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SEVENTH GRADE / MATHEMATICS /INTEGERS TEST 7.1.1.2

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. Which choice is the result of evaluating the expression (-21:-3)x5:2x4-(7+8:2-4x2)+(-2)x0x10 ?

a) 67
b) 76
c) 38
d) 17
Evaluate the value of each paranthesis with priority of powers (none yet), divisions and multiplications and subtractions and additions . In case of equal priorities then in the order you read.
(-21:-3)x5:2x4 = 7x5:2x4 = 35:2x4 = 17.5x4 = 70 ; (7+8:2-4x2) = 7+4-8 = 3 ; (-2)x0x10 = 0 .
 
2. What is the product of integers having an absolute value less than 7 ?

a) 0
b) 110
c) 129600
d) 518400
e.g. : |6|=|-6|=6. But take care of 0 .
-6x-5x...x0x...x6x7 =...
 
3. What is the product of factorials of integers having an absolute value less than 3 ?

a) 0
b) 2
c) Not defined.
d) 12
http://mathforum.org/library/drmath/view/60851.html.
Factorial is not defined for negative natural numbers .
 
4. Which number is to be in the red circle ?

!


a) 2
b) 1
c) 1/3
d) 1/2
-4:2x3-(-7)=-6+7=1 and 3!=6 olduğuna göre ... In addition (-2)2=4 ... .
 
5. A≤B≤C are given as consecutive even integers. (A-C)x(A-B)/(B-C)x(C-B) = ?

!


a) -4
b) 2
c) -2
d) 4
Let A=-6. Then A-C = -6 - (-2)= -4 ; A-B = -2 ; B-C=-2 and C-B=2 . If we choose a positive number, the result will not change because of the differences.
 
y
6. Which choice gives the rule of the pattern 6, 6, 20/3, ..., 56/6, ... if 0≤n≤7 is known ?

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



a) nx(n+1)/(n-1)
b) 2xn
c) (2n+1)/(n-1)
d) none


Try a and c ... .
 
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7. |-42| - [(|-7x4| - |-7|):(3!-|3|)]2 = ?

a) -7
b) -5
c) 7
d) 11
42-[(21):(3)]2 = ?
8. Which choice gives the solution set of the expresssion |A-3|-|A-2| = -2 in case A is an integer ?

a) {1}
b) Φ
c) {1,2}
d) {1,2,3,4}
There are 4 possibilities :
A<2 , then a contradiction because |A-3|=3-A and |A-2|=2-A which implies 3-A-(2-A)=-2 .
A=2 gives 1=-2 also contradictary.
A=3 implies -1=-2 .
A>3 gives A-3-A+2=-2 , also not possible.
9. What is the set of solutions of the equality |A-7|=11 ?

a) {18}
b) {1,18}
c) {-4,18}
d) {14,18}
If A-7 = 11 then A=18 and if 7-A=11 then A=... .
10. |A-2| + |B+4| = 0 What will be the value of A-B if |A-2| + |B+4| = 0 ?

a) 16
b) 8
c) 4
d) 2
Both absolute values must be zero ...
11. (|(A+1):B-C-2|)! + (-5)3 = ?

!


a) -3
b) -5
c) 3
d) 8
A, B and C are respectively supposed to be 7, 8 and ... olmalıdırlar .
y
12. Which choice gives the factorial of the difference of the max. and min. numbers that make the result of the expressiion (A+9)/A an integer ?

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

RY1 RY2



a) 6 402 373 705 728
b) 6 402 373 705 728 000
c) 6 402 373 705
d) 6 402 373 705 728 999
(A+9)/A = 1 + 9/A. Possibilities for an integer 9/A : A=-9, -3, -1, 1, 3 and 9 . ry1 for further help .
Having a look at the factors, you should be able to see that the number asked has 15 or more digits.
13. What will A3 be if A is the number of terms of the expression given in the figure below ?

!


a) 2081
b) 1981
c) 81
d) 2197
133=13x13x13=169x13=1690+3x169=1690+510-3= ... .
14. Which number is the least of the integers satisfying the inequality A<(795:3):(1:5) ?

a) 1324
b) 324
c) 24
d) 2649


(795/3):(1/5)=265:(1:5)=2650:2=... .
15. Which of the followings will be an even number if [(5!-4!)/4!x(2!-0!)-1]xA is ?

a) A-13
b) 3xA+11
c) A+(-1)3
d) A+8
Determine first if the multiplier of A is even or odd .
16. The absolute value of the sum of 5 consecutive even integers is given as 770. Which is the set of means of these consecutive evens ?

a) {-54,54}
b) {-15,15}
c) {-554,154}
d) {-154,154}
ın case integers are positive, 770/5 gives the mean .
17. A and B are integers with AxB=9 . Which is the minimal value anyone of these numbers may take ?

a) -7
b) 11
c) -9
d) 18
(-9)x(-1)=9 and -9<-1 .
y
18. Find please A,B and C from the figure below. Find then the product AxBxC. Let D be the number of prime factors of AxBxC and E be the number of primes from 100 to 120.
Dx(E-1)/(B-A) = ?


!


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


a) -2
b) -8
c) -4
d) -12
A=8 and B=5 which implies C=3 .
Prime factors of 120 are 2,3 and 5 .
To find E make please use of ry1. 119=7x17 .
19. Given www.alo[336:(-3)+6].com , which address belongs to the web site ?

a) www.alo18.com
b) www.alo118.com
c) www.alo177.com
d) www.alo155.com
Just evaluate the algebraic expression .
20. Let A be the set of even integers having at most an absolute value less then the greatest digit. What will be the minimal value for any binary addition on this set ?

a) 0
b) -14
c) 1
d) -24
A = { -8, -6, ..., 0, ..., 6, 8} .
21. Which choice should replace the question mark of the figure below ?

!


a) (28,36)
b) (18,36)
c) (9,36)
d) (19,36)
(38/2,36) ...
y
22. A,B and C are 3 nonzero and different digits with AAC+BBC=894. Which is a possible max. value for ABC ?

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

RY1 RY2



a) 357
b) 627
c) 715
d) 842


Have please a look at ry1 .
23. [7+12:(1:3)-16:2x1]:(5+12:1:3-16:2x1) = ?

a) 54
b) 45
c) 34
d) 35
7+12:(1:3)-16:2x1=35 ve 5+12:1:3-16:2x1=1.
24. (5+12:1:3-16:2x1)x(5+12:1:3-16:2x1)= ?

a) 3
b) 1
c) 9
d) 1/3
5+12:1:3-16:2x1=1 .
25. 3:(7+12:1:3-16:2x1):(7+12:1:3-16:2x1) = ?

a) 1
b) 3
c) 1/3
d) 9
We repeatedly advice to evaluate the paranthesis at first, because they are to avoid ambiguity. Sometimes there may be some simple operations that are attractive to handle first, but keep rather the sure track. Then, after paranthesis, keep the order "powers-multiplication and divisions-addition and subtractions". In case of equal priorities, not usual because we normally use aranthesis, keep the read/write order (left first).
7+12:1:3-16:2x1=3 .
This is the feedback!

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FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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