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2nd Test
1) What is 1 / 3 + 1 / 4 ?
Do not add the denominators. A common wrong answer was 2/7
You need to find a denominator that is the least common multiple of 3 and 4.
This is 12. So 4/12 + 3/12 = 7/12
2) What is 2 / 3 of 1 / 2 ?
Of means multiply. If you take half of 2/3, you get 1/3.
3) What is 20% of 120?
Very few got this even though we just had a discussion about percents.
Percents are fractions. Percent means parts per hundred.
20/100 times 120 = 1/5 of 120 = 24
4) If a @ b = a times (b - a), what is 4 @ 7?
This sort of problem was very common on the continental math league tests.
The @ operation is defined and you need to plug in specific values for a and b
4 ( 7 - 4) = 4 times 3 = 12
5) What is 2 * 4 * 6 * 8 * 10 where (a * b = a times b)?
You can multiply in any order.
8 * 48 * 10 = 384 * 10 = 3,840
6) What is 2 divided by -6 ?
Very few got this. Its almost the same as the problem last time that we went over.
Almost everyone had -3 as their answer for some reason.
One approach is to solve without the negative sign, then add it after. 2/6 = 1/3; 2/-6 = -1/3.
Also note: -2/-6 = 1/3 and -2/6 = -1/3 also.
7) What is 5.1 - 8.23 ?
Many students thought the answer was -4.87 and I'm not quite sure why.
The correct answer is -3.13.
First find the difference by subtracting 5.1 from 8.23 since 8.23 is larger in absolute terms.
Then realize that since you are subtracting a larger number from a smaller, the answer must be negative.
8) If Joe is 2 years less than twice Sally's age, and Sally will be 7 one year from today, how old is Joe?
First convert to an expression:
2 ( 7 - 1 ) - 2 = 10 years old
9) List all the factors of 34.
First you need to learn what a factor is.
A number is a factor of another number if it divides evenly (no remainder) into that number.
The factors are 1, 2, 17, 34 but I gave half credit if you were able to come up with 2 of them..
10) Which of the numbers in this set are prime? {9, 11, 13, 15, 17, 19, 21, 23, 25}
First you need to know what a prime number is.
A prime number has only one and itself as factors.
The primes in this set are 11, 13, 17, 19, 23
11) What is the average of 5, 6, and 12?
To find the average of a set, first sum up the numbers, then divide by how many there are.
(5 + 6 + 12) /3 = 7 2/3
12) What is the average of 3, -10, and 4 ?
( 3 + 4 - 10 ) / 3 = -3
13) If my car gets 30 miles per gallon, how many gallons will I burn if I drive 160 miles?
160 miles / 30 miles/gallon = 5 1/3 gallons
14) What is 5^3 ?
Many got this I am glad to report. On the other hand many still thought it was 5 times 3.
The 3 in the superscript indicates 5 to the power of 3. I know this concept was recently covered in Mrs Kochar's class. The answer is 5 * 5 * 5 = 125
15) If f(y) = 8y + 3, what is f(3) ?
f(y) means a function of y. The idea is to evaluate the expression to the right of the equals sign when y=3.
If you do this, you get 8(3) + 3 = 24 + 3 = 27
16) What is 20,000 times 9,000 divided by 60,000?
I gave half credit on this one if you were close.
You should cancel out the zeros to make this problem much easier.
20000 * 9000 2 * 9000
------------------ = -------------- = 1/3 of 9000 = 3,000
60000 6
17) What is x if 11x + 7 = 52 + 2x ?
One approach is guessing values of x and adjusting your guesses until you get 5.
A better approach is to use algebraic manipulation.
First subtract 2x from both sides to get
9x + 7 = 52
Next subtract 7 from both sides to get
9x = 45
Lastly, divide both sides by 9 to get x = 5
18) What is the area of a right triangle with base (or width) 12 inches and height 5 inches?
Same problem as last time basically.
5 * 12 / 2 = 30 square inches. (area is always in squared units, volume is cubed unites)
19) What is (7 - 4) / (7 + 17) ? 3/24 = 1/8 I don't know why many wrote 8.
20) Estimate how many drops of water there are in a cup of water?
There are 3 teaspoons in a tablespoon. 16 tablespoons in a cup. You don't need to know this to guess though.
I looked up some answers on the web and tried counting drops in a teaspoon.
There are about 50 drops in a teaspoon.
full credit for any guess between 1400 and 4000
half credit if outside that range but within 900 to 9000
One student said there were 5 drops in a cup, and another said there were 999,999,999,999,999.
Do not add the denominators. A common wrong answer was 2/7
You need to find a denominator that is the least common multiple of 3 and 4.
This is 12. So 4/12 + 3/12 = 7/12
2) What is 2 / 3 of 1 / 2 ?
Of means multiply. If you take half of 2/3, you get 1/3.
3) What is 20% of 120?
Very few got this even though we just had a discussion about percents.
Percents are fractions. Percent means parts per hundred.
20/100 times 120 = 1/5 of 120 = 24
4) If a @ b = a times (b - a), what is 4 @ 7?
This sort of problem was very common on the continental math league tests.
The @ operation is defined and you need to plug in specific values for a and b
4 ( 7 - 4) = 4 times 3 = 12
5) What is 2 * 4 * 6 * 8 * 10 where (a * b = a times b)?
You can multiply in any order.
8 * 48 * 10 = 384 * 10 = 3,840
6) What is 2 divided by -6 ?
Very few got this. Its almost the same as the problem last time that we went over.
Almost everyone had -3 as their answer for some reason.
One approach is to solve without the negative sign, then add it after. 2/6 = 1/3; 2/-6 = -1/3.
Also note: -2/-6 = 1/3 and -2/6 = -1/3 also.
7) What is 5.1 - 8.23 ?
Many students thought the answer was -4.87 and I'm not quite sure why.
The correct answer is -3.13.
First find the difference by subtracting 5.1 from 8.23 since 8.23 is larger in absolute terms.
Then realize that since you are subtracting a larger number from a smaller, the answer must be negative.
8) If Joe is 2 years less than twice Sally's age, and Sally will be 7 one year from today, how old is Joe?
First convert to an expression:
2 ( 7 - 1 ) - 2 = 10 years old
9) List all the factors of 34.
First you need to learn what a factor is.
A number is a factor of another number if it divides evenly (no remainder) into that number.
The factors are 1, 2, 17, 34 but I gave half credit if you were able to come up with 2 of them..
10) Which of the numbers in this set are prime? {9, 11, 13, 15, 17, 19, 21, 23, 25}
First you need to know what a prime number is.
A prime number has only one and itself as factors.
The primes in this set are 11, 13, 17, 19, 23
11) What is the average of 5, 6, and 12?
To find the average of a set, first sum up the numbers, then divide by how many there are.
(5 + 6 + 12) /3 = 7 2/3
12) What is the average of 3, -10, and 4 ?
( 3 + 4 - 10 ) / 3 = -3
13) If my car gets 30 miles per gallon, how many gallons will I burn if I drive 160 miles?
160 miles / 30 miles/gallon = 5 1/3 gallons
14) What is 5^3 ?
Many got this I am glad to report. On the other hand many still thought it was 5 times 3.
The 3 in the superscript indicates 5 to the power of 3. I know this concept was recently covered in Mrs Kochar's class. The answer is 5 * 5 * 5 = 125
15) If f(y) = 8y + 3, what is f(3) ?
f(y) means a function of y. The idea is to evaluate the expression to the right of the equals sign when y=3.
If you do this, you get 8(3) + 3 = 24 + 3 = 27
16) What is 20,000 times 9,000 divided by 60,000?
I gave half credit on this one if you were close.
You should cancel out the zeros to make this problem much easier.
20000 * 9000 2 * 9000
------------------ = -------------- = 1/3 of 9000 = 3,000
60000 6
17) What is x if 11x + 7 = 52 + 2x ?
One approach is guessing values of x and adjusting your guesses until you get 5.
A better approach is to use algebraic manipulation.
First subtract 2x from both sides to get
9x + 7 = 52
Next subtract 7 from both sides to get
9x = 45
Lastly, divide both sides by 9 to get x = 5
18) What is the area of a right triangle with base (or width) 12 inches and height 5 inches?
Same problem as last time basically.
5 * 12 / 2 = 30 square inches. (area is always in squared units, volume is cubed unites)
19) What is (7 - 4) / (7 + 17) ? 3/24 = 1/8 I don't know why many wrote 8.
20) Estimate how many drops of water there are in a cup of water?
There are 3 teaspoons in a tablespoon. 16 tablespoons in a cup. You don't need to know this to guess though.
I looked up some answers on the web and tried counting drops in a teaspoon.
There are about 50 drops in a teaspoon.
full credit for any guess between 1400 and 4000
half credit if outside that range but within 900 to 9000
One student said there were 5 drops in a cup, and another said there were 999,999,999,999,999.