SAT SMACK DOWN (Part 2)!!

GEOMETRY

100

−2x + 3y = 6 

In the xy-plane, the graph of what equation is perpendicular to the graph of the equation above?

3x + 2y = 6

200

In the xy-plane, the point (2, 5) lies on the graph of the function f. If f (x) = k − x2, where k is a constant, what is the value of k?

9. Since the point (2, 5) lies on the graph of y = f(x) in the xy-plane, the ordered pair (2, 5) must satisfy the equation y = f(x). That is, 5 = f(2), or 5 = k − 22. This equation simplifies to 5 = k − 4. Therefore, the value of the constant k is 9.

300

The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 1/3 the corresponding original dimension, what is the height of the reproduction, in inches?

29 /3. It is given that the height of the original painting is 29 inches and the reproduction’s height is 1/3 the original height. One-third of 29 is 29/3, or 9.6 . Either the fraction 29/3 or the decimals 9.66 or 9.67 can be gridded as the correct answer.

400

The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?

m=dV

500

x^2 + 20x + y^2 + 16y = -20

The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

(-10, -8)

The standard equation of a circle in the xy-plane is of the form (x − h)2 + (y − k)2 = r2, where (h, k) are the coordinates of the center of the circle and r is the radius. To convert the given equation to the standard form, complete the squares. The first two terms need a 100 to complete the square, and the second two terms need a 64. Adding 100 and 64 to both sides of the given equation yields (x2 + 20x + 100) + (y2 + 16y + 64) = −20 + 100 + 64, which is equivalent to (x + 10)2 + (y + 8)2 = 144. Therefore, the coordinates of the center of the circle are (−10, −8).

ALGEBRA II

100

If x^-2 = 64, what is the value of x^(1/3) + x^0?

3/2

200

x    f(x)

1     5

3     13

5     21

Some values of the linear function f are shown in the table above. Which of the following defines f?

a. f(x)= 2x+3

b. f(x)= 3x+2

c. f(x)= 4x+1

d. f(x)= 5

C

300

What is the value of a where the a is a positive constant and x does not equal -2?

(2x+6)/(x+2)^2 - 2/(x+2) = a/(x+2)^2

2

400

What value of p is the solution of the equation?

2(p+1)+8(p-1) = 5p

1.2 or 

6/5

500

Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?

2 hours and 40 minutes. If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.

WORD PROBLEMS

100

To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

7.5 lbs of chocolate

200

An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

3

300

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, what equation can Alan use to determine how many fewer average miles, m, he should drive each week?

(4/25)m = 5

400

Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, what is the maximum number of hours for which Maria can rent the boat?

4. The equation 60h + 10 ≤ 280, where h is the number of hours the boat has been rented, can be written to represent the situation. Subtracting 10 from both sides and then dividing by 60 yields h ≤ 4.5. Since the boat can be rented only for whole numbers of hours, the maximum number of hours for which Maria can rent the boat is 4.

500

The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of n businesses per year. There were b businesses in the DBA at the beginning of this year. Determine the function that best models the total number of businesses, y, the DBA plans to have as members x years from now?

y=nx+b

ARITHMETIC & ALGEBRA I

100

If 5x+6=10, what is the value of 10x+3?

11

200

If h hours and 30 minutes is equal to 450 minutes, what is the value of h ?

7

300

In one semester, Doug and Laura spent a combined 250 hours in the tutoring lab. If Doug spent 40 more hours in the lab than Laura did, how many hours did Laura spend in the lab?

105

400

At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t = n + 2, how many additional tea bags are needed to make each additional cup of tea?

1

When n is increased by 1, t increases by the coefficient of n, which is 1.

500

For how many integer values of b is b+3>0 and 1>2b-9?

Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.

MISCELLANEOUS

100

In how many different ways can 6 vehicles be parked in three parking spaces?

120   

6X5X4 = 120

200

a = 18t + 15

Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount to the account. The equation above models the amount a, in dollars, that Jane has deposited after t weekly deposits. According to the model, how many dollars was Jane’s initial deposit? 

15

300

Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?

1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.

400

Five students, all of different heights, are randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?

1/20. 1x3x2x1x1=6, 6 ways in which students can be arranged under given conditions. Under no conditions, the ways are 5x4x3x2x1=120. 6/120=1/20.

500

In the xy-plane, the point (3, 6) lies on the graph of the function 

f(x)=3x^2-bx+12

. What is the value of b ?

11