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# Mathematics Lesson Notes SS1 Third Term

SCHEME OF WORK

WEEK 1: SS1 MATHEMATICS THIRD TERM: MENSURATION

WEEK 2: SS1 MATHEMATICS THIRD TERM: VOLUME OF A CONE

WEEK 3: SS1 MATHEMATICS THIRD TERM: CONTENT GEOMETRICAL CONSTRUCTION

WEEK 4: SS1 MATHEMATICS THIRD TERM: CONSTRUCTION OF QUADRILATERAL POLYGON

WEEK 5: SS1 MATHEMATICS THIRD TERM: DEDUCTIVE PROOF

WEEK 6: SS1 MATHEMATICS THIRD TERM: STATISTICS – COLLECTION AND PRESENTATION OF DATA

WEEK 7: SS1 MATHEMATICS THIRD TERM: CALCULATION OF MEAN, MEDIAN AND MODE OF GROUPED DATA

WEEK 8: SS1 MATHEMATICS THIRD TERM: COLLECTION, TABULATION AND PRESENTATION OF GROUPED DATA

WEEK 9: SS1 MATHEMATICS THIRD TERM: STATISTICAL GRAPH

WEEK 10: SS1 MATHEMATICS THIRD TERM: CALCULATION OF MEAN, MEDIAN, MODE OF GROUPED DATA

WEEK 11: SS1 MATHEMATICS THIRD TERM: MEAN DEVIATION FOR GROUPED DATA

COLLECTION, TABULATION AND PRESENTATION OF GROUPED DATA

CALCULATION OF RANGE, MEDIAN AND MODE OF GROUPED DATA

# Below are the 2022 complete SS1 Third Term Mathematics Lesson Note

WEEK 1

Topic: MENSURATION

CUBES

A cube is a solid of a uniform cross-section. It is formed by squares and has 8 vertices. An example is processed cubed sugar.

The length of a side of a cube is ‘e’ which is the length of all sides since a cube is formed with squares.

TOTAL SURFACE AREA OF A CUBE

A cube has 6 faces. The surface area of each side = e2 as each side is a square.

Therefore, Total surface area of a cube (all 6 sides) = 6e2

The surface area of a cube is gotten by the formula

Week 2

Topic: VOLUME OF A CONE

Volume of a cone = 1/3 ×πr2h

This is the formula for the volume of all cones.

RECTANGULAR BASED PYRAMID

A pyramid is a solid whose base is a polygon and has a common point or vertex.  A pyramid is named according to its base, evidently the pyramid in question here has a rectangular base.

TOTAL SURFACE AREA OF A RECTANGULAR BASED PYRAMID

In the case of a pyramid, the total surface area is found by summing up the areas of the common shapes that make up the pyramid.

VOLUME OF A RECTANGULAR-BASED PYRAMID

Since a pyramid is shaped like a cone with the pyramid having a polygonal base, the volume of a pyramid is also 1/3 the base area height.

Therefore, volume of pyramid= 1/3 × the product of base area and perpendicular height. To learn more, click here

Week 3

TopicContent Geometrical Construction

Revision of Construction of Triangle

A triangle can be constructed with a compass, a ruler and a protractor. You also need some squared paper and a pencil.

At first you need an overview of the information about the triangle you have.

A good place to start is by drawing the baseline, which is the basis of the further construction of the triangle.

In the following explanations are the vertices of a triangle called A, B and C, and the side lengths are called |AB|, |AC| and |BC|. We will explain how the construction of the triangle is carried out, depending on which of the mentioned information that are given.

Not all possible situations are explained, but hopefully, it’s enough to give you an idea of what to do, when the triangle’s information is presented to you. To learn more, click here

Week 4

We can identify different quadrilaterals based on the properties sides, diagonals and angles.
Quadrilaterals are made up of ten parts. However, to construct them, you do not need to know the measurements of all of them.
In case of special quadrilaterals, like the rectangle, just two measurements, the lengths of its adjacent sides are enough to construct it.
A kite can be constructed if the lengths of its distinct adjacent sides and one diagonal are known.
Similarly, a square can be constructed with just the length of its side, while a rhombus can be constructed when the lengths of its diagonals are known.

Steps to Construct a Rectangle:
Step 1: Draw a side of given length (say) CL
Step 2: Draw side LU (say) of given length perpendicular to CL at L.
Step 3: Draw side CE (say) of length equal to LU and perpendicular to CL at C.
Step 4: Draw side UE.

Week 5

Topic: Deductive Proof

Sum of Angles of a Triangle

An axiom is a statement that is simply accepted as being true.  We have accepted the following statements as facts:

1.  Alternate angles are equal.  That is:

aº = bº

2.  Corresponding angles are equal.  That is:

bº = cº

3.  The sum of adjacent angles forming a straight line is equal to 180º.   That is:

aº + bº = 180º

In deductive geometry, we do not accept any other geometrical statement as being true unless it can be proved (or deduced) from the axioms.

A statement that is proved by a sequence of logical steps is called a theorem.

To prove a theorem we start by using one or more of the axioms in a particular situation to get some true statements.  We then have to apply logical reasoning to these statements to produce new statements that are true.  The proof ends when we arrive at the statement of the theorem.

Properties of Equality

The relation of equality has the following properties.  We will use these properties in the proofs of some theorems.

1.  Transitive Property

If a = b and b = c, then a = cTo learn more, click here

Week 6

Topic: Statistics

Collection and Presentation of Data

Introduction

To derive conclusions from data, we need to know how the data were collected; that is, we need to know the method(s) of data collection.

Methods of Data Collection

There are four main methods of data collection.

• Census. A census is a study that obtains data from every member of a population. In most studies, a census is not practical, because of the cost and/or time required.
• Sample survey. A sample survey is a study that obtains data from a subset of a population, in order to estimate population attributes.
• Experiment. An experiment is a controlled study in which the researcher attempts to understand cause-and-effect relationships. The study is “controlled” in the sense that the researcher controls (1) how subjects are assigned to groups and (2) which treatments each group receives.In the analysis phase, the researcher compares group scores on some dependent variable. Based on the analysis, the researcher draws a conclusion about whether the treatment (independent variable) had a causal effect on the dependent variable.
• Observational study. Like experiments, observational studies attempt to understand cause-and-effect relationships. However, unlike experiments, the researcher is not able to control (1) how subjects are assigned to groups and/or (2) which treatments each group receives.

Data Collection Methods: Pros and Cons

WEEK 7

Topic: Calculation of Mean, Median and Mode of Ungrouped Data

Mean, median, and mode are three basic ways to look at the value of a set of numbers. You will start by learning about the mean.

The mean, often called the average, of a numerical set of data, is simply the sum of the data values divided by the number of values. This is also referred to as the arithmetic mean. The mean is the balance point of a distribution.

Mean = sum of the values/the number of values

For instance, take a look at the following example. Use the formula to calculate the mean number of hours that Stephen worked each month based on the example below.

Example

Stephen has been working on programming and updating a Web site for his company for the past 15 months. The following numbers represent the number of hours Stephen has worked on this Web site for each of the past 7 months:

24, 25, 31, 50, 53, 66, 78

What is the mean (average) number of hours that Stephen worked on this Web site each month?

Step 1: Add the numbers to determine the total number of hours he worked.

24 + 25 + 33 + 50 + 53 + 66 + 78 = 329 To learn more, click here

WEEK EIGHT

Topic: Collection, Tabulation and Presentation of Grouped Data

In some investigations you may collect an awful lot of information. How can you use this raw data and make it meaningful? This section will help you to collect, organise and interpret the data efficiently.

Imagine that you are asked to carry out a survey to find the number of pets owned by pupils in your school. You decide to ask 50 people, and record your results as follows:

0  2  1  2  0  4  1  0  2  2  1  6  1  1  2  8  0  12

2  1  2  0  3  2  0  1  3  0  1  4  0  3  0  2  3  6

3  3  0  1  2  0  1  1  3  0  2  0  3  2

You now have the information you need, but is this the most efficient way to collect and display the data?

Tallying

Tallying is a method of counting using groups of five. To learn more, click here

WEEK 9

Topic: CALCULATION OF MEAN, MEDIAN, MODE OF GROUPED DATA

Let’s start off with some raw data (not a grouped frequency) .

Example: Alex did a survey of how many games each of 20 friends owned, and got this:

9, 15, 11, 12, 3, 5, 10, 20, 14, 6, 8, 8, 12, 12, 18, 15, 6, 9, 18, 11

To find the Mean, add up all the numbers, then divide by how many numbers there are:

Mean = 9+15+11+12+3+5+10+20+14+6+8+8+12+12+18+15+6+9+18+11/20 = 11.1

To find the Median, place the numbers in value order and find the middle number (or the mean of the middle two numbers). In this case the mean of the 10th and 11th values:

3, 5, 6, 6, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 14, 15, 15, 18, 18, 20:

12 appears three times, more often than the other values, so Mode = 12 To learn more, click here

Grouped Frequency Table

WEEK 10

Topic: STATISTICAL GRAPHS

Bar Chart

A bar graph is a way to visually represent qualitative data. Qualitative or categorical data occurs when the information concerns a trait or attribute and is not numerical. This kind of graph emphasizes the relative sizes of each of the categories being measured by using vertical or horizontal bars. Each trait corresponds to a different bar. The arrangement of the bars is by frequency. By looking at all of the bars, it is easy to tell at a glance which categories in a set of data dominate the others. The larger a category, the bigger its bar will be.

Big Bars or Small Bars?

To construct a bar graph we must first list all the categories. Along with this, we denote how many members of the data set are in each of the categories. Arrange the categories in order of frequency. We do this because the category with the highest frequency will end up being represented by the largest bar, and the category with the lowest frequency will be represented by the smallest bar.

For a bar graph with vertical bars, draw a vertical line with a numbered scale. The numbers on the scale will correspond to the height of the bars. The greatest number that we need on the scale is the category with the highest frequency. The bottom of the scale is typically zero, however, if the height of our bars would be too tall, then we can use a number greater than zero. To learn more, click here

WEEK 11

Topic: MEAN DEVIATION FOR GROUPED DATA

Range and quartile deviations are positional measures of dispersion, wherein all the observations are not taken into account in the calculation. Now we consider a measure of dispersion called mean deviation based on all observations.

Consider the observations 3, 5, 6, 7, 9

A.M. = `(3+5+6+7+9)/(5)` = 6

The sum of the deviations of the items from the mean is zero. Consider the A.M. of the absolute deviations of those observations from their mean.

i.e., = `(3+1+0+1+3)/(5)` = 8/5 = 1.6

This is called the mean deviation from the mean. This tells that on average the observations deviated away from the mean by 1.6 on either side.

Definition of Mean Deviation for Grouped Data:

Let x1, x2, x3,…xn be n values. The mean deviation about the mean of these values is given by

M.D. = `(sum I X i – barxI)/(n)` To learn more, click here

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