Solve for x: x + 3 = 12

Transcription

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Math GED Practice Test
This test includes 50 questions, you have maximum 90 minutes to answer these questions.
1. Solve for x: x + 3 = 12
A.
B.
C.
D.
E.
15
-4
9
4
9
2. Which of the following decimals is equal to 1/100?
A.
B.
C.
D.
E.
0.1
1.1
0.01
1.01
0.001
3. How many degrees form one complete sweep through a circle like noon to midnight on a
clock?
A.
B.
C.
D.
E.
360
270
180
90
45
4. Find y: 5 + y = -15
A.
B.
C.
D.
E.
-20
-3
3
10
-10
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5. Which is equal to 3 and 4/5?
A.
B.
C.
D.
E.
7/5
12/5
19/5
24/10
Both and are correct.
6. Solve for h: h – 9 = 36
A.
B.
C.
D.
E.
27
45
4
-4
25
A.
B.
C.
D.
E.
0.3
0.03
1.03
0.003
1.003
8. What is the probability of tossing at once three coins for all ‘heads’ or ‘tails’?
A.
B.
C.
D.
E.
1/2
3/4
1/4
3/8
5/8
A.
B.
C.
D.
E.
0.4
0.04
0.004
1.004
0.0004
10. Arrange the following absolute values in decreasing order: -2.2, 1.21, -2.10, 3.04, 3.2?
A.
B.
C.
D.
E.
1.21, -2.10, -2.2, 3.04, 3.2
-2.2, -2.10, 3.2, 3.04, 1.21
3.2, 3.04, -2.2, -2.10, 1.21
3.04, 3.2, -2.10, -2.2, 1.21
3.2, 3.04, 1.21, -2.10, -2.2
11. How many degrees make up the four corners of a rectangle?
A.
B.
C.
D.
E.
360
270
180
90
45
12. Which of the following absolute values is smaller than the absolute value of -1/2?
A.
B.
C.
D.
E.
0.10
0.20
-1.02
-0.50
Both and are smaller.
13. Which is incorrect?
A.
B.
C.
D.
E.
4 + (8 – 2) = (4 + 8) – 2
4 x (8 / 2) = (4 x 8) / 2
4 / (8 x 2) = (4 / 8) x 2
4 – (8 + 2) = (4 – 8) + 2
and are each incorrect.
14. Fill in the missing number in the following sequence: 2, 4, 3, 9, ???, 49, 46 …
A.
B.
C.
D.
E.
29
7
18
6
24
15. Which is commutative?
A.
B.
C.
D.
E.
a–b
a/b
b/a
a+b+c
and are each commutative.
16. Which is equal to 54/7?
A.
B.
C.
D.
E.
8 and 2/7
2 and 6/7
5 and 4/7
4 and 4/7
7 and 5/7
17. Fill in the missing number in the following sequence: 3, 5, 7, 11, 13, ???, 19, 23 …
A.
B.
C.
D.
E.
14
15
16
17
18
18. The probability of rolling a pair of dice for a ‘7’ is 1 in 6. Am I guaranteed a ‘7’ within six
rolls? Why or why not?
A.
B.
C.
D.
E.
Yes, because theory works.
No, because theory never works.
Yes, because 1 in 6 means six rolls will produce a ‘7’.
No, because there’s a [5/6]^6 or 30% chance of NOT rolling ‘7’ in six rolls.
No, because nothing is ‘guaranteed’.
19. How can the area of any right triangle be found?
A.
B.
C.
D.
E.
base x height
length x width
1/2 base squared
1/2 base x height
Depends on the shape.
20. How many slices are 1/3 of a 12-slice pizza?
A.
B.
C.
D.
E.
4
8
1/36
6
Cannot split a 12-slice pizza three ways.
21. Fifty is What percent of 40?
A.
B.
C.
D.
E.
1.25%
125%
5/4%
80%
0.80%
22. How can the area of any general triangle be found?
A.
B.
C.
D.
E.
base x height
length x width
1/2 base squared
1/2 base x height
Depends on the shape.
23. Solve for t: 1 = 12/t
A.
B.
C.
D.
E.
11
12
13
1/12
None of the above is correct.
24. Find the equivalent of: sqrt (x^9)
A.
B.
C.
D.
E.
x^3
x^7
x^(9/2)
(sqrt x) ^9
(sqrt x) ^3
25. Solve for x: 3x = 12
A.
B.
C.
D.
E.
9
15
36
4
26. Which is smallest: 9 and 7/9 -or- 89/9 -or- 29/3?
A.
B.
C.
D.
E.
9 and 7/9
89/9
29/3
and are equal and < 89/9
and are equal and < 29/3.
27. What is 5 percent of 50?
A.
B.
C.
D.
E.
10%
25%
0.25
25
2.5
28. Arrange these fractions from big to small: 5/8, 7/16, 17/32
A.
B.
C.
D.
E.
5/8, 7/16, 17/32
5/8, 17/32, 7/16
17/32, 7/16, 5/8
17/32, 5/8, 7/16
7/16, 17/32, 5/8
29. A $25 item now selling for $17.50 is discounted by what percent?
A.
B.
C.
D.
E.
30%
33%
40%
7/10
7/10%
30. Solve for x: 1/3 = 12x
A.
B.
C.
D.
E.
9
4
36
1/4
1/36
31. Solve for y: / 7 – y / = 12
A.
B.
C.
D.
E.
5
-5
-19
19
and form the correct answer.
32. Which triangle pair is NOT similar?
A.
B.
C.
D.
E.
5-12-13 -and- 12.5 – 30 – 32.5
60 deg, 30 deg, 10 -and- 60 deg, 90 deg, 12
3-4-5 -and- 3/5 – 4/5 – 1
35 deg, 90 deg, 12 -and- 35 deg, 55 deg, 19
All are similar pairs.
33. A roof slopes downward 6ʹ per foot. What is the percent slope and the drop over a 10ft run?
A.
B.
C.
D.
E.
0.6 and 60 in
50% and 5 ft
67% and 60 in
133% and 5ft
67% and 60ft
34. Solve: 5 + 9 x 3 – 8
A.
B.
C.
D.
E.
34
-70
-40
24
Need parentheses to compute.
35. Compute: 2 and 1/3 + 3 and 4/9 – 2 and 2/3
A.
B.
C.
D.
E.
7 and 7/15
3 and 3/15
3 and 1/9
3 and 13/9
4 and 4/9
36. Which is larger than 8.15 : 55 / 9 -or- 57 / 7 -or- 41 / 5 -or- 65 / 8?
A.
B.
C.
D.
E.
57 / 7
55 / 9
65 / 8
41 / 5
All are greater than 8.15 except B., which is smaller.
37. Revenues comprise $60 million labor for every $55 million in materials. What total revenue
includes $396 million in material?
A.
B.
C.
D.
E.
432 million
828 million
440 million
920 million
495 million
38. A 16-in diameter pizza weighing 4lb has 8 slices. What is the per-slice crust length?
A.
B.
C.
D.
E.
8pi in
2pi in
1pi in
8 oz
Both and are correct answers.
39. What is the least common multiple (LCM) among 3, 4, and 6?
A.
B.
C.
D.
E.
12
18
24
36
48
40. If a parking lot’s SUV : sedan ratio is 1:3, what percent of the lot is cars and how many SUV’s
park in a 100-vehicle lot?
A.
B.
C.
D.
E.
33% and 33 SUV’s
40% and 40 SUV’s
25% and 25 SUV’s
75% and 25 SUV’s
67% and 33 SUV’s
41. Suppose the average worker’s income grows $2k per year starting from $25k annual
salary. Which equation represents income lower than average?
A.
B.
C.
D.
E.
I > 2000y + 25000
I > -2000y + 25000
I < -2000y + 25000
I < 2000y - 25000
42. Which is greatest: 256% -or- 2 and 11/20 -or- 101/40?
A.
B.
C.
D.
E.
256%
2 and 11/20
101/40
and are equal and greater than C..
and are equal and greater than C..
43. Which inequality is entirely outside the area between lines: y = x + 1 -and- y = 21 – 3x for
0 < x < 5?
A.
B.
C.
D.
E.
y < 20 - 4x
y > 22 – 2x
y < 2x + 2
y < 1/2 x + 2
Both and are correct.
44. Solve for c: / 6 – 3c / > / -12 /
A.
B.
C.
D.
E.
inside of 2, 6
outside -2, -6
outside -2, 6
outside 2, -6
No solution.
45. What is the height of a 1000cc box with a 100 sq.cm base?
A.
B.
C.
D.
E.
100cm
10cm
32cm
16cm
13cm
46. What is the slope of the line: y = 2 – x?
A.
B.
C.
D.
E.
-1
2
-2
1
No solution.
47. What is the approximate volume of a 5-cm diameter, 6cm-high cylinder?
A.
B.
C.
D.
E.
150cc
110cc
60cc
50cc
360cc
48. A boat sails 30 miles north and then 40 miles east. How far has the boat traveled and what
is its location from the start point?
A.
traveled 70 miles and is 70 miles away
B.
traveled 50 miles and is 50 miles away NE
C.
traveled 70 miles and is 50 miles away 37 degrees E of N
D.
traveled 70 miles and is 50 miles away 37 degrees N of E
E.
traveled 50 miles and is 50 miles away 37 degrees N of E
49. Three one-foot rulers can be split among how many users to leave each with 1/12 of a ruler?
A.
9
B.
15
C.
36
D.
4
E.
50. One-third of students totaled 12 in attendanc Each pupil was what fraction of the group?
A.
9
B.
4
C.
36
D.
1/4
E.
1/36
1. Answer: Think what temperature ‘x’, when increased 3 degrees, gives 12 degrees.
2. Answer: Since one dollar is $1.00, and 1/100 of a dollar is a penny -or- $0.01
3. Answer: One rotation is called ‘doing a 360ʹ.
4. Answer: Think what temperature ‘y’, when heated 5 degrees, rises to 15 deg below zero.
5. Answer: Three wholes is 15 fifths, plus 4/5 = 19/5.
6. Answer: Since subtraction makes a number smaller, h must be bigger than 36.
7. Answer: Move the decimal point to the left one place for tenths: 3/10 = 0.3/1.0 = 0.3
8. Answer: Possible results are HHH, HHT, HTH, HTT, TTT, TTH, THT, THH, and 2 out of 8
outcomes present all heads HHH or tails TTT.
9. Answer: Move the decimal point left 4 places: 4/10000 = 0.4/1000.0 = 0.0004/1.0000
10. Answer: $3.20 > $3.04 > /-$2.20/ > /-$2.10/ > $1.21
11. Answer: Four right angles means 4×90 = 360 degrees.
12. Answer: Since / -1/2 / a dollar is $0.50, only and are smaller.
13. Answer: Subtraction and division in only the last terms are unaffected by re-groupings.
However, ‘upstream’ subtraction and division are ‘grouping dependent’.
14. Answer: Sequence is square, subtract 1, square, subtract 2, square, subtract 3 …
15. Answer: Purely addition or multiplication can be done in different order; subtraction or
division, however, is ‘order-dependent’ and is not commutative.
16. Answer: 54/7 = 49/7 + 5/7 = 7 and 5/7.
17. Answer: Sequence is list of increasing prime numbers [note 9 and 21 are skipped].
18. Answer: with the 5 in 6 chance of NOT rolling ‘7’, [5/6]^6 = [25/36]^3 ~ [2/3]^3 ~ 8/27
19. Answer: Since a triangle is half a rectangle, then A = 1/2 bh.
20. Answer: One-third of 12 = 12/3 -or- 4.
21. Answer: Since ‘100 percent’ = 40 / 40 x 100%, then ‘percent’ = 50 / 40 x 100% = 125%
22. Answer: A = 1/2 side length flat on the ground x height of top corner from the ground.
23. Answer: Multiply both sides by ‘t’ to isolate ‘t': 1[t] = 12[t]/t => t = 12
24. Answer: Since sqrt y = y^(1/2) , then sqrt (x^9) = (x^9) ^(1/2) ==> Multiply exponents.
25. Answer: Divide both sides by ‘3’ to isolate ‘x': 3x/3 = 12/3 => x = 4
26. Answer: 29/3 = 87/9 < 88/9 < 89/9.
27. Answer: Since ‘100 percent’ of 50 = 1.00 x 50, then 5% of 50 = 0.05 x 50 = 2.50
28. Answer: Since using a common denominator gives: 20/32, 17/32, and 14/32.
29. Answer: Since 25 falls by 7.5, then 7.5/25 = 15/50 = 30/100 -or- a 30% discount.
30. Answer: Divide both sides by ’12’ to isolate ‘x': [1/3]/12 = 12x/12 => x = 1/36
31. Answer: Need to solve two equations: 7 – y = 12 -and- 7 – y = -12 ==> y = -5, 19
32. Answer: Since is 150% enlargement, a fifth, and B.,specify similar rt. tri’s.
33. Answer: Since slope is drop / run = 6in / 12in = 0.50 = 50% slope ==> 5ft drop / 10ft.
34. Answer: Think ‘PEMDAS': no Parenthesis, no Exponent. ==> Multiply 9 x 3 first.
35. Answer: Since a ‘net’ 1/3 is deducted from the middle term: 3 and 4/9 – 3/9 = 3 1/9.
36. Answer: Since 57/7 is 8 1/7 = 8.143, 55/9 is 6 1/9, 65/8 is 8 1/8, and 41/5 is 8 1/5 = 8.20
37. Answer: Since 55:115, then 110:230 = 440:920, and deducting 10% means 396:828
38. Answer: Since C = pi*d, dividing 16pi by 8 slices = 2pi in
39. Answer: Stair-step each factor: 6,12 – 4,8,12 – 3,6,9,12
40. Answer: Since 1:3 means 3 sedans / 3+1 vehicles, 75% are cars and there are 25 SUV’s.
41. Answer: Since I = 2000y + 25000 is the growth line, and I > applies.
42. Answer: Since 11/20 is exactly 0.55, and 101/40 leaves just 1/40 more than 2.5 at 2.525.
43. Answer: Since the other inequalities trace inside y = 1,21 for x->0, and since looks upward,
starting above y = 22 and does not fall as fast as y = 21 – 3x.
44. Answer: Need to solve two equations: 6 – 3c > 12, 6 – 3c < -12 ==> c < -2, c > 6. Recall
that dividing by a negative factor switches the inequality.
45. Answer: 10×100 = 1000
46. Answer: Slope ‘m’ is ‘y-rise over x-run’ from [0,2] to [2,0] = 0-2 / 2-0 = -2/2 = -1.
47. Answer: V cyl ~ 3/4 V box ~ 3/4 of 5x5x6 ~ 3/4 of 150 ~ 110cc
48. Answer: Since 30-40-d resembles a 3-4-5, 37-53-90 degree triangle, then the boat actually
travels 30 + 40 miles while being displaced 50 miles 37 deg N of E.
49. Answer: Let 3/h = 1/12 and multiply both sides by ‘h’ and 12 to isolate ‘h': [12h][3/h] =
1/12[12h] ===> h = 36 users.
50. Answer: Let 1/3 = 12x and divide both sides by ’12’ to isolate ‘x': [1/3]/12 = 12x/12 => x =
1/36

Solve for x: x + 3 = 12

Transcription

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