June 2024 High School Senior Mock Exam – Probability and Statistics

What is the value of ?

For the function , what is the value of ?

For the sequence , given that and , what is the value of ?

The graph of function is shown in the figure. What is the value of ?

For the function , what is the value of ?

What is the sum of all real values of such that the equation has exactly 2 distinct real roots?

For a geometric sequence where , given that what is the value of ?

For the function when the function is continuous on the entire set of real numbers, what is the value of the constant ?

When the area of the circumcircle of triangle ABC satisfying the following conditions is , what is the area of triangle ABC? (a) (b)

A cubic function with leading coefficient and satisfies When the -intercept of the tangent line to the curve at the point is , what is the value of ? (Note: is a constant.)

As shown in the figure, let A be a point in the first quadrant on the curve . Let B be the point where a line through point A parallel to the y-axis intersects the curve . Let C be the point where a line through point A parallel to the x-axis intersects the curve , and let D be the point where a line through point C parallel to the y-axis intersects the curve . When , what is the area of quadrilateral ABCD?

Let be the area of the region enclosed by the curve , the line , and the -axis, and let be the area of the region enclosed by the curve and the two lines and . When , what is the value of the constant ? (Given that )

What is the sum of all natural numbers that satisfy the following condition? The number of natural numbers such that is positive is .

For a cubic function with leading coefficient and a constant , the function satisfies the following conditions. (a) The function is increasing and differentiable on the set of all real numbers. (b) For all real numbers , and . What is the minimum value of ?

Find the value of real number that satisfies the equation .

For a function , given that and , find the value of .

Given that , find the value of the constant .

A point P starts from the origin at time t=0 and moves along a number line. The velocity v(t) of point P at time t (t ≥ 0) is given by: When the position of point P at the time when its direction of motion changes for the second time is 1, find the value of the positive constant k.

For two natural numbers not exceeding , let be the set of points where the graph of the function defined on the open interval intersects the line , and let be the sets of points where it intersects the lines respectively. For the ordered pairs such that , let be the maximum value of and be the minimum value. Find the value of .

The sequence satisfies , and for all natural numbers : Find the product of all values of such that .

How many ways are there to arrange the four numbers in a row?

Two events are mutually exclusive events and Find the value of .

What is the coefficient of in the expansion of the polynomial ?

When selecting one string at random from all possible strings that can be made by choosing 4 characters from the letters with repetition allowed and arranging them in a row, what is the probability that the selected string contains exactly one letter or exactly one letter ?

There are 6 chairs with natural numbers from 1 to 6 written on them, one number per chair. When arranging these 6 chairs in a circle at regular intervals, find the number of ways to arrange them such that the sum of the numbers on any two adjacent chairs does not equal 11. (Note: Arrangements that are identical after rotation are considered the same.)

There is a bag containing balls. Each ball is either white or black. When randomly drawing balls simultaneously from this bag, let be the probability of drawing white balls, be the probability of drawing white ball and black ball, and be the probability of drawing black balls. When , find the value of . (Note: )