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CTJan27 Online Year 8 Mathematics Reasoning Test 05

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
For what value of x will 8 and x have the same mean (average) as 27 and 5?
A)
1.5
C)
24
B)
8
D)
40
 

 2. 
The image of point mc002-1.jpg when reflected in the y-axis is
A)
mc002-2.jpg
C)
mc002-4.jpg
B)
mc002-3.jpg
D)
mc002-5.jpg
 

 3. 
Which is a factor of mc003-1.jpg?
A)
mc003-3.jpg
C)
mc003-5.jpg
B)
mc003-4.jpg
D)
mc003-6.jpg
 

 4. 
If 0.0154 is expressed in the form mc004-1.jpg, n is equal to
A)
mc004-2.jpg
C)
3
B)
2
D)
mc004-3.jpg
 

 5. 
What is the distance between points mc005-1.jpg and mc005-2.jpg?
A)
mc005-4.jpg
C)
mc005-6.jpg
B)
mc005-5.jpg
D)
mc005-7.jpg
 

 6. 
There are 12 tomato plants in a garden.  Each plant has 7 branches and each branch has four (4) tomatoes growing on it.  If one-third of the tomatoes are picked, how many tomatoes were picked?
A)
23
C)
224
B)
112
D)
336
 

 7. 
In the diagram below, mc007-1.jpg is parallel to mc007-2.jpg.  Transversal mc007-3.jpg intersects mc007-4.jpg and mc007-5.jpg at G and H, respectively.  If mc007-6.jpg and mc007-7.jpg, what is the value of x?

mc007-8.jpg
A)
20
C)
80
B)
40
D)
160
 

 8. 
There are 461 students and 20 teachers taking buses on a trip to a museum.  Each bus can seat a maximum of 52.  What is the least number of buses needed for the trip?
A)
8
C)
10
B)
9
D)
11
 

 9. 
If mc009-1.jpg, the expression mc009-2.jpg is equivalent to
A)
mc009-4.jpg
C)
mc009-6.jpg
B)
mc009-5.jpg
D)
mc009-7.jpg
 

 10. 
The distance from Earth to the Sun is approximately 93 million miles.  A scientist would write that number as
A)
mc010-1.jpg
C)
mc010-3.jpg
B)
mc010-2.jpg
D)
mc010-4.jpg
 

 11. 
A locker combination system uses three digits from 0 to 9.  How many different three-digit combinations with no digit repeated are possible?
A)
30
C)
720
B)
504
D)
1,000
 

 12. 
What is the slope of line mc012-1.jpg in the accompanying diagram?

mc012-2.jpg
A)
mc012-4.jpg
C)
mc012-6.jpg
B)
mc012-5.jpg
D)
mc012-7.jpg
 

 13. 
If mc013-1.jpg, then x equals
A)
mc013-3.jpg
C)
mc013-5.jpg
B)
mc013-4.jpg
D)
mc013-6.jpg
 

 14. 
In a molecule of water, there are two atoms of hydrogen and one atom of oxygen.  How many atoms of hydrogen are in 28 molecules of water?
A)
14
C)
42
B)
29
D)
56
 

 15. 
A car travels 110 miles in 2 hours.  At the same rate of speed, how far will the car travel in h hours?
A)
mc015-1.jpg
C)
mc015-3.jpg
B)
mc015-2.jpg
D)
mc015-4.jpg
 

 16. 
If the length of a rectangular prism is doubled, its width is tripled, and its height remains the same, what is the volume of the new rectangular prism?
A)
double the original volume
C)
six times the original volume
B)
triple the original volume
D)
nine times the original volume
 

 17. 
Which properties best describe the coordinate graph of two distinct parallel lines?
A)
same slopes and same intercepts
C)
different slopes and same intercepts
B)
same slopes and different intercepts
D)
different slopes and different intercepts
 

 18. 
At a school costume party, seven girls wore masks and nine boys did not. If there were 15 boys at the party and 20 students did not wear masks, what was the total number of students at the party?
A)
30
C)
35
B)
33
D)
42
 

 19. 
If one-half of a number is 8 less than two-thirds of the number, what is the number?
A)
24
C)
48
B)
32
D)
54
 

 20. 
If there are four teams in a league, how many games will have to be played so that each team plays every other team once?
A)
6
C)
3
B)
8
D)
16
 

 21. 
A woman has a ladder that is 13 feet long.  If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?
A)
8
C)
11
B)
9
D)
12
 

 22. 
A boy got 50% of the questions on a test correct.  If he had 10 questions correct out of the first 12, and mc022-1.jpg of the remaining questions correct, how many questions were on the test?
A)
16
C)
26
B)
24
D)
28
 

 23. 
A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner.  An association gives a dinner and charges $3 a plate but invites four nonpaying guests.  If each person has one plate, how many paying persons must attend for the association to collect the exact amount needed to pay the hotel?
A)
60
C)
40
B)
44
D)
20
 

 24. 
In the set of positive integers, what is the solution set of the inequality mc024-1.jpg?
A)
mc024-3.jpg
C)
mc024-5.jpg
B)
mc024-4.jpg
D)
mc024-6.jpg
 

 25. 
Which is a rational number?
A)
mc025-3.jpg
C)
mc025-5.jpg
B)
mc025-4.jpg
D)
mc025-6.jpg
 

 26. 
The perimeter of an equilateral triangle varies directly as the length of a side. When the length of a side is doubled, the perimeter of the triangle is
A)
halved
C)
multiplied by 3
B)
doubled
D)
divided by 3
 

 27. 
Which expression is rational?
A)
mc027-2.jpg
C)
mc027-4.jpg
B)
mc027-3.jpg
D)
mc027-5.jpg
 

 28. 
In the accompanying diagram, a circle with radius 4 is inscribed in a square.

mc028-1.jpg

What is the area of the shaded region?
A)
mc028-3.jpg
C)
mc028-5.jpg
B)
mc028-4.jpg
D)
mc028-6.jpg
 

 29. 
Which letter below has point symmetry, but does not have line symmetry?
A)
H
C)
A
B)
N
D)
E
 

 30. 
What is the approximate circumference of a circle with radius 3?
A)
7.07
C)
18.85
B)
9.42
D)
28.27
 

 31. 
The sum of the measures of the interior angles of an octagon is
A)
180°
C)
540°
B)
360°
D)
1,080°
 

 32. 
The exact average of a set of six test scores is 92.  Five of these scores are 90, 98, 96, 94, and 85.  What is the other test score?
A)
92
C)
89
B)
91
D)
86
 

 33. 
A certain car comes in three body styles with a choice of two engines, a choice of two transmissions, and a choice of six colors.  What is the minimum number of cars a dealer must stock to have one car of every possible combination?
A)
13
C)
42
B)
36
D)
72
 

 34. 
In his will, a man leaves one-half of his money to his wife, one-half of what is then left to his older child, and one-half of what is then left to his younger child.  His two cousins divide the remainder equally, each receiving $2,000.  What was the total amount of money in the man’s will?
A)
$40,000
C)
$24,000
B)
$32,000
D)
$16,000
 

 35. 
If mc035-1.jpg is less than mc035-2.jpg, and mc035-3.jpg is less than mc035-4.jpg, then e is
A)
less than c
C)
less than d
B)
equal to c
D)
greater than d
 

 36. 
In a class of 450 students, 300 are taking a mathematics course and 260 are taking a science course.  If 140 of these students are taking both courses, how many students are not taking either of these courses?
A)
30
C)
110
B)
40
D)
140
 

 37. 
Which expression is equivalent to mc037-1.jpg?
A)
mc037-2.jpg
C)
mc037-4.jpg
B)
mc037-3.jpg
D)
mc037-5.jpg
 

 38. 
What is the smallest integer greater than 1 that is both the square of an integer and the cube of an integer?
A)
8
C)
36
B)
9
D)
64
 

Short Answer
 

 1. 
Find, to the nearest tenth of a foot, the height of the tree represented in the accompanying diagram.

sa001-1.jpg
 

 2. 
A school district offers hockey and basketball.  The result of a survey of 300 students showed:
120 students play hockey, only
90 students play basketball, only
30 students do not participate in either sport
Of those surveyed, how many students play both hockey and basketball?
 

 3. 
In the accompanying diagram, parallel lines sa003-1.jpg and sa003-2.jpg are intersected by transversal sa003-3.jpg at points X and Y, and sa003-4.jpg.  Find sa003-5.jpg.

sa003-6.jpg
 

 4. 
Triangle ABC, with side sa004-1.jpg extended to D, is shown in the accompanying diagram.  If sa004-2.jpg and sa004-3.jpg, what is sa004-4.jpg?

sa004-5.jpg
 

 5. 
How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36 feet from the ground?
 



 
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