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. 

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

2. 

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

3. 

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

4. 

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

5. 

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

6. 

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

7. 

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

8. 

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

9. 

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

10. 

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

11. 

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

12. 

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

13. 

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

14. 

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

15. 

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

16. 

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

17. 

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

18. 

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

19. 

$$(2-\sqrt{-25})(-7+\sqrt{-4})=x+yi$$
In the equation above, what is the value of y?
write your answer in numbers only

20. 

If 27^{x}=9^{y-1}, then

21. 

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

22. 

Which of the following is equal to \(y^{\frac{3}{2}}\) for all values of y for which the
expression is defined?

23. 

(y²+ ky − 3)(y − 4) = y³ + by²+ 5y + 12
In the equation above, k is a nonzero constant. If the equation is true
for all values of y, what is the value of k?

24. 

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

25. 

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

26. 

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

27. 

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

28. 

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

29. 

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

30. 

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

31. 

The expression \(\frac{x^{2}}{\sqrt{x^{3}}}\)is equivalent to

32. 

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

33. 

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

34. 

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

35. 

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

36. 

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

37. 

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

38. 

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

39. 

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

40. 


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)

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