Mathematics SAT test paper 3

                Mathematics SAT  Paper

1)  If Alex can fold 12 napkins in x minutes, how many napkins can he fold in y hours?

• A. 
• B. 
• C. 
• D. 

Correct Answer: C

Explanation:

C    12 napkins in x minutes=  12/x

so now the y hours convert into minutes therefore

y *60 = 60y minutes

(60y * 12) /x = 720y/x

2)Of all the houses in a certain neighborhood, 80% have garages. Of those houses with garages, 60% have two-car garages. If there are 56 houses with garages that are not two-car garages, how many houses are there in the neighborhood?

• A. 93
• B. 117
• C. 156
• D. 175

Correct Answer: D

Explanation:

D 80x houses have garages.

60% of those have two-car garages, 

(100- 60)% = 40%=0.40 have garages that are not two-car.

80x * 0.40 = 56 

x = 175

3) Let the function f be defined such that f(x) = x² - c, where c is a constant. If f(-2) = 6, what is the value of c ?

• A. -10
• B. -2
• C. 0
• D. 2

Correct Answer: B

Explanation:

B Start by plugging in what you know into the function given. If f(x) = x² - c, and

 f(-2) = 6.......(1).(given)

then plug put x=-2 for x in the function: f(-2) = (-2)² - c = 4- c ..........(2)

Solve equate (1) and (2) equations 

6 = 4 - c; 

2 = -c; and c = -2.

4) If f (x) = , what is the smallest possible value of f (x) ?

• A. 0
• B. 
• C. 1
• D. 2

Correct Answer: A

Explanation:

A  pic from the options smallest value of f(x)=0

 If 0 = , \

square both sides    0 = 3x - 2  

 2 = 3x, and

x = . Since this is a real value, the equation works, so the smallest value of f(x) is 0. Choice (A) is correc

5) If b is two more than one-third of c, which of the following expresses the value of c in terms of b ?

• A. c = 
• B. c = 
• C. c = 3(b - 2)
• D. c = 3(b - 6)

Correct Answer: C

Explanation:

 b = 2 + (1/3)c

Multiply everything by 3

3b = 6 + c

Subtract 6

3b - 6 = c

6) 3x = 12, what is the value of ?

• A. 
• B. 
• C. 4
• D. 6

Correct Answer: D

Explanation:

D First, solve for x. Divide both sides of the equation by 3, and you get x = 4. Then divide 24 by 4, which gives you 6, which is (D).

7) A coat was on sale for 50% off. Katie bought the coat, using a "$10 off the current price" coupon. If she paid $35 for the coat, what was its original price?

A. $45
B. $70
C. $80
D. $90
E. $95

Correct Answer: D

Explanation:

D. The easiest approach to this problem is to start at the end: Katie used her $10 coupon and paid $35, so the price was $45 without the coupon. Because this price was 50% off the original price, it originally cost twice as much, or $90

8) If i = , what is the product of (4 + 7i) and ?

• A. 16 -  i
• B. 14 +  i
• C. 2 - 8i - 14i²
• D. 

Correct Answer: A

Explanation:

A Use FOIL to multiply the two binomials together. The expression becomes 4  - 8i + 7i - 14i². Simplify the result by multiplying through where you can to get 2 - 8i + i - 14i². To combine the i terms, multiply 8 by  to get . Now the expression is 2 - i + i - 14i², which can be further simplified to 2 - i - 14i². Substitute -1 for i² and combine like terms: 2 - i + 14 = 16 - i, which is (A)

9)  How many solutions exist to the equation |x| = |2x - 1| ?

• A. 0
• B. 1
• C. 2
• D. 3

Correct Answer: C

Explanation:

C If |x| = |2x - 1|, either x = 2x - 1 or -x = 2x - 1. The solutions to these equations are 1 and , respectively. However, the only thing you need to recognize is that the equation has two different solutions to establish that the answer is (C).

10)   If 

 = 2, what is the value of x ?

• A. 4
• B. 16
• C. 16
• D. 32

Correct Answer: D

Explanation:.

vx = 4.

Square both sides to get

x = 16 × 2 = 32.

11)  If y = 3^x and x and y are both integers, which of the following is equivalent to 9^x + 3^{x + 1} ?

• A. y³
• B. 3y + 3
• C. y(y + 3)
• D. y² + 3

Correct Answer: C

Explanation:

C 9^x + 3^{x + 1} 

(3²)^x+3^x3¹

3^x(3^x+3) 

Y(y+3)                          [put y = 3^x]

.

12)   A beverage store charges a base price of x dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression 1.07x + 17, then what is the sales tax, expressed as a percentage of the base price?

• A. 0.07%
• B. 1.07%
• C. 7%
• D. 17%

Correct Answer: C

Explanation:

C You can plug in to make sense of this equation. Say that x = $100. The amount of the keg would then be $107 + $17. The $17 must be the untaxed deposit since it is a flat fee rather than percentage based. Therefore, the tax is $7, which is 7% of the original $100 base price. The answer is (C).

13) The rotation rate of a mixing blade, in rotations per second, slows as a liquid is being added to the mixer. The blade rotates at 1,000 rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less than three times the square of the height of the liquid. If h is the height of liquid in the mixer, which of the following represents R(h), the rate of rotation?

• A. 4 - 9h²
• B. 1,000 - (4 - 3h)
• C. 1,000 - (9h - 4)
• D. 1,000 - (3h² - 4)

Correct Answer: D

Explanation:

D Treat this question as a translation problem. According to the question, R(h) = four rotations per second less than three times the square of the height of the liquid. The height of the liquid is represented by h. Therefore, three times the square of the height of the liquid = 3h². Four less than this amount is 3h² - 4. Since the original speed was 1,000, subtract this value from 1,000 to get the current rate of rotation. The correct answer is (D).

14)  What number divided by two is equal to that same number minus 15 ?

Correct Answer: 30

Explanation:

30 Translate English to math. "What number divided by two is equal to that same number minus 15?" can be written as an equation, with x representing the missing number:  = x - 15.Add 15 to both sides of the equation to get  + 15 = x. Subtract  from both sides to get 15 = . Multiply both sides by 2 to get x = 30.

16)    If f(x) = x², then 

A. 0
B. h
C. 2x
D. 2x + h
E. 

Correct Answer: D

Explanation:

(D) First note that f(x + h) = (x + h )² = x² + 2xh + h². So f(x + h) – f(x) = 2xh + h². Divide this expression by h to get the correct answer choice. [1.1]

17)  If the ratio of k to m is the same as the ratio of m to n, then which of the following must be true?

A. kn = m2
B. k + m = m + n
C. kn = 2m
D. km = mn
E. k - m = m - n

Correct Answer: A

Explanation:

A. Ratio is just a fancy name for fraction, so this problem says that k/m = m/n. Cross-multiplying gives you kn = m2, or Choice (A).

18)    A train leaves the station at 10:45 p.m. and arrives at its destination at 2 a.m. the next day (without changing time zones). The train was stopped for 1/2 hour while it had engine trouble; the rest of the time, its average speed was 80 miles per hour. What total distance did the train travel?

A. 120 miles
B. 140 miles
C. 220 miles
D. 240 miles
E. 260 miles

Correct Answer: C

Explanation:

C. From 10:45 p.m. to midnight is 1 hour 15 minutes, and from midnight to 2 a.m. is another 2 hours. Thus, the train was moving for 3 hours 15 minutes minus the 30 minutes (1/2 hour) it was stopped, for a total of 2 hours 45 minutes. Two hours × 80 miles per hour is 160 miles. Because 45 minutes is 3/4 of an hour, you need to add another 3/4 × 80 = 60 miles, giving you 220 miles.

19)   Getting ready for a party, Nandan expected to set up 1/3 of the tables needed. Unfortunately, one of the people helping him did not show up. As a result, he now had to set up 1/2 of the tables. If he had to set up 4 more tables than he expected, what was the total number of tables set up for the party?

A. 8
B. 12
C. 20
D. 24
E. 30

Correct Answer: D

Explanation:

D. You could write an algebra equation for this problem, but reasoning it out works fine, too. The fraction of the tables that Nandan had to set up changed from 1/3 to 1/2. In math, change is always a cue to subtract, and 1/2 - 1/3 = 1/6. (Solve this without a calculator just for the practice.) So Nandan had to set up 1/6 more tables than he expected — 4 tables, according to the problem. If 4 is 1/6 of the total, then the total number of tables is 4 × 6 = 24.

20)   A certain shipping company charges $3.99 per pound for packages of 15 pounds or less, and $3.49 per pound for packages weighing more than 15 pounds. If Lyle sends two 10-pound packages, and Gretchen sends one 20-pound package, what is the difference between their total costs?

A. $0
B. $0.50
C. $7.50
D. $10
E. $69.80

Correct Answer: D

Explanation:

D. Lyle's cost is 2 packages × 10 pounds × $3.99 = $79.80. Gretchen's cost is 20 pounds × $3.49 = $69.80, and the difference between them is $79.80 - $69.80 = $10.