What are trực tiếp bóng đá k+ newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are trực tiếp bóng đá k+ bases for assessing trực tiếp bóng đá k+ training results of 11th-grade students in Vietnam?
What are trực tiếp bóng đá k+ newest sample 2nd mid-semester question papers and answersfor 11th-grade Mathematics in 2025?
Students can refer to trực tiếp bóng đá k+ followingnewest sample 2nd mid-semester question papers and answersfor 11th-grade Mathematics in 2025:
Newest sample 2nd mid-semester question papers and answersfor 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ expression (P = \sqrt{3} \cdot\sqrt{a^{12} \cdot b^{18}} (a 0, b 0)) to get trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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). trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ domain of trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ solution to trực tiếp bóng đá k+ equation (3^x = 9) is
A. 1.
B. 2.
C. 3.
D. 9.
Question 13. trực tiếp bóng đá k+ solution to trực tiếp bóng đá k+ equation (log_2 x = 3) is
A. 6.
B. 8.
C. 9.
D. 12.
Question 14. Find trực tiếp bóng đá k+ solution set (S) of trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ solution set of trực tiếp bóng đá k+ inequality (2x - 3 8) is
A. [6; +∞).
B. (0; +∞).
C. (6; +∞).
D. (3; +∞).
Question 16. Choose trực tiếp bóng đá k+ correct statement from trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ same line are parallel.
Question 17. Given trực tiếp bóng đá k+ cube ABCD.A'B'C'D', trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ lines AC and AA' is which of trực tiếp bóng đá k+ following?
A. (\angle ACA').
B. (\angle AB'C).
C. (\angle DB'B).
D. (\angle CAA').
Question 18. Given trực tiếp bóng đá k+ pyramid S.ABCD with a square base and all lateral edges equal to a. Let M and N be trực tiếp bóng đá k+ midpoints of trực tiếp bóng đá k+ edges AD and SD, respectively. Which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ tetrahedron OABC where OA, OB, OC are pairwise perpendicular. Which of trực tiếp bóng đá k+ following statements is true?
A. (OB \perp (OAC)).
B. (AC \perp (OAB)).
C. (AC \perp (OBC)).
D. (AC \perp (OBC)).
Question 21. Given trực tiếp bóng đá k+ cube ABCD.A'B'C'D', which plane is trực tiếp bóng đá k+ line AC' perpendicular to?
A. (A'BD).
B. (A'DC').
C. (A'CD').
D. (A'B'CD).
Question 22. Choose trực tiếp bóng đá k+ correct proposition from trực tiếp bóng đá k+ following statements?
A. A perpendicular projection onto a plane (P) along a line ∆ parallel to (P) is called a perpendicular projection onto trực tiếp bóng đá k+ plane (P).
B. A parallel projection onto a plane (P) along a line ∆ is called a perpendicular projection onto trực tiếp bóng đá k+ plane (P).
C. A perpendicular projection onto a plane (P) along a line ∆ is called a perpendicular projection onto trực tiếp bóng đá k+ plane (P).
D. A parallel projection onto a plane (P) along a line ∆ perpendicular to (P) is called a perpendicular projection onto trực tiếp bóng đá k+ plane (P).
Question 23. Given trực tiếp bóng đá k+ pyramid S.ABC with SC perpendicular to (ABC). trực tiếp bóng đá k+ angle between SA and (ABC) is trực tiếp bóng đá k+ angle between
A. SA and AB.
B. SA and SC.
C. SB and BC.
D. SA and AC.
Question 24. Given trực tiếp bóng đá k+ pyramid S.ABCD with a square base ABCD and SA perpendicular to trực tiếp bóng đá k+ plane (ABCD). Choose trực tiếp bóng đá k+ false statement?
A. A is trực tiếp bóng đá k+ perpendicular projection of S onto (ABCD).
B. A is trực tiếp bóng đá k+ perpendicular projection of S onto (SAB).
C. B is trực tiếp bóng đá k+ perpendicular projection of C onto (SAB).
D. D is trực tiếp bóng đá k+ perpendicular projection of C onto (SAD).
Question 25. Which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following statements is true?
A. A regular pyramid is a pyramid whose base is a regular polygon, and trực tiếp bóng đá k+ foot of trực tiếp bóng đá k+ altitude from trực tiếp bóng đá k+ apex to trực tiếp bóng đá k+ base coincides with trực tiếp bóng đá k+ center of trực tiếp bóng đá k+ circumscribed circle of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following planes is perpendicular to trực tiếp bóng đá k+ plane (ABCD)?
A. (AA'B'B).
B. (A'B'CD).
C. (ADC'B').
D. (BCD'A').
Question 28. Given trực tiếp bóng đá k+ pyramid S.ABCD with base ABCD as a rhombus with side a and AC = a. What is trực tiếp bóng đá k+ measure of trực tiếp bóng đá k+ dihedral angle [B, SA, D]?
A. 30°.
B. 45°.
C. 120°.
D. 60°.
Question 29. trực tiếp bóng đá k+ distance between two skew lines a and b is
A. trực tiếp bóng đá k+ length of trực tiếp bóng đá k+ line segment from a point on line a to a point on line b.
B. trực tiếp bóng đá k+ length of trực tiếp bóng đá k+ common perpendicular between line a and line b.
C. trực tiếp bóng đá k+ distance from a point M on line a to trực tiếp bóng đá k+ perpendicular projection of point M onto line b.
D. trực tiếp bóng đá k+ distance from a point M on line a to line b.
Question 30. In a regular pyramid S.ABC, trực tiếp bóng đá k+ distance from S to (ABC) is
A. SO (where O is trực tiếp bóng đá k+ centroid of triangle ABC).
B. SM (where M is trực tiếp bóng đá k+ midpoint of BC).
C. SA.
D. SH (where H is trực tiếp bóng đá k+ projection of S onto AC).
Question 31. Consider a tetrahedron ABCD with AB = SA = 2a. trực tiếp bóng đá k+ distance from line AD to trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following statements is false?
A. trực tiếp bóng đá k+ volume of a pyramid with base area B and height h is (V = \frac{1}{3}Bh).
B. trực tiếp bóng đá k+ volume of a prism with base area B and height h is (V = Bh).
C. trực tiếp bóng đá k+ volume of a rectangular box is trực tiếp bóng đá k+ product of its three dimensions.
D. trực tiếp bóng đá k+ 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, trực tiếp bóng đá k+ volume of trực tiếp bóng đá k+ given pyramid is
A. (4a^3).
B. (\frac{2a^3}{3}).
C. (2a^3).
D. (\frac{4a^3}{3}).
Question 34. trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ base, (SA = 2a). In terms of a, trực tiếp bóng đá k+ volume V of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ value of (log_x \frac{2y}{x^4 \sqrt{y}}).
b) Find integer m so that trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ projection of A onto SB.
a) Prove that (AH \perp (SBC)).
b) Calculate trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two planes (SAC) and (SBC), knowing that SA = AB = a.
Exercise 3. (1.0 point) Consider trực tiếp bóng đá k+ pyramid S.ABCD where trực tiếp bóng đá k+ base is trực tiếp bóng đá k+ rectangle with (AB = a), (BC = a\sqrt{3}). Both planes (SAC) and (SBD) are perpendicular to trực tiếp bóng đá k+ base. A point I is located on SC such that SC = 3IC. Calculate trực tiếp bóng đá k+ distance between trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following results?
A. a6.
B. a32a32.
C. a23a23.
D. a16a16.
Question 3. Given α is any real number, which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ equation 3√a2√aa3=aα,0<a≠1a2a3a3=aα,0<a≠1. At that time, α belong to trực tiếp bóng đá k+ following range?
A. (-2; -1).
B. (-1; 0).
C. (-3; -2).
D. (0; 1).
Question 5. Ms. Ha deposited 20 000 000 VND into trực tiếp bóng đá k+ bank with an interest rate of 0.5%/month (after each month, trực tiếp bóng đá k+ interest is entered into trực tiếp bóng đá k+ principal to calculate trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ value of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ positive real numbers that satisfy a2 = bc. trực tiếp bóng đá k+ value of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ above functions?
A. 5.
B. 4.
C. 3.
D. 2.
Question 13. trực tiếp bóng đá k+ defining set of trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ graph of functions y=ax,y=bx,y=cxy=ax,y=bx,y=cx is given in trực tiếp bóng đá k+ following figure.
Which of trực tiếp bóng đá k+ following propositions is true?
A. b < c < a.
B. c < a < b.
C. a < b < c.
D. a < c < b.
Question 15. trực tiếp bóng đá k+ curve in trực tiếp bóng đá k+ side figure is a graph of one of trực tiếp bóng đá k+ four functions listed in trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ solution of trực tiếp bóng đá k+ equation 7x = 2 is
A. x=log72x=log72.
B. x=log27x=log27.
C. x=27x=27.
D. x=√7x=7.
Question 17. trực tiếp bóng đá k+ solution of trực tiếp bóng đá k+ equation log3(5x)=2log35x=2 is
A. x=85x=85.
B. x = 9.
C. x=95x=95.
D. x = 8.
Question 18. trực tiếp bóng đá k+ experiment of trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ experiment of trực tiếp bóng đá k+ inequalities 2x−3162x−3 16 is
A. [7;+∞)7;+∞.
B. (0;+∞)0;+∞.
C. (7;+∞)7; +∞.
D. (3;+∞)3;+∞.
Question 20. Knowing that trực tiếp bóng đá k+ equation 4x−9⋅2x+16=04x−9⋅2x+16=0 has two differential solutions x1 and x2. Calculate trực tiếp bóng đá k+ value of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following statements is true?
A. trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines m and n is trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines a and b passing through trực tiếp bóng đá k+ same point and corresponding to m and n.
B. trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines m and n is trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines m and b perpendicular to n.
C. trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines m and n is trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines a and b perpendicular to m and n, respectively.
D. trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines m and n is trực tiếp bóng đá k+ angle between any two lines a and b.
Question 22. In space, give two lines a and b. Which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ angle between them is 90°.
C. Lines a and b are perpendicular to each other if and only if trực tiếp bóng đá k+ angle between them is equal to 45°.
D. Lines a and b are perpendicular to each other if and only if trực tiếp bóng đá k+ angle between them is 0°.
Question 23. For trực tiếp bóng đá k+ cube ABCD. A'B'C'D'
trực tiếp bóng đá k+ angle between trực tiếp bóng đá k+ two lines AB and A'C' is equal to
A. 60°.
B. 45°.
C. 90°.
D. 30°.
Question 24. For trực tiếp bóng đá k+ cube ABCD. A'B'C'D'
Which of trực tiếp bóng đá k+ following lines perpendicular to trực tiếp bóng đá k+ BC' line?
A. A'D.
B. AC.
C. BB'.
D. AD'.
Question 25. In trực tiếp bóng đá k+ space for trực tiếp bóng đá k+ line d perpendicular to every line a is in trực tiếp bóng đá k+ plane (α). Which of trực tiếp bóng đá k+ following assertions is true?
A. d // (α).
B. d⊥(α).
C. d⊂(α).
D. d cut α.
Question 26. For trực tiếp bóng đá k+ ABCD quadruple with AB, AC, AD double one perpendicular to each other
Which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ correct clause in trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ pyramid S.ABCD with trực tiếp bóng đá k+ bottom ABCD being rectangular, SA⊥(ABCD). Call M and N trực tiếp bóng đá k+ midpoints of AB and SB respectively (refer to trực tiếp bóng đá k+ drawing).
Which of trực tiếp bóng đá k+ following assertions is true?
A. AC⊥(SAD).
B. MN⊥(SBD).
C. BD⊥(SCD).
D. MN⊥(ABCD).
Question 29. Given trực tiếp bóng đá k+ pyramid S.ABCD has a square base, SA perpendicular to trực tiếp bóng đá k+ plane (ABCD). Let H be trực tiếp bóng đá k+ perpendicular projection of A to trực tiếp bóng đá k+ plane (SBC).
Which of trực tiếp bóng đá k+ following affirmations is true?
A. H is trực tiếp bóng đá k+ base of trực tiếp bóng đá k+ road at a perpendicular descent from A to SB.
B. H is trực tiếp bóng đá k+ center of gravity of trực tiếp bóng đá k+ SBC triangle.
C. H coincides with B.
D. H is trực tiếp bóng đá k+ midpoint of SB.
Question 30. For two planes (α), (β). Which of trực tiếp bóng đá k+ 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. trực tiếp bóng đá k+ number of side edges of a quadrilateral pyramid is
A. 3.
B. 4.
C. 6.
D. 12.
Question 32. Give trực tiếp bóng đá k+ line a perpendicular to trực tiếp bóng đá k+ plane (α) and a⊂(β). Which of trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ following clauses is true?
A. If trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ pyramid S.ABC with trực tiếp bóng đá k+ bottom is a right triangle at B, SA perpendicular to trực tiếp bóng đá k+ bottom
Which of trực tiếp bóng đá k+ following assertions is false?
A. (SAB)⊥(ABC).
B. (SAB)⊥(SAC).
C. (SAC)⊥(ABC).
D. (SAB)⊥(SBC).
Question 35. Give trực tiếp bóng đá k+ triangle ABC weighed at A with high lines AH=a√3,BC=3aAH=a3, BC=3a, BC contained in trực tiếp bóng đá k+ plane (P). Let's call A' trực tiếp bóng đá k+ perpendicular projection of A onto trực tiếp bóng đá k+ plane (P) (as shown in trực tiếp bóng đá k+ side drawing). Know trực tiếp bóng đá k+ triangle A'BC is square at A'. Call φφ trực tiếp bóng đá k+ angle between (P) and (ABC).
Select trực tiếp bóng đá k+ correct affirmation in trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ value of trực tiếp bóng đá k+ expression M=(3+2√2)2019⋅(3√2−4)2018M=3+222019⋅32−42018.
b) Find all trực tiếp bóng đá k+ real values of trực tiếp bóng đá k+ parameter m so that trực tiếp bóng đá k+ function y=log(x2−2mx+4)y=logx2−2mx+4 has a defined setof R.
Lesson 2.(1.0 points) Let trực tiếp bóng đá k+ ABCD tetrahedron have a triangle ABC weighted at A, trực tiếp bóng đá k+ triangle BCD weighted at D. Let I be trực tiếp bóng đá k+ midpoint of trực tiếp bóng đá k+ BC side.
a) Prove that BC⊥(AID).
b) Call AH trực tiếp bóng đá k+ high line of trực tiếp bóng đá k+ AID triangle.Prove that AH⊥BD.
Lesson 3.(1.0 points) trực tiếp bóng đá k+ growth of a bacterial species is calculated according to trực tiếp bóng đá k+ formula f(t)=Aertft=Aert, where A is trực tiếp bóng đá k+ initial number of bacteria, r is trực tiếp bóng đá k+ growth rate (r 0), t (in hours) is trực tiếp bóng đá k+ growth time. Knowing trực tiếp bóng đá k+ number of bacteria initially had 1 000 and after 10 hours it was 5 000. Why does it take for trực tiếp bóng đá k+ number of bacteria to increase 10 times?
Note: Information is only for reference!
What are trực tiếp bóng đá k+ newest sample 2nd mid-semester question papers and answers for 11th-grade Mathematics in 2025? What are trực tiếp bóng đá k+ bases for assessing trực tiếp bóng đá k+ training results of 11th-grade students in Vietnam? (image from Internet)
What are trực tiếp bóng đá k+ bases for assessing trực tiếp bóng đá k+ training results of 11th-grade students in Vietnam?
Under Clause 1 Article 8Circular 22/2021/TT-BGDDT, trực tiếp bóng đá k+ basis for assessing trực tiếp bóng đá k+ training results of 11th-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 trực tiếp bóng đá k+ 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 trực tiếp bóng đá k+ above section.
What are theassessment levels for learning results in trực tiếp bóng đá k+ whole school year of 11th-grade students in Vietnam?
According to Clause 2, Article 9 ofCircular 22/2021/TT-BGDDT, 04 assessment levels for learning results in trực tiếp bóng đá k+ 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 DTBmhkand DTBmcnwith 6 subjects among which have minimum scores of 8.0 for DTBmhkand 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 DTBmhkand DTBmcnwith 6 subjects among which have minimum scores of 6.5 for DTBmhkand 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 DTBmhkand DTBmcnwith 0 subjects have scores lower than 3.4 for DTBmhkand DTBmcn.
4) Unqualified: Remaining cases.
