practice questions
4 1/2 make it an improper fraction
9/2
To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 7 minutes, how much time will it take her to reach her destination?
90=5/7x
A number is divisible by 2 if
the last digit is even
A number is divisible by 8 if
the number formed by the last three digits is divisible by 8.
A number is divisible by 4 if
the number formed by the last two digits is divisible by 4
prime numbers are only
divisible by themselves
one cup of butter makes 12 cookies. 1c sugar makes 8. if she used 5 more c of sugar than butter how many cookies?
combine the ratios 2:24:3 then multiply cookies by 5
Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control. how do you figure it out
have it or dont 2*2*2*2*2
when asked what the percent increase or decrease is, ALWAYS
subtract 1 at the end
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k? how to solve?
(-2,0) (0,3) plug in either inthe answers
25,002² - 24,998²=
(25002+24998) (25002-25008) simplify
how to find the number of distinct prime factors ie 20⁶
factor 20 into (2²*5)⁶=2^12*5⁶, so it has 2 distinct prime factors
greatest prime factor ie: 2*3*3*3
factor it out and whatever prime number is biggest 3
If \sqrt{28}+\sqrt{175}=a\sqrt b√ 28 +√ 175 =a√ b where a and b are integers each greater than one, then what is the value of (a + b)?
factor out and simplify
In triangle FGH, the base has a length of FH = 126.3, and the altitude from G to FH is constructed and has a length of h. What could be the value of h if we know that the area of the triangle is an integer? Indicate all possible values of h.
1/2b needs to be a multiple of 10 so plug in
the price of an item decreases from 250 to 200. what is the percent decrease?
20%
on a hs team sop to jr 2:3 and jr to sen 5:6. what fraction is sophmores of the whole team?
find common factor of same one, (Jr) and multiply both ratios then add ratios and set soph over whole
5 5/8 make it an improper fraction
45/8
If x4 = y16, then y =
4√x
5√2 percent of√200/1=
5√2 /100*√200/1 then simplify
the price of an item increases from 60 to 102. what is the percent increase
70%
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?
find the slope by using y2-y1/x2-x1
if you are looking for remainders after simplifying and have a whole number and a fraction which one has the greater remainder
fraction bc bottom is not a divisor
Whenever Art Dealer sells a sculpture, he earns a 20 percent commission on the first $12,000 of the sale price plus 15 percent of the sale price in excess of $12,000. If Art earned a $3,900 commission on the sale of a certain sculpture, what was the sale price?
commission=20%*12000+15%(x-12000)
to compare two fractions
cross multiply
associative property
a + (b + c) = (a + b) + c a*(b*c) = (a*b)* c
when you have two fractions equal to eachother what should you do
cross multiply
If a, b, and c are real numbers, and a ≠ 0, which of the following must be true? comm property
a*(b + c) = a*b + a*c a*(b - c) = a*b - a*c (b + c)/a = b/a + c/a (b - c)/a = b/a - c/a
if a/b=c/d then
a*d=b*c
In the downtown of a certain city, there are 8,000 apartments for rent. Here is their breakdown by total area: The median area falls into what group?
add the percents from the top and percents from the bottom until you get 50% or above
30% of 50 is what fraction of 75% of 80?
calculate each then set them over each other and simplify
If x>21/40 then x could be which of the following?
change it to 20/40+1/40 and reduce to 1/2+1/40 then reduce all other fractions
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
combination for boys combination for girls and multiply
if order does not matter:
combination: nCr=n!/r!(n-r)!
undefined fraction means
denominator is zero
In the quadrilateral shown here, a+b+c+d=
inside angles equal 360 so 4*260-360
A number is divisible by 6 if
it is divisible by 2 AND it is divisible by 3.
Both P and Q are positive numbers, and S is a negative number. Which of the following fractions could be undefined? how to solve
look at denominators and see pos+neg, pos-pos because they could equal zero
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 ½ inches. In total, how many marbles must be added to the aquarium to raise the water 2 ¾ inches?
marbles/ inches=x/inches
if you have a complex fraction
multiply num and denom by bottom most denom
compound interest use
percent increase 1.whatever
Which of the following lines intersects the vertical line x = 3 between (3, 1) and (3, 2)?
plug in x=3 and see what is bigger than 1 smaller than 2
From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ? Indicate all such values. how to solve
r values of n / r!
when interest is compounded more than once a year what do you do? _ and _
rate/how many times per year AND years*how many times per year
concrete is made in 1:2:3 ratio. if we have 150 sand, how much concrete can be made?
set sand proportion over whole 2/6=150/x
For which values of x is 5x + 9 < 7x + 6? Indicate all possible values of x. What do you do
simplify, to compare turn into mixed numbers
A number is divisible by 3 if
the sum of the digits is divisible by 3
A number is divisible by 9 if
the sum of the digits is divisible by 9
An integer is randomly selected from the integers from 200 to 900 inclusive.
when you see inclusive the answer must be between 0&1
If x ≠ -2, x ≠ 7 and x-3/x+2=x+3/x-7 , then x =
x-3*x-7=x+3*x+2
In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 for all n > 2. If t1 = -2 and t2 = -1 , then t4 =
you have to plug in 3 for n in order to find t4