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Which of the following is the smallest prime number greater than 200? A. 201. B. 205. C. 211. D. 214. A prime number is a number larger than 1 that has only itself and 1 as factors. (It can be evenly divided only by itself and by 1.) 201 is divisible by 3; 205 is divisible by 5; 211, however, is a prime number If 40% is equal to the fraction x/30, what is the value of x? A. 0. B. 15 C. 1, D. 12 Change 40% to a decimal and write an equation to solve for x. 0.4 = x/30. Multiply both sides by 30. You are "undoing" the division. The expression "5 factorial" equals A. 125. B. 120. C. 25. D. 10. The product of all integers from 1 to x is called the x factorial. The product of all numbers from 1 to 5 is 5 factorials. Thus (5)(4)(3)(2)(1) = 20 (3)(2)(1) = 60 (2)(1) = 120 (1) = 120. The expression 5 factorial" is equal to 120 What is the result of subtracting 3x² - 5x - 1 from 8x² + 2x - 9? A. 5x² - 3x - 10
B. -5x² - 3x - 10 C. 5x² +7x - 8 D. - 5x² - 7x + 8 To subtract one polynomial from another, you change the signs of the terms in the subtrahend. First write the example as a subtraction in arithmetic. (From) 8x² + 2x - 9 (Take) – (3x² - 5x – 1) Then change the signs of the terms in the bottom row (the subtrahend) and combine terms that are alike. 8x² + 2x - 9 -3x² + 5x + 1 5x² + 7x - 8 What is the meaning of the statement -30 < -5? A. 30 is greater than 5. B. 30 is less than minus 5. C. Negative 30 is less than negative 5. D. Negative 30 is greater than negative 5. On the number line above, -5 is to the left of 0 and is, therefore, less than 0, but -50 is to the left of -5. This makes -30 less than -5. The < sign is a symbol of inequality, meaning "less than". The statement (-30 < -5) means "negative 30 is less than negative 5." Solve for x: 8x - 2 - 5x = 8. A. x = 1. B. x = 2½ C. x = 3 and 1/ D. x = - To solve for x, combine all similar terms, and set the equation equal to zero. (8x - 5x) + (-2 - 8) = 0 Do the operations inside the
3x - 10 + 10 = 0 + 10 3x = 10 Finally, divide each side by 3 to find the value of x> You are undoing the multiplication. John is paid $26.00 for 8 hours of work. How much should he be paid for working 37 hours at the same hourly wage? We must find out how much John is being paid for each hour he works. To do this we divide the amount he had gained by the number of hours he worked. 26/8=3. $3.25perhour Then we multiply by 37 to get the amount he has earned in 37 hours 3.25⋅37=120. He should be paid $120.25 for 37 hours of work A woman has $500 in a bank account. Every week, she writes out a check for $50. If she doesn't make any new deposits, what will her bank account hold x weeks from now? A. $500 + $50x B. $
- $50x C. $500 - x D. $500 + $50 + x In x weeks, she will make out check’s tor x times $50, or $50x. To find out how much she still has after writing these checks, she would subtract $50x from $500. Thus, her bank account will hold $500 - $50x. When the temperature is 20ºC, what is it the Fahrenheit (F) scale? (Use the following formula). F = (9/5 • C) + A. 93 and 3/5 degrees
B. 78 degrees C. 62 and 7/ degrees D. 68 degrees Use the formula F = (9/5 • C) + 32 Substitute 20 degrees for C. F = (9/5 • 20) + 32 F = 36 + 32 = 68 degrees. The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width. A. 17½ inches B. 8 inches C. 11 inches D. 14½ inches If Length = Width + 3, then l = w + 3 so, 2l + 2w = 2(w + 3) + 2w = 2w + 6 + 2w = 4w + 6 = 4w = 32 W= 8 The perimeter of a rectangle is the sum of its four sides. If x equals its width, then x + 3 equals the length. (The length is 3 inches more than the width.) From this, you can write an equation to find the perimeter. (Use the formula 2w + 2l = P.) x + x + (x + 3) + (x
- = 38 To solve for x, combine similar terms. 4x + 6 = 38 4x = 38 - 6
Find the square root of 85 correct to the nearest tenth. A. 9. B. 9. C. 9. D. 9. One way to solve this is to square each of the suggested answers to see which is close to 85. Thus 9.1 • 9.1 = 82.81 9.2 • 9.2 = 84. 9.3 • 9.3 = 86. 9.4 • 9.4 = 88. To find squares of 9.2 and 9.3 are near 85. Find the difference between the square of each of these numbers and 85. (9.2) 85.00 - 84.64 = 0. (9.3) 86.49 - 85.00 = 1.49. The square 9.2 is closer to 85 than the square 9.3. Therefore, the square root of 85, to the nearest tenth, is 9.2. If 5x = 30, then x is equal to A. 150 B. 25 C. 6 D.
The statement 5x = 30 means "5 times a certain number is equal to 30." To find the number, divide each side by 5. This is to undo the multiplication. 5x/5 = 30/5 x = 6 What is the product of (a - 5) and (a + 3)? A. a² - 15 B. a² + 2a - 15 C. a² - 2a
- 15 D. a² - 2 Set this up as a multiplication example in arithmetic. Remember that
when you multiply terms with unlike signs, the product has minus sign. (a - 5) • (a + 3) =
B. 60 degrees, 45 degrees C. 60 degrees, 90 degrees D. 45 degrees, 90 degrees Every right triangle contains an angle of 90 C. 60 degrees, 90 degrees. This particular right triangle also has an angle of 30 C. 60 degrees, 90 degrees. To find the third angle, subtract the sum of these two angles from 180 degrees. 180 - (30 + 90)) = 180 - 120 = 60 degrees in third angle. The other two angles are 60 and 90 degrees. What is the value of x in the equation x/2 = 7? A. x = 14 B. x = 3½ C. x = 9 D. x = 5 To solve for x in this equation, multiply both sides by 2. This is to undo the division. 2 • (x/2) = 2 • 7 x = 14 Divide 15a³b²c by 5abc. A. 10abc B. 3abc C. 5a²b ² D. 3a²b Divide only similar terms. First divide numbers, then letters. When dividing powers of a letter, just subtract the exponents. (15a³b²c) /5abc = 15/5 • a³/a • b²/b • c/c = 3a²b Two circles have the same center. If their radii are 7 inches and 10 inches, find the area that is part of the larger circle but not the smaller one. A. 3 square inches
B. 17 square inches C. 51π square inches D. 70π square inches The formula for the area of a circle is π • R². Find the area of the larger circle first. π • 10² = 100π square inches. Then find the area of the smaller circle. π • 7² = 49π square inches. To find the part of the larger circle that the smaller one doesn't touch, subtract the two areas. 100 - 49 = 51π square inches. My average grade on a set of five tests was 88%. I can remember only that the first four grades were 78%, 86%, 96%, 94%. What was my fifth grade? A. 88 B. 86 C. 84 D. 82 The easiest way to solve this is to form an equation using x as the unknown grade. (78 + 86 + 96 + 94 + x) / 5 = 88 (354 + x) / 5 = 88 Multiply both sides by 5. This is to undo the division. 5 • [(354 + x) / 5] = 88 • 5 Simplify both sides of the question. 354 + x = 440 x = 440 - 354 x = 86 (grade) How many cubic yards of concrete are needed to make a cement floor that is 9 feet by 12 feet by 6 inches thick?
C. 54
D. 648
First change all measurements to yards 9 feet = 3 yards; 12 feet = 4 yards; 6 inches = 1/6 yard To find the volume of the concrete, multiply the length by the width by the height. 3 • 4 • 1/6 = 12 • 1/6 = 2 cubic yards A wildlife preserve is laid out in the shape of a perfect circle whose radius is 14 miles. The lions' territory in this preserve is shaped like a wedge and has a fence around it. Two inner sides of a fence meet at a 90-degree angle in the center of the preserve. How much territory do the lions have? A. 140 square miles B. 3½ square miles C. 210 square miles D. 154 square miles First find the area of the entire wildlife preserve. Since it is a circle, use the formula for the area of a circle. (Area equals π times the square of the radius.) A = π •R² = 22/7 • (14) ² = 22/7 • 196 = 22 • 28 = 616 square miles The lions' territory is a wedge formed by a 90-degree angle at the center of the circle. Since a circle has 360 degrees, we can find the part of the preserve inhabited by lions. 90/360 = 1/ Next find what equals in square miles. 1/4 • 616/1 = 154 square miles Find the value of (-3) to the 4 power + (-2) to the 4 power + (-1) to the 4 power.
The wall, the ladder, and the ground in the tennis court form a right triangle. The ladder is on a slant and is opposite the right angle formed by the wall and the ground. In this position, the ladder is the "hypotenuse" of the triangle. In geometry, the Pythagorean Theorem states that the square of the hypotenuse (c²) equals the sum of the squares of the other two sides (a² + b²). Thus, a² + b² = c² 8² + x² = 10² Solve by doing the arithmetic operations, and by clearing one side of the equation for x². 64 + x² = 100 x² = 100 - 64 x² = 36 Then find the square root of x² and 36. x = 6 The base of the ladder is 6 feet from the wall. Ten ounces of liquid 20% fruit juice and 80% water. The mixture is diluted by adding 40 additional ounces of water. What is the percentage of fruit juice in the new solution? A. 4% B. 10% C. 20% D. 40% First find how many ounces of the original mixture were fruit juice. 10 • 20 = 10 • .2 = 2 ounces. Next find the total number of ounces in the new mixture. 10 + 40 = 50 ounces Then find what part of the new mixture is fruit juice and convert it to a percentage. 2/50 = 1/25 = 4/100 = 4% If b - 3 = 7, then b is equal to A. 10. B. 4.
C. 21.
D. 8.
This equation means "a number, decreased by 3, is equal to 7" b - 3 = 7 To arrive at a true statement for b, we want to eliminate -3 on the left side of the equation. We do this by adding 3. (This in undoing the subtraction.) We then add 3 to the other side so that the statement remains an equation. (b - 3) + 3 = 7 + 3 By simplifying both sides, we isolate 'b' and thus find the solution. b = 10 What is the product of (z + 2) (2z - 3)? A. 3z - 6 B. z + 4z - 3 C. z² + 4z - 6 D. 2z² + z – 6 An easy way to perform the multiplication is to do four separate multiplications. Then the procedure looks like ordinary multiplication in arithmetic. Use the FOIL (z + 2) (2z - 3) 2z² - 3z + 4z - 6 2z² + z – 6 An artist sold 4 of his paintings. These represented 0.05 of all the artwork he had done. How many paintings had he made? A. 100 B. 80 C. 50 D. 20 Let p stand for the number of paintings the artist made. The 4 paintings he sold are equal to 0.05 of all his paintings. This can be expressed as an equation. 0.05p = 4
0.05 and 'p'. 0.05p/0.05 = 4/0.05 (Clear the decimal in the divisor.) 1p/1 = 400/ p = 80 (paintings made) One of the equal angles of an isosceles triangle is 40 degrees. What is the angle opposite the unequal side? A. 40 degrees B. 90 degrees C. 100 degrees D. 140 degrees In an isosceles triangle, two of the sides are equal. This means that the angles opposite them are equal, too. If one is 40 degrees, then so is the other. To find the angle opposite the unequal side, begin by adding the equal angles. 40 + 40 = 80 degrees To find the third angle, subtract this amount from 180 (the number of degrees in any triangle). 180 - 80 = 100 degrees (third angle) If you divide 24x³ + 16x² - 8x by 8x, how many x's will be there in the quotient? A. 0 B. 5 C. 2 D. - An easy way to do this example is to break it into three examples, dividing each term by 8x. Divide the numbers first, and then the letters. However, to divide the exponents for 'x', just find the difference between them. (Thus, x³ / x = x³-² = x².) 24x³/8x + 16x²/8x - 8x/8x = 3x² + 2x - 1 Since the equation asks only how many x's there are in the quotient (not how many x²'s), the answer is 2.
A room is 19 feet long, 10 feet wide, and 8 feet high. If you want to paint the walls and ceiling, how many square feet of surface will you have to cover with paint? A. 232 square feet B. 422 square feet C. 464 square feet D. 654 square feet First, find the area (surface) of the ceiling. Since it is opposite the floor, it has the same length and width (A = I • w). 19 feet • 10 feet = 190 square feet (ceiling) Next find the combined area of two matching (opposite) walls. Start with the walls formed by the length and height of the room. 19 feet • 8 feet = 152 square feet (first wall) 152 feet • 2 = 304 square feet (matching walls) Then find the area of the walls formed by the width and height of the room. 10 feet • 8 feet = 80 square feet (second wall) 80 feet • 2 = 160 square feet (matching walls) finally, combine all surfaces to be painted. 190 + 304 + 160 = 654 square feet. If a car traveled 200 miles at an average rate of speed of 'r' miles per hour, the time it took for the trip could be written as A. 200/r B. r/ C. 200r D. r/ The basic formula for travel is "distance equals rate multiplied by time," or D = rt. The car traveled 200 miles (D); therefore 200 = rt. To solve for 't' (time), divide both sides of the equation by r. (You are undoing the multiplication.) 200/r = rt/r 200/r = t (time it took for trip)
