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. 

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

2. 

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?

3. 

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)?

4. 

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?

5. 

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

6. 

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?

7. 

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

8. 

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

9. 

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

10. 

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

11. 

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

12. 

Which of the following expressions is equivalent to
2/4(a²-a-3) + 1/3 (a²+2a+6)

13. 

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

14. 

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?

15. 

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?

16. 

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?

17. 

A linear equation in the xy-plane intercepts the y-axis at − 3. For every 2 units the y-coordinate of the line increases, the x-coordinate decreases by 7 units. Which of the following is the correct equation for this line?

18. 

The equation a + b = 15 relates the number of hours, a, Kevin
spends doing homework each week and the number of hours he
spends watching television each week. If Kevin spends a total of
15 hours doing homework and watching television each week,
what does the variable b represent?

19. 

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

20. 

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

21. 

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

22. 

What value of x is a solution to the equation below?
$$\frac{3x^{2}-27}{3x-9}=5$$
write answer only in numbers

23. 

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

24. 

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

25. 

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

26. 

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

27. 

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?

28. 

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

29. 

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?

30. 

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?

31. 

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

32. 

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

33. 

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

34. 

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

35. 

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

36. 

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

37. 

In 2014, the United States Postal Service charged €0.48 to mail a first-class letter weighing up to 1 oz. and €0.21 for each additional ounce.
Based on these rates, which function would determine the cost, in
dollars, c(z), of mailing a first-class letter weighing z ounces where z is
an integer greater than 1?

38. 

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

39. 

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

40. 

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

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