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.

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

5x²

x²+y²

4x²+y²

x²-y²

None

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

$$y=\frac{3}{2}x+1$$

$$y=\frac{1}{2}x+\frac{2}{3}$$

$$y=\frac{3}{2}x+\frac{1}{2}$$

$$y=\frac{3}{2}x+2$$

None

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

4/7

3/7

6/7

5/7

None

(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?

-2

-1/2

None

If $4^{y}+4^{y}+4^{y}+4^{y}=16^{x}$, then y

x-2

2x-1

x+2

2x+1

None

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

None

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

$$\frac{17}{28}$$

$$-\frac{19}{33}-\frac{25}{33}i$$

$$\frac{1}{33}-\frac{5}{13}i$$

$$\frac{1}{33}+\frac{5}{13}i$$

None

If a, b, and c are positive numbers such that $\sqrt{\frac{a}{b}}=8c$ and ac = b, what is the value of c?

1/3

1/4

1/2

1/5

None

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

$$\frac{3}{xy^{3}}$$

$$\frac{1}{3xy^{3}}$$

$$3xy^{3}$$

$$\frac{xy^{3}}{3}$$

None

10.

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

52 − 126i

–12

115 − 89i

116

None

11.

If $\frac{6+4i}{1-3i}$, what is the value of a + b?

8/5

9/8

8/3

8/7

None

12.

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

−6xi

−8xi

−2x + 8i

2x − 8i

None

13.

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

1/10

3/10

7/10

9/10

None

14.

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

-i

-1

None

15.

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

16.

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

$$\frac{y^{3}}{x^{2}}$$

$$\frac{y^{3}}{16x^{2}}$$

$$-\frac{y^{3}}{x^{2}}$$

$$-\frac{y^{3}}{16x^{2}}$$

None

17.

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

18.

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

$$\frac{xy}{x-y}$$

$$\frac{x+y}{xy}$$

$$\frac{5y^{2}}{x-y}$$

$$\frac{y^{2}}{x-y}$$

None

19.

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

$$\frac{b}{b^{2}}$$

$$\frac{1}{\sqrt{2b}}$$

$$\frac{\sqrt{b}}{b}$$

$$\frac{1}{2}b$$

None

20.

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

1/5

1/3

1/2

1/4

None

21.

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

22.

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

4√6i

-24

-4√6

24i

None

23.

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

7/3

7/8

7/6

7/2

None

24.

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

-2

-2+4xi

4xi

None

25.

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

$$\frac{1}{\sqrt{x}}$$

$$\sqrt{x}$$

$$\sqrt[3]{x}$$

$$\frac{1}{\sqrt[3]{x^{2}}}$$

None

26.

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

$$\sqrt{y^{3}}$$

$$\sqrt[3]{y^{\frac{1}{2}}}$$

$$3\sqrt{y}$$

$$\sqrt[3]{y^{2}}$$

None

27.

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

5/3

7/3

5/2

7/2

None

28.

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

29.

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

1/5

1/4

1/3

1/2

None

30.

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?

II only

I only

I and III

III only

None

31.

In an electrical circuit, the voltage, E, in volts, the current, I, in amps,
and the opposition to the flow of current, called impedance, Z, in ohms,
are related by the equation E = IZ. What is the impedance, in ohms, of
an electrical circuit that has a current of (3 + i) amps and a voltage of
(−7 + i) volts?

$$\frac{16}{25}t$$

$$-\frac{11}{25}-\frac{1}{5}t$$

$$-2+i$$

$$1-2i$$

None

32.

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

33.

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

34.

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

f(x) = (x + 4)(1 − x ² )

f(x) = (x − 4)(1 + x ²)

f(x) = (x − 1)( x² + 3x − 4)

f(x) = (x − 1)( x² − 3x − 4)

None

35.

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

16t√2

4t√2

3t√2

-t√2

None

36.

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

I and III, only

I, II, and III

I and II, only

II and III, only

None

37.

When $x^{-1}-1$ is divided by x − 1, the quotient is

-1

1/x²

-1/x

1/(x-1)²

None

38.

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

30i

-900

-30

900i

None

39.

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

$$2-3i$$

$$-2-3i$$

$-2+3i$$

$$2+3i$$

None

40.

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

6/7

5/4

7/4

9/4

None