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Linear Equations and Graphs: Practical Exercises, Exercises of Mathematics

Mathematics

Exercises focused on linear equations and their graphical representation. Problems provide a linear equation, requiring users to complete a table, draw the graph, and interpret the gradient. Scenarios include water volume decrease, data depletion, transport card balance reduction, movie credits consumption, class package usage, and phone battery decline. Designed to reinforce the relationship between linear equations and real-world situations, enhancing students' ability to apply mathematical concepts. Suitable for high school students learning about linear functions, providing a hands-on approach to mastering these concepts and improving analytical skills.

Typology: Exercises

2024/2025

Uploaded on 08/07/2025

jaswika
jaswika 🇲🇾

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1) The volume of water, V (in litres) left in a tank after ‘t’ hours is given by
V = 1,000 - 70t
where ‘t’ is time in hours.
a) Complete the table for t = 0, 1, ..., 10 and draw the graph of V against t on graph paper.
t
0
1
2
3
4
5
6
7
8
9
V
b) What is the initial volume in the tank?
c) What is the water volume after
(i) 2 hours,
(ii) 5 hours,
(iii) 10 hours?
d) Find the gradient of the graph.
e) What does the gradient represent in this context?
pf3
pf4
pf5

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1 ) The volume of water, V (in litres) left in a tank after ‘t’ hours is given by V = 1,000 - 70t where ‘t’ is time in hours. a) Complete the table for t = 0, 1, ..., 10 and draw the graph of V against t on graph paper. t 0 1 2 3 4 5 6 7 8 9 10 V b) What is the initial volume in the tank? c) What is the water volume after (i) 2 hours, (ii) 5 hours, (iii) 10 hours? d) Find the gradient of the graph. e) What does the gradient represent in this context?

  1. A phone plan's free data balance, D in GB after t days is given by D = 30 0 - 2 5t where ‘t’ is the number of days since activation. a) Complete the table for t = 0, 1, ..., 10 and draw the graph. t 0 1 2 3 4 5 6 7 8 9 10 D b) What is the initial data balance? c) Find the remaining data after (i) 1 day, (ii) 6 days, (iii) 10 days. d) Find the gradient of the graph. e) What does the gradient represent?
  1. A user receives a fixed amount of movie credits, and each movie watched reduces the balance: C = 20 0 - 1 5t where C is credits remaining after watching t movies. a) Complete the table for t = 0, 1, ..., 10 and plot the graph. t 0 1 2 3 4 5 6 7 8 9 10 C b) What are the starting credits? c) Credits remaining after (i) 2 movies, (ii) 5 movies, (iii) 10 movies? d) Find the graph’s gradient.

e) Interpret the gradient’s meaning in this context.

  1. You buy a package of classes where each class attended reduces your credit: F = 15 - t where F is classes remaining after attending t classes. a) Complete the table for t = 0, 1, ..., 10, then draw the graph. t 0 1 2 3 4 5 6 7 8 9 10 F b) How many classes did you start with? c) Find credits after (i) 1 class, (ii) 6 classes, (iii) 10 classes. d) Find the gradient of the graph.