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SIXTH GRADE / ALGEBRAIC EXPRESSIONS / TEST 4.1.3

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.

 Algebraic Expressions

    ♦ 
We somehow knew these days would come, so we used these kind of expressions before.
    ♦ Whenever we used a character like "A", "b", "♦" etc. instead of a number, we happened to have written down an algebraic exprssion indeed.
    ♦ We need to inform that the algebaric expressions use tradionally a, b,c ... (the first letters of the alphabet) for coefficients and ... x,y,z for the variables. In addition we will not use "x" for product sign, it is from now on a variable.

    Ref.-1
    Ref.-2
1. Muhammet Daghan German dropped a stone from a definite height as shown in the figure below and the fall is recorded via a special camera that records 50 frames per second. Frames pertaining to 1st, 2nd, 3rd and 4th seconds are overlapped with a result shown. How is the fall distance to be expressed as a function of time ?

!


a) (1/2)·10·t2
b) 10·t2
c) 2·10·t2
d) (1/2)·10·t
It is certainly not directly proportional with time .
2. The same place and technique as in question-1 but the stone is given an horizontal kick. How about the time dependency of the horizontal motion ?

!


a) y=5·t2
b) y=5·t
c) y=10·t
d) y=(5/2)·t
This time it is directly proportional with time.
3. Which choice decodes the pattern ... , -1 , 0 , 3 , 8 , 15 , ... ?

a) n2·(n-2)
b) n·(n-1)
c) (n-2)2
d) n·(n-2)
n·(n-2) = n2 - ... .
4. Which of the following choices is true regarding the left side of the statement 7·s - 5·t + 2·u = 3·s + 11 ?

a) It has a constant term.
b) The sum of it's coefficients is 4.
c) The coefficient of 2nd term is 5.
d) The first variable is greater than the second.
7·s - 5·t + 2·u is the expression being questioned .
5. Which choice gives the area of the purple region ?

!


a) (27/64)·π·x2
b) (27/32)·π·x2
c) (27/32)·π·x3
d) (27/64)·π·x3
The purple part is 1/4 ths of the ring.
y
6. What will be the sum of the elements of the set of remainders of (10112·m+n2)/11 as m and are natural numbers (0 excluded) ?

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



a) 34
b) 32
c) 28
d) 41


1011 is not divisible by 11 but 990, 1001 and 1012 are. Consider the first term as (1012-1)2·m .
If (1012-1)2·m is expanded, the constant term will be "+1" because the powers are even. And all other terms are multiples of 11 .
The term n2 will have a residue of 0 if multiple of 11. Have please a look at ry1 for further help.
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7. Which of the two following algebraic expressions seen in red rectangles in the figure below is approximately (better then 5% approximate) justified by the numbers given ?

!


a) all
b) the one at left
c) the one at right
d) none
The questions may be complex or may seem to be complex, right choice is to try to attain the maximum possible out of them .
Looking carefully it is possible to see that h1 and h2 are not among the given data, which of course means only the second (at right) may be tried/questioned.
Be careful about the units. Density is given as 1 g /cm3 which is the same as 1000 kg/m3 . Velocities are given as cm./s. and are to be converted to m./s. (2 m./s. and .6 m./s.) because pressure is given as Newton/m2. Then we have to compare 1037 + 500·22 = 3037 and 2932 + 500·(.6)2 = 3112. 3112-3037 = 75 and 75/3037 is .024 (rounded, 2% approximate).
8. Which of the choices is the set of coefficients of ( the simplified form) the algebraic expression a + 3·a + 5·b - 6·c + 4·d + 7 ?

a) {4,5,-6,7}
b) {1,3,5,-6,7}
c) {4,5,-6,4,7}
d) {1,3,4,5,-6,7}
the unknown a has a coeff of 4 ...
9. Which of the statements in the following figure are correct ?

!


a) all
b) none
c) 1, 2 and 4
d) 1 and 2
5 will only be correct if A=B .
10. The greater one of the sides of a rectangle whose sides are a and b the greater is decreased by 5 cm. and a square with a side a is obtained. Which algebraic expression gives the area of this triangle (a2) in terms of b ?

a) b2-5·b+5
b) b2-10·b+5
c) b2-5·b+25
d) b2-10·b+25
(b-5)2= ?
11. Which of the following algebraic expressions gives the minimal value if evaluated for a=10 ?

a) (1 - a)3
b) (a-10)10
c) 10·a - 99
d) (a-9)4
(a-10)10 = (10 - 10)10 = 010 = 0·0 ... 0·0 .
y
12. What will be obtained if 1+x·(1+x·(1+x·(1+x·(1+x·(1+x·(1+x·(1+x·(1+x)))))))) is evaluated for x=2 ?

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

RY1 RY2



a) 28 + 1
b) 210 + 1
c) 28 - 1
d) 210 - 1
Have please a look at ry1 .
13. The milk yield of a specific dairy cow is x kg. per day just after it gives birth and this yield decreases by 5% each month after birth. Which algebraic expression gives the expected yield after 2 months ?

!


a) x·(1-1/10)3
b) x·(1-1/20)3
c) x·(1-1/10)2
d) x·(1-1/20)2
After a month the yield will be x - x/20 = x·(1-1/20) .
14. The grid below consists of squares of side lenth "x" . What will be the total distance traveled by an ant which has gone through all possible shortest distances between A and B only once ?

!


a) 56·x
b) 560·x
c) 840·x
d) 188·x


The shortest distance is of length 8·x . There are ... of them .
This is a rather hard question. If not solved, have please a look at the web page "http://www.test-dr.com/education/6th-Grade-Mathematics/probability-5.1.1.html" /question-18 and it's helps.
15. It has been determined that the result of the sum k·a + l·b is maximal as a and b are 2-digit non equal numbers and k, l are constant elements chosen from the set of natural numbers. Which choice will then be an equal of x+a·b ?

a) x+9702
b) x-9702
c) x+4851
d) x-4851
a and b may be any natural number between 10 and 99 ...
16. Which of the followings is the product of 3 consecutive even numbers ?

a) n3 - 2·n
b) n3 - 4·n
c) n2 - 4·n
d) n2 - 2·n
Take the representation (n-2)·n·(n+2).
17. What is the total area of blue filled regions ?

!


a) π·R/2
b) π·(R/2)2
c) π·(R/4)2
d) 1+π·(R/2)2
The sum is 1/4 ths of ...
y
18. If the daily yield of the cow mentioned in question-13 drops 0.17% per day it happens to be about 5% in a month. What will be milk yield of this cow the second day after the birth ?

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


a) x2=x·(1+2·0.0017)
b) x2=x·(1-4·0.0017)
c) x2=x·(1-2·0.0017)
d) x2=x·(1+4·0.0017)
The first day after the birth it will be x1 = (1- 1.7/1000)·x . For further help have please a look at ry1 .
19. Marcus took a Greyhound bus from Indianapois to Lafayette which is approximately 70 miles northwest of Indianapolis. The bus halted in Lebanon for t minutes and took the whole distance in between, say 120 km., in 100 minutes. Which algebraic expression is to be used for the average driving speed of the bus ?

!


a) 3600/(50-t)
b) 7200/(100-t)
c) (100-t)/7200
d) (50-t)/3600
The duration of drive is 100-t minutes i.e. (100-t)/60 hours. Average drive velocity 60·120 / (100-t) km./h .
20. Simplify the expression 23·x + 91 + 12·x - 21 + x2 . Which result did you get ?

a) x2+35·x+70
b) x2+25·x+70
c) x2-35·x+70
d) x2+35·x+35
The constant term is 91-21=70 .
21. Which result is to be obtained if the statement - 16·n - 7 - 14·(n - 2) = n + r is solved for r ?

a) - 31·n + 21
b) - 31·n - 21
c) 31·n + 21
d) 31·n - 21
Subtract "n" from both sides to get -17·n - 7 - 14·(n - 2) = r and simplify .
y
22. How many prime numbers less than 10 exits which makes the evaluation of the expression 2·p4 - 7·p2 +1 the square of a natural number ?

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

RY1 RY2



a) 0
b) 3
c) 1
d) 2


Primes less than 10 are 2,3,5 and 7 . For the time being, trial and error is must . Excellent if you do without having a look at ry1.
23. What is the simplified form of - 27·x - 27 + 54·(x + 27) ?

a) 7·x - 1431
b) 27·x - 1431
c) 27·x + 1431
d) 7·x + 1431
27·x + ...
24. How many "m" will "8·n - 4·m" be if n = 6·m ?

a) 22
b) 88
c) 66
d) 44
8·n - 4·m = 8·6·m - 4·m. = ...
25. Which choice below gives the simplified form of the algebraic expression (x+1)·(2·x-3) ?

a) 2·x2 - x - 3
b) 2·x2 - 2·x - 3
c) 2·x2 - 2·x + 3
d) 2·x2 - 4·x - 3
(x+1)·(2·x-3) = 2·x2 - 3·x + 2·x - 3 = ...
This is the feedback!

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© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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