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Midterm exam 1st grade Math 6th grade Creative Horizon book for the school year 2022 – 2023
Midterm exam 1 in Math 6th grade Creative Horizons book is a set of exam questions with answers included for students to review and practice knowledge to achieve the best results in the midterm math test. This is a set of ĐH KD & CN Hà Nội.vn exam questions collected and synthesized with the content closely following the new textbook program, please refer to the detailed 2 sets of 6th grade math test questions mid-term 1 below.
6th grade math midterm exam
- 1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
- Answers to the midterm exam 1 of Grade 6 Maths book No. 1 Creative Horizons
- 2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
- Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
(Title 2)
I. Multiple choice section
Question 1: Write the following set A = {x∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Question 3: Factor 300 into prime factors
A) 2^{3}.3.5^{2}
B) 2^{2}.3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3}.3.5
Question 4: The result of the calculation: 250 – 5^{2} – (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) The number -5 is to the left of the number -4 so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Verse 8: Set A = {a ∈ Z | -5 < a < 2}
A) 5
B) 7
C) 6
D) 8
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Question 10: The result of the calculation: 2^{3} – 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
II. Essay
Lesson 1: Do the math
a) (4 + 32 + 6) + (10 – 32 – 2)
b) (56.35 + 56.18): 53
c) 12:{400:[500 – (125 + 25.7)]}
d) 303 – 3. {[655 – (18:2 + 1). +5]}: ten^{}
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
b) 125 – 5(4 + x) = 15
c) (15 + x):3 = 3^{15} : 3^{twelfth}
d) 2^{x+1}_{ }– 2^{x} = 32
Lesson 3: Vinh has 48 red marbles, 30 green marbles, and 66 yellow marbles. Vinh wants to equally divide the number of marbles into the bags so that each bag contains all three types of marbles. Ask Vinh how many bags can be divided at most. How many marbles of each type are there in each bag?
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13
AnswerMidterm exam 1 Math 6th grade book Creative Horizons No. 1
I. Multiple choice section
Question 1: Write the following set A = {x ∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Since 8 ≤ x ≤ 12, x ∈ {8; 9; ten; 11; twelfth}
Attention: we take the equal sign at 8 and 12
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Since every natural number divided by 10 leaves a remainder 5 of the form 10k + 5 where k belongs to N.
Question 3: Factor 300 into prime factors
A) 2^{3} .3.5^{2}
B) 2^{2} .3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3} .3.5
300 = 2.2.3.5.5 = 2^{2}.3.5^{2}
Question 4: The result of the calculation: 250 – 5^{2} – (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
250 – 5^{2} – (3 .)^{2} +12):3
= 250 – 25 – (9 + 12):3
= 250 – 25 – 21:3
=250 – 25 – 7
= 225 – 7
= 218
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) On the number line, -5 is to the left of -4, so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Sentence C is wrong because the numbers on the number line on the left will be smaller than the numbers on the right, so -5 is on the left of the number -4, so -5 is less than -4
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Because answer A has 1 non-prime number, answer C has 1 non-prime number, and answer D has 9 non-prime numbers. Answer B All 4 numbers are prime.
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Since answer D the numbers are sorted in ascending order.
Verse 8: Set A = {a ∈ Z | -5 < a < 2}. How many elements does set A have?
A) 5
B) 7
C) 6
D) 8
We have: A = {a ∈ Z | -5 < a < 2}
A = {-4; -3; -2; -first; 0; 1} set A has 6 elements
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Explain
2x = 17 – 35
2x = -18
x = -18:2
x = -9
Question 10: The result of the calculation: 2^{3} – 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
2^{3} – 2.(-3) + 5^{2}
= 8 – (-6) + 25
= 8 +6 + 25
= 14 + 25
= 39.
II. Essay section
Lesson 1:
a) (4 + 32 + 6) + (10 – 32 – 2)
= 4 + 32 + 6 + 10 – 32 – 2
= (4 – 2) + (32 – 32) + (10 + 6)
= 2 + 0 + 16
= 18
b) (56.35 + 56.18): 53
= [56.(35 + 18)]:53
= [56.53]:53
= 2968:53
= 56
c) 12:{400:[500 – (125 + 25.7)]}
= 12:{400:[500 – (125 + 175)]}
= 12:{400:[500 – 300]}
= 12:{400:200}
=12:2 = 6
d) 303 – 3.[655 – (18:2 + 1). +5]:
= 303 – 3.[655 – (9 + 1).64 + 5]:ten^{}
= 303 – 3.[655 – 10.64 + 5]:ten^{}
= 303 – 3[655 – 640 + 5]:ten^{}
= 303 – 3[15 + 5]:ten^{}
= 303 – 3.20:1
= 303 – 60
= 243
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
4 + (x + 3) = 25
x + 3 = 25 – 4
x + 3 = 21
x = 21 -3
x = 18
So x = 18
b) 125 – 5(4 + x) = 15
5(4 + x) = 125 – 15
5(4 + x) = 110
4 + x = 110: 5
4 + x = 22
x = 22 – 4
x = 18
So x = 18
c) (15 + x):3 = 3^{15} : 3^{twelfth}
(15 + x): 3 = 3^{3}
15 + x = 3^{3}.3
15 + x = 3^{4}
15 + x = 81
x = 81 – 15
x = 66
So x = 66
d) 2^{x + 1} – 2^{x} = 32
2^{x}.2 – 2^{x} = 32
2^{x}.(2 – 1) = 32
2^{x} = 32
2^{x} = 2^{5}
x = 5
So x = 5
Lesson 3:
The answer:
Let the number of your bag of marbles Vinh be x (x ∈ N^{*})
Because 48 red marbles, 30 blue marbles and 66 yellow marbles are equally divided into the bags of marbles, 48 x; 30 x; 66 x or x is a common divisor of 48; 30, 66.
Since the maximum number of bags of marbles can be divided, x is the greatest common divisor of 48; 30; 66.
We have:
48 = 2.2.2.2.3 = 2^{4}.3
30 = 2.3.5
66 = 2.3.11
CCLN (48; 30; 66) = 2.3 = 6
So at most 6 bags of marbles can be divided such that the number of marbles of each color in the three bags is equal.
The number of red marbles in each bag is:
48:6 = 8 (tablets)
The number of blue marbles in each bag is:
30:6 = 5 (tablets)
The number of yellow marbles in each bag is:
66:6 = 11 (tablets)
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13.
The answer:
We have:
2xy + x + 2y = 13
⇒ 2xy + x + 2y + 1 = 13 +1
(2xy + 2y) + (x + 1) = 14
2y(x + 1) + (x + 1) = 14
(x + 1)(2y + 1) =14
Since x, y are natural numbers, x + 1 and 2y + 1 are also natural numbers
We have: (x + 1)(2y + 1) = 1.14 = 2.7
Case 1: With x + 1 = 1 and 2y + 1 = 14
We have: x + 1 = 1 x = 0
2y + 1 = 14 2y = 13 y = (discard because x, y are natural numbers)
Case 2: With x + 1 = 14 and 2y + 1 = 1
We have: x + 1 = 14 x = 14 – 1
2y + 1 = 1 2y = 0 ⇒ y = 0 (satisfied)
Case 3: With x + 1 = 2 and 2y + 1 = 7
We have: x + 1 = 2 x = 1
2y + 1 = 7 2y = 6 y = 3 (satisfied)
Case 4: With x + 1 = 7 and 2y + 1 = 2
We have: x + 1 = 7 x = 6
2y + 1 = 2 2y = 1⇒ y = (discard because x, y are natural numbers)
So we find two pairs of numbers (x; y) satisfying (13; 0) and (1; 3)
2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Question 1. Write the set A of natural numbers greater than 5 and less than 10
A. A = {6, 7, 8, 9}
B. A = {5, 6, 7, 8, 9}
C. A = { 6, 7, 8, 9, 10}
D. A = {6, 7, 8}
Verse 2. Write the following set A = {x ∈ N | 9 < x < 13} by enumerating the elements:
A. A = {10, 11, 12}
B. A = {9, 10, 11}
C. A = { 9, 10, 11, 12, 13}
D. A = {9, 10, 11, 12}
Question 3: Of the following numbers: 59; 101; 355; 1341; 119; 29 which numbers are prime?
A. 59; 101; 29
B. 101; 355; 119; 29
C. 59; 355; 1341; 29
D. 59; 101; 355
Question 4: The natural number m divided by 45 leaves 20 in the form:
A. 45 + 20k
B. 45k + 20
C. 45 – 20k
D. 45k – 20
Question 5: Analyzing 126 into prime factors, we get the following results:
A. | B. |
C. | D. |
Question 6: Find the correct statement among the following:
A. A number that is divisible by 9 is always divisible by 3
B. If two numbers are divisible by 3, the sum of those two numbers is divisible by 9
C. Any even number is always divisible by 5
D. A number that is divisible by 2 is a number ending in zero; 2; 3; 4; 6; 8
Verse 7: Which of the following properties does a parallelogram not have?
A. Two opposite sides are parallel to each other
B. Two opposite sides are congruent
C. Four equal sides
D. The two main diagonals are equal
Verse 8: The area of a rhombus whose diagonals are 10cm and 12cm respectively is:
A. 60cm^{2} | B. 60m |
C. 60m^{2} | D. 60cm |
II. Essay section (6 points)
Question 1. Do the following calculations:
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
b) 5 . 2^{2} – 18 : 3
c) 18 : 3 + 182 + 3.(51 : 17)
d) 25 . 8 – 12.5 + 170 : 17 – 8
Verse 2: Find x knows:
a) 12 + (5 + x) = 20
b) 175 + (30 – x) = 200
c) 10 + 2x = 4^{5} : 4^{3}
d) 10x + 2^{2}.5 = 10^{2}
Question 3: Class 6A has 54 students, class 6B has 42 students and class 6C has 48 students. On the first day of school, three classes lined up in equal rows to parade without any odd people in each class.
a. Calculate the maximum number of vertical rows that can be stacked
b. How many students are there in each row?
Question 4: Write as a power with base 2
Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Sentence | Question 1 | Verse 2 | Verse 3 | Verse 4 | Question 5 | Verse 6 | Verse 7 | Verse 8 |
Answer | A | A | A | REMOVE | REMOVE | A | OLD | A |
II. Essay section (6 points)
Question 1
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
12 : { 400 : [500 – (125 + 25 . 7)]} = 12 : { 400 : [500 – (125 + 175)]}
= 12 : { 400 : [500 – 300]} = 12 : { 400 : 200} = 12 : 2 = 6
b) 5 . 2^{2} – 18 : 3 = 27 . 75 + 25 . 27 – 150 = 27. (75 + 25) – 150 = 27,100 – 150 = 270 – 150 = 120
c) 18 : 3 + 182 + 3.(51 : 17) = 197
d) 25 . 8 – 12.5 + 170 : 17 – 8 = 285
Verse 2.
a) 12 + (5 + x) = 20
5 + x = 20 – 12
5 + x = 8
x = 8 – 5 = 3
b) 175 + (30 – x) = 200
30 – x = 200 – 175
30 – x = 25
x = 30 – 25 = 5
c) 10 + 2x = 4^{5} : 4^{3}
Answer: x = 11
d) 10x + 2^{2}.5 = 10^{2}
Answer x = 61
Verse 3
a) Since the number of students is enough, the number of vertical rows is a common divisor of the number of students in 3 classes
The maximum number of vertical rows is also the greatest common divisor of the number of students in three grades
We have: 54 = 2.3^{3}
42 = 2.3.7
48 = 2^{4}.3
CCLN (54; 42; 48) = 2.3 = 6
So the maximum number of vertical rows that can be arranged is 6 rows
Verse 4
We have
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Midterm exam 1st grade Math 6th grade Creative Horizon book for the school year 2022 - 2023
6th grade math exam in middle school year 1 book Creative Horizons
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Midterm exam 1 in Math 6th grade Creative Horizons book is a set of exam questions with answers included for students to review and practice knowledge to achieve the best results in the midterm math test. This is a set of ĐH KD & CN Hà Nội.vn exam questions collected and synthesized with the content closely following the new textbook program, please refer to the detailed 2 sets of 6th grade math test questions mid-term 1 below.
6th grade math midterm exam
1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
- Answers to the midterm exam 1 of Grade 6 Maths book No. 1 Creative Horizons
2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
- Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
(Title 2)
I. Multiple choice section
Question 1: Write the following set A = {x∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Question 3: Factor 300 into prime factors
A) 2^{3}.3.5^{2}
B) 2^{2}.3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3}.3.5
Question 4: The result of the calculation: 250 - 5^{2} - (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) The number -5 is to the left of the number -4 so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Verse 8: Set A = {a ∈ Z | -5 < a < 2}
A) 5
B) 7
C) 6
D) 8
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Question 10: The result of the calculation: 2^{3} - 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
II. Essay
Lesson 1: Do the math
a) (4 + 32 + 6) + (10 – 32 – 2)
b) (56.35 + 56.18): 53
c) 12:{400:[500 – (125 + 25.7)]}
d) 303 – 3. {[655 – (18:2 + 1). +5]}: ten^{}
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
b) 125 – 5(4 + x) = 15
c) (15 + x):3 = 3^{15} : 3^{twelfth}
d) 2^{x+1}_{ }- 2^{x} = 32
Lesson 3: Vinh has 48 red marbles, 30 green marbles, and 66 yellow marbles. Vinh wants to equally divide the number of marbles into the bags so that each bag contains all three types of marbles. Ask Vinh how many bags can be divided at most. How many marbles of each type are there in each bag?
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13
AnswerMidterm exam 1 Math 6th grade book Creative Horizons No. 1
I. Multiple choice section
Question 1: Write the following set A = {x ∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Since 8 ≤ x ≤ 12, x ∈ {8; 9; ten; 11; twelfth}
Attention: we take the equal sign at 8 and 12
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Since every natural number divided by 10 leaves a remainder 5 of the form 10k + 5 where k belongs to N.
Question 3: Factor 300 into prime factors
A) 2^{3} .3.5^{2}
B) 2^{2} .3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3} .3.5
300 = 2.2.3.5.5 = 2^{2}.3.5^{2}
Question 4: The result of the calculation: 250 - 5^{2} - (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
250 - 5^{2} - (3 .)^{2} +12):3
= 250 – 25 – (9 + 12):3
= 250 – 25 – 21:3
=250 – 25 – 7
= 225 – 7
= 218
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) On the number line, -5 is to the left of -4, so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Sentence C is wrong because the numbers on the number line on the left will be smaller than the numbers on the right, so -5 is on the left of the number -4, so -5 is less than -4
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Because answer A has 1 non-prime number, answer C has 1 non-prime number, and answer D has 9 non-prime numbers. Answer B All 4 numbers are prime.
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Since answer D the numbers are sorted in ascending order.
Verse 8: Set A = {a ∈ Z | -5 < a < 2}. How many elements does set A have?
A) 5
B) 7
C) 6
D) 8
We have: A = {a ∈ Z | -5 < a < 2}
A = {-4; -3; -2; -first; 0; 1} set A has 6 elements
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Explain
2x = 17 – 35
2x = -18
x = -18:2
x = -9
Question 10: The result of the calculation: 2^{3} - 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
2^{3} - 2.(-3) + 5^{2}
= 8 – (-6) + 25
= 8 +6 + 25
= 14 + 25
= 39.
II. Essay section
Lesson 1:
a) (4 + 32 + 6) + (10 – 32 – 2)
= 4 + 32 + 6 + 10 – 32 – 2
= (4 – 2) + (32 – 32) + (10 + 6)
= 2 + 0 + 16
= 18
b) (56.35 + 56.18): 53
= [56.(35 + 18)]:53
= [56.53]:53
= 2968:53
= 56
c) 12:{400:[500 – (125 + 25.7)]}
= 12:{400:[500 – (125 + 175)]}
= 12:{400:[500 – 300]}
= 12:{400:200}
=12:2 = 6
d) 303 – 3.[655 – (18:2 + 1). +5]:
= 303 – 3.[655 – (9 + 1).64 + 5]:ten^{}
= 303 – 3.[655 – 10.64 + 5]:ten^{}
= 303 – 3[655 – 640 + 5]:ten^{}
= 303 – 3[15 + 5]:ten^{}
= 303 – 3.20:1
= 303 – 60
= 243
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
4 + (x + 3) = 25
x + 3 = 25 – 4
x + 3 = 21
x = 21 -3
x = 18
So x = 18
b) 125 – 5(4 + x) = 15
5(4 + x) = 125 – 15
5(4 + x) = 110
4 + x = 110: 5
4 + x = 22
x = 22 – 4
x = 18
So x = 18
c) (15 + x):3 = 3^{15} : 3^{twelfth}
(15 + x): 3 = 3^{3}
15 + x = 3^{3}.3
15 + x = 3^{4}
15 + x = 81
x = 81 – 15
x = 66
So x = 66
d) 2^{x + 1} - 2^{x} = 32
2^{x}.2 - 2^{x} = 32
2^{x}.(2 - 1) = 32
2^{x} = 32
2^{x} = 2^{5}
x = 5
So x = 5
Lesson 3:
The answer:
Let the number of your bag of marbles Vinh be x (x ∈ N^{*})
Because 48 red marbles, 30 blue marbles and 66 yellow marbles are equally divided into the bags of marbles, 48 x; 30 x; 66 x or x is a common divisor of 48; 30, 66.
Since the maximum number of bags of marbles can be divided, x is the greatest common divisor of 48; 30; 66.
We have:
48 = 2.2.2.2.3 = 2^{4}.3
30 = 2.3.5
66 = 2.3.11
CCLN (48; 30; 66) = 2.3 = 6
So at most 6 bags of marbles can be divided such that the number of marbles of each color in the three bags is equal.
The number of red marbles in each bag is:
48:6 = 8 (tablets)
The number of blue marbles in each bag is:
30:6 = 5 (tablets)
The number of yellow marbles in each bag is:
66:6 = 11 (tablets)
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13.
The answer:
We have:
2xy + x + 2y = 13
⇒ 2xy + x + 2y + 1 = 13 +1
(2xy + 2y) + (x + 1) = 14
2y(x + 1) + (x + 1) = 14
(x + 1)(2y + 1) =14
Since x, y are natural numbers, x + 1 and 2y + 1 are also natural numbers
We have: (x + 1)(2y + 1) = 1.14 = 2.7
Case 1: With x + 1 = 1 and 2y + 1 = 14
We have: x + 1 = 1 x = 0
2y + 1 = 14 2y = 13 y = (discard because x, y are natural numbers)
Case 2: With x + 1 = 14 and 2y + 1 = 1
We have: x + 1 = 14 x = 14 – 1
2y + 1 = 1 2y = 0 ⇒ y = 0 (satisfied)
Case 3: With x + 1 = 2 and 2y + 1 = 7
We have: x + 1 = 2 x = 1
2y + 1 = 7 2y = 6 y = 3 (satisfied)
Case 4: With x + 1 = 7 and 2y + 1 = 2
We have: x + 1 = 7 x = 6
2y + 1 = 2 2y = 1⇒ y = (discard because x, y are natural numbers)
So we find two pairs of numbers (x; y) satisfying (13; 0) and (1; 3)
2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Question 1. Write the set A of natural numbers greater than 5 and less than 10
A. A = {6, 7, 8, 9}
B. A = {5, 6, 7, 8, 9}
C. A = { 6, 7, 8, 9, 10}
D. A = {6, 7, 8}
Verse 2. Write the following set A = {x ∈ N | 9 < x < 13} by enumerating the elements:
A. A = {10, 11, 12}
B. A = {9, 10, 11}
C. A = { 9, 10, 11, 12, 13}
D. A = {9, 10, 11, 12}
Question 3: Of the following numbers: 59; 101; 355; 1341; 119; 29 which numbers are prime?
A. 59; 101; 29
B. 101; 355; 119; 29
C. 59; 355; 1341; 29
D. 59; 101; 355
Question 4: The natural number m divided by 45 leaves 20 in the form:
A. 45 + 20k
B. 45k + 20
C. 45 – 20k
D. 45k - 20
Question 5: Analyzing 126 into prime factors, we get the following results:
A. | B. |
C. | D. |
Question 6: Find the correct statement among the following:
A. A number that is divisible by 9 is always divisible by 3
B. If two numbers are divisible by 3, the sum of those two numbers is divisible by 9
C. Any even number is always divisible by 5
D. A number that is divisible by 2 is a number ending in zero; 2; 3; 4; 6; 8
Verse 7: Which of the following properties does a parallelogram not have?
A. Two opposite sides are parallel to each other
B. Two opposite sides are congruent
C. Four equal sides
D. The two main diagonals are equal
Verse 8: The area of a rhombus whose diagonals are 10cm and 12cm respectively is:
A. 60cm^{2} | B. 60m |
C. 60m^{2} | D. 60cm |
II. Essay section (6 points)
Question 1. Do the following calculations:
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
b) 5 . 2^{2} – 18 : 3
c) 18 : 3 + 182 + 3.(51 : 17)
d) 25 . 8 - 12.5 + 170 : 17 - 8
Verse 2: Find x knows:
a) 12 + (5 + x) = 20
b) 175 + (30 – x) = 200
c) 10 + 2x = 4^{5} : 4^{3}
d) 10x + 2^{2}.5 = 10^{2}
Question 3: Class 6A has 54 students, class 6B has 42 students and class 6C has 48 students. On the first day of school, three classes lined up in equal rows to parade without any odd people in each class.
a. Calculate the maximum number of vertical rows that can be stacked
b. How many students are there in each row?
Question 4: Write as a power with base 2
Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Sentence | Question 1 | Verse 2 | Verse 3 | Verse 4 | Question 5 | Verse 6 | Verse 7 | Verse 8 |
Answer | A | A | A | REMOVE | REMOVE | A | OLD | A |
II. Essay section (6 points)
Question 1
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
12 : { 400 : [500 – (125 + 25 . 7)]} = 12 : { 400 : [500 – (125 + 175)]}
= 12 : { 400 : [500 – 300]} = 12 : { 400 : 200} = 12 : 2 = 6
b) 5 . 2^{2} – 18 : 3 = 27 . 75 + 25 . 27 – 150 = 27. (75 + 25) – 150 = 27,100 – 150 = 270 – 150 = 120
c) 18 : 3 + 182 + 3.(51 : 17) = 197
d) 25 . 8 - 12.5 + 170 : 17 - 8 = 285
Verse 2.
a) 12 + (5 + x) = 20
5 + x = 20 – 12
5 + x = 8
x = 8 – 5 = 3
b) 175 + (30 – x) = 200
30 – x = 200 – 175
30 – x = 25
x = 30 – 25 = 5
c) 10 + 2x = 4^{5} : 4^{3}
Answer: x = 11
d) 10x + 2^{2}.5 = 10^{2}
Answer x = 61
Verse 3
a) Since the number of students is enough, the number of vertical rows is a common divisor of the number of students in 3 classes
The maximum number of vertical rows is also the greatest common divisor of the number of students in three grades
We have: 54 = 2.3^{3}
42 = 2.3.7
48 = 2^{4}.3
CCLN (54; 42; 48) = 2.3 = 6
So the maximum number of vertical rows that can be arranged is 6 rows
Verse 4
We have
Above is the document for the 6th grade math test midterm 1 with answers. I wish you all the best in your studies and good results in this midterm exam.
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Midterm exam 1 in Math 6 books Connecting knowledge with life
Midterm exam 1 Math 6 book Wings
Midterm exam 1st grade 6 book Connecting knowledge with life - All subjects
Midterm exam 1st grade Math 6th grade Creative Horizon book for the school year 2022 – 2023
Midterm exam 1 in Math 6th grade Creative Horizons book is a set of exam questions with answers included for students to review and practice knowledge to achieve the best results in the midterm math test. This is a set of ĐH KD & CN Hà Nội.vn exam questions collected and synthesized with the content closely following the new textbook program, please refer to the detailed 2 sets of 6th grade math test questions mid-term 1 below.
6th grade math midterm exam
- 1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
- Answers to the midterm exam 1 of Grade 6 Maths book No. 1 Creative Horizons
- 2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
- Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
1. Midterm exam for grade 6 Maths book No. 1 Creative Horizons
(Title 2)
I. Multiple choice section
Question 1: Write the following set A = {x∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Question 3: Factor 300 into prime factors
A) 2^{3}.3.5^{2}
B) 2^{2}.3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3}.3.5
Question 4: The result of the calculation: 250 – 5^{2} – (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) The number -5 is to the left of the number -4 so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Verse 8: Set A = {a ∈ Z | -5 < a < 2}
A) 5
B) 7
C) 6
D) 8
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Question 10: The result of the calculation: 2^{3} – 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
II. Essay
Lesson 1: Do the math
a) (4 + 32 + 6) + (10 – 32 – 2)
b) (56.35 + 56.18): 53
c) 12:{400:[500 – (125 + 25.7)]}
d) 303 – 3. {[655 – (18:2 + 1). +5]}: ten^{}
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
b) 125 – 5(4 + x) = 15
c) (15 + x):3 = 3^{15} : 3^{twelfth}
d) 2^{x+1}_{ }– 2^{x} = 32
Lesson 3: Vinh has 48 red marbles, 30 green marbles, and 66 yellow marbles. Vinh wants to equally divide the number of marbles into the bags so that each bag contains all three types of marbles. Ask Vinh how many bags can be divided at most. How many marbles of each type are there in each bag?
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13
AnswerMidterm exam 1 Math 6th grade book Creative Horizons No. 1
I. Multiple choice section
Question 1: Write the following set A = {x ∈ N | 8 ≤ x ≤ 12} by enumerating the elements:
A) A = {8; 9; ten; 11; twelfth}
B) A = {9; ten; 11; twelfth}
C) A = {9; ten; 11}
D) A = {9; ten; 11; twelfth}
Since 8 ≤ x ≤ 12, x ∈ {8; 9; ten; 11; twelfth}
Attention: we take the equal sign at 8 and 12
Verse 2: A natural number divided by 10 leaves 5 with the form
A) 5k + 10 (with k N)
B) 5k -10 (with k N)
C) 10k + 3 (with k N)
D) 10k + 5 (with k N)
Since every natural number divided by 10 leaves a remainder 5 of the form 10k + 5 where k belongs to N.
Question 3: Factor 300 into prime factors
A) 2^{3} .3.5^{2}
B) 2^{2} .3.5^{2}
C) 2.3^{2}.5^{2}
D) 2^{3} .3.5
300 = 2.2.3.5.5 = 2^{2}.3.5^{2}
Question 4: The result of the calculation: 250 – 5^{2} – (3 .)^{2} +12):3
A) 218
B) 268
C) 232
D) 240
250 – 5^{2} – (3 .)^{2} +12):3
= 250 – 25 – (9 + 12):3
= 250 – 25 – 21:3
=250 – 25 – 7
= 225 – 7
= 218
Question 5: Which of the following statements is false?
A) The opposite of -6 is 6.
B) The opposite of 0 is 0.
C) On the number line, -5 is to the left of -4, so we say -5 is greater than -4.
D) The number 0 is neither a negative integer nor a positive integer.
Sentence C is wrong because the numbers on the number line on the left will be smaller than the numbers on the right, so -5 is on the left of the number -4, so -5 is less than -4
Question 6: Which of the following sequences of numbers are only prime numbers?
A) 1; 3; 5; 7
B) 2; 3; 5; 7
C) 1; 2; 3; 5; 7
D) 3; 5; 7; 9
Because answer A has 1 non-prime number, answer C has 1 non-prime number, and answer D has 9 non-prime numbers. Answer B All 4 numbers are prime.
Verse 7: Given the following integers: 0; -3; 2; 5; -4; 4; 6. Sort the given integers in ascending order
A) -3; -4; 0; 2; 4; 5; 6
B) 0; -3; -4; 2; 4; 5; 6
C) 6; 5; 4; 2; 0; -3; -4
D) -4; -3; 0; 2; 4; 5; 6
Since answer D the numbers are sorted in ascending order.
Verse 8: Set A = {a ∈ Z | -5 < a < 2}. How many elements does set A have?
A) 5
B) 7
C) 6
D) 8
We have: A = {a ∈ Z | -5 < a < 2}
A = {-4; -3; -2; -first; 0; 1} set A has 6 elements
Verse 9: Find the number x ∈ Z satisfying: 2x + 35 = 17
A) 12
B) 9
C) 26
D) -9
Explain
2x = 17 – 35
2x = -18
x = -18:2
x = -9
Question 10: The result of the calculation: 2^{3} – 2.(-3) + 5^{2}
A) 39
B) 25
C) 27
D) 14
2^{3} – 2.(-3) + 5^{2}
= 8 – (-6) + 25
= 8 +6 + 25
= 14 + 25
= 39.
II. Essay section
Lesson 1:
a) (4 + 32 + 6) + (10 – 32 – 2)
= 4 + 32 + 6 + 10 – 32 – 2
= (4 – 2) + (32 – 32) + (10 + 6)
= 2 + 0 + 16
= 18
b) (56.35 + 56.18): 53
= [56.(35 + 18)]:53
= [56.53]:53
= 2968:53
= 56
c) 12:{400:[500 – (125 + 25.7)]}
= 12:{400:[500 – (125 + 175)]}
= 12:{400:[500 – 300]}
= 12:{400:200}
=12:2 = 6
d) 303 – 3.[655 – (18:2 + 1). +5]:
= 303 – 3.[655 – (9 + 1).64 + 5]:ten^{}
= 303 – 3.[655 – 10.64 + 5]:ten^{}
= 303 – 3[655 – 640 + 5]:ten^{}
= 303 – 3[15 + 5]:ten^{}
= 303 – 3.20:1
= 303 – 60
= 243
Lesson 2: Find x ∈ Z know:
a) 2^{2} + (x + 3) = 5^{2}
4 + (x + 3) = 25
x + 3 = 25 – 4
x + 3 = 21
x = 21 -3
x = 18
So x = 18
b) 125 – 5(4 + x) = 15
5(4 + x) = 125 – 15
5(4 + x) = 110
4 + x = 110: 5
4 + x = 22
x = 22 – 4
x = 18
So x = 18
c) (15 + x):3 = 3^{15} : 3^{twelfth}
(15 + x): 3 = 3^{3}
15 + x = 3^{3}.3
15 + x = 3^{4}
15 + x = 81
x = 81 – 15
x = 66
So x = 66
d) 2^{x + 1} – 2^{x} = 32
2^{x}.2 – 2^{x} = 32
2^{x}.(2 – 1) = 32
2^{x} = 32
2^{x} = 2^{5}
x = 5
So x = 5
Lesson 3:
The answer:
Let the number of your bag of marbles Vinh be x (x ∈ N^{*})
Because 48 red marbles, 30 blue marbles and 66 yellow marbles are equally divided into the bags of marbles, 48 x; 30 x; 66 x or x is a common divisor of 48; 30, 66.
Since the maximum number of bags of marbles can be divided, x is the greatest common divisor of 48; 30; 66.
We have:
48 = 2.2.2.2.3 = 2^{4}.3
30 = 2.3.5
66 = 2.3.11
CCLN (48; 30; 66) = 2.3 = 6
So at most 6 bags of marbles can be divided such that the number of marbles of each color in the three bags is equal.
The number of red marbles in each bag is:
48:6 = 8 (tablets)
The number of blue marbles in each bag is:
30:6 = 5 (tablets)
The number of yellow marbles in each bag is:
66:6 = 11 (tablets)
Lesson 4: Find the natural numbers x; y knows 2xy + x + 2y = 13.
The answer:
We have:
2xy + x + 2y = 13
⇒ 2xy + x + 2y + 1 = 13 +1
(2xy + 2y) + (x + 1) = 14
2y(x + 1) + (x + 1) = 14
(x + 1)(2y + 1) =14
Since x, y are natural numbers, x + 1 and 2y + 1 are also natural numbers
We have: (x + 1)(2y + 1) = 1.14 = 2.7
Case 1: With x + 1 = 1 and 2y + 1 = 14
We have: x + 1 = 1 x = 0
2y + 1 = 14 2y = 13 y = (discard because x, y are natural numbers)
Case 2: With x + 1 = 14 and 2y + 1 = 1
We have: x + 1 = 14 x = 14 – 1
2y + 1 = 1 2y = 0 ⇒ y = 0 (satisfied)
Case 3: With x + 1 = 2 and 2y + 1 = 7
We have: x + 1 = 2 x = 1
2y + 1 = 7 2y = 6 y = 3 (satisfied)
Case 4: With x + 1 = 7 and 2y + 1 = 2
We have: x + 1 = 7 x = 6
2y + 1 = 2 2y = 1⇒ y = (discard because x, y are natural numbers)
So we find two pairs of numbers (x; y) satisfying (13; 0) and (1; 3)
2. Mid-term exam papers for Grade 6 Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Question 1. Write the set A of natural numbers greater than 5 and less than 10
A. A = {6, 7, 8, 9}
B. A = {5, 6, 7, 8, 9}
C. A = { 6, 7, 8, 9, 10}
D. A = {6, 7, 8}
Verse 2. Write the following set A = {x ∈ N | 9 < x < 13} by enumerating the elements:
A. A = {10, 11, 12}
B. A = {9, 10, 11}
C. A = { 9, 10, 11, 12, 13}
D. A = {9, 10, 11, 12}
Question 3: Of the following numbers: 59; 101; 355; 1341; 119; 29 which numbers are prime?
A. 59; 101; 29
B. 101; 355; 119; 29
C. 59; 355; 1341; 29
D. 59; 101; 355
Question 4: The natural number m divided by 45 leaves 20 in the form:
A. 45 + 20k
B. 45k + 20
C. 45 – 20k
D. 45k – 20
Question 5: Analyzing 126 into prime factors, we get the following results:
A. | B. |
C. | D. |
Question 6: Find the correct statement among the following:
A. A number that is divisible by 9 is always divisible by 3
B. If two numbers are divisible by 3, the sum of those two numbers is divisible by 9
C. Any even number is always divisible by 5
D. A number that is divisible by 2 is a number ending in zero; 2; 3; 4; 6; 8
Verse 7: Which of the following properties does a parallelogram not have?
A. Two opposite sides are parallel to each other
B. Two opposite sides are congruent
C. Four equal sides
D. The two main diagonals are equal
Verse 8: The area of a rhombus whose diagonals are 10cm and 12cm respectively is:
A. 60cm^{2} | B. 60m |
C. 60m^{2} | D. 60cm |
II. Essay section (6 points)
Question 1. Do the following calculations:
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
b) 5 . 2^{2} – 18 : 3
c) 18 : 3 + 182 + 3.(51 : 17)
d) 25 . 8 – 12.5 + 170 : 17 – 8
Verse 2: Find x knows:
a) 12 + (5 + x) = 20
b) 175 + (30 – x) = 200
c) 10 + 2x = 4^{5} : 4^{3}
d) 10x + 2^{2}.5 = 10^{2}
Question 3: Class 6A has 54 students, class 6B has 42 students and class 6C has 48 students. On the first day of school, three classes lined up in equal rows to parade without any odd people in each class.
a. Calculate the maximum number of vertical rows that can be stacked
b. How many students are there in each row?
Question 4: Write as a power with base 2
Answers to the midterm exam 1 of 6th grade Maths book No. 2 Creative Horizons
I. Multiple choice (4 points)
Sentence | Question 1 | Verse 2 | Verse 3 | Verse 4 | Question 5 | Verse 6 | Verse 7 | Verse 8 |
Answer | A | A | A | REMOVE | REMOVE | A | OLD | A |
II. Essay section (6 points)
Question 1
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
12 : { 400 : [500 – (125 + 25 . 7)]} = 12 : { 400 : [500 – (125 + 175)]}
= 12 : { 400 : [500 – 300]} = 12 : { 400 : 200} = 12 : 2 = 6
b) 5 . 2^{2} – 18 : 3 = 27 . 75 + 25 . 27 – 150 = 27. (75 + 25) – 150 = 27,100 – 150 = 270 – 150 = 120
c) 18 : 3 + 182 + 3.(51 : 17) = 197
d) 25 . 8 – 12.5 + 170 : 17 – 8 = 285
Verse 2.
a) 12 + (5 + x) = 20
5 + x = 20 – 12
5 + x = 8
x = 8 – 5 = 3
b) 175 + (30 – x) = 200
30 – x = 200 – 175
30 – x = 25
x = 30 – 25 = 5
c) 10 + 2x = 4^{5} : 4^{3}
Answer: x = 11
d) 10x + 2^{2}.5 = 10^{2}
Answer x = 61
Verse 3
a) Since the number of students is enough, the number of vertical rows is a common divisor of the number of students in 3 classes
The maximum number of vertical rows is also the greatest common divisor of the number of students in three grades
We have: 54 = 2.3^{3}
42 = 2.3.7
48 = 2^{4}.3
CCLN (54; 42; 48) = 2.3 = 6
So the maximum number of vertical rows that can be arranged is 6 rows
Verse 4
We have
Above is the document for the 6th grade math test midterm 1 with answers. I wish you all the best in your studies and good results in this midterm exam.
Invite students to visit the group Have you studied yet? Ask questions and share quality learning. Group is an opportunity for students from all over the country to exchange, exchange learning, make friends, guide each other in learning experiences,…
Please refer to other lesson plans in the For Teachers section of the Materials section.
- Midterm exam 1 in Math 6 books Connecting knowledge with life
- Midterm exam 1 Math 6 book Wings
- Midterm exam 1st grade 6 book Connecting knowledge with life – All subjects
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