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

2. 

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

3. 

$$\frac{16a^{4}-81b^{4}}{8a^{3}+12a^{2}b+18ab^{2}+27b^{3}}$$
Which of the following expressions is equivalent to the expression
above?

4. 

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

5. 

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

6. 

Which of the following functions have zeros −1, 1, and 4?

7. 

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

8. 

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

9. 

$$g(x)=a\sqrt{41-x^{2}}$$
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?

10. 

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

11. 

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

12. 

$$\frac{y^{3}+3y^{2}-y-3}{y^{2}+4y+3}$$
The expression above is equivalent to

13. 

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

14. 


Which equation(s) represent(s) the graph above?
I. y = (x + 2)(x²− 4x − 12)
II. y = (x − 3)(x²+ x − 2)
III. y = (x − 1)(x²− 5x − 6)

15. 

Which of the following is equivalent to 2i(xi − 4i²)?

16. 

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

17. 

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

18. 

If x = 2i, y = −4, z = 3i, and i = √-1 then √x³yz =

19. 

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

20. 

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

21. 

When resistors R1and R2 are connected in a parallel electric circuit,
the total resistance is
\(\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}}\) 
This fraction is equivalent to

22. 

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

23. 

$$\frac{3}{2}=\frac{-(5m-3)}{3m}+\frac{7}{12m}$$
What is the solution for m in the equation above?

24. 

Which of the following is equal to (13 + 17i)(4 − 9i)?

25. 

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

26. 

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

27. 

A meteorologist estimates how long a passing storm will last by using
the function\(t(d)=0.08d^{\frac{3}{2}}\) where d is the diameter of the storm, in miles, and t is the time, in hours. If the storm lasts 16.2 minutes, find its diameter, in miles

28. 

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

29. 

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

30. 

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

31. 

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

32. 

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

33. 

If \(g(x)=(x\sqrt{1-x})^{2}\), what is g(10)?

34. 

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

35. 

If \(\sqrt{m} = 2p\; then\: m^{\frac{3}{2}}=\)

36. 

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

37. 

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

38. 

When \(x^{-1}-1\) is divided by x − 1, the quotient is

39. 

Function g is defined by the equation below. If g (−8) = 375, what is
the value of a?
$$g(x)=a\sqrt{a(1-x)}$$

40. 

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

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