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

2. 

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

3. 

Two lines are graphed in the xy-plane. The lines have the same slope and different y-intercepts. How many solution(s) would the equations represented by this pair of lines have?

4. 

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

5. 

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?

6. 

If |x − 16| ≤ 4 and |y – 6| ≤ 2, what is the greatest possible value of x − y?
write answers only in number

7. 

Let the function f be defined by f(x) = x²+ 12. If n is a positive number
such that f(3n) = 3f(n), what is the value of n?

8. 

The point whose coordinates are (4, −2) lies on a line whose slope is .
Which of the following are the coordinates of another point on this
line?

9. 

The lines y = ax + b and y = bx + a are graphed in the xy-plane. If a and
b are non-zero constants and a + b = 0, which statement must be true?

10. 

If \(\frac{|a+3|}{2}\) =1 and 2|b + 1| = 6, then |a + b| could equal any of the
following EXCEPT

11. 

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?

12. 

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

13. 

What is the slope of a line with the equation 5x + 4y = 2?

14. 

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

15. 

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?

16. 

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

17. 

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

18. 

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?

19. 

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

20. 

For the inequality below, what is a possible value of x-3?
$$-\frac{5}{3}< \frac{1}{2}-\frac{1}{3}x<\frac{-3}{2}$$

21. 

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

22. 

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)?

23. 

Which of these represents a linear equation in the xy-plane that has the
points (5, 17) and (2, 5)?

24. 

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?

25. 

If the below system of equations has infinitely many solutions, what is
the value of  p/q?
6x+py = 21
qx+5y=7

26. 

Which of the following expressions is NOT
equivalent to p - 2/3 (2p - 3q) - 1/3 (p + 4q)

27. 

The net profit for the sales of a product is equal to
the total revenue from the sales of that product
minus the total cost for the sales of that product. If a
particular model of calculator sells for €98, and the
cost for making and selling n of these calculators is
€(35n + 120,000), which of the following equations
expresses the net profit in dollars, P, for making and
selling n of these calculators?

28. 

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?

29. 

If ax + by = 5 is a line in the xy-coordinate plane in which a and b are constants, which of the following expresses the slope of the line?

30. 

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?

31. 

The annual profit from the sales of an item is equal
to the annual revenue minus the annual cost for
that item. The revenue from that item is equal to
the number of units sold times the price per unit.
If n units of a portable heart monitor were sold in
2012 at a price of €65 each, and the annual cost to
produce n units was €(20,000 + 10n), then which
of the following statements indicates that the total
profit for this heart monitor in 2012 was greater
than €500,000?

32. 

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

33. 

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

34. 

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

35. 

If 2 times an integer x is increased by 5, the result is always greater than 16 and less than 29. What is the least value of x?

36. 

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

37. 

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

38. 

If the function f is defined by f(x) = 3x + 2, and if f(a) = 17, what is the
value of a?

39. 

An ocean depth finder shows the number of feet in the depth of water
at a certain place. The difference between d, the actual depth of the
water, and the depth finder reading, x, is |d − x| and must be less than
or equal to 0.05d. If the depth finder reading is 620 feet, what is the
maximum value of the actual depth of the water, to the nearest foot?
write answers only in number

40. 

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

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