Module Title and Code: Mathematics C20193 (Level 5)

Brief

Module Title and Code: Mathematics C20193 (Level 5)

Assessment Technique: Assignment

Weighting: 30%

Title: Assignment 1

Guidelines: The required number of questions must be answered.

All necessary work must be clearly shown.

All hand drawn graphs must be presented on graph paper.

Answers involving calculations to be shown correct to 2 decimal places unless otherwise stated.

Assessment criteria: as per individual candidate marking sheet.

Issue Date:

Deadline:

MATHEMATICS

LEVEL 5

C20193

ASSIGNMENT 1

VALUE: 30%

The following research was carried out in a college of further education to obtain a picture of the life of a typical student.

250 students were chosen at random and asked to fill out a questionnaire which sought information on their part-time work, study habits, weekly expenditure, involvement in sport and leisure activities, time spent at college per day, car ownership, satisfaction level with their course and plans for the future.

80% of the students completed the questionnaire.

Some of the data that was gathered is shown below.

Half of the students who completed the questionnaire had part-time jobs. The hours worked during term time were as follows:

Table A

To examine the relationship between part-time work and study habits 20 students with part time jobs were chosen at random. The hours these students worked and their weekly study habits are contained in the table below;

Table B

Table C

The study habits of the 80% of students who completed the questionnaire are shown below;

Table D

When asked to identify the activities in which they regularly participated the following ten were the most popular activities identified.

(i)Calculate the number of students who completed the questionnaire.

(ii)Represent the data from tables A,B and D using 2 graphs from the following list:

Bar charts, trend graphs, histograms, cumulative frequency curves, pie charts and scatter diagrams.

(iii)In the case of table C represent the data given using a cumulative frequency curve and find the mean and standard deviation of the data correct to 2 decimal places.

(iv)Answer the following questions based on Table D

1. a student is selected at random what is the probability that they play basketball?
2. a student is selected at random what is the probability that they play soccer or tennis?
3. A student decides to take up 3 of the activities in listed in the table, in how many ways can the student select 3 activities if the order in which the activity is selected is not important.

Using data collected on the number of cars in the student carpark from 8am - 6pm on a particular day, researchers derived the following function f : - x2 + 3x + 4, with the domain being -1 ≤ x ≤ 4 .

Each unit on the y - axis represents 100 cars.

Each unit on the x – axis represents 2 hours, where 8am = -1, 10am = 0, 12pm = 1 ....etc.

(i)Draw the graph of the function in the given domain.

(ii)Use your graph to estimate

1. the number of cars in the carpark at 1.30pm
2. the times when the carpark contained 400 cars
3. the times the carpark contained no cars.

(iii)Discuss the relationship between the number of cars in the carpark and the time.

(v)Draw the axis of symmetry and write down its equation.