Act Mathmatics

What is the difference between 1.8 and 1.08? (Note: A bar indicates a digit pattern that is repeated.)

0.719. Take 1.08 and repeat the pattern several times, then subtract that from 1.8. 1.8 - 1.08080808 ≈ 0.7191919. Realizing that the pattern should repeat, you can conclude that 0.719 is the correct answer.

What is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o'clock?

One complete rotation of a clock hand is 360°, and there are 12 hourly markings on a clock. When the hands read exactly 1 o'clock, the degree measure of the angle formed by the clock hands is of a complete rotation, or (360°) = 30°.

What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 ?

Since 12, 72, and 108 are the only numbers in the list divisible by both 2 and 3, the probability that the number selected at random is divisible by both 2 and 3 is ⅜

Which of the following statements must be true whenever n, a, b, and c are positive integers such that n < a, c > a, and b > c ?

Since b > a, subtracting n from each side, b - n > a - n, will not change the relationship between b and a.

The measure of ∠ABC in the figure is x°. Which of the following is an expression for β° ? Individual Question

The angles of the rectangular pieces of lumber measure 90°, so the sum of the measure of the angles at β is 360°. β + 90 + x + 90 = 360, or β = 180 - x.

A neighborhood recreation program serves a total of 280 children who are either 11 years old or 12 years old. The sum of the children's ages is 3,238 years. How many 11-year-old children does the recreation program serve?

of 11-year-olds to be 122. If you let e = number of 11-year-olds and t = number of 12-year-olds, then you can solve the system e + t = 280 and 11e + 12t = 3,238. Substitution, elimination, and matrices are just some of the methods you could use to solve the system. Just remember, in the end, you want to solve for e.

The distribution of Jamal's high school grades by percentage of course credits is given in the circle graph below. What is Jamal's grade point average if each A is worth 4 points; each B, 3 points; and each C, 2 points?

since 4(0.7) + 3(0.2) + 2(0.1) = 3.6.

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.

After arranging the flower bed, Taher decides that the flower bed would look more attractive if 1 of the angles in the triangle were a right angle. He decides to place the right angle at vertex A and to leave the lengths of AB and AC as 4 and 5 feet, respectively. To the nearest 0.1 foot, how long of a piece of lumber would he need to replace the 6-foot piece represented by BC ?

6.4 is the correct answer. Using the Pythagorean theorem, 42 + 52 = (BC)2. Then BC = √(42 + 52) = √41 ≈ 6.4.

Which of the following equations represents the linear relationship between time, t, and velocity, v, shown in the table below?

A linear relationship means the associated graph is a line. So, you can think of the ordered pairs (t,v) as points on the line. Since (0,120), (1,152), and (2,184) are points on the line, the slope of the line is = 32. Therefore, v = 32t + b, where b is the y-intercept of the line. Since (0,120) is a point on the line, 120 = 32(0) + b, or b = 120. Thus, an equation for the line is v = 32t + 120.

Points A, B, C, and D are on a line such that B is between A and C, and C is between B and D. The distance from A to B is 6 units. The distance from B to C is twice the distance from A to B, and the distance from C to D is twice the distance from B to C. What is the distance, in units, from the midpoint of to the midpoint of ?

BC = 2AB = 2(6) = 12 and CD = 2BC = 2(12) = 24. The distance between the midpoints of BC and CD is BC + CD = (12)+ (24) = 18

Quadrilateral ABCD is drawn on the standard (x,y) coordinate plane as shown below, with points E and F on AD. Point G is the center of rectangle BCEF. How many coordinate units long is AG ?

By drawing in rectangle BCEF and diagonal BE, you can find the coordinates of G by finding the midpoint of BE. So G is at , or (9,2). Using the distance formula, AG = √((9 - 0)2 + (2 - 0)2) = √(81 + 4) = √85.

In the figure below, A, B, C, and D are collinear, FC is parallel to ED, BE is perpendicular to ED, and the measures of ∠FAB and ∠EBA are as marked. What is the measure of ∠FCB ?

Correct! B is the correct answer. Since FC and ED are two parallel line segments cut by transversal BE, ∠E and ∠BGC are corresponding angles. So, the measure of ∠BGC is 90°. Since ∠ABG ∠GBC are supplementary angles, the measure of ∠GBC = 180° - 147° = 33°. Looking at ΔBGC, the sum of the measures of angles ∠GCB, ∠BGC, and ∠GBC is 180°. So, the measure of ∠GCB + 90° + 33° = 180°, or 180° - 90° - 33° = 57°.

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?

Correct! This 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.

Which one of the following expressions has an even integer value for all integers a and c ?

F. 8a + 2ac is even because it is divisible by 2, 8a + 2ac = 2(4a+ ac), and 4a + ac is an integer because a and c are integers.

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?

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.

An industrial cleaner is manufactured using only the 3 secret ingredients A, B, and C, which are mixed in the ratio of 2:3:5, respectively, by weight. How many pounds of secret ingredient B are in a 42-pound (net weight) bucket of this cleaner?

If you let 3x be amount of secret ingredient B, you can set up the equation 2x + 3x + 5x = 42. Since 10x = 42, x = 4.2, and B = 3x = 12.6.

Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane?

The correct answer is K. The radius of the circle is the distance between (0,0) and (3,4), which is √((3-0)2+ (4-0)2) = 5. An equation of a circle where (h,k) is the center and r is the radius is (x - h)2 + (y - k)2 = r2. So (x - 0)2 + (y - 0)2 = 52 or x2 + y2 = 25.

A circle has a circumference of 16 feet. What is the radius of the circle, in feet?

The formula for the circumference of a circle with radius r is 2r. So 2r= 16 , or r = 8.

Use the following information to answer questions 3-5.Taher has decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular lumber with lengths 4, 5, and 6 feet, as shown in the figure below. Points A, B, and C are located at the corners of the flower bed. Taher plans to cut the 3 pieces of lumber for the flower bed border from a single piece of lumber. Each cut takes inch of wood off the length of the piece of lumber. Among the following lengths, in inches, of pieces of lumber, which is the shortest piece that he can use to cut the pieces for the flower bed border?

The number of inches of wood needed if there were no cuts is 4 + 5 + 6 = 15 feet, or 180 inches. However, you need to add 2(<) for 2 cuts that are needed so that you have lumber for each of the 3 sides. Since 180 + 2() = 180 + , the minimum piece needed to construct the flower bed border including the 2 cuts would be 181 inches

In the standard (x,y)coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (-3,0) and (7,4) ?

To find the midpoint, you need to take the average of each of the coordinates, = (2,2).

If n = 8 and 16 • 2m = 4n - 8, then m = ?

When n = 8, 4n - 8 = 48 - 8 = 40 = 1, and 16 · 2m = 24 · 2m = 24 + m. So, 24 + m= 1, and any number to the zeroth power is 1, so 4 + m = 0, or m = -4.

Which of the following expressions is the closest approximation to the height h, in feet, of the roof truss shown below?

YZ = XZ = 30) = 15. So, tan 20° = = . Then h = 15 tan 20°.

The geometric figure shown below consists of a square and 4 semicircles. The diameters of the semicircles are the sides of the square, and each diameter is 10 centimeters long. Which of the following is the closest approximation of the total area, in square centimeters, of this geometric figure?

You found the area of the square, the area of 4 semicircles (or the area of 2 full circles), and added them. 102 + 2pi(5)2 double tilde 257. The closest answer is 260.