ACT math practice questions

2.When x = 3 and y = 5, by how much does the value of 3x2 - 2y exceed the value of 2x2 - 3y ?

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.

5.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?

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.

11.What is the x-intercept of the graph of y = x2 - 4x + 4 ?

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.

1.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?

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.

4.A rectangle with a perimeter of 30 centimeters is twice as long as it is wide. What is the area of the rectangle in square centimeters?

50 is the correct answer. If w = width, then 2w = length. So, the perimeter is 2(w + 2w) = 30, and w = 5. Since the width is 5, the length is 2(5) = 10. Then the area is 5(10) = 50

6.A boat departs Port Isabelle, Texas, traveling to an oil rig. The oil rig is located 9 miles east and 12 miles north of the boat's departure point. About how many miles is the oil rig from the departure point?

The answer is 15. Using the Pythagorean theorem, 92 + 122 = c2. 92(squared) + 122(squared) 81 + 144= 225 The square root of 225 is 15.

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?

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.

4.What is the greatest common factor of 42, 126, and 210 ?

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.

A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year?

54 is the correct answer. For each member of the track team to consume 20% less sugar, the track member will consume 100% - 20% = 80% of the level of a typical high school student. 80% of 67.5 = 0.80(67.5) = 54.

2.If xy = 144, x + y = 30, and x > y, what is the value of x - y ?

The answer is 18. Solve the first equation for y, y = . Then substitute for y in the second equation: x + = 30. Multiplying each side by x, x2 + 144 = 30x. Subtracting 30x from each side, x2 - 30x + 144 = 0. You could solve this equation by factoring: (x - 24)(x - 6) = 0, and then setting each factor equal to zero, x = 24 or x = 6. However x = 6 will not work (if x = 6 then y = 24, but the problem says that x > y). So, x = 24. Putting this value of x back into either of the original equations, y = 6. Then x - y = 24 - 6 = 18.

11.A DVD player with a list price of $100 is marked down 30%. If John gets an employee discount of 20% off the sale price, how much does John pay for the DVD player ?

The answer is 56.00 100(0.70) = 70 is the amount that would be paid if the DVD was marked down 30%, but there is another discount of 20%, so the price is going to be 80% of the marked-down price. The price will be 70(0.80) = 56.

3.What is the value of x when 2x + 3 = 3x - 4 ?

The answer is 7. You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x - 4. Then add 4 to each side, so x = 7.

10.How many irrational numbers are there between 1 and 6 ?

The answer is Infinately many.If you chose this answer, you know 1 and 6 are real numbers and that there are an infinite number of irrational numbers between any two real numbers.

7.Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of + 4D - 250 gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?

The correct answer is 1,250.If you substitute D with 150 in the expression, you get + 4(150) - 250 = + 600 - 250 = 1,250.

8.Which of the following is a factor of the polynomial 2x2 - 3x - 5 ?

The correct answer is 2x-5. . 2x2 - 3x - 5 = (x + 1)(2x - 5).