SAT Algebra

Mastering SAT Algebra :  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. 

If the function k is defined by k(h) = (h + 1)2, then k(x − 2) =
x²-x

2. 

If \(\frac{1}{2}|x|\) and |y| = x + 1, then y² could be
write answers only in number

3. 

The graph of the inequality y ≤ 2x will include all of the points in
which quadrant?

4. 

Which of the following expressions is equivalent
to 5.4(x-2y)-2.7(x-3y)?

5. 

Which of the following expressions is equivalent
to a(b - c)-b(a + c)-c(a - b)

6. 

Which of the following is equivalent to 10 + 2(x − 7)?

7. 

Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum number of rides he can go on?

8. 

Which of the following expressions is equivalent to
1/2(2a+3b+4c) - 3/2(b+2c)?

9. 

A family kept a log of the distance they traveled during a trip, as represented by the graph below in which the points are ordered pairs of the form (hour, distance). During which interval was their average speed the greatest?

10. 

Let h be the function defined by h(x) = x + 4x. What is the value of 
$$h(\frac{-1}{2})$$

11. 

In the xy-plane, which of these linear equations has a y-intercept of 12?

12. 

Which ordered pair (x, y) satisfies the system of equations
shown below?
3x - (y/3) = 21
x = y+7

13. 

Let g be the function defined by g(x) = x − 1. If \(\frac{1}{2}\)g (c) = 4, what is the
value of g(2c)?
write answers only in numbers

14. 

The inequality |1.5C − 24| ≤ 30 represents the range of monthly
average temperatures, C, in degrees Celsius, during the winter months
for a certain city. What was the lowest monthly average temperature, in
degrees Celsius, for this city?
write answers only in number

15. 

Which of the following expressions is NOT
equivalent to 3 [6a-3(1 - a) - 5(a + 1)

16. 

Which of the following represents an equation of the line that is the perpendicular bisector of the segment whose endpoints are (–2, 4) and (8, 4)?

17. 

Which of the following is equivalent to the expression below?
x²− 8x + 5

18. 

If |x| ≤ 2 and |y| ≤ 1, then what is the least possible value of x − y?

19. 

what is the value of
$$\frac{7\div (q)^{2}\times 2}{2p}\times \frac{-p+6q-r}{-q}$$
if p =4, q= 1/2 and r = 2?

20. 

In a certain greenhouse for plants, the Fahrenheit temperature, F, is
controlled so that it does not vary from 79° by more than 7°. Which of
the following best expresses the possible range in Fahrenheit
temperatures of the greenhouse?

21. 

Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine the number of packages of hot dogs Roger must buy?

22. 

In 2012, a retail chain of fast food restaurants had 68 restaurants in
California and started to expand nationally by adding 9 new restaurants
each year thereafter. At this rate, which of the following functions f
represent the number of restaurants there will be in this retail chain n
years after 2012 assuming none of these restaurants close?

23. 

According to market research, the number of magazine subscriptions
that can be sold can be estimated using the function
$$n(p)=\frac{5,000}{4p-k}$$
where n is the number of thousands of subscriptions sold, p is the price
in euros for each individual subscription, and k is some constant. If
250,000 subscriptions were sold at €15 for each subscription, how
many subscriptions could be sold if the price were set at €20 for each
subscription?

24. 

For the system of equations below, which of the following statements
is true?
3x + 5 = 2y
\(\frac{x}{3}+\frac{y}{2}=\frac{2}{3}\)

25. 

If function f is defined by f(x) = 5x + 3, then which expression
represents 2f(x) – 3?

26. 

A function f is defined such that f(1) = 2, f(2) = 5, and f(n) = f(n − 1) − f(n − 2) for all integer values of n greater than 2. What is the value of f(4)?

27. 

Which of the following equations represents a line in the xy-coordinate plane with a
y-intercept of 6 and a slope of − 3?

28. 

Which of the following is an equation of a line that is parallel to the
line (1/2 )y - (2/3)x = 6in the xy-plane?

29. 

(4 − a²) − (2a² − 6)
Which of the following expressions is equivalent to the one
above?

30. 

For what value of k does the system of equations below have no
solution?
4x + 6y = 12
y = 8 − kx

31. 

For the equation 1/2 y= 2/3 x -4, what is the x-intercept?

32. 

The graph of a line in the xy-plane has slope and contains the point
(0, 7). The graph of a second line passes through the points (0, 0) and
(–1, 3). If the two lines intersect at the point (r, s), what is the value of
r + s?

33. 

The line y + 2x = b is perpendicular to a line that passes through the
origin. If the two lines intersect at the point (k + 2, 2k), what is the
value of k?

34. 

In the system of equations below, k and s are nonzero constants. If the
system has no solutions, what is the value of k?
$$\frac{1}{3}r +4s =1$$
$$kr+6s=-5$$

35. 

The ninth grade class at a local high school needs to purchase a park permit for €250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays €0.75. Each guest pays €1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

36. 

If point E(5, h) is on the line that contains A(0, 1) and B(−2, −1), what
is the value of h?

37. 

What is the slope of the line 2(x + 2y) = 0?

38. 

Which could be the slope of a line that contains (1, 1) and passes
between the points (0, 2) and (0, 3)?

39. 

If  \(a=60(99)^{99}+ 30(99)^{99}, b=99^{100},c=90(90)^{99}\)
then which of the following expresses the correct
ordering of a, b, and c

40. 

Which of the following equations has a slope perpendicular to the slope of a line with the equation y = ax + b, given that a and b are constants?

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