Question 1:
Find the value of each of the following.
1. 6 - 7 + 2 x (4 - 7²)
2. (-2)³ - 12 ÷ 2 - (√36 + 3)
Question 2:
Write down an algebric expression of each of the following.
1. Subtract 11 from the square of g
2. Add 7a to the product of e and f
3. Multiply 4c by 13d
Question 3:
Asad is 5 years older than Raees and Kaleem is thrice as old as Asad. If Raees is 'y' years old, find
1. Asad's present age,
2. Kaleem's present age
Answers
Answer:
Q.3...Since this is a multiple choice question, you can easily deduce the answer from the choices.
If Aslam is 10 years old now, that means Javed would be 3 years old. Since Javed would not be born 5 years ago, this alternative is false.
If Aslam is 12 years old, Javed would be 4 years old. Same reasoning as above.
If Aslam is 24 years old, Javed would then be 8 years old. Five years ago, Aslam would be 19 and Javed would be 3. 3 times 5 is 15, which is not Aslams age, so this is false.
If Aslam is 30 years old, Javed would then be 10 years old. Five years ago, Aslam would be 25 and Javed would be 5. 5 times 5 is 25, which is Aslams age, so this is true.
If Aslam is 36 years old, Javed would then be 12 years old. Five years ago, Aslam would be 31 and Javed would be 7. 5 times 7 is 35, which is not Aslams age. This is false.
Or, the algebraic version. Suppose Aslam is currently x years old, and Javed is currently y years old. Then we are told that Aslam is three times as old as Javed now:
x = 3y (1)
And also, that five years ago Aslam was five times as old as Javed:
x - 5 = 5(y - 5) (2)
Two equations, two unknowns - this means the equation will have one to no solution. Focusing on the second equation, we can find y easily, since x = 3y:
3y - 5 = 5y - 25
2y = 20
y = 10
Then, x has to be 30, the correct answer is therefore 30.
Q.2......ADDING LIKE TERMS
WHEN NUMBERS ARE ADDED OR SUBTRACTED, we call them terms. Like terms are terms that we could combine. Here, for example, is a sum of like terms:
5x + 3x − 2x.
How many x 's are there? 5 + 3 − 2 equals 6 of them. We write:
5x + 3x − 2x = 6x.
We call 5, 3, and −2 the coefficients respectively of each term. Recall that in naming terms we include the minus sign.
Here, on the other hand, is a sum of unlike terms:
x² − 2xy + y²
There is no way that we could combine them.
The most elementary terms that we could combine are a and −a.
5 + (−5) = 0.
Adding like terms
In this sum—
2x − 3y + 4x + 5y
—the like terms are 2x and 4x, y and −5y.
Upon combining, or adding, them:
2x + 3y + 4x − 5y = 6x − 2y.
That has the effect of reducing the number of terms. Which is what we like.
We say that there are two terms "in" x and two "in" y. The preposition "in" indicates which are the like terms.
See Problem 12.
To add like terms, add their coefficients. The order in which the terms are written does not matter.
Problem 1 . 6a − 3b + c − d.
a) What number is the coefficient of a ?
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6
b) What number is the coefficient of b ? −3
c) What number is the coefficient of c ? 1. For c = 1·c.
d) What number is the coefficient of d ? −1. −d = −1·d.
See Lesson 5.
It is the style in algebra not to write the coefficients 1 or −1.
Actually, the coefficient of any factor is all the remaining factors. Thus in the term 4ab, the coefficient of a is 4b; the coefficient of 4a is b; and so on. In this term, x(x − 1), the coefficient of (x − 1) is x.
Problem 2. In the expression 5ayx, name the coefficient of
a) x 5ay b) y 5ax c) yx 5a
d) 5a xy e) 5 ayx
Problem 3. In this product 2(x + y)z
a) name each factor. 2, (x + y), z
b) name the coefficient of z. 2(x + y)
c) name the coefficient of (x + y). 2z
Problem 4. What number is the coefficient of x?
a) x
2 1
2 Compare Lesson 6, Problem 7b.
b) 3x
4 3
4 3x
4 = 3
4 · x Lesson 4.
Problem 5. How do we add like terms?
Add their coefficients.
