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SIXTH GRADE / ALGEBRAIC EXPRESSIONS / TEST 4.1.2

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.

 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. Evaluate 2·x÷2·x÷2·x÷2 for x=2. Which is your answer ?

a) 2
b) no unique answer
c) 4
d) 1
Without making use of parantheses, no sound answer is possible . "Multiplication and division have the same priorities, so do operations from left to right in their order" is not universally accepted.
2. What will be the evaluation of the algebraic expression 3·x(x-2)2 + 1 for x = 2 ?

!


a) 1
b) 2
c) 3
d) 4
2(2-2)2 = 1 .
3. What will be the simplest, without any parenthesis written, form of the algebraic expression x·(x-1)·(x-2) ?

a) x2-3·x2+2·x
b) x3-3·x2+2·x
c) x3-3·x3+2·x
d) x3-3·x2+2·x2
It should have no constant term, otherwise it will not be 0 at x=0.
4. Which result is obtained if x7÷x4 is simplified ?

a) x3
b) x4
c) 1
d) 0
(x3·x4)/x4 .
5. (2·x - 5·y)3 ?

!


a) 8·x2-60·x2·y+150·x·y2-125·y3
b) 8·x3-60·x2·y+150·x·y2-125·y3
c) x3-60·x2·y+150·x·y2-125·y3
d) 4·x3-60·x3·y+150·x·y2-125·y3
Make use of Pascal Triangle by choosing A = 2·x and B = 5·y.
According to the Pascal Triangle (A+B)3 have the coefficients 1, 3, 3 and 1 and is equal to A3+3·A2·B+ 3·A·B2+B3.
y
6. What is the solution set to 81·x4 - 16 = 0 ?

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



a) {2/3,-2/3}
b) {3,-3}
c) {-2/3,3}
d) {1/3,-2/3}


Solution set is the set of values for which the statement is true.
Write in the form (3·x)4 - 24 = 0 and try to bring it to the form A2-B2.
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7. Which of the following statements has 4 as solution ?

1- x2-4 = 0
2- 3·3 - 6·x + 87 - 75 = 0
3- 3·3 - 6·x - 87 + 75 = 0

a) all
b) 1 and 2
c) 2
d) none
The first is not the one ...
8. Which of the followings can not have a real (number as a) solution ?

1- x2 - 27
2- x3 - 27
3- x3 + 27
4- x2 + 27

a) only 4
b) 1 and 4
c) only 2
d) only 3
"3-" can have ...
9. 3 consecutive numbers has 21924 as their product. Which is the first number ?

a) 30
b) 27
c) 15
d) 9
(n-1)·n·(n+1) = n·(n2 - 1) = 21924 i.e. n3 - n = 21924 and this means of course, n3 is supposed to be about 21 924. After this point, for the time being, trial and error is due.
10. What will the sum a2·a0+a1 have for a value if x·(2·x-5)+3·(x-2) = a2·x2 +a1·x +a0 ?

a) 12
b) -12
c) -14
d) 22
Simplifying the left we get 2·x2 - 2·x - 6 .
The previous hint says : a2=2 , a1 = -2 and a0 = -6 .
11. Which of the followings is equal to a2·x2+a1·x+a0 if a2=1, a1=-2 and a0=-3 ?

a) (x+1)·(x-3)
b) (x-1)·(x-3)
c) (x+1)·(x+3)
d) (x+1)·(x-1)
Given is x2-2·x-3 .
y
12. What may be deduced from the following table for the two roots of the statements shown ?

!


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

RY1 RY2



a) x1-x2=-a1
b) x1+x2=a1
c) x1+x2=2·a1
d) x1+x2=-a1
Have please a look at ry1 .
13. What should the value of x be if (x-2)÷3 + (x-1)÷2 = x ?

a) -7
b) 7
c) 14
d) -14
2·x-4+3·x-3 = 6·x
14. Martin has walked 2÷5 of his way from school to home till the park. He then walked 250 m. and found himself halfway to home. How much way does he still have to go ?

!


a) 3 000 m.
b) 2 700 m
c) 2 500 m.
d) 1 500 m.


(2/5)·w + 250 m. but w·(1 - 2/5 - 1/2) = 250 m. is also valid.
15. What is the value of x according to the following figure ?

!


a) 8
b) 6
c) 2
d) 160/33
Take please care of the terms adding up to 0 .
16. What will x2 + y2-4·x+4·y-2·x·y be if x-y=10 ?

a) 60
b) 80
c) 90
d) 45
Try it to bring to the form (x-y-4)·(x-y) .
17. What will be the result of evaluating [56÷(5+5+5+5+5)]·x for x = 1÷5 ?

a) 125
b) 75
c) 90
d) 110
56/53 = ?
y
18. The green curve is the plot of resources and the red of consumers in a closed system. What will be the amount of per capita resource(s) at the year 150 ?

!


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


a) 1.98
b) 1.75
c) 3.05
d) 2.05
Please have a look at ry1.
19. 1/3 of a car's x-gallon fuel tank is full of gasoline. The car consumes 2 gallons per 100 km. and after the car is driven y/2 hundred kilometers the tank is completely filled for an amount of z dollars. Which expression gives then the price of a gallon of gasoline ?

!


a) (2·x + 3·y)/3·z
b) 3·z
c) 3·z/(2·x + 3·y)
d) 2·x + 3·y
x/3 is full. After y gallons consumed x/3 - y is full which means x - (x/3 - y) = 2·x/3 + y is empty. So z dollars is paid for (2·x + 3·y)/3 gallons
20. Please give the result of your evaluation of [3.33·10-3·(1/33.3)·104/10-2]·x3 for x=0.1

a) 10
b) 1
c) 0.1
d) 0.5
Find the coefficient first. The numerator is 1.
21. The distance between the Sun and Earth changes in a year and may be written as 149.6 ± 2.5 million km. where 149.6 million km. is the average distance. On the other hand the average distance from Earth to the Moon is 384 400 km. Let the Sun-Earth distance be D and the lunar distance be d. Which of the following expressions is correct ?

a) D = 149.6·106 km. ± 65·d
b) D = 149.6·106 km. - 6.5·d
c) D = 149.6·106 km. + 6.5·d
d) D = 149.6·106 km. ± 6.5·d
Change in D is 6.5 times the lunar distance . The lunar distance is about 30 times the diameter of Earth.
y
22. How many x,y couples exist in the set of natural numbers that satisfy x3 + 2 = 3·y and y3 + 2 = 3·x ?

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

RY1 RY2



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


x=1 and y=1 openly does. Have please a look at ry1 .
23. What will be the value of n if [7·(n-13)+n] ÷ [2·(1-4)] = 0 ?

a) 91/8
b) 8/91
c) 17/2
d) 3/17
The statement 8·n - 91 = 0 should be valid ; the denominator has no role if different from 0 .
24. What will be the value of [7·(n-13)+n] ÷ [2·(2·n-4)] if evaluated for n=4 ?

a) -17/3
b) 17/3
c) 59
d) -59/8
(+4-63)/8 = ?
25. What will be the value of p3 - q2 for p=q=0 ?

a) 1
b) 0
c) 10
d) 0.1
1-1 = ?
This is the feedback!

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