Buzz
Practical exercises in the section Solving 8th-grade math problems on pages 67, 68, 69, 70 of Kite book volume 1 - Exercise 3: Linear functions y = ax + b (a not equal to 0) will help students memorize the characteristics of linear functions, knowing how to determine the constant term in each linear function. Hopefully, this will be a useful resource to help students study well.
Solving 8th-grade math problems Kite volume 1 page 67, 68, 69, 70
Exercise 3: Linear functions y = ax + b (a not equal to 0)
Solving Grade 8 Cánh Diều Volume 1 page 70
1. Solve problem 1 - Cánh Diều Grade 8 volume 1 page 70
Problem:
Among the following statements, which one is correct, and which one is incorrect?
a) A linear function has the form y = ax + b, where a and b are given numbers.
b) A linear function has the form y = ax + b, where a and b are given numbers, and a is not equal to 0.
c) A linear function has the form y = ax + b, where a and b are given numbers, and b is not equal to 0.
Solution Method:
Definition of a linear function
Answer:
The correct statement is: b
The incorrect statements are: a and c
2. Solve problem 2 - Kite Grade 8 Book 1 page 70
Problem:
Determine the coefficients of x and the constant term in each linear function below:
a) y = 6x + 8
b) Linear function with the form y = -x - 5
c) Linear function with the form y = x/3
Solution Method:
Definition of a linear function
Answer:
3. Solve problem 3 - Kite grade 8 workbook page 70
Issue:
For the linear function f(x) = 3x + 2. Calculate f(1); f(0); f(-2); f(1/2); f(-2/3)
Solution Method:
Substitute values and calculate
Answer:
f(1) = 3.1 + 2 = 5
f(0) = 3.0 + 2 = 3
f(-2) = 3.(-2) + 2 = -4
f(1/2) = 3.(1/2) + 2 = 7/2
f(-2/3) = 3.(-2/3) + 2 = 0
4. Solve problem 4 - Kite Grade 8 Workbook Page 70
Problem:
Currently, Nam has saved 300,000 VND. Nam is planning to buy a bicycle worth 2,000,000 VND. To achieve this, Nam has planned to save 5,000 VND per day. Let m (VND) be the amount Nam saves after t days according to the plan.
a) Write the formula expressing m in terms of t. Is m a linear function of t or not?
b) After how many days from the start of saving can Nam buy the bicycle?
Solution:
Amount saved = Amount saved per day x Number of days + Amount already saved
Answer:
a. Write the formula expressing m in terms of t: m = 5t + 300 (thousand VND)
m is a linear function of t.
b. From the start of saving, Nam can buy the bicycle after the number of days is:
t = (2000 - 300) : 5 = 340 (days)
5. Giải bài 5 - Cánh Diều lớp 8 tập 1 trang 70
Đề bài:
Một người đang sử dụng internet, mỗi phút tốn dung lượng 1 MB. Giả sử gói cước internet của người đó cho phép sử dụng dung lượng 4GB.
a. Write the function f(x) representing the data consumption (MB) over the time of internet usage x (seconds):
b. Write the function g(x) representing the remaining allowed capacity (MB) after using the internet for x seconds:
c) Sau khi sử dụng internet được 2 phút thì dung lượng cho phép còn lại là bao nhiêu MB?
Phương pháp giải:
Áp dụng định nghĩa hàm số rồi thay số để giải bài toán
Đáp án:
a) Mỗi phút tốn dung lượng 1 MB=> mỗi giây tốn dung lượng : 1/60 MB
Viết hàm số f(x) biểu thị dung lượng tiêu tốn (MB) theo thời gian sử dụng internet x(giây):
f(x) = x/60
b) Đổi: 4GB = 4 096MB.
Viết hàm số g(x) biểu thị dung lượng cho phép còn lại (MB) sau khi sử dụng internet được x(giây):
g(x) = 4096 - x/60
c) Sau khi sử dụng internet được 2 phút thì dung lượng cho phép còn lại là:
g(x) = 4096 - 120/60 = 4094 MB
6. Solve problem 6 - Kite grade 8 workbook page 70
Problem:
Dương brings 100,000 VND and a bicycle to the bookstore to buy notebooks. Knowing the price of each notebook is 7,000 VND, and the bicycle parking fee is 3,000 VND.
a) Write a formula representing the total amount y (VND) Dương needs to pay for bicycle parking and buying x notebooks. Is y a linear function of x?
b) Calculate the amount Dương has to pay for parking and buying 12 notebooks.
c) Write a formula representing the remaining total amount t (VND) Dương has after parking the bicycle and buying x notebooks. Is the function given by that formula a linear function?
d) Can Dương buy 15 notebooks with the given amount? Why or why not?
a) Apply the function definition and substitute values to solve the problem.
b) Solution method: Apply the function definition and substitute values to solve the problem.
c) Answer: Apply the function definition and substitute values to solve the problem.
d) Write the formula representing the total amount y (VND) Dương needs to pay for bicycle parking and buying x notebooks:
y = 7x + 3 (thousand VND)
y is a linear function of x.
b) The amount Dương has to pay for parking and buying 12 notebooks:
y = 7x + 3 = 7 * 12 + 3 = 87 (thousand VND)
c) The total amount t (VND) Dương has left after parking and buying x notebooks:
t = 100 - 7x - 3 = -7x - 97 (thousand VND)
The function given by this formula is a linear function.
d) When buying 15 notebooks, Dương needs to pay: y = 7 * 15 + 3 = 108 (thousand VND). Therefore, with the given amount, Dương cannot buy 15 notebooks.
Above is the guide for solving 8th-grade math on pages 67, 68, 69, 70 of Kite Book 1 Linear functions y = ax + b (a not equal to 0). To prepare for the next lesson, you can preview the section on Solving 8th-grade math on pages 71, 72, 73, 74, 75, 76, 77 of Kite Book 1 - Exercise 4: Graph of linear functions y = ax + b (a not equal to 0). Additionally, the section on Solving 8th-grade math on pages 60, 61, 62, 63, 64, 65 of Kite Book 1 - Exercise 2: Coordinate plane - Graph of functions will help reinforce the knowledge you have learned; you can review the answers here. Best of luck in your math studies.
Refer to other 8th-grade math resources:
- 8th-grade math solutions in Kite Book
