Free SAT Maths Test Practice Questions with Answers
Sample 1

A set of 25 Maths questions, with answers and detailed solutions similar to the questions in the SAT maths test. The answers are at the bottom of the page.

1. What is the area, in square feet, of the triangle whose sides have lengths equal to 10, 6 and 8 feet?
   A) 480
   B) 24
   C) 48
   D) 30
   E) 40
   

2. 3¹⁰² + 9×3¹⁰⁰ + 3¹⁰³/3 = ?
   A) 3¹⁰¹
   B) 3¹⁰²
   C) 3¹⁰³
   D) 3¹⁰⁴
   E) 3¹⁰⁵
   

3. Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are not studying any of the three languages?
   A) 27
   B) 18
   C) 53
   D) 62
   E) 36
   

4. In the figure below, AB is a diameter of the large circle. The centers C1 and C2 of the smaller circles are on AB. The two small circles are congruent and tangent to each other and to the larger circle. The circumference of circle C1 is 8 π. What is the area of the large circle?
   

   .

   
   A) 64π
   B) 32π
   C) 156π
   D) 128π
   E) 16π
   

5. Round (202)² to the nearest hundred.
   A) 40,000
   B) 48,000
   C) 40,800
   D) 47,000
   E) 49,000
   

6. If w workers, working at equal rates, can produce x toys in n days, how many days it takes c workers, working at same equal rates, to produce y toys?
   A) y·x·c / w
   B) y·w·c /(w·n)
   C) y·w/(w·n·c)
   D) y·w·n / x
   E) y·w·n / (x·c)
   

7. A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.
   A) 5
   B) 7
   C) 6
   D) 8
   E) 9
   

8. Find a negative value of x that satisfies the equation
   [(x+1)² - (2x + 1)]^1/2 + 2|x| - 6 = 0
   A) -5
   B) -4
   C) -3
   D) -2
   E) -1
   

9. The equation 1/a + 1/|a| = 0 has
   A) an infinite number of solutions
   B) no solutions
   C) 1 solution only
   D) 2 solutions only
   E) 3 solutions only
   

10. The inequality x² - 2x + 1 ≤ 0 has
    A) no solutions
    B) a set of solutions
    C) 1 solution only
    D) 2 solutions only
    E) 3 solutions only
    

11. In the figure below, AC is parallel to DE. AE, FG and CD intersect at the point B. FG is perpendicular to AC and DE. The length of DE is 5 inches, the length of BG is 8 inches and the length of AC is 6 inches. What is the area, in square inches, of triangle ABC?
    

    .

    
    A) 28.8
    B) 20
    C) 24
    D) 15
    E) 36
    

12. Points A, B and C are defined by their coordinates in a standard rectangular system of axes. What positive value of b makes triangle ABC a right triangle with AC its hypotenuse?
    

    .

    
    A) 4
    B) 6
    C) √6
    D) 1 + √6
    E) 1 + 2√3
    

13. Line L passes through the points (-2,0) and (0,a). Line LL passes through the points (4,0) and (6,2). What value of a makes the two lines parallel?
    A) 1/2
    B) -2
    C) 2
    D) -1/2
    E) 0
    

14. a, b, c and d are numbers of different values such that
    a + b = d
    a·b·c = 0
    Which of the 4 numbers MUST be equal to 0?
    
    A) a
    B) b
    C) c
    D) d
    E) none
    

15. 10⁴(5⁴ - 2⁴) / 21 =
    
    
    A) 10,000
    B) 209,000
    C) 289,000
    D) 290,000
    E) 40,000
    

16. For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution?
    
    
    A) 6
    B) 2
    C) 17
    D) -1
    E) 20
    

17. An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?
    
    
    A) 360
    B) 370
    C) 367.5
    D) 600
    E) 960
    

18. 4 / (√20 - √12) =
    
    
    A) 1
    B) 1/2
    C) 4 / √8
    D) √5 - √3
    E) √5 + √3
    

19. In the figure below, DE is parallel to CB and the ratio (length of AE / length of EB) is 4. If the area of triangle AED is 20 square inches, what is the area, in square inches, of triangle ABC?
    

    .

    
    A) 31.25
    B) 80
    C) 320
    D) 1,600
    E) The area of triangle ABC cannot be determined from the given information.
    

20. If f(n) = n + √n, where n is a positive integer, which of the following would be a value of f(n)?
    I) 5
    II) 10
    III) 12
    
    
    A) III only
    B) None
    C) I and III only
    D) I, II and III only
    E) II and III only
    

21. If a and b are both even numbers, which of the following COULD be and odd integer?
    
    
    A) (a + b)²
    B) a² + b²
    C) (a + 1)² + (b + 1)²
    D) (a + 1)*(b + 1) - 1
    E) (a + 1) / (b + 1)
    

22. If x is a negative number, which of the following must be true?
    I) x⁵ < |x|
    II) x < √(-x)
    III) x - 1/|x| < 0
    A) I, II and III
    B) I and II only
    C) None
    D) II and III only
    E) I and III only
    

23. If n is a positive integer such that n! / (n - 2)! = 342, find n.
    
    
    A) 15
    B) 16
    C) 17
    D) 18
    E) 19
    

24. What is the sum of the reciprocals of the solutions to the equation
    x² - (3/5)x = -11/3
    A) 3/5
    B) 5/3
    C) 9/55
    D) -11/3
    E) 94/65
    

25. A number is given as 987562153ab where a and b are digits. Which values of a and b, such that
    
    a + b = 11 and a < b,
    
    would result in 987562153ab being divisible by 4?
    A) a = 0 , b = 8
    B) a = 3 , b = 8
    C) a = 7 , b = 8
    D) a = 5 , b = 6
    E) a = 3 , b = 4

1. B
2. C
3. E
4. A
5. C
6. E
7. B
8. D
9. A
10. C
11. A
12. D
13. C
14. C
15. D
16. C
17. B
18. E
19. A
20. A
21. E
22. A
23. E
24. C
25. D