Buzz
Solving 7th-grade Math on page 35 Volume 2, Connecting Knowledge with Life book provides hints and answers for exercises 7.18, 7.19, 7.20, 7.21, 7.22 in the Focused Practice section of the textbook. 7th-grade students can use this as a reference to easily solve all homework exercises.
Good study materials for 7th-grade Math:
- Solving 7th-grade Math, Connecting Knowledge with Life book
- Solving 7th-grade Math on page 40 of Volume 2, Creative Horizon book - Exercise 4: Multiplication and division of polynomials with one variable
- Solving 7th-grade Math on page 63 of Volume 2, Kite book - Exercise 4: Multiplication of polynomials with one variable
Solving 7th-grade Math on page 35 of Volume 2, Connecting Knowledge with Life book
Focused Practice
1. Solve Exercise 7.18 Page 35 Math Book Grade 7
a) Condense the sum A and arrange the terms to form a polynomial.
b) Find the leading coefficient, the constant term, and the coefficient of x^2 of the resulting polynomial.
Solution Guide:
+ Write polynomial A as the sum of monomials.
+ Combine and simplify similar monomials to condense the polynomial and address the questions in the problem.
Answer:
a) We have:
2. Solve Exercise 7.19 Page 35 Math Book Grade 7
Problem: A water tank has a rectangular shape with dimensions in proportion:
Height : Width : Length = 1 : 2 : 3.
In the tank, there is currently 0.7 m3 of water. Let the height of the tank be x (meters).
Write a polynomial representing the number of cubic meters of water needed to pump into the tank to fill it. Determine the degree of that polynomial.
Solution Guide:
Knowing the height of the tank is x, express the width and length of the tank in terms of x.
The volume of the water tank = length . width . height.
Answer:
3. Solve Exercise 7.20 Page 35 Math Book Grade 7
Solution Guide:
a) Given T(x) = 0, find x.
b) Substitute x = 35, calculate T(x)
c) Given T(x) = 41, find x.
Answer:
4. Solve Exercise 7.21 Page 35 Math Book Grade 7
Problem: Given two polynomials:
a) Determine the degree of the polynomial P + Q and P - Q.
b) Calculate the values of each polynomial P + Q and P − Q at x = 1; x = −1.
c) Which polynomial among P + Q and P − Q has a root at x = 0?
Solution Guide:
a) The degree of the polynomial (excluding the zero polynomial) is the degree of the term with the highest degree.
b) Substitute the values x = 1 and x = -1 into the expression and calculate the value of the expression for each.
c) Substitute x = 0 into the polynomials and calculate the values. Conclude which polynomial has a root at x = 0.
Answer:
a) We have:
Hence, the polynomial P + Q has degree 3, and the polynomial P - Q has degree 4.
b)
5. Solve Exercise 7.22 Page 35 Math Book Grade 7
Problem: A passenger bus travels from Hanoi to Yen Bai (on the Hanoi - Lao Cai highway) with a speed of 60 km/h. After 25 minutes, a tourist car also travels from Hanoi to Yen Bai (on the same route as the passenger bus) with a speed of 85 km/h. Both vehicles do not stop along the way.
a) Let D(x) be the polynomial representing the distance traveled by the tourist car, and K(x) be the polynomial representing the distance traveled by the passenger bus from departure until the tourist car has traveled for x hours. Find D(x) and K(x).
b) Prove that the polynomial f(x) = K(x) − D(x) has a root at x = 1. Explain the significance of the root x = 1 for the polynomial f(x).
Guidance:
a) The distance the passenger bus travels from departure until the tourist car has traveled for x hours = distance traveled by the passenger bus in 25 minutes + distance traveled by the passenger bus in x hours.
b) To demonstrate that x = 1 is a root of the polynomial f(x), we show that for x = 1, the value of the polynomial f(x) = 0.
Answer:
b) The polynomial f(x) = K(x) − D(x)
= 60x + 25 - 85x
= 25 - 25x
Substitute x = 1 into f(x), we get:
f(1) = 25 - 25.1 = 0
The polynomial f(x) = K(x) − D(x) has a root at x = 1. This means that the two vehicles meet after traveling for 1 hour.
Here is the guide to solve 7th-grade Math on page 35 Volume 2. Students can also refer to solving 7th-grade Math on page 38 Volume 2 and review solving 7th-grade Math on page 33 Volume 2 to strengthen their knowledge.
- Solving 7th-grade Math on page 38 Volume 2, Connecting Knowledge with Life book - Exercise 27: Multiplication of polynomials with one variable
- Solving 7th-grade Math on page 33 Volume 2, Connecting Knowledge with Life book - Exercise 26: Addition and subtraction of polynomials with one variable
