What are the newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are the bases for assessing the training results of 11th-grade students in Vietnam?
What are the newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025?
Students can refer to the following newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025:
Newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025
Question Paper. 1:
I. Multiple Choice (7 points)
Question 1. Let a be a positive real number, m ∈ Z, n ∈ N, n ≥ 2. Which of the following statements is false?
A. (a^{mn} = \sqrt[m]{a^n} = a^{mn}).
B. (a^{1/n} = \sqrt[n]{a} = a^{1n} = a^1).
C. (a^{mn} = \sqrt[m]{a^n} = a^{nm}).
D. (a^{1/2} = \sqrt{a} = a).
Question 2. Let x, y be two positive real numbers other than 1, and let n, m be any real numbers.
Which of the following equalities is false?
A. (x^m \cdot x^n = x^{m+n}).
B. (\frac{x^n}{y^n} = \frac{(x \cdot y)^n}{x^n \cdot y^n}).
C. (\frac{x^n}{y^m} = \frac{(x \cdot y)^{n-m}}{x^n \cdot y^m}).
D. (\frac{x^n}{y^n} = \frac{(x \cdot y)^n}{x^n \cdot y^n}).
Question 3. Calculate the value of (2^{3-\sqrt{2}} \cdot 4^{\sqrt{2}}) as
A. 8.
B. 32.
C. (2^{3+\sqrt{2}}).
D. (46\sqrt{2} - 44).
Question 4. Simplify the expression (P = \sqrt{3} \cdot\sqrt{a^{12} \cdot b^{18}} (a > 0, b > 0)) to get the result as
A. (P = a^2 \cdot b^3).
B. (P = a^6 \cdot b^9).
C. (P = a^2 \cdot b^9).
D. (P = a^6 \cdot b^3).
Question 5. (log_3 127) equals
A. -3.
B. (-\frac{1}{3}).
C. (\frac{1}{3}).
D. 3.
Question 6. Given (a, b > 0) and (a ≠ 1). Which of the following propositions is false?
A. (log_a 1 = 0).
B. (log_a a = 1).
C. (log_a \frac{a}{b} = a).
D. (a^{log_a b} = b).
Question 7. Given (a > 0), (a ≠ 1). The expression (a^{log_a a^2}) equals
A. (2a)
B. 2.
C. (2a).
D. (a^2).
Question 8. For all (a, b, x) being positive real numbers satisfying (log_2 x = 5log_2 a + 3log_2 b).
Which of the following propositions is true?
A. (x = 5a + 3b).
B. (x = a^5 + b^3).
C. (x = a^5 b^3).
D. (x = 3a + 5b).
Question 9. Which of the following functions is a logarithmic function?
A. (y = 3logx).
B. (y = log_{\sqrt{2}} x).
C. (y = x^{log_3 2}).
D. (y = (x+3)ln2).
Question 10. The domain of the function (y = 6^x) is
A. [0; +∞).
B. (ℝ \setminus {0}).
C. (0; +∞).
D. ℝ.
Question 11. Which function below is increasing on ℝ?
A. (f(x) = 3^x).
B. (f(x) = 3^{-x}).
C. (f(x) = (1/\sqrt{3})^x).
D. (f(x) = 3^{3x}).
Question 12. The solution to the equation (3^x = 9) is
A. 1.
B. 2.
C. 3.
D. 9.
Question 13. The solution to the equation (log_2 x = 3) is
A. 6.
B. 8.
C. 9.
D. 12.
Question 14. Find the solution set (S) of the inequality (log_{12}(x + 1) < log_{12}(2x - 1)).
A. (S = (2; +∞)).
B. (S = (-1; 2)).
C. (S = (-∞; 2)).
D. (S = (\frac{1}{2}; 2)).
Question 15. The solution set of the inequality (2x - 3 > 8) is
A. [6; +∞).
B. (0; +∞).
C. (6; +∞).
D. (3; +∞).
Question 16. Choose the correct statement from the following:
A. In space, two perpendicular lines can intersect or skew with each other.
B. In space, if two lines are perpendicular, they must intersect.
C. In space, two lines that have no common points are parallel.
D. In space, two distinct lines perpendicular to the same line are parallel.
Question 17. Given the cube ABCD.A'B'C'D', the angle between the lines AC and AA' is which of the following?
A. (\angle ACA').
B. (\angle AB'C).
C. (\angle DB'B).
D. (\angle CAA').
Question 18. Given the pyramid S.ABCD with a square base and all lateral edges equal to a. Let M and N be the midpoints of the edges AD and SD, respectively. Which of the following statements is true?
A. (MN \perp SC).
B. (MN \perp SB).
C. (MN \perp SA).
D. (MN \perp AB).
Question 19. Through a given point O, how many planes are perpendicular to a given line ∆?
A. 1.
B. Countless.
C. 3.
D. 2.
Question 20. Consider the tetrahedron OABC where OA, OB, OC are pairwise perpendicular. Which of the following statements is true?
A. (OB \perp (OAC)).
B. (AC \perp (OAB)).
C. (AC \perp (OBC)).
D. (AC \perp (OBC)).
Question 21. Given the cube ABCD.A'B'C'D', which plane is the line AC' perpendicular to?
A. (A'BD).
B. (A'DC').
C. (A'CD').
D. (A'B'CD).
Question 22. Choose the correct proposition from the following statements?
A. A perpendicular projection onto a plane (P) along a line ∆ parallel to (P) is called a perpendicular projection onto the plane (P).
B. A parallel projection onto a plane (P) along a line ∆ is called a perpendicular projection onto the plane (P).
C. A perpendicular projection onto a plane (P) along a line ∆ is called a perpendicular projection onto the plane (P).
D. A parallel projection onto a plane (P) along a line ∆ perpendicular to (P) is called a perpendicular projection onto the plane (P).
Question 23. Given the pyramid S.ABC with SC perpendicular to (ABC). The angle between SA and (ABC) is the angle between
A. SA and AB.
B. SA and SC.
C. SB and BC.
D. SA and AC.
Question 24. Given the pyramid S.ABCD with a square base ABCD and SA perpendicular to the plane (ABCD). Choose the false statement?
A. A is the perpendicular projection of S onto (ABCD).
B. A is the perpendicular projection of S onto (SAB).
C. B is the perpendicular projection of C onto (SAB).
D. D is the perpendicular projection of C onto (SAD).
Question 25. Which of the following propositions is false?
A. There is a unique plane passing through a given point and perpendicular to a given plane.
B. There is a unique plane passing through a given point and perpendicular to a given line.
C. There is a unique plane passing through a given line and perpendicular to a given plane.
D. There is a unique line passing through a given point and perpendicular to a given plane.
Question 26. Which of the following statements is true?
A. A regular pyramid is a pyramid whose base is a regular polygon, and the foot of the altitude from the apex to the base coincides with the center of the circumscribed circle of the polygonal base.
B. A regular pyramid is a pyramid whose base is a regular polygon, and all lateral edges are equal.
C. A regular pyramid is an equilateral tetrahedron.
D. A regular pyramid is a pyramid whose base is a regular polygon.
Question 27. In space, given a rectangular parallelepiped ABCD.A'B'C'D', which of the following planes is perpendicular to the plane (ABCD)?
A. (AA'B'B).
B. (A'B'CD).
C. (ADC'B').
D. (BCD'A').
Question 28. Given the pyramid S.ABCD with base ABCD as a rhombus with side a and AC = a. What is the measure of the dihedral angle [B, SA, D]?
A. 30°.
B. 45°.
C. 120°.
D. 60°.
Question 29. The distance between two skew lines a and b is
A. The length of the line segment from a point on line a to a point on line b.
B. The length of the common perpendicular between line a and line b.
C. The distance from a point M on line a to the perpendicular projection of point M onto line b.
D. The distance from a point M on line a to line b.
Question 30. In a regular pyramid S.ABC, the distance from S to (ABC) is
A. SO (where O is the centroid of triangle ABC).
B. SM (where M is the midpoint of BC).
C. SA.
D. SH (where H is the projection of S onto AC).
Question 31. Consider a tetrahedron ABCD with AB = SA = 2a. The distance from line AD to the plane (SBC) is
A. (\frac{a\sqrt{63}}{3}).
B. (\frac{2a\sqrt{63}}{3}).
C. (\frac{a}{2}).
D. a.
Question 32. Which of the following statements is false?
A. The volume of a pyramid with base area B and height h is (V = \frac{1}{3}Bh).
B. The volume of a prism with base area B and height h is (V = Bh).
C. The volume of a rectangular box is the product of its three dimensions.
D. The volume of a pyramid with base area B and height h is (V = 3Bh).
Question 33. For a pyramid with a square base and height equal to 2a, the volume of the given pyramid is
A. (4a^3).
B. (\frac{2a^3}{3}).
C. (2a^3).
D. (\frac{4a^3}{3}).
Question 34. The volume of a prism with a base area of 9 and height of 2 is
A. 18.
B. 6.
C. 9.
D. 54.
Question 35. For a pyramid S.ABCD with base ABCD a square with side a, triangle SAB is isosceles at S and lies in a plane perpendicular to the base, (SA = 2a). In terms of a, the volume V of the pyramid S.ABCD is
A. (V = \frac{a^3\sqrt{15}}{12}).
B. (V = \frac{a^3\sqrt{15}}{6}).
C. (V = 2a^3).
D. (V = \frac{2a^3}{3}).
II. Essay (3 points)
Exercise 1. (1.0 point)
a) Given (log_x y = 2), calculate the value of (log_x \frac{2y}{x^4 \sqrt{y}}).
b) Find integer m so that the function (f(x) = \frac{(2x^2 + mx + 2)^3}{2}) is defined for every (x ∈ ℝ).
Exercise 2. (1.0 point) Given a pyramid S.ABC with base triangle ABC being right-angled at B, (SA \perp (ABC)). Let H be the projection of A onto SB.
a) Prove that (AH \perp (SBC)).
b) Calculate the angle between the two planes (SAC) and (SBC), knowing that SA = AB = a.
Exercise 3. (1.0 point) Consider the pyramid S.ABCD where the base is the rectangle with (AB = a), (BC = a\sqrt{3}). Both planes (SAC) and (SBD) are perpendicular to the base. A point I is located on SC such that SC = 3IC. Calculate the distance between the lines AI and SB given that AI is perpendicular to SC.
Question Paper. 2:
I. Multiple Choice (7 points)
Question No. 2:
I. Multiple Choice Test (7 points)
Question 1. Given a is a positive real number. For which set n is affirmed, an=a.a............ anan=a.a............ a⏟n right?
A. n ∈ R.
B. n ∈ Z.
C. n ∈ N.
D. n ∈ N*.
Question 2. Where a is an arbitrary positive real number, √a3a3 equals which of the following results?
A. a6.
B. a32a32.
C. a23a23.
D. a16a16.
Question 3. Given α is any real number, which of the following propositions is false?
A. √10α=(√10)α10α=10α.
B. √10α=10α210α=10α2.
C. (10α)2=(100)α10α2=100α.
D. (10α)2=(10)α210α2=10α2.
Question 4. Give the equation 3√a2√aa3=aα,0<a≠1a2a3a3=aα,0<a≠1. At that time, α belong to the following range?
A. (-2; -1).
B. (-1; 0).
C. (-3; -2).
D. (0; 1).
Question 5. Ms. Ha deposited 20 000 000 VND into the bank with an interest rate of 0.5%/month (after each month, the interest is entered into the principal to calculate the next month's interest). Asked how much money Ms. Ha received after 1 year, she knew that in that 1 year Ms. Ha did not withdraw money and the interest rate did not change (rounded to thousands).
A. 21 233 000 VND.
B. 21 235 000 VND.
C. 21 234 000 VND.
D. 21 200 000 VND.
Question 6. Under what conditions of a and b, it is confirmed that logab=α⇔aα=blogab=α⇔aα=b is correct?
A. a, b > 0, a ≠ 1.
B. a, b > 0.
C. a > 0, a ≠ 1.
D. b > 0, a ≠ 1.
Question 7. Which of the following clauses is true?
A. logabα=αlogablogab=αlogab with all positive real numbers a, b and a ≠ 1.
B. logabα=αlogablogab=αlogab with all positive real numbers a, b.
C. logabα=αlogablogabα=αlogab with every real number a, b.
D. logabα=αlogablogab=αlogab with all real numbers a, b, and a ≠ 1.
Question 8. Where a is the arbitrary positive real number, log3(9a)log39a is equal to
A. 12+log3a12+log3a.
B. 2log3a2log3a.
C. (log3a)2log3a2.
D. 2+log3a2+log3a.
Question 9. Give 0 < a ≠ 1. The value of the expression P=loga(a⋅3√a2)P=logaa⋅a23 is
A. 4343.
B. 3.
C. 5353.
D. 5252.
Question 10. For a, b, c are the positive real numbers that satisfy a2 = bc. The value of the expression S=2lna−lnb−lncS=2lna−lnb−lnc is
A. S=2ln(abc)S=2lnabc.
B. S = 1.
C. S=−2ln(abc)S=−2lnabc.
D. S = 0.
Question 11. Which of the below functions is an exponential function?
A. y=x√3y=x3.
B. y=xlog2y=xlog2.
C. y=log√2xy=log2x.
D. y=(π3)xy=π3x.
Question 12. For the following functions:
y=log2xy=log2x
y=log√3xy=log3x
y=lnxy=lnx, y=log2−3xy=log2−3x
y=logx5y=logx5.
How many logarithmic functions are in the above functions?
A. 5.
B. 4.
C. 3.
D. 2.
Question 13. The defining set of the function y=log2xy=log2x is
A. [0;+∞)0;+∞.
B. (−∞;+∞)−∞;+∞.
C. (0;+∞)0;+∞.
D. [2;+∞)2;+∞.
Question 14. Give three other positive real numbers a, b, c 1. The graph of functions y=ax,y=bx,y=cxy=ax,y=bx,y=cx is given in the following figure.
Which of the following propositions is true?
A. b < c < a.
B. c < a < b.
C. a < b < c.
D. a < c < b.
Question 15. The curve in the side figure is a graph of one of the four functions listed in the four options A, B, C, D below. Ask what function is it?
A. y=log2xy=log2x.
B. y=log2(x+1)y=log2x+1.
C. y=log3x+1y=log3x+1.
D. y=log3(x+1)y=log3x+1.
Question 16. The solution of the equation 7x = 2 is
A. x=log72x=log72.
B. x=log27x=log27.
C. x=27x=27.
D. x=√7x=7.
Question 17. The solution of the equation log3(5x)=2log35x=2 is
A. x=85x=85.
B. x = 9.
C. x=95x=95.
D. x = 8.
Question 18. The experiment of the log23(x−2)≥1log23x−2≥1 is
A. [83;+∞)83;+∞.
B. [2; 83]2;83.
C. (2; 83]2;83.
D. (−∞; 83]−∞;83.
Question 19. The experiment of the inequalities 2x−3>162x−3 > 16 is
A. [7;+∞)7; +∞.
B. (0;+∞)0; +∞.
C. (7;+∞)7; +∞.
D. (3;+∞)3; +∞.
Question 20. Knowing that the equation 4x−9⋅2x+16=04x−9⋅2x+16=0 has two differential solutions x1 and x2. Calculate the value of the expression A = x1 + x2.
A. A = 4.
B. A = log29log29.
C. A = 9.
D. A = 16.
Question 21. In space for two straight lines m and n. Which of the following statements is true?
A. The angle between the two lines m and n is the angle between the two lines a and b passing through the same point and corresponding to m and n.
B. The angle between the two lines m and n is the angle between the two lines m and b perpendicular to n.
C. The angle between the two lines m and n is the angle between the two lines a and b perpendicular to m and n, respectively.
D. The angle between the two lines m and n is the angle between any two lines a and b.
Question 22. In space, give two lines a and b. Which of the following assertions is true?
A. Lines a and b are perpendicular to each other when and only when they intersect.
B. Lines a and b are perpendicular to each other if and only if the angle between them is 90°.
C. Lines a and b are perpendicular to each other if and only if the angle between them is equal to 45°.
D. Lines a and b are perpendicular to each other if and only if the angle between them is 0°.
Question 23. For the cube ABCD. A'B'C'D'
The angle between the two lines AB and A'C' is equal to
A. 60°.
B. 45°.
C. 90°.
D. 30°.
Question 24. For the cube ABCD. A'B'C'D'
Which of the following lines perpendicular to the BC' line?
A. A'D.
B. AC.
C. BB'.
D. AD'.
Question 25. In the space for the line d perpendicular to every line a is in the plane (α). Which of the following assertions is true?
A. d // (α).
B. d ⊥ (α).
C. d ⊂ (α).
D. d cut α.
Question 26. For the ABCD quadruple with AB, AC, AD double one perpendicular to each other
Which of the following assertions is true?
A. AB ⊥ (BCD).
B. AC ⊥ (BCD).
C. AD ⊥ (BCD).
D. AD ⊥ (ABC).
Question 27. For two lines a, b, and mp(P). Point out the correct clause in the following clauses:
A. If a// (P) and b ⊥ a, then b// (P).
B. If a // (P) and b ⊥ (P) then a ⊥ b.
C. If a // (P) and b ⊥ a, then b ⊥ (P).
D. If a ⊥ (P) and b ⊥ a, then b // (P).
Question 28. Given the pyramid S.ABCD with the bottom ABCD being rectangular, SA ⊥ (ABCD). Call M and N the midpoints of AB and SB respectively (refer to the drawing).
Which of the following assertions is true?
A. AC ⊥ (SAD).
B. MN ⊥ (SBD).
C. BD ⊥ (SCD).
D. MN ⊥ (ABCD).
Question 29. Given the pyramid S.ABCD has a square base, SA perpendicular to the plane (ABCD). Let H be the perpendicular projection of A to the plane (SBC).
Which of the following affirmations is true?
A. H is the base of the road at a perpendicular descent from A to SB.
B. H is the center of gravity of the SBC triangle.
C. H coincides with B.
D. H is the midpoint of SB.
Question 30. For two planes (α), (β). Which of the following statements is true?
A. If (α) cuts (β) then (α) ⊥ (β).
B. If ((α), (β)) = 0°, then (α) ⊥ (β).
C. If ((α), (β)) = 45°, then (α) ⊥ (β).
D. If ((α), (β)) = 90°, then (α) ⊥ (β).
Question 31. The number of side edges of a quadrilateral pyramid is
A. 3.
B. 4.
C. 6.
D. 12.
Question 32. Give the line a perpendicular to the plane (α) and a ⊂ (β). Which of the following assertions is true?
A. (α) // (β).
B. (α) coincides with (β).
C. 0°≤((α),(β))<90°0°0°≤α,β<90°.
D. (α) ⊥ (β).
Question 33. Which of the following clauses is true?
A. If the box shape has two sides that are rectangular then it is a rectangular box.
B. If a box with five sides is rectangular, it is a rectangular box.
C. If a box with four sides is rectangular then it is a rectangular box.
D. If a box with three sides is rectangular, it is a rectangular box.
Question 34. For the pyramid S.ABC with the bottom is a right triangle at B, SA perpendicular to the bottom
Which of the following assertions is false?
A. (SAB) ⊥ (ABC).
B. (SAB) ⊥ (SAC).
C. (SAC) ⊥ (ABC).
D. (SAB) ⊥ (SBC).
Question 35. Give the triangle ABC weighed at A with high lines AH=a√3,BC=3aAH=a3, BC=3a, BC contained in the plane (P). Let's call A' the perpendicular projection of A onto the plane (P) (as shown in the side drawing). Know the triangle A'BC is square at A'. Call φφ the angle between (P) and (ABC).
Select the correct affirmation in the following affirmations.
A. φ=60°φ=60°.
B. φ=45°φ=45°.
C. cosφ=√23cosφ=23.
D. φ=30°φ=30°.
II. Essay (3 points)
Lesson 1. (1.0 points)
a) Calculate the value of the expression M=(3+2√2)2019⋅(3√2−4)2018M=3+222019⋅32−42018.
b) Find all the real values of the parameter m so that the function y=log(x2−2mx+4)y=logx2−2mx+4 has a defined set of R.
Lesson 2. (1.0 points) Let the ABCD tetrahedron have a triangle ABC weighted at A, the triangle BCD weighted at D. Let I be the midpoint of the BC side.
a) Prove that BC ⊥ (AID).
b) Call AH the high line of the AID triangle. Prove that AH ⊥ BD.
Lesson 3. (1.0 points) The growth of a bacterial species is calculated according to the formula f(t)=Aertft=Aert, where A is the initial number of bacteria, r is the growth rate (r > 0), t (in hours) is the growth time. Knowing the number of bacteria initially had 1 000 and after 10 hours it was 5 000. Why does it take for the number of bacteria to increase 10 times?
Note: Information is only for reference!
What are the newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are the bases for assessing the training results of 11th-grade students in Vietnam? (image from Internet)
What are the bases for assessing the training results of 11th-grade students in Vietnam?
Under Clause 1 Article 8 Circular 22/2021/TT-BGDDT, the basis for assessing the training results of 12th-grade students in Vietnam is prescribed as follows:
- Assess training results of students based on requirements for traits and general capacity by subjects and education level under general programs and requirements for specific capacity under subject program in formal education program.
- Subject teachers shall rely on Point a of this Clause to provide feedback and assess training results, improvement, advantages, and disadvantages of students during training and learning process of the subjects.
- Class advisors shall rely on Point a of this Clause to monitor training and learning process of students; consult feedback and assessment of subject teachers and feedback of students’ parents, relevant, agencies, organizations, and individuals in educating students; instruct students on how to perform self-assessment; provide feedback and assess training results of students based on categories under the above section.
What are the assessment levels for learning results in the whole school year of 11th-grade students in Vietnam?
According to Clause 2, Article 9 of Circular 22/2021/TT-BGDDT, 04 assessment levels for learning results in the whole school year of 11th-grade students in Vietnam include:
1) Excellent:
- All subjects assessed with feedback are placed in Qualified category.
- All subjects assessed by both feedback and scores have minimum scores of 6.5 for DTBmhk and DTBmcn with 6 subjects among which have minimum scores of 8.0 for DTBmhk and DTBmcn.
2) Good:
- All subjects assessed with feedback are placed in Qualified category.
- All subjects assessed by both feedback and scores have minimum scores of 5.0 for DTBmhk and DTBmcn with 6 subjects among which have minimum scores of 6.5 for DTBmhk and DTBmcn.
3) Qualified:
- Have no more than 1 subject assessed via feedback placed in Unqualified category.
- At least 6 subjects assessed by both feedback and scores have minimum scores of 5.0 for DTBmhk and DTBmcn with 0 subjects have scores lower than 3.4 for DTBmhk and DTBmcn.
4) Unqualified: Remaining cases.
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