ACT MATH PRACTICE QUESTIONS
AND ANSWERS GRADED A+
14 is the correct answer. When you use x = 3 and y = 5 in the given expressions, 3x² -
2y = 3(3)² - 2(5) = 27 - 10 = 17 and 2x² - 3y = 2(3)² - 3(5) = 18 - 15 = 3. Then subtract 3
from 17 to get 14. - ANSWER-When x = 3 and y = 5, by how much does the value of 3x²
- 2y exceed the value of 2x² - 3y ?
16 is If x = sales for the first year, then x + 3 = sales for the second year. Since sales for
the third year were double the sales for the second year, sales for the third year = 2(x +
3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could
first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x =
16. - ANSWER-Sales for a business were 3 million dollars more the second year than
the first, and sales for the third year were double the sales for the second year. If sales
for the third year were 38 million dollars, what were sales, in millions of dollars, for the
first year?
2 is the x-intercept. One way to find the x-intercept is to replace y with 0, and solve for x.
If 0 = x² - 4x + 4, then (x - 2)2 = 0, and x = 2. Another way of doing this problem is to
look at the graph of the equation and see where the graph crosses the x-axis. -
ANSWER-What is the x-intercept of the graph of y = x² - 4x + 4 ?
20 is the correct answer. With every complete turn inch of the screw goes into the wood.
So after 8 complete turns, 1 inch of the screw would be in the wood. So, x() = 2.
Multiplying by 8, x = 8(2) = 8() = 20. - ANSWER-The lead of a screw is the distance that
the screw advances in a straight line when the screw is turned 1 complete turn. If a
screw is 2 1/2 inches long and has a lead of 1/8 inch, how many complete turns would
get it?
408. 04 is the correct answer. If you divide 2,727 miles by 27 miles per gallon you will
get the number of gallons: = 101. Then, multiply the number of gallons by the cost per
gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical
miles. - ANSWER-A car averages 27 miles per gallon. If gas costs $4.04 per gallon,
which of the following is closest to how much the gas would cost for this car to travel
2,727 typical miles?
42 is the correct answer since it is the largest number that is a factor of all three
numbers given. You can find the greatest common factor by writing out the prime
factorization of all three numbers, and then taking each of the common prime factors to
the lowest power that appears for that factor: 42 = 2 × 3 × 7; 126 = 2 × 32 × 7; and 210
= 2 × 3 × 5 × 7. So the greatest common factor is 2 × 3 × 7 = 42. - ANSWER-What is
the greatest common factor of 42, 126, and 210 ?
AND ANSWERS GRADED A+
14 is the correct answer. When you use x = 3 and y = 5 in the given expressions, 3x² -
2y = 3(3)² - 2(5) = 27 - 10 = 17 and 2x² - 3y = 2(3)² - 3(5) = 18 - 15 = 3. Then subtract 3
from 17 to get 14. - ANSWER-When x = 3 and y = 5, by how much does the value of 3x²
- 2y exceed the value of 2x² - 3y ?
16 is If x = sales for the first year, then x + 3 = sales for the second year. Since sales for
the third year were double the sales for the second year, sales for the third year = 2(x +
3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could
first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x =
16. - ANSWER-Sales for a business were 3 million dollars more the second year than
the first, and sales for the third year were double the sales for the second year. If sales
for the third year were 38 million dollars, what were sales, in millions of dollars, for the
first year?
2 is the x-intercept. One way to find the x-intercept is to replace y with 0, and solve for x.
If 0 = x² - 4x + 4, then (x - 2)2 = 0, and x = 2. Another way of doing this problem is to
look at the graph of the equation and see where the graph crosses the x-axis. -
ANSWER-What is the x-intercept of the graph of y = x² - 4x + 4 ?
20 is the correct answer. With every complete turn inch of the screw goes into the wood.
So after 8 complete turns, 1 inch of the screw would be in the wood. So, x() = 2.
Multiplying by 8, x = 8(2) = 8() = 20. - ANSWER-The lead of a screw is the distance that
the screw advances in a straight line when the screw is turned 1 complete turn. If a
screw is 2 1/2 inches long and has a lead of 1/8 inch, how many complete turns would
get it?
408. 04 is the correct answer. If you divide 2,727 miles by 27 miles per gallon you will
get the number of gallons: = 101. Then, multiply the number of gallons by the cost per
gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical
miles. - ANSWER-A car averages 27 miles per gallon. If gas costs $4.04 per gallon,
which of the following is closest to how much the gas would cost for this car to travel
2,727 typical miles?
42 is the correct answer since it is the largest number that is a factor of all three
numbers given. You can find the greatest common factor by writing out the prime
factorization of all three numbers, and then taking each of the common prime factors to
the lowest power that appears for that factor: 42 = 2 × 3 × 7; 126 = 2 × 32 × 7; and 210
= 2 × 3 × 5 × 7. So the greatest common factor is 2 × 3 × 7 = 42. - ANSWER-What is
the greatest common factor of 42, 126, and 210 ?
