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Majorship LET Reviewer

LET Reviewer for Mathematics
LET Reviewer for Mathematics

PRACTICE TEST IN MATHEMATICS

1. What is the slope of the line passing through the points (2,3) and (4,7)?
A) 2
B) 4
C) 5
D) 7

Answer: A) 2

2. If f(x) = x^2 + 4x + 3, what is f(1)?
A) 0
B) 3
C) 8
D) 10

Answer: B) 3

3. What is the solution to the equation 2x + 5 = 11?
A) 2
B) 3
C) 6
D) 7

Answer: B) 3

4. What is the value of sin(45°) + cos(45°)?
A) 0
B) 1
C) √2
D) 2

Answer: C) √2

5. What is the value of log(100) base 10?
A) 1
B) 2
C) 10
D) 100

Answer: B) 2

6. What is the value of (3 + 4i)(2 - i)?
A) 2 + 5i
B) 5 + 10i
C) 10 + 5i
D) 10 + 11i

Answer: D) 10 + 11i

7. What is the area of a circle with a radius of 5 cm?
A) 25π cm^2
B) 50π cm^2
C) 100π cm^2
D) 125π cm^2

Answer: C) 100π cm^2

8. If a rectangle has a length of 8 cm and a width of 3 cm, what is its perimeter?
A) 6 cm
B) 14 cm
C) 16 cm
D) 22 cm

Answer: C) 22 cm

9. What is the value of tan(60°)?
A) √3/2
B) 1/2
C) √2/2
D) 2/√3

Answer: A) √3/2

10. What is the solution to the equation x^2 - 3x - 10 = 0?
A) x = -2, x = 5
B) x = -5, x = 2
C) x = -2, x = -5
D) x = 2, x = 5

Answer: A) x = -2, x = 5

11. What is the equation of the line that passes through the point (3,-2) and has a slope of 4?
A) y = 4x - 14
B) y = 4x - 10
C) y = 4x + 10
D) y = 4x + 14

Answer: D) y = 4x + 14

12. If g(x) = 2x - 5, what is g(4)?
A) -7
B) -3
C) 3
D) 7

Answer: C) 3

13. What is the solution to the equation 3x - 2 = 13?
A) 3
B) 5
C) 7
D) 8

Answer: B) 5

14. What is the value of cos(60°)?
A) 0
B) 1/2
C) √2/2
D) 1

Answer: B) 1/2

15. What is the value of log(1) base 10?
A) 0
B) 1
C) -1
D) undefined

Answer: A) 0

16. What is the value of (2 + 3i)(-1 + 4i)?
A) -14 + 5i
B) -10 + 5i
C) -10 - 5i
D) -14 - 5i

Answer: C) -10 - 5i

17. What is the area of a square with a side length of 6 cm?
A) 6 cm^2
B) 12 cm^2
C) 18 cm^2
D) 36 cm^2

Answer: D) 36 cm^2

18. If a triangle has sides of lengths 5 cm, 8 cm, and 10 cm, what is its perimeter?
A) 8 cm
B) 18 cm
C) 23 cm
D) 25 cm

Answer: D) 25 cm

19. What is the value of sin(30°)?
A) 1/2
B) √2/2
C) √3/2
D) 2/√3

Answer: A) 1/2

20. What is the solution to the equation 2x^2 - 7x + 3 = 0?
A) x = 1/2, x = 3
B) x = -1/2, x = 3/2
C) x = 1/2, x = 2
D) x = -1/2, x = 3

Answer: C) x = 1/2, x = 2

21. What is the equation of the line that passes through the points (-3,5) and (1,-1)?
A) y = -x + 2
B) y = -x - 2
C) y = x + 2
D) y = x - 2

Answer: B) y = -x - 2

22. If h(x) = x^3 - 4x, what is h(2)?
A) -4
B) 0
C) 4
D) 8

Answer: D) 8

23. If f(x) = (x^2 + 1) / (x - 2), what is the sum of the x-intercepts of the graph of f(x)?
a) 0
b) 2
c) 4
d) 6

Answer: a) 0

24. What is the value of the expression (log(base 2) 5)^(log(base 5) 2)?
a) 1/2
b) 1
c) 2
d) 2.5

Answer: b) 1

25. A fair six-sided die is rolled four times. What is the probability that the product of the numbers rolled is a perfect square?
a) 1/12
b) 11/54
c) 11/72
d) 16/81

Answer: c) 11/72


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