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SEVENTH GRADE / MATHEMATICS / TEST 7.1.1.1

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

 INTEGERS
    ♦ 
Whole numbers are counting numbers (1,2,3,...) with the addition of 0; and integers are these plus the negatives of counting numbers: { ...,-2,-1,0,1,2,...}. Counting numbers are also called natural numbers by the way.
    ♦ Integers are very important because all of our calculations are done via integers. Here we will learn the way of well defining consecutive basic operations and evaluating them.
1. What is the result of (7-8:2+64:8)-(7+8:2-4x2)?

a) 4
b) 12
c) -12
d) 8
The order of operations is similar to stack or last-in-first-out memories. The later defined/used operations are done/evaluated earlier. That means evaluation of powers, division and multiplication and subtraction and summation is the correct order.
Paranthesis are blocks and are to be evaluated first in order to be able to continue.
7-7=0 ; - 8:2 - 8:2 = -8 ; 8+8 = 16.
2. (7-8:2+64:8)-(7+8:2-4x2)+(17-8:2x4+64:8)-(7+18:2-4:2)=?

a) 3
b) 18
c) 6
d) 4
Looking at the paranthesis we record (17-8:2x4+64:8) is bit uneasy. The result of 8:2x4 differs depending of the order of operations having equal priorities. Usually extra paranthesis are used but her we will evaluate the operations according to yehir order in print/script and we will adopt evaluating the division first:8:2x4=16.
(7-8:2+64:8)=11; (7+8:2-4x2)=3; (17-8:2x4+64:8)=9; (7+18:2-4:2)=14.
3. How many integers does there exist between the solutions of blue and red expressions seen below ?

!


a) 3
b) 0
c) 1
d) 2
"Between" means here that the limits are excluded. It is usually better to cite this exclusion because language gets sometimes vauge.
The denominator (in both cases) is greater than the numerator, try to see at a glance .
4. Which case states the truth if A=1/0.001 , B=1/0.002 ve C=1/0.008 ?

a) A < B < C
b) C < B < A
c) B < C < A
d) A < C < B
Just expand by 1000 ... It will then be much easier to see .
5. What will be the minimal A+B+C value if A, B and C are all integers and AxB = 24 , BxC = 48 ?

a) -73
b) -18
c) -24
d) -8
If we consider the equality AxB=24, the minimal sum for A+B will be (-24)+(-1)=-25. Integers having a definite sum will have max. product when they are closest and/besides integers do contain negative wholes.
y
6. What will be the minimal A+B-C value if A, B and C are all integers and AxB = 24 , BxC = 48 ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) 0
b) -23
c) -12
d) -1


Since AxB = 24, B=24/A is valid. replace and get (24/A)xC=48, i.e. C=2xA. ry1 makes use of this fact.
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7. The inequalities 1≤A≤3 and 3≤B≤12 are valid for integer A and B. Which of the followings should then be valid for AxB ?

a) 3≤AxB≤36
b) 9≤AxB≤36
c) 3≤AxB≤30
d) 3≤AxB≤6
The least values are A=1 and B=3, whereas the greatest ...
8. The inequalities 1≤A≤3 and 3≤B≤12 are valid for integer A and B. Which of the followings should then be valid for B/A ?

a) 3≤B/A≤12
b) 1≤B/A≤36
c) 1≤B/A≤12
d) 0≤B/A≤12
Least B/A değeri if greatest A and least B; similarly ...
9. Which value should A have according to the figure below if each letter represents a different digit ?

!


a) 8
b) 5
c) 7
d) 9
The first addition implies C=0 .
The second addition implies A+B=10 and B=1 .
10. A and B are inequal natural numbers with A<9 and B<10. Which min. value may then the expression (A-B)/(A+B) take ?

a) -1
b) 1/15
c) 1
d) -15
If A-B>0, take the greatest A+B under A-B=1.
If A-B<0 ... And compare the reults.
11. A and B are inequal integers with A<9 and B<10. Which min. value may then the expression (A-B)/(A+B) take ?

a) -14
b) -13
c) -17
d) -21
The question is already answered if A and B are positive integers. The least numerator is to be attained in case B>A in which case the result is negatve integer if A+B>0.
Let A=-1 . B should be among 2 and 9. The least value if B=2 .
Let A=-2 . B should be among 3 and 9. olmalıdır. Values: -5, -6/2, ... , -11/7
...
Let A=-8 olsun. B should be 9 olmalıdır. Value: -17 .
y
12. Lines A and B are perpendicular to each other. On which line will the perpendiculars drawn from equal points on A and B, points having same distances to the origin, intersect ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) Red
b) Purple
c) Green
d) Orange
That is a preperation for coordinate systems; have please a look at ry1 .
13. An operation Δ is defined on ıntegers as AΔB = A4+A2x B2+B4. Which of the followings will then the set of all possible results be ?

a) Rational numbers
b) All numbers
c) Integers
d) Natural numbers
Even powers of integers are whole (natural) numbers .
14. A division without residue is shown at the figure below. Which integers are not likely to be equal to b ?
Note: Numbers at places marked with "-" are not given.

!


a) 0
b) 1, 2 and 3
c) 0 and 4
d) 4


b can not be equal to or grater than 5, because ... .
15. (5!-4!)/4!x(2!-0!)=?

a) 3
b) 1
c) 2
d) 4
5!=5x4x3x2x1 . 0! is defined to be 1.
5! = 5 x 4! i.e. 5!-4! = 4x4! .
16. What is the value of S supposed to be for equality shown below ?

!


a) -4
b) -8
c) -2
d) 2
[1+1/(1+2/S)]=3 i.e. 1/(1+2/S)=2 i.e. 1+2/S=1/2 i.e. 2/S=-1/2 .
17. What is the value of (6xA + B)/(4xB+A), if A/B = 3/5 ?

a) 2
b) 1
c) -1
d) 0
The first equation means 5xA = 3xB, i.e. 6xA = 3xB +A ve 6xA + B = ... .
y
18. Let C=12+22+32+ ... +1002 and let D be to be obtained by decreasing each to be squared number of the right side of the previous equation by 1.
Let A and B further be defined as A=C-D and B=C+D .
B-A = ?


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 676700
b) 338350
c) 328350
d) 656700
ry1 & http://www.9math.com/book/sum-squares-first-n-natural-numbers .
19. The numbers A < B < C are consecutive. How is the expression (A+2xB+3xC+4)/3 to be written in terms of A ?

!


a) A+2
b) A+4
c) 2xA+4
d) 2x(A+1)
For quick answer take A=1. Get(1+4+9+4)/3 = 6 and compare ... (2xA+4 seems to be proper) .
Calculate A+2xA+2+3xA+9+4 = 6xA+12 and divide by 3 if you want to be a sure hand ... .
20. Two operations A*B = 2xA-B and AΔB = A2 - B2 are defined. [1*(-2)]Δ3 = ?

a) 9
b) 7
c) 3
d) -3
1*(-2)= 2x1 - (-2) = 4 and 4Δ3 = 42 - 32 = ... .
21. Which cohice is the replacement of the question mark of the figure ?

!


a) 9
b) 7
c) 5
d) 0
Consider 543-143 = 396 as an example .
Since +10xB+C-100xC-10xB-A = 99x(A-C) , the result should be multiples of 99, i.e. anyone of 99, 198, 297, 396, 495, 594,693, 792 and 891 . They all have ... at tens .
y
22. The operation Ø is defined via table below. (3Ø2)x(2Ø0) = ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 1
b) 3
c) 4
d) 2


The operation is commutative. have please a look at ry1 .
23. Which choice is the least of the numbers having a digit sum of 15 ?

a) 069
b) 960
c) -960
d) -069
3 digits having a sum of 15:0,6,9 and 0,7,8 ; 1,5,9 ; 1,6,8 and 1,7,7 ... .
Connect points A and be to have a 7 sided polygon whose sum of inner angles is (7-2)·180°=900° .
The sum of the angles given is 775° .
24. How much will the number -56490 decrease if the digits at thousands' and hundreds' are interchanged ?

a) -2970
b) 2970
c) -115950
d) 115950
- 56490 + 59460 = 2970 .
25. 3:(7+12:1:3-16:2x1) = ?

a) 3/35
b) 35
c) 1
d) 1/35
This is operation priority: Powers, division and multiplication, addition and subtraction. Paranthesis are blocks whose simplest form or numerical value is first to be determined. Without evaluating the parantehsis, operations can not be performed.
The convention in case of operations having equal priorities is to evaluate the first operation prior to the next. Paranthesis are generally used to avoid ambiguity in such cases .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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