Praxis Test

Associative Property of Addition

(A + B) + C = A + (B + C)

Associative Property of Multiplication

(A × B) × C = A × (B × C)

1 mL

1 cubic centimeter

deci

1/10

centi-

1/100

deca

10

1 decimeter

10 cm ≈ 4 inches

hecto

100

1 meter

100 cm

1 kg

1000 grams 2.2 lbs

1 liter

1000 mL 1 quart (a liter is a little bigger)

1 km

1000 meters

1 pound

16 "dry" ounces

Triangle sum of measures

180 degrees

1 pint

2 cups 16 oz

1 quart

2 pints = 4 cups

1 short ton

2000 lbs

1 yard

3 feet

Isosceles

30-60-30 Hypotenuse measure is twice that of the shorter leg, and the longer leg is S.R. 3 times the measure of the shorter leg

1 gallon

4 quarts = 16 cups 8 pints

Equilateral

45-45-90 The two legs are congruent, the hypotenuse is always S.R. 2 times the measure of a leg

1 mile

5280 feet = 1760 yards 1.6 km

1 cup

8 fluid ounces

Commutative Property of Addition

A + B = B + A

Work problems

A = RT That's amount equals work rate times time.

Distributive Property

A × (B + C) = AB + AC

Commutative Property of Multiplication

A × B = B × A

Which of the following is NOT a multiple of 12?

Although 6 is a factor of 12, 6 is not a multiple of 12. A multiple of a number is a product of the number and an integer. The remaining choices are all multiples of 12.

If q is 1 more than p and p + q = 21, what is the value of p?

An equation with one variable is solvable, but an equation with two variables is not unless more information is given. Since q is p + 1, you can rewrite the given equation as p + p + 1 = 21 and solve it. p + p + 1 = 21 2p + 1 = 21 2p + 1-1 = 21 -1 2p =20 p= 10

Motion problems

D = RT That's distance equals rate times time.

In a game of Office Worker Out, names are picked out of a hat randomly and the person whose name is picked is out of the contest. If 22 office workers are participating in a game of Office Worker Out and Trudy is one of the participants, what is the probability that Trudy's name will be chosen on the second pick?

For Trudy to even be in the game for the second pick, she has to survive the first pick. The probability that she will be picked on the first pick is 1/22, so the probability that she will survive it is 21/22. If she is in the game on the second pick, only 21 players will be left, so the probability she will be picked is 1/21. Both events have to happen, and the probability that they will both happen is the product of their individual probabilities. , which can be simplified as 1/22.

"King Henry Doesn't Usually Drink Chocolate Milk"

Kilo- *1000 Hecto *100 Deka *10 Original Unit Deci *1/10 Centi *1/100 Milli *1/1000

Supplementary Angles

Make up 180 degrees (If you live to be 180, SUPER!)

Complementary

Make up 90 degrees (If you live to be 90, you deserve a compliment!)

If x and y are opposite integers, what is the range of the median and the mean of x and y?

No matter what integers x and y are, they are opposites, so their sum is 0. Therefore, their mean is 0/2, which is 0. Because they are just two numbers, their median is also their mean, so their median is also 0. The range of a set is the greatest number minus the smallest number, so the range of a set with only 0 and 0 is 0 - 0, which is 0.

Surface area of a cone

SA=pie R squared + pie R square root R square + height squared

5451.38 × 10^7 What can be done to the preceding expression to change it to scientific notation?

Scientific notation consists of a number in which a single digit is followed by a decimal point and multiplied by 10 with an exponent. The number in the question has four digits before the decimal, so the decimal must be moved three places to the left. To keep the original value, the exponent of 10 has to increase by three to make up for moving the decimal three places to the left. 5451.38 × 10^7 = 5.45138 × 10^10

Surface area of a rectangular solid prism

Shaped like a Toblerone 2B+Ph

A specific pie chart represents the 238,456 people who live in a city; one of the sectors of the pie chart has a central angle of 45 degrees. How many people does that sector represent?

The central angle of a sector in a pie chart can tell you what portion of the pie chart a sector covers. Simply divide the central angle by 360: is (or 0.125), so the sector covers of the pie chart. The pie chart represents 238,456 people, so take of that number. The sector represents 29,807 people. Choice (B) is the number of 45-degree sectors a pie chart can have. Choice (C) is of the number of people represented by the pie chart, not . Choice (D) is the number of degrees in the sector. Choice (E) results from multiplying 238,456 by 8 instead of (or 0.125).

If Ace walks 724.26 decameters down a trail and then walks back to his starting point, how many kilometers does he walk on the way back to the starting point?

The distance back to the starting point is the same as the distance from the starting point. The distance back is therefore 724.26 decameters. The next question is what that is in terms of kilometers. Keep in mind that any distance contains fewer kilometers than decameters. One kilometer contains 100 decameters, so divide the number of decameters by 100. . (Dividing by 100 is the same as moving the decimal point two places to the left.) The other choices result from moving the decimal incorrectly

How many meters are in 3 millimeters?

The number of meters in a distance is less than the number of millimeters, so you need to move the decimal to the left. Single units and milli are three apart on the metric prefixes list, so you need to move the decimal three places to the left. The result of doing so is 0.003.

In this diagram, two congruent circles share a point, and each shares three points with the rectangle. The radius of each circle is 2 centimeters. What is the area of the shaded region, rounded to the nearest hundredth?

The radius of each circle is half the diameter. The two diameters cover the length of the rectangle, and one diameter covers the width. The area of the rectangle is found using the formula A = lw; therefore, the area of the rectangle is 8 cm by 4 cm, or 32 cm2. The area of a circle is πr2, so each circle in the diagram has an area of 4π cm2. The sum of the areas of the circles is thus 8π cm2. The area of the shaded region is the area of the rectangle minus the area of the two circles, so it's 32 cm2 - 8π cm2. To the nearest hundredth, that is 6.87 cm2. The other choices are miscalculations you can get from using the formulas incorrectly.

A set of data contains all whole numbers through x and the opposites of all of those whole numbers. Which of the following represents the range of the set of data?

The range of a set of data is the resulting value of the highest number minus the lowest number. Since x represents the highest number, -x represents the lowest number because it has the greatest distance from 0 in the negative direction. x - (-x) = 2x.

The preceding pyramid has a square base, a height of 9 cm, and a volume of 432 cm3. What is the surface area of the pyramid rounded to the nearest whole number?

This problem requires you to take what you know and use it to work your way to what you don't know. The formula for the volume of a pyramid is . The volume and height of the pyramid are given, so you can put those values into the formula and solve for B, base area. This process reveals that the base area is 144 cm2. The base is a square, so the sides have equal measures. The measure of a side times itself gives the area of the square, so a side is equal to the square root of the area. The square root of 144 is 12, so each side is 12 cm. That means the distance from the center of the square base to the midpoint of one of its sides is 6 cm. The center-midpoint segment, the segment representing the height of the pyramid, and a segment representing the slant height of the pyramid form a right triangle. By using the Pythagorean theorem, a2 + b2 = c2, you can determine that the slant height of the pyramid is approximately 10.8167 cm (you need to round to at least four decimal places because the number is not the final answer). With the information gathered so far, you have what you need to use the formula for the surface area of a pyramid, which is times perimeter times slant height. By putting the known values into the formula, you can conclude that the surface area of the pyramid, to the nearest whole number, is 260 cm3.

If 4x < 12, which of the following could be the value of x?

You can divide both sides of the inequality by 4 and get the inequality x < 3. The only choices that are less than 3 are 2 and -1.

Natasha is 9 times Eric's age. In 10 years, the sum of their ages will be 60. What is Natasha's age now?

You can use a variable to represent Eric's age and 9 times that variable to represent Natasha's age. Then you can write an equation based on the situation described. The sum of their ages in 10 years can be represented by x + 10 + 9x + 10, which is equal to 60. By solving the equation x + 10 + 9x + 10 = 60, you can determine that x is 4, so Natasha's age is 9(4), or 36. Choice (A) is the sum of their ages in 10 years, Choice (B) is Eric's age in 10 years, Choice (C) is Natasha's age in 10 years, and Choice (D) is Eric's current age.

Dave's age is 6 times greater than Aden's age. Eight years ago, Dave's age was 26 times greater than Aden's. What will Aden's age be in 20 years?

You can use x to represent Aden's current age, in which case you would need to use 6x to represent Dave's current age. Then, you can write an equation representing the situation. Eight years ago, Aden's age was x - 8 and Dave's age was 6x - 8. Because Dave's age was Aden's age multiplied by 26 then, 26(x - 8) = 6x - 8. The solution to that equation is 10, so Aden's age now is 10. In 20 years, he will be 10 + 20, which is 30.

Which of the following is the prime factorization of 210?

You can write 210 as a product of factors and break down those factors into products of factors. If you continue the process until all factors are prime, you get the prime factorization, which is 2 × 3 × 5 × 7. Choice (A) is incorrect because it leaves out 3 and also because 11 isn't a factor of 210. Choice (B) doesn't list the factor 2. Choices (C) and (E) are factorizations but not the prime factorization. Prime #'s: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

72 is 75 percent of what number?

You can write the sentence in mathematical form as 72 = 0.75x and then solve the equation to reveal that the value of x is 96.

Range

max-min

milli-

one thousandth

Slope

rise/run

Mean

sum/number of terms

kilo

thousand