ACT Sample Questions (for Math)

The degree measure of the angles between two sides that are 5 feet long is θ. In terms of x, cosθ =? (Keep in mind: law of cosines).

(50-x²)/50. You must remember that a² = b² + c² - 2bc(cos<A). Therefore, you must plug in terms, subtract from each side, and then divide when necessary. The key is that the cosine term is a PRODUCT, so you cannot cancel 50 - 50.

An angle with vertex at the origin and measure θ is shown in the standard (x,y) coordinate plane below. If one side of the angle includes the positive x-axis and the other side passes through (-12, -5), then what is the sine of θ?

-5/13 The resultant, 13 in this case, will always be positive because of the Pythagorean Theorem. -5 is opposite the angle measure θ on the diagram, therefore, the sine measurement is -5/13. REMEMBER: sin = y, cos = x

In a piggy bank, there are pennies, nickels dimes, and quarters that total $5.29 in value. if there are 3 times as many dimes as there are pennies, 1 more dime than nickels, and 2 more quarters than dimes ,then how many nickels are in the piggy bank?

11 nickels. 0.01p + 0.05n + 0.1d + 0.25q = $5.29 THEN ... convert all to one unit (pennies, in this case) 0.01p + .05(3p-1) + .1(3p) + .25(3p +2) = 5.29 THEN ... multiply by 100 to make easier on yourself p + 5(3p-1) + 10(3p) + 25(3p +2) = 529 121p + 45 = 529, p = 4 3(4)-1 = 11 nickels

If 0°< θ < 90° and tanθ = 2/9, what is sinθ + cosθ?

11/√85. To solve for tanθ = 2/9, plug 2/9 into inverse tan to get the angle measure. Then, plug that angle measure into sinθ + cosθ to get a number value. Then, convert all answer choices into decimals.

A cement walkway will be added along a side measuring 60 feet. The top of the walkway will be a rectangle with a width of 3 feet. The walkway will be 4 inches (1/9 yard) thick. How many cubic YARDS of cement will be needed for this walkway?

2 2/9 yards of cement. Convert all measurements in feet to yards (1 yard = 3 feet). Then, multiply resulting values together.

x is subtracted from 6. That difference is then multiplied by 3. This product is 15 more than half the original integer. What equation represents this relationship?

3(6-x) = (x/2) + 15 Make sure that "more than" is ALWAYS to the right of the equal sign.

If 0˚≤x≤180˚ and 4cos²x = 1, what is the value of x?

60˚. 4cos²x = 1 cos²x = 0.25 (cosx)(cosx) = 0.25 cosx = 0.5, cos⁻¹ = 60˚

A compass has marks for every 10°. If the point of the needle of the compass travels 42mm as it moves in a clockwise direction from "east" to "north," how long is the needle to the nearest tenth of a millimeter.

8.9 mm. This is an arc question, so you must find the diameter of the needle and divide that value by 2. (270/360) * πd = 42 is the equation used to start.

A restaurant decides on following production model, where N. is the number of ounces of flour the restaurant purchases each month N = x² - 600x - 160,000. What is the greatest quantity of flour, in ounces, that the restaurant can use during a month, without buying another bag?

800 ounces. Two ways to solve this question. You can either use the calculator to graph the function. Another possibility is factoring the function, and seeing which x-intercept provides a greater solution.

Melissa is 20 feet ahead of Carl. Melissa runs at a constant rate of 8 ft/second. Carl runs at a constant rate of 9.2 ft/second. Which equation gives the number of seconds Carl will take to catch up to Melissa?

8s + 20 = 9.2s OR 9.2s - 20 = 8s Since Melissa is running AHEAD of Carl, she will add the distance she is ahead to the rate she is running. Since Carl is running BEHIND Melissa, he will subtract the distance he is behind from the rate he is running.

Which of the following expressions gives the area in square feet of <ABC shown below with the given side lengths in feet (AB = 10 and AC = 10) and <BAC = 35°?

Just don't answer this question. It is confused.

For some x and y that satisfy the equation xy = -x².

Normally, if you saw xy = x², you would break up and multiply the terms (x * y = x * x), showing that y = x. In this questions, the negative sign is included, knowing that y = -x. Plug in numbers for x and y, and then plug in those numbers into the answer choices.

If the value, to the nearest thousand, of cosX is -0.385, which of the following could be true about X?

Option C. Solve for X by doing inverse cosine of -0.385. Then, test the answer choices.

If the average for a group of students is 89.3, and the average test scores for the 8 girls was 92, what was the average score for the 5 boys?

Plug values into the weighted average formula. Then isolate the variable to solve for the boys' average scores.

Wherever a, b, and c are positive real numbers, which of the following expressions is equivalent to log₄a -2log₈b + 0.5log₄c?

Use product and power rules to get log₄a√c - log₈b².

If g(x) = cscx * tanx, then which of the following trigonometric functions is equivalent to g(x)?

g(x) = secx cscx * tanx = (1/sin) * (sin/cos) = 1/cos = sec

Which trigonometric function (where defined) is equivalent to sin²x/cosx * tanx?

sinx - ALWAYS put these functions in terms of sine and cosine (sinx)(sinx)/(cosx) * (sinx/cosx) = sinx/(cosx/cosx) = sinx