Untitled Presentation

Multiple Choice

Which of the following statements about the number of ways to select and arrange k elements from a set of n elements is correct?

• The number of ways is given by n!/(n-k)! for both selection and arrangement.

• The number of ways to select is n!/(k!(n-k)!), and to arrange is n!/(n-k)!

• The number of ways to select is n!/(n-k)!, and to arrange is n!/(k!(n-k)!)

• The number of ways to select is k!/(n-k)!, and to arrange is n!/(n-k)!

Multiple Choice

Which of the following topics is most likely to help you solve problems involving the area and volume of 3D shapes?

• Bất phương trình bậc nhất hai ẩn

• Hình học phẳng

• Nhị thức Newton

• Giá trị lượng giác của một góc

Open Ended

Why is it important to have a strong foundation in mathematics before studying advanced topics in grade 12?

Open Ended

Explain the process of dividing the polynomial x^2 - 2x + 2 by x + 1 and interpret the result.

Multiple Choice

Which of the following is a correct factorization of the expression (A^2 - B^2)?

• (A + B)(A - B)

• (A + B)^2 - 2AB

• (A - B)^2 + 2AB

• (A^2 + B^2)

Fill in the Blank

The Pythagorean theorem states that in a right triangle, BC^2 = ___ + AC^2.

Multiple Select

Which of the following statements about similar triangles are correct?

• If three sides of one triangle are proportional to three sides of another triangle, the triangles are similar.

• If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

• If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are similar.

• If the ratio of the areas of two similar triangles is k^2, then the ratio of their corresponding sides is k.

Open Ended

Describe the conditions under which a plane and a sphere in space will not intersect.

Multiple Choice

Which of the following best describes the centroid of a triangle?

• The intersection of the medians

• The intersection of the altitudes

• The intersection of the angle bisectors

• The intersection of the perpendicular bisectors

Multiple Choice

What is the formula for the surface area of a sphere with radius R?

• S = 2πR^2

• S = 4πR^2

• S = πR^2

• S = 3πR^2

Fill in the Blank

The cross-section of a cone when cut by a plane perpendicular to its axis is a ___

Multiple Choice

Which of the following are formulas for the volume of a cone with base radius r and height h?

• V = πr^2h

• V = 1/3πr^2h

• V = 2πrh

• V = 1/2πr^2h

Open Ended

Explain the difference between a mặt nón tròn xoay (rotational cone) and a hình nón tròn xoay (rotational cone shape) as described in the images.

Multiple Choice

Given a cylinder with height h and base radius r, what is the formula for its lateral surface area?

• S = 2πrh

• S = πr^2h

• S = 2πr^2

• S = πrh

Open Ended

Describe how the area of a parallelogram and a rhombus are calculated and compare their formulas.

Multiple Select

Which of the following are correct ways to specify a set?

• Listing all elements.

• Describing a property that elements satisfy.

• Using a Venn diagram.

• Using a formula.

Multiple Choice

Which of the following statements best describes a subset?

• A subset contains all elements of another set.

• A subset contains some or all elements of another set.

• A subset contains only one element of another set.

• A subset contains no elements of another set.

Fill in the Blank

The set of all real numbers is denoted by ___ .

Multiple Choice

What is the result of the intersection of two sets A and B?

• All elements in A or B

• All elements in A and B

• All elements not in A or B

• All elements in A but not in B

Open Ended

Explain how to determine the solution set (miền nghiệm) for a linear inequality in two variables.

Multiple Choice

Which condition must be true for the function f(x) = 1/√A to be defined?

• A > 0

• A < 0

• A = 0

• A ≠ 0

Open Ended

Explain how the sign of the coefficient 'a' in the quadratic function y = ax^2 + bx + c affects the direction in which the parabola opens.

Multiple Choice

Which of the following statements about the vertex of the quadratic function y = ax^2 + bx + c is correct?

• The vertex is at (b/2a, Δ/4a)

• The vertex is at (-b/2a, -Δ/4a)

• The vertex is at (b/2a, -Δ/4a)

• The vertex is at (-b/2a, Δ/4a)

Fill in the Blank

Fill in the blank: The discriminant of the quadratic equation ax^2 + bx + c = 0 is given by Δ = ___ .

Open Ended

According to Viète's formulas, if x1 and x2 are the roots of ax^2 + bx + c = 0, what is the value of x1 + x2 and x1*x2 in terms of a, b, and c?

Multiple Choice

Which of the following conditions must be satisfied for the quadratic equation ax^2 + bx + c = 0 to have two distinct real roots?

• Δ < 0

• Δ = 0

• Δ > 0

• a = 0

Multiple Choice

Which of the following topics is NOT mentioned in the table of contents for the mathematics handbook?

• Hàm số bậc ba

• Bất phương trình bậc nhất hai ẩn

• Nhị thức Newton

• Hình học phẳng

Open Ended

After studying the topics listed in the table of contents, which area of mathematics do you feel most confident about, and which area would you like to explore further?