SAT Algebra part 2

Mastering SAT Algebra :  Part 2

  • 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. 

Sara correctly solves a system of two linear equations and finds that
the system has no solution. If one of the two equations is (y/6) - (x/4)= 1,
which could be the other equation in this system?

2. 

Which of the following would be a solution to this equation?
21 - √x = 10
Write answer only in numbers 

3. 


If the slope of line p shown in the figure above is , what is the value of b?

4. 

If \(3^{2x}+3^{2x}+3^{2x}=(\frac{1}{3})^{x}\)
What is the value of x?

5. 


The figure above shows the graph of function h. If function f is defined by f(x) = h(2x) + 1, what is the value of f(−1)?
write answers only in numbers

6. 

What is the value of ƒ(−2) if 
ƒ(x) =  \(\frac{x^{2}+4x-8}{x-2}\)

7. 

In the figure below, the slope of line ℓ1 is and the slope of line ℓ2 is 5/6. What is the distance from point A to point B?

8. 

The graph of a line in the xy-plane passes through the points (5, –5)
and (1, 3). The graph of a second line has a slope of 6 and passes
through the point (–1, 15). If the two lines intersect at (p, q), what is
the value of p + q?

9. 

For what positive value of x is this function undefined?
$$f(x)=\frac{1}{x^{2}-1}$$
Write answer only in numbers 

10. 

Which of the following is an equation of the line that contains diagonal AC of square ABCD shown in the accompanying figure?

11. 

Which of the following is an equation of the line that is parallel to the
line y − 4x = 0 and has the same y-intercept as the line y + 3 = x + 1?

12. 

Find an integer value of x that satisfies
both of the inequalities below:
|3x-5|<20 and
|x+2| > 8
write answer only in numbers

13. 

If \( ( \frac{1}{3} )^{x}=(81)^{x-1}\)

14. 

What are the solutions to the equation 5x²− 7x + 1 = 0 ?

15. 

If f(x) = x² + x – 42 and f(p – 1) = 0,
what is a positive value of p?
write answer only in numbers  

16. 

If x²− 3x − 10 = 0, for what value of x is this equation true given that x > 0?
Write answer only in numbers 

17. 

A statistics class investigated the cost of cheesecakes at different bakeries around
town. Given that P(x) was the cost, in dollars, of a cheesecake with diameter x,
the function that best fit the data collected by the class was
$$P(x)=\frac{1}{2}x^{2}-5x+20$$
write answer only in Decimal numbers

18. 

What is the remainder when 2x²+ 3x − 1 is divided by x − 4?

19. 

The accompanying figure shows the graph of y = f(x). If function g is defined by g(x) = f(x + 4), then g(−1) could be

20. 

Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs £ 22 per share and stock Y, which cost £ 35 per share.  His budget for buying stock is no more than £ 4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?

21. 

Let ƒ(x) = –x² + 2x +3
If g(x) = f(–x),
then a point on the graph of g(x) is

22. 

A function ƒ(x)is defined as follows:
ƒ(x) = $$\left\{\begin{matrix}
\frac{3}{x-2}\times x<0\\
|x|\times x\geq 0
\end{matrix}\right.$$

 
What is the domain of ƒ(x)?

23. 

Ben correctly solves a system of two linear equations and finds that the
system has an infinite number of solutions. If one of the two equations
is 3(x + y) = 6 − x, which could be the other equation in this system?

24. 

In the accompanying figure, what is the y-coordinate of the point at which the line that is perpendicular to AB (not shown) at point M crosses the y-axis?


Write answer only in numbers 

25. 

Which of the following is an equation of a line that is perpendicular to
the line y = −2(x + 1)?

26. 

If in the accompanying figure (p, q) lies on the graph of
y = f(x) and 0 ≤ p ≤ 5, which of the following represents the set of corresponding values of q?

27. 

Which of the following graphs shows a line where each value of y is three more than half of x?

28. 

f(2n) = 4f(n) for all integers n
f(3) = 9
If function f satisfies the above two conditions for all positive integers n, which equation could represent function f ? 

29. 

Which of the following statements must be true for
all values of x, y, and z ?
I. (x + y) + z = (z + y) + x
II. (x - y) - z = (z - y) - x
III. (x ÷ y) ÷ z = (z ÷ y) ÷ x

30. 

For i = √-1, which of the following complex numbers is
equivalent to (10i − 4i²) - (7 − 3i)?

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