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. 

Let [[x]] = the greatest integer that does
not exceed x. If f(x) = x + [[x]], then ƒ(-3.2) =

2. 

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

3. 

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

4. 


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

5. 

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

6. 

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

7. 

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)?

8. 

Let f(x) = x
2 – 5x + 2 and g(x) = f(x – 4).
Find the positive root of the equation
f(x) = g(2)
write answer only in numbers

9. 

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?

10. 

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

11. 

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?

12. 

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

13. 

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

14. 

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

15. 

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

16. 

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

17. 

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

18. 

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

19. 

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?

20. 

Which of the following is equivalent to the expression below, where p > 1 and q > 1?
$$\frac{p^{\frac{1}{4}}q^{-3}}{p^{-2}q^{\frac{1}{2}}}$$

21. 

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?

22. 

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

23. 


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

24. 

The table below represents the number of hours a student worked and the amount of money the student earned. Which equation represents the number of dollars, d, earned in terms of the number of hours, h, worked

25. 

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

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. 

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?

28. 

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 

29. 

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

30. 

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?

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