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Solving Grade 7 Mathematics pages 110, 111, 112, 113 Volume 2 'Connecting Knowledge with Life' providing solutions for exercises 1 to 13 in the end-of-year review. Review these to reinforce understanding of solving various exercises throughout the curriculum, enabling proficiency in tackling any encountered problems.
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Solving Grade 7 Mathematics pages 110, 111, 112, 113 Volume 2 'Connecting Knowledge with Life'
End-of-Year Review Exercises
NUMBERS AND ALGEBRA
1. Solve Exercise 1 Page 110 Mathematics Grade 7
Problem: Calculate the values of the following expressions:
Solution Guide:
+ For expressions without parentheses, follow the order:
Exponents => Multiplication and division => Addition and subtraction.
+ For expressions with parentheses, evaluate inside the parentheses first, then outside. In cases with multiple parentheses, follow the order ( ) => [ ] => { }.
Answer:
2. Solve Exercise 2 Page 110 Math Grade 7
Problem: Calculate reasonably:
Solution Guide:
For expressions without parentheses, perform in the following order:
Exponents => Multiplication and division => Addition and subtraction.
Answer:
3. Solve Exercise 3 Page 110 Math Grade 7
Guidelines:
a) Apply the rule of transposition and change signs to find x.
b) Calculate |x| and draw a conclusion.
c) Estimate the positive value of x and then use a handheld calculator to verify.
Answers:
a) We have:
The estimated difference from the calculator result is: 3.6 - 3.5 = 0.1.
4. Solve Exercise 4 on Page 110 of Math Grade 7 Textbook
Problem: Two workers together produced a total of 136 items (equal time). How many items did each worker produce, knowing that the first worker takes 9 minutes to make one item, while the second worker takes 8 minutes?
Solution:
+ Let x and y be the number of items produced by the first and second workers, respectively (x, y > 0).
+ Represent the given conditions in the form of equations.
+ Apply the property of equal ratios to find x, y.
Answer:
Let x and y be the number of items produced by the first and second workers, respectively (x, y > 0). We have:
Since the working time of both workers is the same, we get: 9.x = 8.y.
So the first worker produces 64 items, and the second worker produces 72 items.
5. Solve Problem 5 on Page 110 of Math Grade 7 Textbook
Problem: Three blocks, 6, 7, 8, of a secondary school participate in donating notebooks to students in difficult areas. Knowing that the number of donated notebooks by the three blocks is directly proportional to 8, 7, 6 in order, and the number of notebooks donated by block 8 is less than the number donated by block 6 by 80 notebooks. How many notebooks did each block donate?
Guide:
+ Let the number of notebooks donated by blocks 6, 7, 8 be x, y, z (x, y, z > 0).
+ Represent the given conditions in a formula.
+ Apply the property of equal ratio to find x, y.
Answer:
Let x, y, z represent the number of notebooks donated by blocks 6, 7, 8, respectively (x, y, z > 0). We have:
x - z = 80.
Since the number of donated notebooks is in direct proportion to 8, 7, 6, we obtain:
Thus, x = 40 * 8 = 320; y = 40 * 7 = 280; z = 40 * 6 = 240.
The 6th block contributed 320 notebooks, the 7th block contributed 280 notebooks, and the 8th block contributed 240 notebooks.
6. Solve Exercise 6 on page 110 of Math Grade 7 textbook
a) Determine the highest coefficient and the constant term in each given polynomial.
b) Calculate the value of the polynomial A + B at x = -2.
c) Prove that x = 0, x = -1, and x = 2 are three roots of the polynomial A - B.
d) Perform the multiplication of A and B in two ways.
e) Find the polynomial R with a degree less than 2 such that the difference A - R is divisible by B.
Guidance:
+ The leading coefficient of the polynomial (excluding zero, already simplified) is the coefficient of the highest-degree term.
+ The constant term of the polynomial (excluding zero, already simplified) is the coefficient of the term with degree 0.
+ x = a is a root of the polynomial P(x) if P(a) = 0.
+ If A - R is divisible by B, then R is the remainder of the polynomial division of A by B.
Answer:
7. Solve Problem 7 Page 110 Math Grade 7
Problem: A rectangular prism-shaped tank is filled with water, and then a solid cube (dense) with edges of length x (cm) is submerged into the tank. It is known that the width, length, and height of the tank are respectively x + 1, x + 3, and x + 2 (see the figure below).
a) Find the polynomial representing the remaining volume of water in the tank.
b) Determine the degree, leading coefficient, and constant term of the polynomial in part a.
c) Use the result from part a to calculate the remaining volume of water in the tank (unit: dm3) when x = 7 dm.
Guide to solve:
The volume of the rectangular prism = length x width x height.
The volume of the cube = side x side x side.
Answer:
GEOMETRY AND MEASUREMENT
8. Solve Exercise 8 Page 111 Mathematics Grade 7
Guidance:
a) Prove that the two triangles ADM and BDC are congruent using the side-angle-side case.
b) Identify the line cutting AN and BC in the formed angles having a pair of alternate interior angles equal.
c) Apply Euclid's postulate for the proof.
Answer:
9. Solve Exercise 9 on page 111 of Math Grade 7 Textbook
Guidance:
a) In an isosceles triangle, the median corresponding to the base is also the altitude corresponding to that base.
b) Prove that the triangles ABM and ACN are congruent using the side-side-side (SSS) condition.
c) Show that AI = IK. Hence, deduce that IK is parallel to MN.
Answer:
10. Solve Exercise 10 on page 111 of Math Grade 7 Textbook
Guidance:
a) Prove that the triangles ABH and DBH are congruent using the side-side-side (SSS) condition.
b) Demonstrate that EA = ED.
c) Prove that E is the centroid of triangle MBC.
Answer:
STATISTICS AND PROBABILITY
11. Solve Exercise 11 on page 112 of Math Textbook Grade 7
Problem: Binh collects data on the number of secondary students nationwide from 2015 to 2020 and creates the following chart:
a) Determine the trend (increase or decrease) in the number of secondary students nationwide from 2015 to 2020.
b) Create a statistical table showing the quantity of secondary students nationwide from 2015 to 2020.
c) According to the student, what method do you think Binh used among the ones learned to collect this data?
d)
Guidance: Observe the chart and answer the questions.
Answer:
a) The number of secondary students nationwide from 2015 to 2020 shows an increasing trend.
b) Statistical table on the quantity of secondary students nationwide from 2015 to 2020:
c) In my opinion, Binh collected data from reference documents.
12. Solve Problem 12 Page 112 Math Grade 7
Problem: The following chart shows the total number of world medals that Vietnam sports achieved in the years from 2015 to 2019:
a) Compile a statistical table on the number of world medals that Vietnamese sports achieved from 2015 to 2019.
b) In which year did Vietnamese sports achieve the fewest world medals?
c) The proportion of each type of world medal for Vietnamese sports in 2019 is shown in the following chart:
Calculate the quantity of each type of world medal that Vietnamese sports achieved in 2019.
Solution: Observe the charts to answer the questions.
Results:
a) Table of the world medals that Vietnamese sports achieved from 2015 to 2019.
b) Among those years, 2018 witnessed the fewest world medals for Vietnamese sports.
c) The number of gold medals that Vietnamese sports achieved is:
The number of silver medals earned by Vietnamese sports is:
238 - 113 - 65 = 60 (medals).
Results:
Problem: In the Lucky Spin game, players spin a circular wheel divided into 12 equal sectors as shown in the figure. Each sector is marked with a certain number of points that the player will receive. There are two sectors with 100 points, two sectors with 200 points, two sectors with 300 points, two sectors with 400 points, one sector with 500 points, two sectors with 1000 points, and one sector with 2000 points. When the wheel stops, the arrow (fixed at the top) points to a specific sector, and the player receives the number of points indicated in that sector.
Mai participates in the game and spins once. Calculate the probability that the arrow points to a sector:
a) With a score less than 2000.
b) With a score less than 100.
c) With a score greater than 300.
d) With a score of 2000.
Guidance: In a game or experiment, if there are k equally likely events, and only one of these events always occurs, then the probability of each event is 1/k.
Answer:
Since the wheel is divided into 12 equally likely sectors, the probability of the arrow pointing to each sector is the same.
a) There are 11 sectors with scores less than 2000. So, the probability of the arrow pointing to a sector with a score less than 2000 is 11/12.
b) There is no sector with a score less than 100 on the wheel, so the event 'arrow points to a sector with a score less than 100' is impossible. Therefore, the probability of this event is 0.
c) There are 4 sectors with scores less than 300. So, the probability of the arrow pointing to a sector with a score less than 300 is 1/3.
d) There is 1 sector with a score of 2000. So, the probability of the arrow pointing to a sector with a score of 2000 is 1/12.
Here is the solution for Grade 7 Mathematics pages 110, 111, 112, 113 in the Knowledge Connection Textbook. Students can review the exercises on page 102 to grasp various problem-solving techniques, making it easier to tackle similar questions.
- Grade 7 Mathematics Solution Page 102 Volume 2 Knowledge Connection Textbook - End-of-chapter exercises 10
