). 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 5, Co-ordinate Geometry (contd.). 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY Two Point Form: Given two points (x1, y1) and (x2, y2), the equation can be obtained using the formula: (y2 – y1)/(x2 – x1) = (y – y1)/(x – x1) Example: Find the equation of the line passing through (2,-5) and (3,6). Solution 6 – (-5)/3 – 2 = y – (-5)/x ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 6, Co-ordinate Geometry (contd.). 2021/2022 Academic Year

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MATHEMATICS CO-ORDINATE GEOMETRY Angles between Lines Parallel lines: The angle between parallel lines is 00 because they have the same gradient   Perpendicular Lines: Angle between two perpendicular lines is 900 and the product of their gradients is – 1. Hence, m1m2 = – 1 Examples: Show that the lines y = -3x + 2 ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 7, Co-ordinate Geometry (contd.). 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS CO-ORDINATE GEOMETRY The gradient of y = mx + c is tan θ.    Hence m = tan θ can be used to calculate angles between two intersecting lines. Generally the angle between two lines can be obtained using:                   tan θ = m2 -m1/(1+m1m2) Example: Calculate the ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 8, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION Consider the curve whose equation is given by y = f(x) Recall that m = y2 – y1/x2 – x1= f(x+x)-f(x) /x As point B moves close to A, dx becomes smaller and tends to zero. The limiting value is written on Lim f(x +x) – f(x)/dx and is denoted by as x ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 9, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

https://youtu.be/d1_PQJcQog0MATHEMATICS  DIFFERENTIATION  Derivative of algebraic functions Let f, u, v be functions such that f(x) = u(x) + v(x) f(x +x ) = u(x +x ) + v(x + x) f(x + x) – f(x) = {u(x+ x) + v(x+ x) – v(x + x) – u(x) – v(x)} = u (x +x ) – ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 8b, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 8c, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION Find from first principle, the derivative of   y = x2 Solution Example 1 Find from first principle, the derivative of   y = x2 Solution y = x2 y + Δy = (x + Δx)2 y +Δ y = x2 + 2Δx + (Δx)2 Δy =  x2 + 2xΔx+ (Δx)2  –  y Δy = ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 8d, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS Differentiation from first principle

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 9, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION   Rules of Differentiation:     Let            y = xn y + dy = (x + dx)n = xn + nxn-1dx + n(n -1) xn-2(dx)2 + … (dx)n 2!   = xn + n xn-1dx + n(n-1) xn-2  (dx)2+ — + (dx)n – xn 2! = nxn-1dx + n (n – 1) xn–1 (dx)2 2! ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 10, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION Rules of differentiation(contd.) Function of a function (chain rule) Suppose that we know that y is a function of u and that u is a function of x, how do we find the derivative of y with respect to x? Given that y = f(x) and u = h(x), what is dy/dx? dy/dx ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Area of concentration. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS AREA OF CONCENTRATION For the forth coming mid-term test, here are the area of concentration; Coordinate Geometry of straight line: Cartesian coordinate graphs, distance between two points, midpoint of the line joining two points. Coordinate Geometry of straight lines: Gradient and Intercepts of a line, angle between two intersecting straight lines and application. Differentiation ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics Test. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS TEST Find the distance between the points in each of the following pairs leaving your answers in surd form:  (7, 2) and (1, 6) What is the value of r if the distance between the points (4, 2) and (1, r) is 3 units? Find the coordinates of the mid-point (-3, -2) and (-7, ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 11, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION PRODUCT RULE We shall consider the derivative of y = uv where u and v are function of x. Let y = uv Then y + y = (u +u )(v + v) = uv + uv + vu +uv y = uv + uv + vu+ uv – uv y= uv + ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 11B, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 12, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS Quotient Rule: If y = u           v then; dy =  vdu – udv          dx        dx     dx                           v2 Examples: Differentiate the following with respect to x.  (a)x2 + 1     (b)(x – 1)2 1 – x2               √x Solution: y = x2 + ….  Read More

## HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 13, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS Differentiation Velocity and Acceleration Velocity: The velocity after t seconds is the rate of change of displacement with respect to time. Suppose; s = distance and t = time, Then; Velocity = ds/dt Acceleration: This is the rate of change of velocity compared with time. Acceleration = dv/dt Example: A moving body goes s ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics, Lesson 12B, Differentiation. 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS DIFFERENTIATION Quotient rule

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics Assignment . 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS  1. What is the gradient and y intercept of the line equation 3x -5y +10=0 ? 2. Find the equation of the line with gradient – 9 and y-intercept 4.                           3. Find the equation of the line with gradient 5 and point(-2, ….  Read More

## YHWH HAMASCHIAC School, 2nd/ Resurrection Day (Easter) Term, SSS3 Mathematics Mock Examination . 2021/2022 Academic Year

Length: 0 minutesAuthor: Mary Okoh

MATHEMATICS Express 302.10495 correct to five significant figures          WAEC 2012 A. 302.10 B. 302.11 C. 302.105 D. 302.1049 2. Simplify; 35√×46√22√×32√35×4622×32                           WAEC 2012 A. 2–√2 B. 5–√5 C. 22–√2 D. 25–√5 3. In 1995, the enrollment of two schools X and Y were 1,050 and 1,190 respectively. Find the ration of the enrollments of X and Y                         WAEC 2012 A. 50:11 B. 15:17 C. 13:55 D. 12:11  4. ….  Read More