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SAT Math - Advanced Math Practice Test

Test your SAT Math - Advanced Math skills with 30 random practice test questions. Great for students preparing for the SAT Math - Advanced Math Analysis section!

1 / 30

1. What is f⁻¹(x) if f(x) = 3x − 6?

A) (x+2)/3

B) (x−6)/3

C) (x+6)/3

D) 3x+6

2 / 30

2. For f(x)=2^x and g(x)=log₂(x), what is f(g(x))+g(f(x))?

A) x+log₂(2ˣ)=x+x=2x

B) x+2x

C) 2x

D) x+x

3 / 30

3. If p(x) = x³ - 5x² + 6x, what are its zeros?

A) x=1, 2, 3

B) x=0, 1, 6

C) x=0, -2, -3

D) x=0, 2, 3

4 / 30

4. The function f(x)=e^(-x²) has inflection points at:

A) x=±1

B) x=0 only

C) x=±2

D) x=±1/√2

5 / 30

5. What is the sum of all coefficients of (x-2y+3z)⁴?

A) 0

B) 2^4

C) Requires expansion

D) 16

6 / 30

6. If g(x)=3x-2 and g(h(x))=x, what is h(x)?

A) (x-2)/3

B) 3/(x-2)

C) 3x+2

D) (x+2)/3

7 / 30

7. Which function has a vertical asymptote at x = 3?

A) Both B and C

B) f(x)=x/(x²−9)

C) f(x)=1/(x+3)

D) f(x)=1/(x−3)

8 / 30

8. The polynomial p(x)=x⁴+1 factors over reals as:

A) (x²+√2x+1)(x²-√2x+1)

B) Both B and C show it factors

C) Cannot factor

D) (x²+1)²-2x²

9 / 30

9. For f(x) and g(x) both even, (f∘g)(x) is:

A) Even

B) Odd

C) Cannot determine

D) Neither

10 / 30

10. The parabola y=2(x-3)²-5 has vertex at:

A) (-3,5)

B) (3,5)

C) (-3,-5)

D) (3,-5)

11 / 30

11. What is the degree of the polynomial (x² + 1)(x³ − x + 2)?

A) 7

B) 6

C) 4

D) 5

12 / 30

12. The average rate of change of f(x) = x³ from x=2 to x=4 is:

A) 28

B) 30

C) 24

D) 26

13 / 30

13. If f(x) = x² - 4 and g(x) = √(x + 4), what is (g∘f)(x) simplified?

A) √(x²-4)

B) x

C) x+4

D) √(x²)=|x|

14 / 30

14. Which function is odd?

A) f(x)=x²+x

B) f(x)=x³+x

C) f(x)=x³+1

D) f(x)=x²

15 / 30

15. The generating function for Fibonacci numbers is:

A) x/(1-x-x²)

B) 1/(1-x)

C) 1/(1-x-x²)

D) x/(1-x)²

16 / 30

16. What is i⁰+i¹+i²+i³?

A) 1

B) −i

C) 0

D) i

17 / 30

17. The number of local extrema of f(x) = x⁵ − 5x³ + 4x is:

A) 5... f'=5x⁴-15x²+4=0. Let u=x²: 5u²-15u+4=0. u=(15±√(225-80))/10=(15±√145)/10. Two positive u values → 4 real x values → 4 local extrema.

B) 2

C) 4

D) 3

18 / 30

18. The number of solutions to f(x)=f(f(x)) for f(x)=x² is:

A) 2

B) 4... wait: f(x)=x². f(f(x))=x⁴. x²=x⁴. x²(x²-1)=0. x=0,±1. Three solutions.

C) 1

D) 3

19 / 30

19. The function f(x) = 2^x has y-intercept at:

A) (1,2)

B) (0,2)

C) (0,1)

D) (0,0)

20 / 30

20. If a_n=(2n-1)/(2n+1), find lim(n→∞) of a_n.

A) 0

B) 2

C) 1/2

D) 1

21 / 30

21. If f(x)=x²-4x and g(x)=f(f(x)), what is g'(0)?

A) 4

B) −16

C) −4

D) 16

22 / 30

22. What is the leading coefficient of f(x) = -3x⁴ + 5x² - 1?

A) 4

B) -3

C) 5

D) -1

23 / 30

23. Simplify: √(72)

A) 6√3

B) 8√2

C) 6√2

D) 9√2

24 / 30

24. If f(x) = x^(1/3) - x^(-1/3), what is f(x)³?

A) x - 3f(x) - x⁻¹

B) x - 3x^(1/3) + 3x^(-1/3) - x^(-1)

C) Both A and B are equivalent

D) x-x⁻¹-3f(x)

25 / 30

25. Simplify: (x²-4)/(x+2) for x≠-2

A) 2

B) x²-2

C) x-2

D) x+2

26 / 30

26. What is the value of log₂(3)×log₃(4)×log₄(8)?

A) 3

B) 6... wait: change of base: log₂3×log₃4×log₄8=log₂8=3

C) 2

D) 4

27 / 30

27. The equation x² = -9 has how many real solutions?

A) 3

B) 0

C) 1

D) 2

28 / 30

28. For the rational function f(x)=(3x²+2)/(x²-4), what is the value of lim f(x) as x→∞?

A) 3

B) 2

C) 0

D) 4

29 / 30

29. What is the exact value of log₄(8) + log₄(2)?

A) 3/2

B) 5/2

C) 3... wait: log₄(16)=2

D) 2

30 / 30

30. The function f(x)=|x²-9| is not differentiable at:

A) x=0 and x=±3

B) x=0

C) x=±3

D) x=3 only

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