Train Set 2 - Authentic Problems for Perfect Score

Q: What topics does Train Set 2 practice in the geometry section?

It practices equilateral triangle perimeter-area relationships, right triangle similarity with tangent-based calculations, and reading coordinates from the unit circle using an angle.

Q: How does Train Set 2 assess algebraic reasoning with systems and constants?

It includes problems where a linear and a quadratic equation must have exactly one common solution, requiring solving for an unknown constant.

Q: How is probability handled in the conditional probability question?

A random student is selected from 100 students, and the probability of living less than 4 km is computed given that the student is a boy, using the table counts.

Aug 25, 2026

Uploaded by Skyler

Train Set 2 focuses on authentic problem-solving practice in SAT Math style. It covers geometry perimeter and area of equilateral triangles, algebraic manipulation of linear and polynomial systems, function behavior classification under growth rules, probability using conditional information, and composition of functions via tables. The set also includes similarity and trigonometry for triangle side ratios, unit-circle coordinate determination, and inequality constraints from triangle side lengths, ending with quadratic-function conditions.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Geometry and Similarity

Equilateral Triangle Perimeter-Area Relationship

Similar Right Triangles and Trigonometry

Unit Circle Coordinate from an Angle

Algebra and Functions

Linear and Polynomial Systems

Function Composition from Tables

Function Growth Behavior

Quadratic Function Vertex Conditions

Probability and Inequalities

Conditional Probability with a Table

Triangle Inequality Constraints

Train Set 2 Compiler: Mr. Yokubjon,telegram channel @sat800 1 Train Set 2.Authentic problems for perfect score 1. The perimeter of an equilateral triangle is 32 cm, and the area is M√3 cm2 , what is the value of M? A) ~~25~~9~~6 ~~B) ~~64~~9 C) ~~6~~8~~4~~1 D) ~~2~~8~~5~~1~~6~~ 2. 2 5k + 7m = (6m + n) 3 For the given equation, m, n and k are positive variables, what is the value of m, in terms of other variables? A) ~~2n+~~9~~15k~~ B) ~~4n~~~~k~~ C) 4nk D) ~~2n~~−9~~15k~~ 3. For right similar triangles ABC and DEF, the angles A and D are right angles. The angles B and C are corresponding to angles E and F. If tan(C) = 0 .75 and |DE| = 24cm, what is the length of EF, in cm? 1 Train Set 2 Compiler: Mr. Yokubjon,telegram channel @sat800 4. For x > 0, when x increases by 2 units f (x) increases by 0.8% . Which of the following could describe the function? A) Increasing linear B) Decreasing linear C) Increasing exponential D) Decreasing exponential 5. | | Less than 4 km | More than 4 km | Total | | --- | --- | --- | --- | | Boys
Girls
Total | 17
48
65 | 15
20
35 | 32
68
100 | A survey was conducted among 100 students from a certain school to determine how far students live from the school. If a student is chosen randomly, what is the probability that student lives less than 4 km from the school, given that the student is a boy? A) 1~~1~~0~~7~~0 B) ~~1~~6~~7~~5 C) ~~1~~3~~7~~2 D) ~~3~~10~~2~~0 6. For the system: y = x + 11 y = x2 + 11x + c where c is a constant. If the system has exactly one solution, what is the value of c? 7. A square base regular prism has height of 20 cm and surface area is A cm² . If we dye whole surface area except base, the dying area is ~~43~~46A cm² . What is the area of the base, in cm²? 2 Train Set 2 Compiler: Mr. Yokubjon,telegram channel @sat800 8. The functions f and g both have a domain of all real numbers. The table gives values for f(x) and g(x) at selected values of x. Which gives a solution to f (g(x)) = 4? | x | −2 | −1 | 0 | 1 | 2 | | --- | --- | --- | --- | --- | --- | | f (x)
g (x) | -4
-2 | -2
4 | -1
2 | -1
-4 | 4 3 | A) x = 0, because f(0) = −1 and g(−1) = 4 B) x = 0, because g(0) = 2 and f(2) = 4 C) x = 1, because f(1) = −1 and g(−1) = 4 D) x = 1, because g(1) = −4 and f(1) = −1 9. Point P lies on the unit circle and its position is determined by constructing an angle of ~~119~~6~~π~~ radians with the positive x-axis. What is the x-coordinate of Point P? A) −~~ ~~√2~~3~~ B) ~~2~~√3~~3 ~~C) √2~~3~~ D) − ~~1~~2 10. A content creator conducted a survey and selected a random sample of 800 Nepalese SAT Math students. The selected students were asked whether they approved of the change to a digital testing format, and 496 students responded that they approved of the new digital format. Which of the following is the largest population to which the results of the study can be generalized? A) The 800 Nepalese SAT Math students in the sample B) All Nepalese students C) All SAT Math students D) All Nepalese SAT Math students 3 Train Set 2 Compiler: Mr. Yokubjon,telegram channel @sat800 11. In triangle DEF, angle F is a right angle, point Q lies on DE , point J lies on EF, and QJ is parallel to DF. If the length of EF is 45 units, the length of FJ is 24 units, and the area of triangle DEF is 630 square units, what is the perimeter of triangle QEJ, in units? 12. 23 − 7x = √ 3k − 2x In the given equation, k is a constant. The equation has exactly one real solution. What is the minimum possible value of 56k? 13. The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. A triangle has side lengths of 4x + 20 , 2x + 8, and 7x − 11. Which inequality represents all possible values of x? A) x < 39 B) 8 < 2x < 78 C) 3 < x < 38 D) 23 < 5x < 195 14. f (x) = −2x2 + bx + c In the g

FAQs

What topics does Train Set 2 practice in the geometry section?

It practices equilateral triangle perimeter-area relationships, right triangle similarity with tangent-based calculations, and reading coordinates from the unit circle using an angle.

How does Train Set 2 assess algebraic reasoning with systems and constants?

It includes problems where a linear and a quadratic equation must have exactly one common solution, requiring solving for an unknown constant.

How is probability handled in the conditional probability question?

A random student is selected from 100 students, and the probability of living less than 4 km is computed given that the student is a boy, using the table counts.

Aug 25, 2026

Uploaded by Skyler