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. 

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?

2. 

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

3. 

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?

4. 

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?

5. 

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

6. 

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

7. 

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

8. 

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

9. 

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

10. 

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

11. 

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

12. 

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

13. 

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?

14. 

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

15. 

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

16. 

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

17. 

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

18. 

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

19. 

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?

20. 

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

21. 

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

22. 

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

23. 

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)?

24. 


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

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. 

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?

27. 

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 ? 

28. 

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

29. 

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

30. 

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?

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