Identifying Kinds of Math Problems

The Earth is 149,600,000 kilometers from the sun. What is this distance in scientific notation?

1.496 ×10⁸ km To compute Scientific Notation, move the decimal so that there is only one digit in the ones place. The number of times you moved the decimal is the exponent that is put next to the ×10. Note that BIG numbers will have a positive exponent. Tiny numbers with a 0 (zero) in the ones places will have a negative exponent. This can be done by putting your calculator in Scientific mode using the "mode" button. Do clear your calculator's memory after you do the Scientific Notation problem so that all your answers will not be in Scientific Notation.

Sara deposits $1244 in her checking account each week. If she currently has $287 in her account, which equation represents her balance (B) at week w?

w= week and B=balance, use these variables to set up the equation. Since the only thing that changes is that each week $1244 is added, this is the variable amount. So the equation would be: B = 1244w + 287

Eighty-four percent of student athletes attended a preseason meeting. If there are 175 student athletes, how many attended the meeting?

84% of 175, "of" means multiply; 84% ×175 =147 If you are using a calculator you can use the function button and the percent key after the number 84. If you are doing this as a non-calculator question, remember to change 84% to the decimal 0.84. *Note when multiplying that you multiply 175 ×0.84 as whole numbers. After you have the answer you count how many decimal places are in the two factors (two in this problem) and then put that many decimal places in your answer.

If f(x)= x²-4 divided by 4x, for which of the following values will the expression be undefined? A. x = -1 B. x = 0 C. x = 1 D. x = -2

B. x = 0 is the answer. Undefined is the answer when you try to divide by 0 (zero) so the denominator (what you would be dividing by is 4x and when we substitute in a 0 in place of the x it results in 0 which would make you divide by 0 and give you an answer of undefined.

A ticket to a fair costs $20. Tokens are sold in packs of 10 for $15. Edward takes $100 to the fair. He has to buy his ticket, and he also wants to buy tokens to win prizes for his family. Which inequality represents the possible number of packs of tokens that he can buy? A. 100-20≤x B. 20≥100-x C. 20x-15<80 D. 15x + 20≤100

D. 15x + 20≤100 Let x represent the packs of tokens bought. The total tokens bought plus the fair ticket must be less than or equal to $100.

Anna can knit a scarf in 1 2/3 hours. How many scarves can she knit in 4 hours?

Division Problem: 4 ÷ 1 2/3= 2 2/5 (without a calculator turn both numbers into fractions: 4/1 ÷5/3. Now use the division of fractions method: Keep, Change, Flip. 4/1 ×3/5= 12/5 = 2 2/5

A group of 426 people is going to a rally. Each bus can take 65 people. What is the minimum number of buses needed?

Division problem: 426÷65 = 6.55 cannot take 0.55 of a bus so will need to take 7 buses.

If a cardboard box has the dimensions of length 15ft, width 3 ft, and height 8 ft and each dimension is doubled, what would the volume of the box be?

Doubled means multiplied by 2. The new dimensions would be length 30ft, width 6 ft, and height 16 ft. Now, use the formula for volume of a rectangular prism: V= lwh . Using this you will multiply 30×6×16= Which will give you an answer of 2880 ft³.

Darren places an 18-foot ladder so that it reaches 14 feet above the ground. What is the distance between the wall and the base of the ladder?

Drawing a picture will help you see that the ladder placed against the wall (and with the floor) makes a right triangle so you will need to use Pythagorean theorem: a²+b²=c² The ladder is the hypotenuse side for the triangle and the 14 feet is one of the legs. So using the numbers you will put in 14²+b²=18², 196+b²=324, Subtract 196 from both sides gives you: b²=128. Now to get the variable by itself take the square root of both sides which gives you the simplified radical 8√2. Press the "toggle" button results in the decimal 11.31. You could also use the shortcut method: √18²-14²=8√2 and then "toggle" to 11.31.

A single six-sided die is rolled, and two coins are tossed at the same time. What is the probability, expressed as a fraction, of coming up with a three on the die, and two heads on the coins?

Find the probability of each independent event and then multiply. So the probability of rolling a 3 on the die is 1/6, the probability of getting heads when you flip a coin is 1/2. So for all three events, you will multiply: 1/6 ×1/2×1/2= The answer will be 1/24. (Remember when multiplying fractions you do not get a common denominator, you multiply across the top and multiply across the bottom and then simplify if needed.)

If 2(y-4)=4-3y, what is the value of y?

First undo the parenthesis using distributive property which results in 2y-8=4-3y. Now combine the like terms (variables and constants) putting all the variables on one side of the equation and all of the constants on the other. This results in y = -12

A right triangle has an area of 216cm². One of the sides that forms the right angle is 24 cm long. What is the perimeter of the triangle?

First use the area of a triangle formula to find the missing side length. You know that the 24 cm side must be one of the legs of the right triangle so you can substitute that in place of the b or h in the formula since they are both legs. A=1/2bh, will look like this: 216=1/2×24×h Do the multiplication on the right side of the equation, resulting in 216=12h. Dividing by 12 on both sides gives you the answer of 18. Now use the 18 in the Pythagorean Theorem formula as one of the legs. a²+b²=c²= 18²+24²= c² 900 = c² then take the square root of both sides which results in 30 =c OR the shortcut method would be √18²+24²=30.

A radio station has a fundraiser and here are the results for the week so far: Monday $5400, Tuesday $6200, Wednesday $4900, Thursday $4400, and Friday $7600. What is the median of the fundraiser results for the first five days?

Median means to find the middle of the data set. First put the numbers in order from least to greatest, 4400, 4900, 5400, 6200, 7600, then cross off two numbers on each end. So you will find the median number is 5400.

Which number is a solution to the inequality 2(1-x)<8? A. -2 B. -3 C. -4 D. -5

Inequalities are solved the same way as equations in that your goal is the isolate the variable and whatever you do to one side, you must do to the other. There are two differences in solving inequalities: 1. the special negative number rule which says IF you multiply or divide by a negative number on both sides of the inequality you must FLIP your sign; 2. you get a solution SET, not just one answer; So first undo your parenthesis by using the distributive property. This results in 2-2x<8. Now subtract the 2 from both sides which leaves you with -2x<6. Next you have to divide by negative 2 on both sides which will mean you need to FLIP your sign (because you divided by a negative number) and the answer will be x >-3. Reread the question to see that the only answer that is part of the solution SET is A. -2 because the answer must be greater than -3.

Two-thirds of Mrs. Jensen's class passed the science exam. If there are 24 students in her class, how many passed the exam?

Multiplication of fractions problem: 2/3 × 24 =16

The Martins drove 210.5 miles on the first day of their trip and 135.8 on the second day. How many more miles did they drive the first day than the second day?

Key words: how many more means to subtract: 210.5-135.8 = 74.7 (be sure to line up decimals)

The number of people voting in an election who were over 25 years old was 56 less than twice the number of those voting who were under 25 years old. Which expression represents the number of people who were over 25 years old who voted in the election? A. 56x - 25 B. 2x - 56 C. x + 56 D. 56x + 25

Let x = voters under 25. Use the information in the problem to describe the relationship of voters over 25, which would be 2x -56. (Choice B.)

A radio station has a fundraiser and here are the results for the week so far: Monday $5400, Tuesday $6200, Wednesday $4900, Thursday $4400, and Friday $7600. What is the mean for the fundraiser for the first five days?

Mean means the same thing as average. To compute mean you will add all the numbers together and divide by how many numbers you added, which would be 5400+6200+4900+4400+7600=. This will give you 28,500 which you will then divide by 5. The answer will be 28,500.

A trapezoid has a perimeter of 58 feet. Three of the sides are: 13 feet, 11 feet, and 13 feet. What is the length of the 4th side?

Perimeter means ADD all the sides together. Add together the three known sides which gives you 37 ft. Now take the perimeter number 58-37= which gives you the answer of 21 feet for the missing side length.

What is the probability of rolling an even number on a regular die (with digits 1-6)?

Probability problem: make a fraction with the possible outcomes on top and the total number of outcomes on the bottom. 3 even numbers on a die and 6 numbers total on a die so write the fraction 3/6 and reduce to lowest terms, ½. If asked to write this as a percent, use the function button and the change to a percent key to change it to 50%.

The proportion of students to chaperones for a school trip is required to be no more than 7 to 1. If 45 students go on the trip, what is the minimum number of chaperones that must accompany the students?

Proportion question: 7/1=45/x. Cross multiply to get 7x=45. Now divide to get x=6.42. Cannot take 0.4 of a chaperone so must take at least 7 chaperones.

The ratio of men to women in a chorus is 2:3. If there are 180 women in the chorus, how many men are in the chorus?

Proportion question: men/women=2/3=x/180. Cross multiply to get 360=3x. Divide to get the answer of 120.

Kara invested $1250 in the production of a friend's music CD. Her friend paid her back at 6% simple annual interest after 36 months. How much money did Kara get back?

Use the simple interest formula: I=PRT. Calculate the interest and THEN add the interest amount to the principal to give you the TOTAL paid back. (Remember that time should always be expressed as years so in this case 36 months = 3 years.) I = 1250×6%×3= 225; 1250 +225 =1475

A radio station has a fundraiser and here are the results for the week so far: Monday $5400, Tuesday $6200, Wednesday $4900, Thursday $4400, and Friday $7600. What is the range of the results?

Range means to take the greatest number in the data set and the smallest number in the data set and subtract the two. Therefore you would compute the range by 7600-4400 =. Which would give you the answer of 3200.

A summer family camp costs $230 for adults. The cost for a child is $30 less than one half the cost for adults. What is the cost for 3 children?

Set up an equation and let x=the adult cost. Then use the information in the problem to describe the child's cost so 1/2x-30. Now substitute the value 230 in place of x in the expression as 1/2(230)-30. This would equal 85. Now reread the question and see that you were asked to compute the price for 3 children so multiply 85 ×3=255.

Francisco has a total of twenty $5 and $1 bills in his wallet. The total value of the bills is $52. How many $5 bills does Francisco have in his wallet?

Set up an equation. You know that some of the bills were $5 bills and some were $1 bills and that there were 20 bill altogether that equaled $52. If you make x the number of $5 bills then you could make 20-x the number that would be $1 bills. Now multiply these times the value of each bill and add them together to equal $52 resulting in the equation, 5x + 1(20-x) = 52 Undo the parentheses and combine like terms which will give you 4x +20 = 52. Now isolate the x which gives you an answer of 8.

If 10x+3.15 = 58.15, what is the value of x?

Solve the equation by isolating the variable. First take away 3.15 from both sides. Then you will have 10x = 55. Next divide by 10 on both sides which results in x =5.5

Ken needs a cable that is 4 3/4 meters long. He has a cable that is 5 1/3 meters long> What fraction of a meter will Ken need to cut off?

Subtraction of mixed numbers, use calculator if allowed and mixed number button (with function button) or if non-calculator section, 5 1/3-4 3/4. Will need to get common denominator (12) and then borrow from the whole number to solve. Answer: 7/12

What is the surface area of a sphere with a diameter of 3.5 inches? Round your answer to the nearest square inch.

Use the surface area of a sphere formula. SA=4πr² Plug in the values that you know from the problem.

What is the smallest whole number that has both 6 and 8 as factors?

Think of multiples of both numbers, example: 6, 12, 18, 24, 30... and 8, 16, 24, 32, 40.... Find the lowest factor they share which is 24.

A triangular ramp is 12 feet long and rises 2 ft from the ground. To the nearest tenth of a foot, what is the horizontal length of the ramp?

Triangle question - draw a picture and see that this would be a right triangle. So use the Pythagorean theorem to compute the length of the missing side. You will need to figure out that you already know one side and the hypotenuse. So substituting those values into Pythagorean theorem would look like this: 2²+ b²=12². Now compute the squared numbers. 4 +b²=144. Isolate the variable by subtracting 4 from both sides (b²=140) and then taking the square root of each side(b=2√35). Use the toggle button to get the decimal 11.83. Reread the question to see that you were supposed to round this to the nearest tenth place(11.8). You may also use the "short cut" method: √12²-2² =2√35use ("toggle")= 11.8

To the nearest tenth, what is the diameter of a circle with area of 254 square centimeters?

Use the Area of a Circle formula, A=πr² Put the 254 in place of the A(area) in the formula. 254 =3.14r² Now work to isolate the variable first by dividing both sides by 3.14. This gives you 80.89 = r² Next take the square root of both sides. This gives you 8.99 = r. Reread the question to see that they were asking for the DIAMETER of the circle. Since the radius is only goes from the edge of the circle to the center, we must multiply the radius of 8.99 ×2 = 17.987 (rounded to the nearest tenths place = 18.0)

Maggie is baking a pie in a dish with a 9 inch diameter. She needs to roll the pie crust so that it extends 1 inch beyond the dish. Rounded to the nearest tenth, what area of pie crust does she need?

Use the Area of a Circle formula. A=πr² The pie crust must extend 1 inch beyond the dish, all the way around, so add 1 inch to each end of the diameter of the pie dish to find the diameter of the crust: 9+1+1=11 inches. So the radius is needed in the formula, which we can find by dividing the diameter by 2. 11÷2=5.5 inches. So using the formula, A=3.14×5.5²=94.98 rounded to the nearest tenths place would be 95.0 inches².

A rectangular dining table is 8 feet long and 4.5 feet wide. What area of wood was used to create the table top?

Use the formula A=lw. 8×4.5=36 square feet

A cardboard box has the dimensions of length 15ft, width 3 ft, and height 8 ft. What is the volume of the box?

Use the formula for volume of a rectangular prism: V= lwh . Using this you will multiply 15×3×8= Which will give you an answer of 360ft³.

A chocolate company sells its specialty hot cocoa in cylindrical canisters. The canister holds 3740 cm³of cocoa. If the canister is 17.5 cm high, what is the diameter of the canister rounded to the nearest centimeter?

Use the volume of a cylinder formula. V=πr²h Plug in the values that you know from the problem. 3740=3.14×r²×17.5 3740=54.95r² Now work to isolate the variable "r²" by dividing by 54.95 on both sides of the equation which gives you 68.06=r² Now take the square root on both sides to get that r all by itself. 8.25 =r

Container A is a cube. What is the volume of Container A in cubic centimeters if the side length equals 8 cm?

Volume of a Cube (which means all sides are squares) can be computed as V=lwh OR V=s³. 8×8×8= 512 or 8³= 512

A square has an area of 50 square feet. What is the perimeter of the square, rounded to the nearest foot?

We know that you can calculate the area of a square using the formula A=s² (all of the sides of a square are the same length). So if the area is 50 we can take the square root of 50 to find one side length. Use the function button and the square root button to take the square root of 50 which give you the simplified radical of 5√2. You will want to use the "toggle" button to get the decimal approximation. This gives you 7.07. Now a perimeter is found by adding ALL the sides so multiply 7.07×4(sides of a square) which gives you the answer of 28.28. The directions in the problem say to round to the nearest foot which means the nearest ones place so that would be an answer of 28.