Download BLAST Math, Senior High, 2005 1 BLAST Math Test Senior High 1

BLAST Math, Senior High, 2005
1
BLAST Math Test
Senior High
1. Three less than a number
is two more than twice the number. What is the
number?
a. −5
b. 13
c. 1
d. 43
e. 3
2. 2005 is 25% of what number?
a. 510.25
b. 1604
e. 50125
c. 2506.25
d. 8020
3. Find the solution to the equation 12(x − 15) + 7 = 19 − 2(x − 2).
a. x = 12
b. x = 14
c. x = 94
7
d. x =
4. Expand (x − 5)(x + 2)(x − 3).
a. x3 − 6x2 − x + 30 b. x3 + 6x2 − x + 30
c. x3 −6x2 +31x+30
d. x3 +6x2 −31x+30
e. x3 −6x2 −19x+30
c. (x − 1)(x2 + x − 1)
d. (x − 1)(x2 − x − 1)
e. (x − 1)(x + 1)(x − 2)
(x + 1)(x2 + x − 1)
(x + 2)(x − 3)(x + 3)
5.
94
5
e. x =
98
5
Factor x6 − 1.
a. (x2 + 1)(x4 − 1)
b. (x − 1)(x2 − x + 1)
2
2
(x + 1)(x + x + 1)
(x + 1)(x + x + 1)
6. Determine the tenth term of the following sequence of numbers: 1, -3, 9, -27, 81, -243, ...
a. -59049
b. -19683
c. -729
d. 19683
e. 59049
7.
A musician spends 40 hours each week practicing her bass guitar. She spends 2 more hours practicing scales than
she spends on fingering. She spends 12 more hours working on grooves than she does practicing scales. How many hours
does she spend on fingering?
a. 6
b. 8
c. 10
d. 14
e. 22
8. The tens digit of a two digit number is two more than the units digit. The number itself is 10 less than 21 times the
units digit. What is the sum of the digits of the number?
a. 3
b. 6
c. 8
d. 10
e. 14
9.
The cost of fuel per hour for running an airplane is directly proportional to the square of the speed. If the cost is
$900 to fly at 150mph, what is the cost to fly at 200mph?
a. $1200
b. $1300
c. $1400
d. $1500
e. $1600
10.
Two-thirds of the women and seven twelfths of the men in a particular town are married. If marriage is always
between one man and one woman and no-one who is married is married to someone outside the town, what fraction of
the town’s
residents are married?
a. 12
b. 24
c. 85
d. 28
e. 56
47
45
75
11.
a.
1
2
12.
a. 1
13.
a.
25
36
Suppose you flip a coin three times. What is the probability that exactly two of the flips are heads?
5
b. 23
c. 65
d. 38
e. 12
v
u v

s r
u u
q p
u
u
t t
√ 

What is the value of log7 
 7 7 7 7 7 7 7?
b.
127
128
c.
63
64
d.
7
8
e. e
A room is measured and determined to be 25 square yards. How large is the room is square inches?
b. 900
c. 1800
d. 3600
e. 32400
14. Find the area of a triangle√with sides that are 5 inches, 7 inches and 8 inches.
√
a. 28in2
b. 10 5in2
c. 20 in2
d. 10 3in2
√
e. 10 2in2
15. On what day of the week will Christmas, 2010 fall?
a. Sunday
b. Tuesday
c. Wednesday
d. Friday
e. Saturday
16. Which of the following is largest?
b. 2100
a. 100!
d. 1002
e. (10!)10
c. 1010!
BLAST Math, Senior High, 2005
2
17. You have a strip of paper that you wish to cut into 30 pieces. After making a cut, you are allowed to overlap the
resulting pieces before making your next cut, but you are not allowed to fold the paper. Under these conditions, what is
the fewest number of cuts you must make?
a. 3
b. 4
c. 5
d. 8
e. 29
18. What is the volume of a pyramid which has a square base with side length of 5cm and height of 6cm?
a. 15cm3
b. 30cm3
c. 50cm3
d. 100cm3
e. 150cm3
19. Jim would like to tape a 3 hour program using his VCR. Jim’s VCR has two modes: SP mode fills up a tape with
120 minutes of video, EP mode fills up a tape with 360 minutes of video. Jim can switch between modes at any time
during the taping. If Jim starts taping in SP mode, after how many minutes should he switch to EP mode in order to fill
up the tape?
a. 60
b. 75
c. 90
d. 100
e. 120
20. When the 3 digit number 91068 is viewed upside down, it reads 89016. How many 3 digit numbers read the same
when viewed upside-down? Assume that the digit 1 looks like a 1 when it is upside down.
a. 9
b. 12
c. 15
d. 20
e. 25
21. Let a and b be the solutions to the equation x2 − 3x + 1 = 0. Determine the value of a + b − (ab)2005
a. -2
b. -1
c. 0
d. 1
e. 2
22.
The circle in the picture at right is constructed so that it is tangent to one side of the square and
intersects the square at two of its corners. If the radius of the circle is 5cm. Find the area of the
square.
a. 25cm2
b. 64cm2
c. 72cm2
d. 81cm2
e. 100cm2
23. Suppose a map has a scale of 1cm=50m. How many square kilometers are represented by an area that has an area
on the map of 120 square centimeters?
a. 0.3
b. 0.6
c. 6
d. 48
e. 300
Suppose 3a = 2 and 3b = 5. Determine the value of 4(b/a) .
log3 (4)
log3 (4)
b. log
c. 5
d. 10
5
3( 2 )
√
65
25. Suppose f ( x − 5) = x2 − 13x + 1−x
. Determine the value of f (3).
a. 9
b. 11
c. 13
d. 14
6
24.
a.
5
2
e. 25
e. 15
26.
Suppose ABC is a triangle and that there is a point D on side AB such that 6 ADC = 90◦ , 6 ACD = 30◦ ,
BCD√= 45◦ and segment AC√is 8 units long. Compute
in square units.
√ the area of the triangle √
√
a. 16 3
b. 8( 3 + 3)
c. 32 3
d. 8(2 3 + 3)
e. 16( 3 + 3)
27. How many consecutive zeros are at the end of 25! ?
a. 4
b. 5
c. 6
d. 7
e. 8
28. Determine the sum of the coefficients of the terms of the expansion of ( 12 x2 − 3x + 2)92 (4x3 + x2 − 3x)94
a. − 129
b. − 12
c. 0
d. 4
e. 29056
2
29. Three logicians are shown a basket containing 3 red hats and 2 white hats. The logicians are blindfolded and each
is given a hat from the basket then the basket is covered by a blanket. The first logician’s blindfold is removed so that he
can see the other two logicians hats but not his own. When asked for the color of his hat, he says that he doesn’t know.
The second logician’s blindfold is removed and he also cannot determine the color of his hat. From this information, what
conclusion can the third logician make before his blindfold is removed?
a. The first logician b. The first logician c. The second logi- d. The third logician e. The third logician
has a white hat
has a red hat
cian has a red hat
has a white hat
has a red hat
30. f (x) = sin(cos(x)) and g(x) = cos(sin(x)). Which of the following is true of the graphs of f and g for 0 ≤ x ≤ 2π?
a. f (x) = g(x)
b. f (x) < g(x)
c. f (x) > g(x)
d. They cross exactly e. They cross exactly
once.
twice.
BLAST Math, Senior High, 2005
3
BLAST Math Test
Senior High
Name
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Church
BLAST Math, Senior High, 2005
4
BLAST Math Test
Senior High
ANSWERS
1. a
2. d
3. b
4. a
5. b
6. b
7. b
8. c
9. e
10. d
11. d
12. b
13. e
14. d
15. e
16. c
17. c
18. c
19. c
20. b
21. e
22. b
23. a
24. e
25. a
26. b
27. c
28. d
29. e
30. b