SAT Math Study
Claire traveled from City C to D. The first half of the way, she drove at a constant speed of 20 miles per hour. Then she increased her speed and traveled the remaining distance at 60 miles per hour. What is her average speed, in miles per hour, for the trip? (round to tenths)
30.3
Linear function - find what b is: x - 2, 4, 8, a y - 5, a, 23, b
32(3n-1)
To solve a high imaginary exponent, divide (long division) by ___ and take the remainder to replace the old power
4
If the sum of consecutive numbers from -40 to x, inclusive, is 83, what is the value of x?
42
If 2a + 3b is equal to 250 percent of 6b, what is the value of a/b - how to set up?
2a + 3 = 2.5 x 6 (plug in 1 for b and solve for a)
How to set up to find the intersection of these two equations? y=2x+3 y=-1/2x-80
2x+3=-1/2x-80
In this equation, a and b are constants. If the equation above is true for all values of x, what is the value of a? a(x + 1) + b=(x - 1) = 2x + 4 - whats the answer?
3 (plug in values)
For SYSTEMS, if the system has INFINITELY MANY solutions, what are the relationships between the two equations using a, b, and c.
a1/a2 = b1/b2 = c1/c2
For SYSTEMS, if the system has NO solutions, what are the relationships between the two equations using a, b, and c.
a1/a2 = b1/b2 ≠ c1/c2
nth sequence formula?
an = a1+(n-1)xd
whats the formula to find the maximum value of an ax^2 + bx + c?
c - (b^2/4a)
A certain job can be completed by p persons in h hours. How long would it take n persons, working at the same rate to complete the same job? - how to set it up?
ph/n
If (x-3) is a factor of x^3 - 4x + k, what is the value of the constant k? - what is the first step?
plug in 3 for x
distance formula
sqrt(x2-x1)^2+(y2-y1)^2
to compare ratios easier, _______ the values will help
squaring
2 equations with 2 variables? setting up a ________ equation might be useful
system
y = 4x + 1 reflected across the x axis, new equation?
y = -4x - 1 (flip signs)
What is vertex form?
y=a(x-h)^2+k
formula for area of circle
πr^2
The length of a rectangle varies inversely with the width. If the length is 10 when the width is 20, what is the length when the width is 40? - how to set it up?
(10)(20)=x(40)
Midpoint formula?
(x1 + x2 / 2, y1 + y2 / 2)
What is the equation for y = 2x + 3 when flipped over y axis?
-
how to find the vertex from standard form in terms of b and a?
-b/2a
whats 10% in decimal form and whats 5% in decimal form?
.1 and .05
If point f (1, 2) is the line segment connecting point a (2a, b) and point B(b, a), what is the value of a? - set it up? (try a system)
1 = 2a + b / 2 and 2 = b + a / 2
What is i^0, i^1, i^2, i^3?
1, i, -1, -i
rewrite k^-3
1/k^3
The midpoint of AB is (10 , 4) and the coordinates of A is (5 , 1). What is the coordinates of B? -- How do you set this up?
10 = 5 + x / 2, and 4 = 1 + x / 2
The tickets for a movie cost $10 for kids and $5 for elders. If the total of 900 tickets were sold and the total amount of $8000 was collected, how many kid tickets were sold? - how do you set this up?
10k + 5e = 8000 and k + e = 200 (system)
Jackson drove a car from Amherst to Boston at a constant speed of 80 miles per hour. On the way back along the same route, he drove at a constant speed of 30 miles per hour. If he took 5 hours in the entire trip, what is the distance in miles from Amherst to Boston? (round to tenths)
112
If a is divisible by 2, b is divisible by 5, and a / b = 7 / 9, where are positive numbers, and a + b < 200, what is a possible value of a + b?
160
To make orange dye, 5 parts of red dye are mixed with 3 parts of yellow dye. To make green dye, 4 parts of blue dye are mixed with 2 parts of yellow dye. If equal amount of green and orange dye are mixed, what fraction of the new mixture is yellow dye?
17/48
Mixture equation formula of two mixtures (percentages)
1stx+2ndy = mix(x+y)
When f(x) = x^2 + 5x + k is divided by x-4, the remainder is 38, what is k?
2
The ratio of the circumference of two circles, circle O to the circumference of circle P, is 2:3. If the area of circle O is 20, what is the area of circle P? - how to set this up using ratios?
4:9 and 20:x (better doing this than using proportions for these types of questions)
If 5 people take d days to install plumbing, how many days would it take 2 people to complete one third of the same job? - how to set it up?
5d/6
This table gives a linear function. Whats a + b? - set it up? : x - 2, 3, 4 y - a, 6, b
6 - a = b - 6 (then a + b = 12)
Bob makes 7 cookies (x) in 9 hours. If Bob takes 13 hours, how many cookies can he make? - how to set it up?
7 / 9 = x / 13
Two triangles. Triangle T has a 1 side labeled a. Triangle Z has 1 side labeled b. If a / b = 9 / 2 and the AREA of triangle T is 60, what is the AREA of triangle Z? - how to set using proportions?
81 / 4 = 60 / x (square the a / b because finding comparing with area.)
