Mathematics SAT test paper 2
Mathematics SAT
Total 25 Questions
1 1) If 7 times a number is 84, what is 4 times the number?)
16
28
48
56
X = 84/7 = 12
4x = 4*12 = 48
2) If 
- A. 4
- B. 16
- C. 32
- D. 256
Correct Answer: D
Explanation:
(
3) For the equation 
- A. {-3, 3}
- B. {-2}
- C. {-2, -7}
- D. {3, 6}
Correct Answer: B
Explanation:
put m=-3
-3x - 5 = x2 + 6x + 9.
X2+6x+9+3x+5=0
X2+9x+14=0
(x + 2) (x + 7)=0
X=-2 or -7 ,
put m=-3(given) and x= -2 in (i)
you get 
put m=-3(given) and x = -7. we get
4) rx2 = 
A quadratic equation is provided above, where r and s are constants. What are the solutions for x ?
- A.
- B.
- C.
- D.
Correct Answer: A
Explanation:: rx3 -
formula is x = 
5) If x + 6 > 0 and 1 - 2x >
-1, then x could equal each of the following EXCEPT
·
A. -6
·
B. -4
·
C. 0
·
D. 1/2
Correct Answer: A
Explanation: x + 6 > 0 and 1 - 2x > -1
x > -6
and - 2x > -2
x > -6
and x < 1
The values in (B), (C), and (D) fit
this requirement as well, so they are values for x and not the
correct answer.
6) If the product of x and y is
76, and x is twice the square of y, which of the
following pairs of equations could be used to determine the values of x and y ?
·
A. xy = 76
x = 2y2
·
B. xy = 76
x = (2y)2
·
C. x + y = 76
x = 4y2
·
D. xy = 76
x = 2y
Correct Answer: A
Explanation:
A Translate each statement, piece by piece. The first part tells us that "the product of x and y is 76."
Since product means multiplication, the first equation must be xy = 76,
The second part says that "x is
twice the square of y," which translates to x =
2y2,
7) If - 6 < - 4r + 10 ≤ 2, what is the least possible
value of 4r + 3 ?
·
A. 2
·
B. 5
·
C. 8
·
D. 11
Correct Answer: D
Explanation:
D Starting with the
-6 < -4r + 10,
multiply both sides of the inequality by -1,
we get 6 > 4r - 10.
Add "13" to each side to get
19 > 4r + 3.........(i)
Then solve the right side of the inequality.
- 4r + 10 ≤ 2
multiply both sides of the inequality by -1,
we get get 4r - 10 ≥ -2.
Now add 13 to each side of the equation:
4r + 3 ≥ 11........(ii)
Finally, combine the equations (i) and (ii) to get the range for
11≤ 4r + 3<19
Since the question asks for the least possible value of the expression, 11, (D)
8) 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 1/3, respectively. However, the only
thing you need to recognize is that the equation has two different solutions to
establish that the answer is (C).
9) The sum of three numbers, a, b, and c, is
400. One of the numbers, a, is 40 percent less than the sum
of b and c. What is the value of b + c ?
·
A. 40
·
B. 60
·
C. 150
·
D. 250
Correct Answer: D
Explanation:
D Write the equation a + b + c = 400. ........(i)
a, is 40 percent less than the sum of b and c.
a= (100-40)%(b+c)
a= 60%(b+c)
a=0.60(b+c)
a=0.6b+0.6c
a-0.6b-0.6c=0.......(ii)
From (i) and (ii)
a + b + c =
400
-1(a - 0.6b - 0.6c) = 0(-1)
Now solve
Simplify by dividing both sides by 1.6 to get b + c = 250. The correct answer is (D
10)If 
- A. 4
- B. 16
- C. 16
- D. 32
Correct Answer: D
Explanation:
Square both sides to get
x = 16 × 2 = 32.
11) If y = 3x and x and y are
both integers, which of the following is equivalent to 9x + 3x + 1 ?
·
A. y3
·
B. 3y + 3
·
C. y(y + 3)
·
D. y2 + 3
Correct Answer: C
Explanation:
9x + 3x +
1
=[(3)2]x+
3x.31
=32x+ 3x.3
=3x+x+3x.3
=3x[3x+ 3]=y(y+3)
12) There are k gallons of gasoline available to fill a tank. After d gallons have been pumped, in terms of k and d, what percent of the gasoline has been pumped?
- A.
- B.
- C.
- D.
Correct Answer: A
Explanation:
A Variables in the answer choices? Plug in!
This is a percent question, so make k = 100 and d =
40. If 40 out of the 100 gallons have been pumped, that equals 40%. So 40% is
your target answer. When you plug k = 100 and d =
40 into the answers, only (A) gives you 40. Plugging In turns a hard question
into a much easier question.
13)
In the equation above, what is the value of d ?
- A. -4
- B. 2
- C. 4
- D. 6
Correct Answer: C
Explanation:Whenever the question includes variables and the answer choices are numbers, think Plugging In the Answers. In (A), d = -4, and the equation becomes 
14) Which of the following is equivalent to 
- A.
- B.
- C.
- D. m - 6
Correct Answer: D
Explanation:
D Whenever there are variables in the question and answers, think Plugging In. If m = 2, the expression becomes 
15)
Bryan,
who works in a high-end jewelry store, earns a base pay of $10.00 per hour plus
a certain percent commission on the sales that he helps to broker in the store.
Bryan worked an average of 35 hours per week over the past two weeks and helped
to broker sales of $5,000.00 worth of jewelry during that same two-week period.
If Bryan's earnings for the two-week period were $850.00, what percent
commission on sales does Bryan earn?
·
A. 1%
·
B. 2%
·
C. 3%
·
D. 4%
Correct Answer: C
Explanation:
C (total worked hour in two weeks 35 x 2 = 70hrs) he worked a total of 70 hours.
At a rate of $10.00 per hour base pay, this would add up to $700.00 (70 × 10 = 700).
Since Bryan's earnings were actually $850.00, that means he must have earned $150.00 of commission (850 - 700 = 150).
At this point, you can calculate the percent commission algebraically or simply work backwards from the answers. Algebraically, you know that $150.00 is equal to a certain percent of $5,000.00 in sales, which can be represented as follows: 150 = (x/100) (5,000)
x=15000/5000
x= 3 %
16)
If 
- A. 3(1 + x)
- B. x2 + 2x - 24
- C.
(x + 6)(x - 4)
- D.
Correct Answer: C
Explanation:
C Cross-multiply to get 3(C + x) = (x - 3)(x + 8).
we get 3(C + x) = x2 + 5x - 24.
3C + 3x = x2 + 5x - 24.
Subtract 3x from both sides of the equation to get
3C = x2 + 2x - 24.
we get 3C = (x + 6)(x - 4).
get
C = 
The correct answer is (C).
3 + 
Which of the following ordered pairs (j, k) is the solution to the system of equations above?
- A. (6, -6)
- B. (3, 0)
- C. (0, 2)
- D. (-4, 1)
Correct Answer: A
Explanation:
A Whenever there are variables in the question and numbers in the answer choices, think Plugging In the Answers. In (A), j = 6, and k = -6. Plug these two values into the first equation to get -24 - 8(6) = 12(-6). Solve for both sides of the equation to get -24 - 48 = -72, or -72 = -72. Therefore, the values work for the first equation. Plug the values into the second equation to get 3 + 
18) If
two times a number is equal to that number minus 4, what is the number?
·
A. -7
·
B. -6
·
C. -4
·
D. -3
Correct Answer: C
Explanation:
C Translate the question into an equation.
Let x equal the number, and then 2x = x -
4. Solving for x, we find that x = -4. This is
(C).
19) Which of the following is equivalent to 2x2 - 6x -
8 ?
·
A. 2(x - 4) (x + 1)
·
B. 3(x + 4) (x - 1)
·
C. 2(x - 3) (x + 2)
·
D. 3(x - 4) (x - 2)
Correct Answer: A
Explanation:
A This question requires factoring the
expression 2x2 - 6x - 8. Begin by factoring 2 from the expression: 2(x2 - 3x - 4). This expression is
further factorable, giving 2(x - 4)(x + 1), which is
(A).
20) If 3a + 2b = 24 and 4a + 5b =
53, what is the value of a + b ?
·
A. 2
·
B. 7
·
C. 9
·
D. 11
Correct Answer: D
Explanation:
3a+2b=24.....(i)
4a+5b=53......(ii)
Adding this to (i) and (ii)
7a+7b=77
7(a+b)=77
(a+b) =11
21) 2c + 3d = 17
6c + 5d = 39
In the system of linear equations above, what is the value of 4c -
4d ?
·
A. -4
·
B. 1
·
C. 4
·
D. 13
Correct Answer: C
Explanation:
6c + 5d = 39......(i)
2c + 3d = 17........(ii)]3
we get 6c +9d =51
6c +5d =34
subtracting we get
4d =12
d= 3
put d= 3 in (i) we get
6c+5(3) =39
6c=24
c= 4
Therefore, 4c - 4d = 4(4) - 4(3) = 16 - 12 = 4. This is (C).
22) If x2 + 2xy + y2 = 64
and y - x = 12, which of the following could
be the value of x ?
·
A. -10
·
B. -4
·
C. 2
·
D. 10
Correct Answer: A
Explanation:
A Factoring the left side of the equation x2 + 2xy + y2 = 64 gives (x + y)2 = 64.
Taking the square root of both sides of the equation, we find that x + y = 8 or -8.
The other equation provides that
y - x = 12,
so y = x + 12 .
Substitute this value of y into the first equation: either
x + (x + 12) = 8, so
2x + 12 = 8, 2x = -4,
and x = -2, or else or
x + (x + 12) = -8, so
2x + 12 = -8, so
2x = -20, and
x = -10.
Therefore, x could be either -2 or -10, and only -10 is an
option in the answers, so (A) is correct.
23) Officer
Blake drives his squad car 1 mile per minute while patrolling local highways
during his shift. If he has driven 480 miles by the end of his shift, how many
total hours did he drive his car at the above rate?
·
A. 8
·
B. 12
·
C. 16
·
D. 20
Correct Answer: A
Explanation:
A Since Officer Blake drives 480 miles at a rate of 1 mile per minute, his total drive time was 480 minutes.
you need to convert those minutes into hours. Since there are 60 minutes in 1 hour,
you can divide 480
minutes by 60 to determine that Officer Blake drove for 8 hours, which is (A).
24) What is the value of (2x2 + 4x +
8) - (2x2 - 4x + 7) ?
·
A. 4x2 + 8x + 15
·
B. 2x2 + x + 1
·
C. 8x + 1
·
D. 8x + 15
Correct Answer: C
Explanation:
(2x2 + 4x + 8) - (2x2 - 4x + 7)
(2x2 + 4x + 8 - 2x2 + 4x - 7
8x+1
25) As part of a project for his cartography elective, Adam climbs
several hills to create a relief map for the woods surrounding his house. He
records the vertical heights of the five hills he climbed at 55 feet, 42 feet,
38 feet, 50 feet, and 48 feet. For his project, Adam must convert his
measurements to inches. If 1 foot = 12 inches, what is the measurement, in
inches, of the tallest hill Adam will have on his map?
·
A. 660
·
B. 600
·
C. 576
·
D. 456
Correct Answer: A
Explanation:
A The tallest hill that Adam measures is 55
feet high. Since 1 foot is equivalent to 12 inches, simply multiply 55 × 12 =
660 inches, (A).
Comments
Post a Comment