SAT Advanced Math part1

Mastering Advanced Math: SAT Test - part 1

  • The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
  • Please note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.
  • Each question is meticulously crafted to mirror the complexity and diversity of  problem-solving you'll encounter in the SAT.
  • Use it as a targeted practice tool to identify and address specific areas of improvement.
  • Track your progress and see your proficiency grow.
1. 

If \(64^{2n+1}=16^{4n-1}\), what is the value of n?

2. 

$$\left ( \frac{10x^{2}y}{x^{2}+xy} \right )\times \left ( \frac{(x+y)^{2}}{2xy} \right )+\left ( \frac{x^{2}-y^{2}}{y^{2}} \right )$$
Which of the following is equivalent to the expression above?

3. 

$$i^{13}+i^{18}+i^{31}+n=0$$
In the equation above, what is the value of n in simplest form?

4. 

$$\frac{t}{t-3}-\frac{t-2}{2}=\frac{5t-3}{4t-12}$$
If x and y are solutions of the equation above and y > x, what is the
value of y − x?

5. 

If m and p are positive integers and
\((2\sqrt{2})^{m}=32^{p},\, what \, is\, the \, value \, of\, \frac{p}{m}\)

6. 

If (1 − 3i)(7 + 5i + i²) = a + bi, what is the value of a + b?
write your answer in numbers only

7. 

Which of the following is equal to (x + i)²− (x − i)²?

8. 

If \(3^{x}=81 \, and\, 2^{x+y}=64,\, then\, \frac{x}{y}=\)

9. 

What is the value of \(\left ( \frac{1}{2}+i\sqrt{5} \right )\left ( \frac{1}{2}-i\sqrt{5} \right )\)

10. 

If x = 3i, y = 2i, z = m + i, and i =√-1 , then the expression xy²z =

11. 

Which of the following complex numbers is equivalent to \(\frac{3+i}{4-7i}\)?

12. 

The expression below is equivalent to
$$\frac{\frac{x-y}{y}}{y^{-1}-x^{-1}}$$

13. 

(9 + 2i)(4 − 3i) − (5 − i)(4 − 3i)
The expression above is equivalent to which of the following?

14. 

If \(4^{y}+4^{y}+4^{y}+4^{y}=16^{x}\), then y

15. 

Which expression is equivalent to \((9x^{2}y^{6})^{-\frac{1}{2}}\)

16. 

If y is not equal to 0, what is the value of \(\frac{6(2y)^{-2}}{(3y)^{-2}}\)?

17. 

x

F(x)

G(x)

-3

3

0

-1

0

3

0

-4

4

2

0

-2


. Several values of x, and the corresponding values for polynomial
functions f and g are shown in the table above. Which of the following
statements is true?
I. f(0) + g(0) = 0
II. f(x) is divisible by x + 2
III. g(x) is divisible by x + 3

18. 

Which of the following is equivalent to 2i²+ 3i³?

19. 

If (x − yi) + (a + bi) = 2x and i = √-1, then (x + yi)(a + bi) = 

20. 

f(x) = x³+ 5x²− 4x − 20
How many of the zeros of function f defined by the equation above are
located in the interval −4 ≤ x ≤ 4?
write your answer only in number

21. 

x³+ 150 = 6x²+ 25x
What is the sum of all values of x that satisfy the equation above?
write your answer only in number

22. 

$$g(x)=a\sqrt{41-x^{2}}$$
Function g is defined by the equation above where a is a nonzero real
constant. If g(2t)=√5, where i =√-1 , what is the value of a?

23. 

Expressed in simplest form, \(2\sqrt{-50}-3\sqrt{-8}\) is equivalent to

24. 

The expression below is equivalent to
$$\frac{x^{2}+9x-22}{x^{2}-121} \div (2-x)$$

25. 

Which expression is equivalent to \(\frac{(2xy)^{-2}}{4y^{-5}}\)

26. 

What is the sum of the zeros of function f defined by the equation
below?
f(x) = (2 − 3x)(x + 3) + 4(x²− 6)

27. 

In how many different points does the graph of the function f(x) = x³−2x²+ x − 2 intersect the x-axis?

28. 

If 10^k= 64, what is the value of \(10^{\frac{k}{2}+1}\)

29. 

The polynomial \(x^{3}-2x^{2}-9x+18\) is equivalent to

30. 

$$\frac{k}{6}+\frac{3(1-k)}4{}=\frac{k-5}{2}$$
What is the solution for k in the equation above?
write your answer only in number

31. 

If p(x) is a polynomial function and p(4) = 0, then which statement is
true?

32. 

If the zeros of function f defined above are represented by r, s, and t,
what is the value of the sum r + s + t?

33. 

\(\frac{\sqrt[3]{a^{8}}}{(\sqrt{a})^{3}}=a^{x}\), where a>1
In the equation above, what is the value of x?

34. 

Which of the following is equal to for all values of \(b^{\frac{1}{2}}\) for which the expression is defined?

35. 


A polynomial function contains the factors
x, x − 2, and x + 5. Which of the graph(s) above could represent the graph of this function?

36. 

If \(x^{\frac{1}{2}}=\frac{1}{8}\) , what is the value of x^{\frac{2}{3}}?
Write your answer only in numbers

37. 

$$p(t)=t^{5}-3t^{4}-kt+7k^{2}$$
In the polynomial function above, k is a nonzero constant. If p(t) is
divisible by t − 3, what is the value of k?

38. 

If \( k=8\sqrt{2}\, and\, \frac{1}{2}k=\sqrt{3h}\) what is the value of h?

39. 

If n is a negative integer, which statement is always true?

40. 

If x is a positive integer greater than 1, how much greater than
\(x^{2}\, is\, x^{\frac{5}{2}}\)

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