Sat Mathematics Level2 Test (PRACTICE PROBLEM)

8/3/2019 Sat Mathematics Level2 Test (PRACTICE PROBLEM)

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SAT MATHEMATICS LEVEL 2

Directions: For each of the following problems, identify the BEST answer of the choices given. If the

exact numerical value is not one of the choices, select the answer that is closest to this value. Then fill

in the corresponding oval on the answer sheet.

USE THE SPACE FOR SCRATCHWORK

1. What is the volume of a cube whose surface area is A cube with volume 1 has a side of length√ 1=1

twice that of a cube with volume 1？ and thus a surface area of 61=6. A cube

(A)√ 2 whose surface area is 62=12 has a side of

(B)2 length 12/6 = √ 2 and a volume of (√ 2)3

(C)2√ 2 =2√ 2.

(D)4

(E)8

2. If y is the measure of an acute angle such that sin( y) The correct answer is (B).

=a/5, tan( y)=？

(A)√ 2 5 − /5

(B)a/√ 2 5 −

(C)5/√ 2 5 −

(D)a/5a

(E) a/√ 2 5 +

3. Which number is NOT in the domain of The correct answer is (C). The function y is

f ( x)=？ defined for all numbers except where x +3 = 0,

(A) 2 which is when x = 3.

(B) 2

(C) 3

(D) 3

(E) 0

4.Find the value of the reminder obtained when Since (6 x4 + 5 x3 – 2 x + 8)=( x(1/2))Q( x)+ R.

6 x4

+ 5 x3

– 2 x + 8 is divided by x(1/2). Hence R=8.

(A) 2

(B) 4

(C) 6

(D) 8



(E) 10 USE THE SPACE FOR SCRATCHWORK

5. Solve the equation 2 x+ √ 1=0. Since √ =12 x

(A) 1 and 1/4 Square both sides: x=14 x+4 x2

(B) 1/4 4 x2 5 x +1=0 (4 x 1)( x 1)

(C) 1 We obtain x= 1/4,1.

(D) 0 Check x=1, 1= 1 (does not check)

(E) 4 Thus x = 1/4 is the only root.

6.Express the infinite decimal 0.212121… as a common 0.212121…=0.21 = 21/99 = 7/33.

fraction.

(A)7/10

(B)7/11

(C)7/33

(D)21/100

(E)7/99

7. In figure 1, RT is a diameter of the semicircle. If The correct answer is (C).

RS = 2 and ST = 3, then the area of the semicircle is

(A)13/2

(B)13/4

(C) 13/8

(D) 13/12

(E)cannot be determined from the information given.

8. The radiator of a car contains 10 quarts of a 20% The correct answer is (B). In the original solution

solution of alcohol. If 2 quarts of water are added, there are 0.20 10 = 2 quarts of alcohol. After 2

what percent of the resulting solution is alcohol ? quarts of water are added, the resulting solution has

(A)18% the same 2 quarts of alcohol in 12 quarts of solution.

(B) %3

216 %

3

216

6

1

12

2

.

(C) %4

115

(D)14%



(E) %2

112


9. A triangle with vertices (0, 0), (4, 3), and (–3, 4) belongs The correct answer is (C).

to which of the following classes?

I—Scalene Triangles

II—Isosceles Triangles

III—Right Triangles

IV—Equilateral Triangles

(A) none

(B) I only

(C) II and III only

(D) IV only

(E) III only

10. Which of the following is the approximate equation The correct answer is (E). First find the slope

of a line perpendicular to47.0

x+

53.0

y= 1and passing of the given line

47.0

x+

53.0

y= 1. Multiply

through the point(2

1,

2

1 ). the entire equation by (0.47)(0.53), therefore

(A) )21(13.1

21 x y we have 0.53 x +0.47 y =(0.47)(0.53),

(B) )2

1(89.0

2

1 y x y =1.128 x +0.53. A perpendicular line has

(C) )2

1(13.1

2

1 x y the negative reciprocal as its slope, so that

(D) )2

1(13.1

2

1 x y m=

128.1

1 =0.887. Through the point

(E) )2

1(89.02

1

x y ( 2

1, 2

1

),thus )2

1(89.02

1

x y .

11. Alicia earns 20 dollars per hour, of which 1.45% is 20 dollars is the same as 2000 cents, and 1.45%

deducted to pay local taxes. How many cents per hour of 2000 is 0.01452000=29cents.The correct

of Alicia ‘s wages are used to pay local taxes？ answer is (E).

(A)0.0029

(B)0.029

(C)0.29

(D)2.9



(E)29 USE THE SPACE FOR SCRATCHWORK

12.What is the value of x if | − 1|=| − 2|？ The correct answer is (A).

(A) 1/2

(B) 1/2

(C) 1

(D) 3/2

(E) 2

13. The axis of symmetry for f ( x)= x2 2 x +3 is x = f ( x)= x2 2 x +3=( x 1)2 +2, thus the axis of

(A) 2 symmetry for f ( x) is x =1.

(B) 1

(C) 2

(D) 1

(E)1/2

14. The equation of the tangent to a circle at point The correct answer is (A). We use the property

(6, 6) if the circle has its center at point (3, 3), would of tangents to circles here, which states that the

Be tangent to a circle at any point on the circle is at

(A) x + y 12 = 0 right angles to the line joining that point and

(B) x = y the center of the circle. (C) x + y = 0

(D) x + y + 12 = 0

(E) x y 12 = 0

15.(a + 2i)(b i)= (a + 2i)(b i)= ab + (2b a)i + 2

(A) a + b i

(B) ab + 2

(C) ab + (2b a)i + 2

(D) ab 2

(E) ab + (2b a)i 2

16. In the figure below, the circle has a radius of 7.07. The given problem, the hypotenuse (which is

AC is a diameter, and AB = BC. The area of triangle the diameter of the circle) is of length 14.14.

ABC is Also, it is given that AB = BC . Using this

(A) 100 information and the Pythagorean theorem,

(B) 200 we have ( AC )2=( AB)2 + ( BC )2 ⇒ AB = BC =

(C) 50 10.Therefore, the area of the triangle is 50



(D) 75 USE THE SPACE FOR SCRATCHWORK

(E) 25 square units.

17. If f (t )=

, f (t )= The correct answer is (D.)

(A) f (t )

(B) f (1/t )

(C) f (1/t )

(D)(1/t ) f (1/t )

(E)none of these.

18.If 2 x=7, then 2

x+3=？ 2

x+3=2

x 2

3=78=56, the correct answer is (B).

(A)63

(B)56

(C)14

(D)49

(E)343

19. AB and AC are tangents to a circle at points B and C , Let m BOC = n, 7=(n/360)2

respectively. Minor arc BC is 7in. and the radius of then n=70. m BOC =18070=110.

the circle is 18 in. What is the number of degrees in The correct answer is (E). angle BAC ?

(A) 90

(B) 95

(C) 70

(D) 100

(E) 110

20. A right circular cylinder is circumscribed about a S =4r 2, T=2r 2+(2r )(2r )= 6r 2

sphere. If S represents the surface area of the sphere ∴S=

.

and T represents the total area of the cylinder, then

(A) S=

T

(B) S<

(C) S>



(D) S


(E) S

21. The graph of f ( x)=104e2 x

is shown below. What is Since triangle OAB is an isosceles triangle, we

the area of triangle ABC if OA= AB ? know that the perpendicular bisector of side

OB will pass through the vertex A. If AX is the

perpendicular bisector of side OB, then the

coordinates of point X will be (3, 0).

Thus, the height of the triangle 104e2310.

The area of triangle OAB =(1/2)(10)(6)=30.

(A)25

(B)60

(C)45

(D)50

(E)30

22. What is the probability that the first 2 draws from a Therefore, the total probability of drawing two

pack of cards are clubs and the third is a spade ? clubs and a spade successively without replacing

(Assume all cards are drawn without replacement.) the cards will be ( 1352

)( 1251

) 1350

)= 2028132600

.

(A)2028

132600

(B) 28

132600

(C) 1716

132600

(D) 2028

140608

(E) 1716

140608

23. What is the present age of John’s son if 2 years If John’s present age is x years, his age two years

ago it was one-third of John’s age. Take John’s ago would be (x 2) years. His son’s age two years

present age to be x years. ago was 1/3 of his age. So, two years ago, John’s

(A)

x 2

3 +2 son’s age was

x 2

3 . This means that John’s son’s



(B) x

3+2 USE THE SPACE FOR SCRATCHWORK

(C) x

3 present age would be

x 2

3+2.

(D) x 2

3

(E) x

3 2

24.The next three terms in the sequence of the geometric The common ratio r = 12/(36)= 1/3.

progression 36, 12,4,4/3,…,are The correct answer is (A).

(A) 4/9, 4/27, 4/81

(B)4/9, 4/27, 4/81

(C) 1/3, 1/9, 1/27

(D)1/3, 1/9, 1/27

(E)1/3, 0, 1/3

25.What are the asymptotes of the hyperbola 4 x2 9 y

2 We see that the given equation is

= 36 ? equivalent to 149

22

y x

.The asymptotes

(A) y = 9 x and y = 9 x are y2 =9

42

x or y = 2 x 3

. The correct

(B) y =2 x

3and y =

2 x

3answer is (B).

(C) y = 2 x and y =2 x

(D) y =3 x

2and y =

3 x

2

(E) y =4 x and y = 4 x

26. What is the period of y = 3cos (2 x) + 4 ? 2 x =2 x x=1.

(A) 2/3 The period is p =1.

(B)

(C) 1

(D) 2

(E) /2

27. The graph of the function y= x2 + x12 cuts the x2 + x12=0, ( x + 4 )( x 3 )=0

x-axis at the points x= 4, 3. The correct answer is (A).



(A) (3, 0) and (4, 0) USE THE SPACE FOR SCRATCHWORK

(B) (0, 0) and (3, 0)

(C) (3, 0) and (4, 0)

(D) (0, 0) and (4, 0)

(E) (0, 0) and (12, 0)

28. Which of the following equations represents the The correct answer is (C).

curve in the figure below ?

(A) y=sin x

(B) y=2sin ( x/3)

(C) y=0.5sin3 x

(D) y=0.5sin ( x/3)

(E) y= 0.5sin ( x/3)

29. In the figure below, the coordinates of the center, P , The correct answer is (B).

of the circle are

(A) (3, 2)

(B) (3, 8)

(C) (3, 6)

(D) (3, 4)

(E) (3, 5)

30. If the population of a city is increasing by 3 percent The correct answer is (A). This problem can

every year, and the current population is 300,000, what be solved using the formula of exponential

was the population five years ago? growth, which is A = P (1+r )t , where A = the

(A) 258,783 amount present finally, P =the initial amount, r

(B) 250,000 = the rate of growth, and t = the total time. Thus,

(C) 265,956 for our problem, we have 300,000

(D) 311,569 = P (1 + 0.03)5 P = 258,783.

(E) 303,214

31.How many possible five-digit zip codes can be formed The correct answer is (B). Since no zip

from the set of digits {0, 1, 2 . . ., 9} such that no code codes can begin with a zero, we have nine

begins with a zero? digits to choose from for the first of the

(A) 100,000 five-digit code. Also, since there is no

(B) 90,000 restriction on repeating the digits, the

(C) 256 remaining four digits of the five-digit code

(D) 128 can each take 10 values. Therefore, we have



(E) 1,024 USE THE SPACE FOR SCRATCHWORK

a total of 9(10)(10)(10)(10)=90,000 options.

32. Convert the binary number 101,101 to a base 10 The correct answer is (A).

number. 101,101

(A) 45 = 125 + 0 24 +1 23 + 1 22 + 0 21 + 120

(B) 18 = 32 + 8 + 4 + 1 = 45

(C) 46

(D) 22

(E) 90

33. The graph of y = f ( x) is shown below. The correct answer is (D).

The graph of y =| ()| would be

(A)

(B)

(C)

(D)

(E)

34. If (3.5) x = (4.2) y, then

=



(A)1.15 USE THE SPACE FOR SCRATCHWORK

(B) 1.25 The correct answer is (A).

(C) 1.35

(D) 1.45

(E) 1.55

35. If arcsin(sin x)=/6, and 0 x /2, then x could be The correct answer is (C). By definition,

(A)0 arcsin( sin u)= u. Therefore, if arcsin( sin u)

(B)1/2 =/6, then u =/6.

(C)/6

(D)/3

(E)/2

36. If triangles ABC and CDE are similar and other The correct answer is (A).

dimensions are as shown below, what is the length

of segment AE ?

(A) 18.03

(B) 17.05

(C) 16.86

(D) 19.85

(E) 18.28

37. In the figure below, the coordinates of point P are The correct answer is (B).

(A) (3.46, 3.46)

(B) (3.46, 2)

(C) (2, 2)

(D) (2, 3.46)

(E) (3, 1.73)

38. A solid box is 15cm by 10cm by 8cm. A new solid The volume of the original box is

is formed by removing a cube 3cm on a side from 15108=1200. The volume of each cube that

each corner of this box. What percent of the original is removed is 33=27. Since there are 8 corners

volume is removed ? on the box, 8 cubes are removed. So the total

(A)4.5% volume removed is 827=216 . Therefore, the

(B)9% desired percentage is

×100=18%.

(C)12%

(D)18%



(E)24% USE THE SPACE FOR SCRATCHWORK

39.Which of the following numbers is a perfect square ? The correct answer is (C).

(A)98!99!

(B)98!99!

(C)99!100!

(D)99!101!

(E)100!101!

40. Simplifies The fraction()()

()()=(()())()() =9.

()()

()()

=? The correct answer is (E).

(A)1

(B)9/4

(C)3

(D)9/2

(E)9

41. A right triangle has perimeter 32 and area 20. What From the problem, we know that

is the length of its hypotenuse ? a +b +c =32 and 2ab=80(A)57/4 a +b =32c

(B)59/4 Squaring both sides, we get

(C)61/4 a2+b2+2ab =102464c+c2

(D)63/4 80=102464c, c=944/64=59/4.

(E)65/4 The correct answer is (B).

42. What is the domain of the function defined by The correct answer is (E).

1 ,51 ,3)(

2 x x x x x f

.

(A)0< x <1

(B) x < 1

(C) x 1

(D) x 0

(E)All rea numbers.

43. The mean of fifteen integers is 102. On adding



another integer, the mean reduces to 100. What is USE THE SPACE FOR SCRATCHWORK

the new integer added? Let S is the sum of the fifteen integers and the

(A) 90 new added integer be x. Now, if the mean

(B) 85 of the 15 numbers before we added the new

(C) 70 integer was 102, then we have：

(D) 65

=120S =1530.

=100, x=70.

(E) 60 The correct answer is (C).

44. In triangle ABC below, AB=10 and BC =8, while By sine’s law, we get the measure of

∠m A = ∠40°. The measure of ACB is ∠ ACB=53°.

(A) 50° The correct answer is (B).

(B) 53°

(C) 60°

(D) 48°

(E) 65°

45.What is the area of the shaded region in the figure The area is equal to 48=4.57.

below? The correct answer is (C).

(A) 12.57

(B) 8(C) 4.57

(D) 7.89

(E) 6.32

46. If sin2 x cos2 x =0.5, then sin4 x cos4 x = ? The correct answer is (A).

(A) 0.5

(B) 1.5

(C) 0.25

(D)√ 0.5

(E) 0

47.√

is the same as

√

= tan , The correct answer is (C).

(A) cos

(B) sec

(C) tan

(D) csc



(E) cot USE THE SPACE FOR SCRATCHWORK

48. When the sun is 20° above the horizon, how long is If x is the length of the shadow cast by the tree, then

the shadow that is cast by a tree 150 feet tall? tan 20°=150/ x, x= 412 ft.

(A) 374 feet The correct answer is (C).

(B) 391 feet

(C) 412 feet

(D) 405 feet

(E) 402 feet

49. If an angle measured counterclockwise from the The correct answer is (D).

positive x-axis terminates in the third quadrant, which

of the following is true?

(A) sin is positive, and cos is negative.

(B) sin is positive, and cos is positive.

(C) sin is negative, and cos is positive.

(D) sin is negative, and cos is negative.

(E) None of the above.

50. Define a@b= abb2and a#b= a +bab2

. What is@#

=

=

= −

.

@#

? The correct answer is (A).

(A)1/2

(B)1/4

(C)1/8

(D)1/4

(E)1/2

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Sat Mathematics Level2 Test (PRACTICE PROBLEM)