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ACT Math - Advanced Math Practice Test
Test your Advanced Math skills with 30 random practice test questions.
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1. What is (1+i)²?
(1+i)²=1+2i+i²=1+2i-1=2i.
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2. What is the value of (−i)⁴?
(-i)⁴=((-1)(i))⁴=(-1)⁴(i)⁴=1×1=1.
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3. What is the general formula for sum of first n terms of arithmetic series?
Sₙ=n/2(a₁+aₙ).
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4. What is the domain of f(x)=log(2x-6)?
2x-6>0→x>3.
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5. What is the 7th term of arithmetic sequence with first term 4 and common difference 5?
a₇ = 4 + (7-1)(5) = 4 + 30 = 34.
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6. What is the equation of the directrix of y=x²?
y=(1/4p)x². p=1/4. Directrix: y=-p=-1/4.
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7. What is the product (3+i)(3-i)?
(3+i)(3-i) = 9 - i² = 9 - (-1) = 10.
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8. Which polynomial has roots 1, -2, and 3?
Roots 1,-2,3 → factors (x-1)(x+2)(x-3).
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9. What is the 6th term of the geometric sequence 1, -2, 4, -8...?
r=-2. a₆=1×(-2)⁵=-32.
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10. What is the sum of the first 20 terms of 1,2,3,...,20?
S=20×21/2=210.
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11. What is f⁻¹(x) if f(x) = 3x + 6?
y = 3x+6 → x = 3y+6 → y = (x-6)/3 = x/3 - 2.
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12. Which function is ODD?
f(-x) = -x³ = -f(x). Odd function.
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13. What is the value of ln(e)+log₁₀(100)?
1+2=3.
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14. What is the common ratio of 5, 15, 45, 135?
r = 15/5 = 3.
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15. For what values is f(x)=(x+1)/(x²-4) undefined?
x²-4=0 → x=±2.
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16. A geometric sequence has a₁=5 and a₄=40. What is r?
5×r³=40. r³=8. r=2.
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17. What is the value of log(1/100)?
1/100=10⁻². log=−2.
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18. What is the graph of |y|=x?
y=x for y≥0 and y=-x for y≤0: two rays.
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19. What is the value of ∑(k=1 to 4) 2k?
2+4+6+8=20.
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20. What is the remainder when x³ - 2x + 1 is divided by (x-1)?
By Remainder Theorem: f(1) = 1 - 2 + 1 = 0.
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21. What is the product (1+i)(1-i)(1+2i)?
(1+i)(1-i)=2. 2(1+2i)=2+4i.
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22. What is the value of e^(ln(3)+ln(4))?
e^(ln(12))=12.
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23. What is the conjugate of the denominator needed to rationalize 1/(2+3i)?
Multiply by conjugate 2-3i.
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24. Which function is EVEN?
f(-x) = (-x)²+1 = x²+1 = f(x). Even function.
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25. What are the roots of x³ - 8 = 0 (real roots only)?
x³=8. Real cube root: x=2.
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26. What is the amplitude of y = -5cos(2x)?
Amplitude = |-5| = 5. Amplitude is always positive.
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27. What is the value of (1-√3i)² ?
(1-√3i)²=1-2√3i+3i²=1-2√3i-3=-2-2√3i.
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28. What is the sum of the first 8 terms of 2+4+8+16...?
S₈ = 2(2⁸-1)/(2-1) = 2(255) = 510.
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29. What type of conic is y=x²+3x-2?
y=ax²+bx+c is a parabola.
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30. What is the value of log₅(125/25)?
125/25=5. log₅(5)=1.
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