MAT1510
Assignment 2
Due date: Friday, 31 May 2024
, DISCLAIMER
This comprehensive document offers a detailed analysis, providing
valuable insights and explanations for students seeking to deepen their
understanding. It’s clear and concise explanations make it an invaluable
study resource, helping students grasp complex concepts with ease.
With well-organized sections and illustrative examples, the document
caters to various learning styles, making it accessible to a wide range of
students. The inclusion of practice questions and exercises enhances its
utility, allowing students to reinforce their knowledge and test their
comprehension. Whether used for exam preparation or as a
supplementary learning aid, this document equips students with the
tools they need to succeed academically in this unit.
,UNIQUE ASSIGNMENT NUMBER: 186115
, ASSIGNMENT 02
Due date: Friday, 31 May 2024
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 186115
ONLY FOR YEAR MODULE
This assignment covers chapter 2 of the prescribed book as well as the study guide
DO NOT USE A CALCULATOR.
Question 1: 13 Marks
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give
an example that disproves the statement.
(1.1) If f is a function, then f (s + t ) = f (s) +f (t ). (3)
(1.2) If f (s) = f (t ), then s = t . (2)
(1.3) If f is a function, then f (3x ) = 3f (x ). (3)
(1.4) A vertical line intersects the graph of a function at most once. (2)
1
(1.5) If f is one-to-one, then f − 1 (x ) = . (3)
f (x )
Question 2: 9 Marks
The perimeter of a rectangle is 16 meters.
(2.1) If the length of one of the sides of the rectangle is (1 + x ) meters, express the area A of the (4)
rectangle in terms of x .
(2.2) Calculate the maximum area of the rectangle. (3)
(2.3) What are the dimensions of the rectangle when its area is a maximum? (2)
Question 3: 6 Marks
Suppose a stone is thrown vertically upwards with a velocity of u meters per second. Then its height is h (in
meters) after t seconds is given by the formula
h = ut − 4.8t 2 .
(3.1) Suppose the stone is thrown upwards with a velocity of 24 meters per second. Sketch the (5)
graph of the function defined by
h = ut − 4.8t 2 .
Label the axes properly, and show the coordinates of the critical points on the graph clearly.
16
Assignment 2
Due date: Friday, 31 May 2024
, DISCLAIMER
This comprehensive document offers a detailed analysis, providing
valuable insights and explanations for students seeking to deepen their
understanding. It’s clear and concise explanations make it an invaluable
study resource, helping students grasp complex concepts with ease.
With well-organized sections and illustrative examples, the document
caters to various learning styles, making it accessible to a wide range of
students. The inclusion of practice questions and exercises enhances its
utility, allowing students to reinforce their knowledge and test their
comprehension. Whether used for exam preparation or as a
supplementary learning aid, this document equips students with the
tools they need to succeed academically in this unit.
,UNIQUE ASSIGNMENT NUMBER: 186115
, ASSIGNMENT 02
Due date: Friday, 31 May 2024
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 186115
ONLY FOR YEAR MODULE
This assignment covers chapter 2 of the prescribed book as well as the study guide
DO NOT USE A CALCULATOR.
Question 1: 13 Marks
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give
an example that disproves the statement.
(1.1) If f is a function, then f (s + t ) = f (s) +f (t ). (3)
(1.2) If f (s) = f (t ), then s = t . (2)
(1.3) If f is a function, then f (3x ) = 3f (x ). (3)
(1.4) A vertical line intersects the graph of a function at most once. (2)
1
(1.5) If f is one-to-one, then f − 1 (x ) = . (3)
f (x )
Question 2: 9 Marks
The perimeter of a rectangle is 16 meters.
(2.1) If the length of one of the sides of the rectangle is (1 + x ) meters, express the area A of the (4)
rectangle in terms of x .
(2.2) Calculate the maximum area of the rectangle. (3)
(2.3) What are the dimensions of the rectangle when its area is a maximum? (2)
Question 3: 6 Marks
Suppose a stone is thrown vertically upwards with a velocity of u meters per second. Then its height is h (in
meters) after t seconds is given by the formula
h = ut − 4.8t 2 .
(3.1) Suppose the stone is thrown upwards with a velocity of 24 meters per second. Sketch the (5)
graph of the function defined by
h = ut − 4.8t 2 .
Label the axes properly, and show the coordinates of the critical points on the graph clearly.
16
