PSAT Math › PSAT Mathematics
Give the coefficient of in the binomial expansion of
.
If the expression is expanded, then by the binomial theorem, the
term is
or, equivalently, the coefficient of is
Therefore, the coefficient can be determined by setting
:
Shannon decided to go to nearby café for lunch. She can have a sandwich made on either wheat or white bread. The café offers cheddar, Swiss, and American for cheese choices. For meat, Shannon can choose ham, turkey, bologna, roast beef, or salami. How many cheese and meat sandwich options does Shannon have to choose from?
10
20
25
30
35
2 bread choices * 3 cheese choices * 5 meat choices = 30 sandwich choices
In the 30-day month of January, for every three days it snowed, there were seven days it did not snow. The number of days in January on which it did not snow was how much greater than the number of days in January on which it snowed?
10
11
12
13
14
The question tells us that for every ten-day period in January (a three-day period plus a seven-day period), it snowed on 3 of those days and did not snow on 7 of those days. Since January has 30 days, it has 3 ten-day periods, so we multiply the numbers given for the 10-day period by 3 to find the number of days with and without snow during the 30-day period. Doing this, we see that it snowed 3 * 3 = 9 days and did not snow 7 * 3 = 21 days during the 30-day period. Since the question asks how much greater the number of days on which it did not snow is than the number of days on which it snowed, we subtract as follows: number of days it did not snow - number of days it snowed = 21 – 9 = 12.
Simplify the radical expression.
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
In the 30-day month of January, for every three days it snowed, there were seven days it did not snow. The number of days in January on which it did not snow was how much greater than the number of days in January on which it snowed?
10
11
12
13
14
The question tells us that for every ten-day period in January (a three-day period plus a seven-day period), it snowed on 3 of those days and did not snow on 7 of those days. Since January has 30 days, it has 3 ten-day periods, so we multiply the numbers given for the 10-day period by 3 to find the number of days with and without snow during the 30-day period. Doing this, we see that it snowed 3 * 3 = 9 days and did not snow 7 * 3 = 21 days during the 30-day period. Since the question asks how much greater the number of days on which it did not snow is than the number of days on which it snowed, we subtract as follows: number of days it did not snow - number of days it snowed = 21 – 9 = 12.
If a car travels at 30 mph, how many feet per second does travel?
44 ft/s
2,640 ft/s
4,400 ft/s
440 ft/s
264 ft/s
30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec
x is 75% of y, which is 8 times the amount of 150% of z. What is x in terms of z?
None of the other answers
7.5z
6z
12z
9z
Just take this step by step. First write out each equation:
x = 0.75y
y = 8(1.5z)
First, simplify the second equation:
y = 12z
Then, substitute y from this equation into the first:
x = 0.75(12z) = 9z
The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:
Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.
A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?
100
200
500
750
1000
A cube with a side length of 25m has a surface area of:
25m * 25m * 6 = 3,750 m2
(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)
Each square tile has an area of 5 m2.
Therefore, the total number of square tiles needed to fully cover the surface of the cube is:
3,750m2/5m2 = 750
Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:
s3/n3
If , what is the solution set for
?
To find the solution set, you must solve the equation; in this case, solving the equation means isolating on one side of the equation, and the numbers on the other side of the equation.
That is done like this:
K = -9 or 9 because either number is the square root of 81. To see that that's true, square both numbers. and
.
This is very important to remember: whenever you're isolating a variable by taking the square root of a squared number, the answer can be a positive OR negative value, as long as they share an absolute value!