(A)
(B) 15
(C) -15
(D) 0(E) 1
2. Find the solution of
(A) 0
(B)
(C)
(D) 1(E)
3. What is the solution of equation
(A)
(B) 2
(C)
(D) 22(E) 11
Exercise 4.8.
1. If x and y are positive integers, and , what is the average (arithmetic mean) of x and y?
(A) 8.5
(B) 17
(C) 9
(D) 1
(E) 16
2. If x and y are positive integers, and , what is the average (arithmetic mean) of x and y?
(A) 9
(B) 8
(C) 6
(D) 10
(E) 7
3. If x and y are positive integers, and , what is the average (arithmetic mean) of x and y?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 6
Exercise 4.9.
Which of the following equations have exactly one solution?
(1) |x| = 1
(2) =1(3)
(A) 1 only
(B) 2 only
(C) 3 only
(D) 2 and 3 only
(E) 1, 2, and 3
Exercise 4.10.
Which of the following equations is equivalent to ?
(A)
(B)
(C)
(D)
(E)
Exercise 4.11.
1. Find the solution
(A) - 2
(B) 2(C) 3(D) - 3(E) 1
2. Find the value of
(A) - 25
(B) 25(C) 7(D) 9(E) 27
3. (=
(A) - 1
(B) 1(C) 2(D) -2(E) 0
4. Which of the following is equal to 9 =
(A) 0.3
(B) (C) 4(D) 3(E) 1
Exercise 4.12.
Which of the following are equal to for any real number b?
1. b
2.
3.
(A) 1 only
(B) 2 only(C) 3 only(D) 1 and 3 only(E) 1, 2, and 3
Exercise 4.13.
1. Which of the following is not an irrational number?
(A) р
(B) (C)
(D) (E) 1/р
Exercise 4.14.
1. What fraction of 36 is of 50?
(A)
(B) (C)
(D) (E)
2. What fraction of 52 is of 90?
(A)
(B) (C)
(D) (E)
3. What fraction of 44 is of 88?
(A)
(B) (C)
(D) (E)
Exercise 4.15.
1. Which of the following lists the numbers , , and in increasing order?
(A) , ,
(B) , , (C) ,
(D) , , (E) , ,
2. Which of the following lists the numbers , , and in decreasing order?
(A) , ,
(B) , , (C) , ,
(D) , , (E) , ,
Exercise 4.16.
1. If 0 < z < 1, which of the following could be less than z?
I.
II. of z
III.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2 only
(E) 1 and 3 only
2. If (- 2) < x < 2, which of the following could be further (больше) than x?
I.
II.
III.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2 only
(E) 1 and 3 only
3. If 5 ? y > - 1, which of the following could be further than y?
I. 10y% of y
II.
III.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2 only
(E) 1 and 3 only
Exercise 4.17.
1. Which of the following numbers satisfies the inequality < <
I.
II.
III.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2 only
(E) 1 and 3 only
Exercise 4.18.
Find the fraction of the number (verbally):
1) from 32; 3) from 25; 5) from 35;
2) from 100; 4) from 60; 6) from 15
Exercise 4.19.
Find the fraction of the number (verbally):
1) from 15; 4) from 60; 7) from 30;
2) from 20; 5) from 45; 8) from 120;
3) from 48; 6) from 70; 9) from 150.
Exercise 4.20.
Find the number if (verbally):
1) of its equal to 80; 4) of it is equal to 20; 7) of it is equal to 10;
2) of its equal to 10; 5) of it is equal to 60; 8) of it is equal to 50;
3) of its equal to 30; 6) of it is equal to 90; 9) of it is equal to 30.
Exercise 4.21.
Find the fraction of the values (verbally):
1) from 8 m; 3) from 10 t; 5) from 8h;
2) from 12 dm; 4) from 5 kg; 6) from 20 min
Exercise 4.22.
4. If 2x = 6 and 3y = 5, what is the value of ?
(A) 5/9
(B) 3/5
(C) 9/5
(D) 6/5
(E) 4/7
5. If and 5y = 20, what is the value of x - y?
(A) 6
(B) 5
(C) 1
(D) 4
(E) 0
6. If 5x = 8 and 4y = 3, what is the value of ?
(A) 256/75
(B) 75/276(C) 3/5(D) 2/3(E) 4/3
Exercise 4.23.
1) From 75 m of fabric, went to the sewing of dresses. How many meters of fabric were spent on dresses?
2) Water is of the mass of a person. How much water is contained in the human body, if its mass is 75 kg?
3) There are 30 students in the class. Of these, are girls. How many girls are there in the class?
Exercise 4.24.
1) The life span of a squirrel is 6 years, which is of the life span of a hare. How many years does a hare live?
2) How many tons of beet need to be processed to get 12 tons of sugar, if of sugar beet is sugar?
3) What is the greatest distance of an artificial satellite of the Earth, if of its distance from the Earth is equal to 380 km?
Exercise 4.25.
There are 80 words in the exercise. Of these, of the words are nouns, are verbs, and the rest are other parts of speech. How many nouns are there in the exercise? verbs? other parts of speech?
Exercise 4.26.
The width of the rectangle is 4 cm, which is of its length. Find the perimeter of the rectangle.
Exercise 4.27.
The sum of three numbers is 324. The first term is of the sum, the second is of the sum. Find the third term.
Exercise 4.28.
1) Marat bought the book with of the money available to him. He has 50 tenge left. How much money did Marat have initially (изначально)?
А. 180 tg; В. 175 tg; С. 178 tg; D. 165 tg.
2) When the tourist has completed of the entire planned path, he has 85 km to go. How many kilometers did the tourist plan to walk?
Exercise 4.29.
Find (verbally) the number if:
1) 1% of it is equal to 8;
2) 2% of it is equal to 6;
3) 10% of it is equal to 0.8;
4) 20% of it is equal to 12;
5) 25%, its equal to 8;
6) 50% of it is equal to 90.
Exercise 4.30.
Find the number:
1) 3% of which are equal to 12; 15; 21; 24; 36;
2) 10% of which are equal to 0.4; 8.5; 9.25; 12.7; 28;
3) 60% of which are equal to 42; 72; 84; 102; 114;
Exercise 4.31.
1) The farmer planted 72 hectares of apple trees, which is 40% of the total area of the farm. How many hectares does a farmer's farm cover?
2) There are 2890 textbooks in the school library, which is 85% of all books available in the library. How many books are there in the school library?
3) There are 12 girls in the class. This is 40% of all students in the class. How many students are there in the class?
Exercise 4.32.
The master made 295 parts, exceeding the plan by 18%. How many parts did the master have to make according to the plan?
Exercise 4.33.
After a 10% markdown (падение цен), the price of the refrigerator became 72,900 tenge. What is the price of the refrigerator before the markdown?
Exercise 4.34.
The tourist left from point A to point B. When he has covered 74% of the distance, he still has 65 km to cover. Find the distance between points A and B.
Exercise 4.35.
The seller, having sold vegetables in the amount of 14,758 tenge, suffered losses (потерпел убытки) of 6%. How much did the seller buy the vegetables for?
Exercise 4.36.
Use the microcalculator to find the number if:
1) 12% of it is equal to 10.8; 4) 60% of it is equal to 45;
2) 15% of it is equal to 8.4; 5) 110% of it is equal to 93.5;
3) 40% of it is equal to 22.4; 6) 180% of it is equal to 64.8.
Exercise 4.37.
Find the value:
1) 12%, which is equal to 18 m; 75 m;
2) 8% of which is equal to 56 kg; 4 kg;
3) 15% of which is equal to 12 cm; 2.7 cm;
4) 24% which is equal to 9.6 tons; 42 tons;
5) 35% of which is equal to 21 km; 11.2 km;
6) 75% of which is equal to 15 c; 90 c.
Exercise 4.38.
What is the natural number that increases by 40% and increases by 3.2?
Exercise 4.39.
The width of the rectangle is 6 cm. This is 75% of its length. Find the area of the rectangle.
Exercise 4.40.
The driver transported 133.4 tons of wheat in 5 days, exceeding the plan by 15%. How many more tons of wheat did the driver transport in one day than he was supposed to transport according to the plan?
Exercise 4.40.
If the of teachers ratio to administrators on a committee is 4:5, what percent of the committee members are administrators?
Exercise 4.41.
1) What is the value of when a = 4 and b = 2?
(A) 5
(B) -5
(C) 6
(D) - 4
(E) 4
2) What is the value of when a = 4 and b = -3?
(A) 5
(B) 7
(C) 6
(D) 8
(E) 9
3) If and (a - b, what is the value of ab?
(A) 1
(B)
(C) 2
(D) 3
(E) 4
Exercise 4.42.
What is the result when (x+3)(x - 5) is subtracted from (2x + 3)(2x - 5)?
(A) x(3x - 2)
(B) x(2 - 3x)
(C) 3
(D) 5
(E)
Exercise 4.43.
If , what is the value of ?
(A) 10
(B) 98
(C) 100
(D) 102
(E) 110
Exercise 4.44.
1. If 5x+12 = 6 - 3x, what is the value of x?
(A) 1
(B)
(C) -1
(D) 2
(E) 3
2. If , what is the value of x?
(A) 5
(B) 7
(C) 9
(D) 3
(E) 11
3. For what values of x is |2x - 3| - 4 < 7?
(A) x < 7
(B) 0 < x < 3
(C) - 4 < x < 7
(D) x < 0 or x > 3
(E) x < - 4 or x > 7
Exercise 4.45.
1. If has exactly one solution, what is the value of c?
(A) 0
(B) 6.25
(C) 3.75
(D) - 6.25
(E) - 2.25
2. Find the solution of equation
I. 1
II. 2
III.
IV. 1
V.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 3
(E) 1, 2, and 3 only
(F) 1, 2, 3, 4, and 5
3. Find the solution of equation
(A) 0
(B) 1; - 1
(C) 1
(D) - 1
(E) 0; - 1
Plane geometry
Exercise 5.1.
Figure 6.5 shows the lines intersecting at point O. When those lines intersect, they are created angles: ?1; ?2; ?3; ?4; ?5. Find a vertical angle pairs.
Fig 6.5 Fig 6.6 Fig 6.7
Exercise 5.2.
Lines a and b intersects at point O (Fig. 6.6). ?2 = 40 °. Find the degree measures of ?1, ?3 and ?4.
Exercise 5.3.
In Figure 6.7 ?EOD = 40 °; ?EOB = 130 °. Find the degree measure of angle AOC.
Exercise 5.4.
1) When two straight lines intersect at point O, they form equal angles between themselves. What is the degree measure of each angle?
2) At the intersection of three straight lines at point O, equal angles appear. What is the degree measure of each angle?
Exercise 5.5.
The sum of one pair of vertical angles formed at the intersection of two straight lines is 126 °. Find the degree measure of each angle obtained at the intersection of these two lines.
Exercise 5.6.
When two straight lines intersect, one of the obtained angles is equal to:
1) 75°; 2) 120°.
Find the degree measures of the remaining angles.
Exercise 5.7.
At the intersection of two straight lines AB and CD at point O, the angles AOC and COB are formed, the degree measures of which are 5: 7. Find the degree measures of the angles AOD and BOD.
Exercise 5.8.
Lines AB, CD and EF meet at point O. ?AOE = 40 °; ?DOF = 80. Find the degree measure of the COB angle (fig. 6.8).
Fig 6.8.
Exercise 5.9.
Lines NP, KL and EF meet at point O. The EOK angle is 35°, and the NOK angle is 85 °. Find the degree measures of the angles FOP, KOP (Fig.6.9).
Fig.6.9
Exercise 5.10.
The sum of the three angles formed at the intersection of two straight lines is 284 °. Find the degree measure of each angle.
Exercise 5.11.
How many degrees is the angle between the hour and minute hands of the watch if the clock shows 9 hours 10 minutes?
Exercise 5.12.
Lines AB, CD and EF meet at point O (Fig. 6.10). ?AOE =55 °, ?DOF = 25 °. Find the degree measure of the angles BOE and BOD.
Fig.6.10
Exercise 5.13.
Lines MN, KL and FT intersect at point O. ?FOL = 110 ° and ?KOM = 35°.
Find the degree measures of the MOT angles and KOF (fig. 6.11).
Fig 6.11
Exercise 5.14.
1. In below, what is the value of x?
(A) 75
(B) 60(C) 45
(D) 30
(E) 15
2. In the triangle below, what is the value of x?
(A) 20
(B) 30(C) 40
(D) 50
(E) 60
3. In the figure below, what is the value of c?
(A) 100
(B) 110(C) 120
(D) 130
(E) 140
Exercise 5.15.
7. What is the value of w in the figure below?
(A) 60
(B) 90(C) 105
(D) 120
(E) 150
8. What is the area of an equilateral triangle whose altitude (высота) is 6?
(A) 18
(B) 12(C) 18
(D) 36
9. What is the area of ?
(A) 3
(B) 4.5(C) 6
(D) 7.5
(E) 10
Exercise 5.16.
1. What is the perimeter of trapezoid PMNR?
(A) 3
(B) 2 + (C) 3 +
(D) 5
(E) 8
2. What is the area of trapezoid PMNR?
(A) 1.5
(B) 1.75(C) 4
(D)
(E)
3. The length of a rectangle is 5 more than the side of a square, and the width of the rectangle is 5 less than the side of the square. If the area of the square is 45, what is the area of the rectangle?
(A) 20
(B) 25(C) 45
(D)
(E)
Exercise 5.17.
1. In rhombus PQRS, the ratio of m?P to m?Q is 1 to 5 and PQ = 6. What is the area of the rhombus?
(A) 6
(B) 12(C) 18
(D) 24
(E) 30
2. If the length of a rectangle is 5 times its width and if its area is 180, what is its perimeter?
(A) 6
(B) 36(C) 60
(D) 72
(E) 144
3. What is the average (arithmetic mean) of the measures of all the interior angles in a decagon?
(A) 18
(B) 36(C) 72
(D) 90
(E) 144
Exercise 5.18.
In the figure below, the two diagonals divide square WXYZ into four small triangles. What is the sum of the perimeters of those four triangles?
(A) 4 +
(B) 16 + (C) 16 +
(D) 32
(E) 48
Exercise 5.19.
1. In the figure above, if O is the center of the circle, what is the value of w?
(A) 21
(B) 38(C) 42
(D) 69
(E) 111
2. In the figure below, if O is the center of the circle, what is m?C?
(A)
(B) (C)
(D)
(E) It cannot be determined from the given information.
3. What is the length of arc ?
(A) 6
(B) (C)
(D)
(E)
Exercise 5.20.
1. What is the area of shaded sector?
(A) 12
(B) (C)
(D)
(E)
2. What is the area of a circle whose circumference is ?
(A)
(B) (C)
(D)
(E)
3. What is the circumference of a circle whose area is 100р?
(A)
(B) (C)
(D)
(E)
Заключение
Разработка теоретических основ курса «Методические основы подготовки будущих учителей математики в условиях полиязычного образования» привела к следующим выводам:
1. На данный момент, в ВУЗах Республики Казахстан существует актуальная проблема, связанная с нехваткой учебной и методической литературы на английском языке для эффективной реализации программы «Триединство языков».
2. Исследуя опыт зарубежных систем оценки знаний, основанный на экзаменах и тестировании на иностранном языке, предметов как гуманитарного, так и технического цикла, можно выделить факт лидерства SAT среди других международных экзаменов и, что данная система оценки является максимально приближенной к формату Единого Национального Тестирования.
3. Одним из важнейших факторов в реализации процесса внедрения английского языка в преподавании технических предметов является продуктивная и органичная программа обучения и использования математических терминов и понятий на иностранном языке, основанная на методике Hard-CLIL и критическом мышлении, позволяющие изучать технический английский язык, обладая минимальным уровнем знаний.
4. С целью эффективного и быстрого формирования структуры взаимодействия технического предмета и языковой составляющей, нужно задействовать необходимые области мозга, отвечающие за математическое мышление и за знание языка, как вместе, так и по отдельности. Для того, чтобы успешно реализовать данную слаженную работу мозга необходимо использовать ряд упражнений и заданий для развития и закрепления.
5. Для реализации процесса обучения техническому английскому языку, отвечающего международным требованиям, были разработаны вводные задания и теоретический материал, необходимый для развития профессионально-компетентностной подготовки будущих преподавателей математики. математический англоязычный пример преподаватель
В данном учебном пособии были обоснованы основные принципы и факторы необходимые для реализации процесса преподавания математики в полиязычной среде, рассмотрен опыт зарубежного тестирования, а также разработана собственная программа преподавания математики на английском языке, с теоретическими объяснениями и необходимым минимумом заданий по темам, задействованным в данном учебном пособии.
Список использованных источников
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2. Bakhyt Aubakirova, Kinga M. Mandel, Balбzs Benkei-Kovбcs Multilingual Education in Kazakhstan and Model of Multilingual Education in the European Context. - 2019. - № 2. - С. 25 - 36.
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4. Richard Barwell, Philip C Clarkson Researching mathematics education in multilingual contexts: theory, methodology and the teaching of mathematics // Conference: PME. - 2004. - № 28. - С. 225 - 256.
5. Marie Hofmannovб, Jarmila Novotnб, Judit Moschkovich, Working with theories from outside mathrmatics education // Conference: PME. - 2004. - № 28. - С. 229 - 236.
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8. Anjum Halai Teaching and Learning Mathematics in Multilingual Classrooms. - 2016. - С. 3 - 10.
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