Buzz
Product (noun): tích – kết quả phép nhân
Khái niệm
Trong toán học, product (tích) là kết quả của một phép nhân. Để tìm tích của hai hoặc nhiều hơn hai số, ta cần thực hiện phép nhân giữa hai hay các số đó.
Function (noun): hàm số (khái niệm)
Khái niệm
Trong toán học, function (hàm số) là một quan hệ toán học trong đó mỗi phần tử của tập xác định (domain) x, tạo ra ít nhất một phần tử của tập giá trị (range) y, và không có hai giá trị x nào tạo ra cùng một giá trị y.
Bên dưới là đồ thị của một số hàm số khác nhau:
Kiến thức liên quan
1. Domain: tập xác định, là tập hợp các giá trị của biến số x.
2. Range: tập giá trị, là tập hợp tất cả các giá trị y.
Ví dụ: Xét hàm số: f(x) = x + 2 có:
- Tập xác định (domain) là các số thực (R);
- Tập giá trị (range) là các số thực (R) vì với mọi x thuộc R ta sẽ có mọi y thuộc R.
Horizontal axis (x-axis): trục hoành (trục x).
Vertical axis (y-axis): trục tung (trục y).
Linear function: hàm số bậc nhất – có dạng y = f(x) = ax + b và có đồ thị là một đường thẳng trên mặt phẳng tọa độ. Trong đó:
- a là hệ số góc (độ dốc - slope) của đường thẳng;
- b là giao điểm với trục tung (trục y).
Ví dụ: Xét hàm số bậc nhất y = 2x + 1, có:
- Đường thẳng này dốc lên vì có hệ số góc a = 2.
- Nó cắt trục y tại điểm A (0,1).
Ôn tập từ vựng - product
Exercise 1: Which sentence uses product as a mathematical term?
A. The store just released a new beauty product.
B. Their success was the product of good communication.
C. The product of 4 and 7 is 28.
D. She promotes her handmade products on Instagram.
Exercise 2: Fill in the blank with one of these words: sum, product, subtraction.
1. The ________ of 7 and 5 is 35.
2. To find the total of two numbers, you calculate their ________.
3. When you take one number away from another, it is called ________.
Ôn tập từ vựng - function
Exercise 1: Which sentence uses function as a mathematical term?
A. That laptop is attractive because it has a lot of unique functions.
B. The function of the heart is to pump blood.
C. The function f(x) = 2x + 3 is a linear function.
D. She likes to study the function of different machines.
Exercise 2: Fill in the blank with one of these words: function, linear function, domain, range.
1. The ________________ of the website is to allow users to search for books.
2. A price increase as the number of items sold goes up is an example of a ________________.
3. The ________________ of the graph includes all the possible output values for 𝑦.
4. The ________________ of the system is all the possible input values, like the numbers you can enter.
Bài toán ứng dụng thực tế - product
Exercise 1: In a biology experiment, a student observes that the product of the number of bacterial cells and the nutrient concentration determines the growth rate.
1. What is the growth rate if there are 500 cells and a nutrient concentration of 0.8?
2. If the student wants to keep the growth rate at 400, what nutrient concentration is needed for 800 cells?
Exercise 2: A clothing store sells a new product, a basic cotton T-shirt, for $15 each. The cost to make one shirt is $6. On a weekend promotion, the store sold 120 shirts.
1. What is the total profit the store made from selling 120 T-shirts, given that profit is the subtraction of cost from revenue?
2. If the store wants to increase its total profit by 25% next weekend while keeping the price and cost the same, how many shirts must it sell?
Exercise 3: A candy factory employs 150 workers, and each worker can produce 40 boxes of candy per day.
1. What is the total number of boxes produced by the factory in one day?
2. If the factory wants to produce 8,000 boxes daily, how many additional workers are needed? (Assume each worker’s productivity stays the same)
Exercise 4: A school is organizing graduation photos. Each student group has 18 students, and there are 12 groups in total.
What is the total number of students in the graduation photos?
If each student pays $5 for their photo, what is the total amount collected?
Bài toán ứng dụng thực tế - function
Exercise 1: Minh wants to rent a bicycle to explore the city. The bike shop uses the following formula to calculate the total rental cost: C(t) = 10 + 3t.
where:
C(t) is the total cost in thousand VND.
t is the number of hours the bike is rented.
10 is the base rental fee (in thousand VND).
3 is the cost per hour (in thousand VND).
1. What is the total cost if Minh rents the bike for 4 hours?
2. If Minh only has 25 thousand VND, what is the maximum number of hours he can rent the bike?
Exercise 2: A contractor uses the function f(x) = 50x + 200 to estimate the total cost for x hours of labor. The $200 is the base fee, and $50 is charged per hour.
1. What is the total cost for 8 hours of labor?
2. If the client has a budget of $1200, what is the maximum number of hours they can afford?
Exercise 3: A taxi company charges a fee described by the function: C(d)=5+2d.
where:
C(d) is the total fare in dollars
d is the distance traveled in kilometers
$5 is the base fee and $2 is charged per km traveled
1. What is the fare for a 10 km ride?
2. If a customer has $25, what is the maximum distance they can travel?
Exercise 4: A plant scientist models the height of a sunflower using the function: H(w) = 5w + 10.
Where:
H(w): height of the sunflower in centimeters
w: number of weeks since planting
The plant grows 5 cm per week, starting at 10 cm tall
1. What is the height of the sunflower after 6 weeks?
2. If a sunflower is 45 cm tall, how many weeks has it been growing?
Key đáp án - product
Exercise 2:
1. product
2. sum
3. subtraction
Exercise 1:
1. 400
2. 0.5
Exercise 2:
1. $1,080
2. 150 shirts
Exercise 3:
1. 6,000 boxes
2. 50 workers
Exercise 4:
1. 216 students
2. 1080 dollars
Key đáp án - function
Exercise 2:
function, linear function, range, domain
Exercise 1:
1. 22,000 VND
2. 5 hours
Exercise 2:
1. $600
2. 20 hours
Exercise 3:
1. $25
2. 10km
Exercise 4:
1. khoảng 40 cm
2. khoảng 7 weeks
Tác giả: Lê Cát Gia Linh (biên soạn)
