SAT® Math Sample Test - Đề thi thử có đáp án gợi ý

SAT là một trong những chứng chỉ uy tín được công nhận tại nhiều trường học trên thế giới. Bài thi SAT bao gồm 2 phần: Math và Reading & Writing. Trong đó, phần thi Math đòi hỏi người học phải luyện tập nhiều để làm quen với các dạng toán và thành thạo cách giải. Bài viết dưới đây sẽ cung cấp một đề thi thử SAT Math với cấu trúc bám sát với đề thi Digital SAT mới nhất kèm đáp án tham khảo, qua đó người học có thể tự ôn luyện để chuẩn bị cho kỳ thi.

Theo College Board [1], cấu trúc đề thi Digital SAT Math bao gồm 44 câu hỏi chia thành 2 module với các dạng toán được phân bố như sau:

• Algebra (Đại số): 13-15 câu

• Advanced Math (Toán nâng cao): 13-15 câu

• Problem Solving and Data Analysis (Giải quyết vấn đề và phân tích dữ liệu): 5-7 câu

• Geometry and Trigonometry (Hình học và lượng giác): 5-7 câu

SAT Math Sample Test - Đề thi thử

Bài thi digital SAT Math hiện nay được thiết kế theo hình thức adaptive testing bao gồm 2 module. Độ khó của các câu hỏi thuộc module 2 được hệ thống lựa chọn dựa trên kết quả của thí sinh trong module 1 sao cho phù hợp với trình độ của thí sinh đó. Trong đề thi dưới đây, module 2 có độ khó thuộc mức dễ-trung bình, phù hợp với người học cấp độ 1000.

Module 1

Question 1:

5(3x+2)=40

Which equation has the same solution as the given equation?

A. 3x+2=8
B. 3x+2=40
C. 3x+10=40
D. 3x+10=8

Question 2:

If 6x−15=21, what is the value of x+2?

A. 3
B. 5
C. 7
D. 8

Question 3:

A catering company charges customers based on the number of standard meals and premium meals they order. The total cost is given by the equation: 5s+8p=52, where s is the number of standard meals and p is the number of premium meals. If a customer ordered 4 standard meals, how many premium meals were ordered?

A. 4
B. 5
C. 6
D. 7

Question 4:

A factory produces two types of items: gadgets and widgets. It takes 2.4 hours to manufacture one gadget and 3.2 hours to manufacture one widget. If the factory spent a total of 72 hours producing g gadgets and w widgets, which equation represents this situation?

A. 3.2g+2.4w=72
B. 2.4g+3.2w=72
C. g+w=72
D. 24g+32w=72

Xem thêm: Tổng hợp từ vựng SAT Math theo chủ đề [PDF]

Question 5:

The total cost g(x), in dollars, to rent a workspace for 24 months is given by the equation: g(x)=24x+500, where x represents the monthly rent payment in dollars. What is the total cost when the monthly payment is $350?

A. $8,900
B. $9,500
C. $8,400
D. $9,900

Question 6:

The function f(x) is given by: f(x)=5x+20. The graph of y=f(x) in the xy-plane has an x-intercept at (a,0) and a y-intercept at (0,b), where a and b are constants. What is the value of a+b?

A. 18
B. 16
C. 24
D. 25

Question 7:

The graph of a system of linear equations is shown below. What is the solution (x,y) to the system?

A. (2,6)
B. (3,5)
C. (4,4)
D. (5,3)

Question 8:

Lisa has two bags of marbles. In the first bag, 40% of the marbles are blue, and in the second bag, 60% of the marbles are blue. Together, the two bags contain at least 500 blue marbles.

Which inequality represents this relationship, where x is the total number of marbles in the first bag and y is the total number of marbles in the second bag?

A. 0.4x + 0.6y ≥ 500
B. 0.6x + 0.4y ≤ 500
C. x/4 + y/6 ≤ 500
D. 40x + 60y ≥ 500

Question 9:

If p=4x+3 and v=x+2, which of the following is equivalent to pv−3p+2v?

A. 4x²+2x+1
B. 4x²+x+2
C. 4x²+2x+2
D. 4x²+x+1

Question 10:

x²−4x−7=0

One solution to the equation above can be written as \(2+\sqrt{k}\), where k is a constant. What is the value of k?

A. 3
B. 5
C. 7
D. 11

Question 11:

The function Q(t)=15.2(1.042)^t gives the predicted population, in millions, of a certain city for the period from 1990 to 2025, where t is the number of years after 1990.

According to the model, what is the best interpretation of the statement “Q(10) is approximately equal to 22.5”?

A. In 1990, the predicted population of this city was approximately 22.5 million.
B. In 1990, the predicted population of this city was approximately 10 million.
C. 10 years after 1990, the predicted population of this city was approximately 22.5 million.
D. 22.5 years after 1990, the predicted population of this city was approximately 10 million.

Question 12:

Which of the following expressions is(are) a factor of 2x²+5x-3?

I. x+3
II. 2x−1

A. I only
B. II only
C. I and II
D. Neither I nor II

Question 13:

If r and s are the two solutions of the equation below, what is the value of r+s?

3x²−7x+2=0

A. 7/3
B. −7/3​
C. 2/3​
D. −2/3​

Question 14:

If ∣5x−7∣=85, what is the positive value of x-2?

Question 15:

The graph of a system of a linear function and a quadratic function is shown. What are the solutions (x;y) to this system of two equations?

A. (-1;2) and (2;-1)
B. (0;2) and (2;0)
C. (1; 2) and (2; 1)
D. (-1;-2) and (-2;-1)

Question 16:

A factory machine produces items at a constant rate of 75 items per hour. At this rate, how many items will the machine produce in 4 hours?

Question 17:

The table below shows the average price of a gallon of gasoline in different years.

What was the percent increase in the average gas price from 1990 to 2000?

A. 25%
B. 34.5%
C. 40%
D. 50%

Question 18:

The table below shows the prices of one gallon of milk at five different grocery stores on the same day.

What is the median price of the milk prices recorded?

A. $3.79
B. $3.89
C. $3.94
D. $3.99

Question 19:

A cube-shaped container has edges that are 15 inches long. Each face of the container is a square, and the container is open at the top. What is the exterior surface area of this open container in square inches?

Question 20:

In △ABC, the measure of ∠A is 35°, and the measure of ∠B is 48°. What is the measure of ∠C?

A. 87°
B. 97°
C. 107°
D. 113°

Question 21:

For the right triangle shown, which of the following expressions represents the value of the b?

A. \(\sqrt{17^2-8^2}\)

B. \(17^2-8^2\)

C. \(\sqrt{17^{}-8^{}}\)

D. 17−8

Question 22:

In the xy-plane, a circle with radius 7 has center (4, -3). Which of the following is an equation of the circle?

A. (x−4)²+(y+3)²=49

B. (x+4)²+(y−3)²=49

C. (x−4)²+(y+3)²=7

D. (x+4)²+(y−3)²=7

Tham khảo thêm: SAT Math formulas - Tổng hợp các công thức thường gặp trong SAT Math

Module 2

Question 1:

For what value of b does the equation have no solution?

5x+7=b(x+2)+3

A. 5
B. 4
C. 7
D. 3

Question 2:

Line q is defined by the equation:

3y+12x=15

Line s is perpendicular to line q in the xy-plane. What is the slope of line s?

A. −4-
B. −1/4
C. 1/4​
D. 4

Question 3:

A city's population was 40,000 in the year 2000 and 88,000 in the year 2015. Assuming the population grows at a constant rate, estimate the population in 2025 to the nearest whole number.

A. 104,000
B. 112,000
C. 120,000
D. 128,000

Question 4:

A plumber charges a flat fee of $150 for the first hour of service and an additional hourly rate for each extra hour. The total charge for 4 hours of service is $390. Which function f gives the total cost, in dollars, for x hours of service, where x≥1?

A. f(x)=80x+70
B. f(x)=80x+150
C. f(x)=120x
D. f(x)=120x+150

Question 5:

\(\frac32y-\frac14x=\frac56-\frac32y\)

\(\frac12x+\frac32=qy+\frac92\)

In the given system of equations, q is a constant. If the system has no solution, what is the value of q?

A. 2
B. 3
C. 6
D. 8

Question 6:

A number a is at most 5 less than 4 times the value of b. If the value of b is −3, what is the greatest possible value of a?

Question 7:

A company requires employees to complete 120 hours of training. The equation 8x+12y=120 represents this situation, where x is the number of in-person training sessions and y is the number of virtual training sessions an employee has attended. How many more hours does each virtual training session take than each in-person training session?

Question 8:

In the expression 4(3x²+qx+5)−10x(q+2), q is a constant. This expression is equivalent to the expression 12x²−98x+20. What is the value of q?

A. −4
B. 6
C. 8
D. 13

Question 9:

How many distinct real solutions does the given equation have?

x²−8x+16=0

A. Exactly two
B. Exactly one
C. Zero
D. Infinitely many

Question 10:

q(x)+42=x²

The given equation relates the value of x and its corresponding value of q(x) for the function q. What is the minimum value of the function q?

A. −1,764
B. −42
C. 42
D. 1,764

Question 11:

(x−5)(x+3)(x−2)=0

What is the product of the solutions to the given equation?

A. 10
B. -30
C. -10
D. 30

Question 12:

The expression below can be written in the form ay²+b, where a and b are constants.

(6400+80y²)+5(20y²−500)

What is the value of a+b?

Đọc thêm: Phương pháp giải các dạng bài trong SAT Math (P1)

Question 13:

In the equation below, m and k are positive constants: y=mx²−k

How many times does the graph of this equation intersect the graph of the equation y=m−k in the xy-plane?

A. Zero
B. One
C. Two
D. More than two

Question 14:

Which function illustrates the graph below?

A. y=-x²+3x+2
B. y=x²+3x+2
C. y=-x²+2
D. y=x²+2

Question 15:

The function g is defined by g(x)=−(a^x)+b, where a and b are constants. In the xy-plane, the graph of y=g(x)−15 has a y-intercept at (0,−85/9). The product of a and b is 425/9​. What is the value of a?

A. 59/9
B. 425/59
C. 59/425
D. 9/59

Question 16:

The scatterplot below shows the relationship between two variables, x and y. A line of best fit is also drawn. Determine which of the following is closest to the slope of the line of best fit.

A. 0.825
B. 0.75
C. 0.45
D. 0.1875

Question 17:

A pet adoption center collected data on the fur pattern and eye color of 60 puppies available for adoption. The data is summarized in the table below.

What fraction of the solid-colored puppies have blue eyes?

A. 10/60
B. 10/28
C. 10/30
D. 18/30

Question 18:

A local library surveyed a class of 30 students about their reading habits. 40% of the students reported that they borrowed at least one book from the library in the past month. The average class size in the school district is 30, and there are 2,000 classes in the district. If this class is representative of all students in the district, which of the following best estimates the number of students in the district who did not borrow a book from the library in the past month?

A. 24,000
B. 30,000
C. 36,000
D. 48,000

Question 19:

Residents of a town were surveyed to determine whether they were satisfied with their internet service provider. A random sample of 300 residents was selected. All 300 responded, and 82% said they were satisfied. Based on this information, which of the following statements must be true?

I. Among all town residents, 82% would report being satisfied with their internet service provider.
II. If another random sample of 300 residents were surveyed, 82% would report being satisfied.

A. Neither
B. I only
C. II only
D. I and II

Question 20:

A right circular cylinder has a radius of r and a height of h. A second right circular cylinder has a volume that is 300 times as large as the volume of the first cylinder.

Which of the following could represent the radius R, in terms of r, and the height H, in terms of h, of the second cylinder?

A. R=10r and H=3h
B. R=5r and H=12h
C. R=6r and H=8h
D. R=15r and H=2h

Question 21:

In the figure below, line m is parallel to line n, and both are intersected by transversal t. The angle formed at the intersection of t and m is 65°. Another angle on line n is labeled as y.

If y=2x+5, what is the value of x?

A. 65
B. 110
C. 55
D. 225

Question 22:

An isosceles right triangle has a hypotenuse of 40 inches. What is the perimeter, in inches, of this triangle?

A. \(20\sqrt2\)

B. \(40\sqrt2\)

C. \(40+40\sqrt2\)

D. \(40+80\sqrt2\)

Đáp án

Module 1

1. A

2. D

3. A

4. B

5. A

6. B

7. B

8. A

9. D

10. D

11. C

12. C

13. A

14. 82/5 or 16.4

15. A

16. 300

17. B

18. B

19. 1125

20. B

21. A

22. A

Module 2

1. A

2. C

3. C

4. A

5. C

6. -17

7. 4

8. D

9. B

10. B

11. B

12. 4080

13. C

14. A

15. B

16. D

17. C

18. C

19. A

20. A

21. C

22. C

Luyện tập thêm:

• Bài tập dạng bài lượng giác trong SAT Math kèm đáp án

• Bài tập dạng bài Phương trình tuyến tính trong SAT Math

• Bài tập về lũy thừa (Exponents) trong SAT Math có đáp án

Tổng kết

Bài viết trên đã cung cấp một đề thi thử SAT Math (Sample Test) theo cấu trúc Digital SAT kèm đáp án. Người học cần làm bài và kiểm tra đáp án cẩn thận cũng như tìm kiếm thêm các nguồn tài liệu ôn tập và đề thi thử khác để làm quen với nhiều dạng bài hơn. Người học có thể đăng ký tham gia các khoá học SAT tại ZIM Academy trong thời gian sắp tới để có cơ hội rèn luyện đầy đủ các phần Toán, Đọc hiểu và Viết với đội ngũ giảng viên giàu kinh nghiệm.

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