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MAT1510 ASSIGNMENT 2 ANSWERS 2024

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MAT1510 ASSIGNMENT 2 ANSWERS 2024

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  • May 21, 2024
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  • 2023/2024
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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

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