Introduction to Algebra

Q.

Two students appeared at an examination. One of them secured $9$ marks more than the other and his marks were $56\%$ of the sum of their marks. What are the marks obtained by both of them?

1. $25and78$

2. $58and77$

3. $33and42$

4. $56and63$

Q. Which of the following is an expression with numbers only?

1. m + 4
2. y/17
3. 2(14 - 7) + 6
4. 7x + 3

Q. Solve the given equation by the trial and error method:
2x + 5 = 13

1. 8
2. 11
3. 3
4. 4

Q. 4 chairs and 3 tables cost Rs.2100 and 5 chairs and 2 tables cost Rs 1750 then the costs of a chair and a table separately would be? Kindly use one variable only.

Q. There are $15$ fruits in a basket. Basket contains 'a' number of apples, 'b' number of grapes and 'c' number of kiwis. The value of a+b+c would be

1. 10
2. 15
3. 20

Q. What is the diameter of the clock in Ben's shop, if it's radius is r?

1. 2r
2. 3r
3. 4r
4. 5r

Q. A Beetle's basket contains $20$ fruits in total which includes bananas, apples and oranges. If there are $10$ bananas and $5$ apples, how many oranges are there in the basket?

1. $10$
2. $15$
3. $5$
4. $20$

Q. Which among the following values satisfies the equation 3n + 11 = 35?

1. 9
2. 6
3. 7
4. 8

Q. Ben is 't' years old. His cousin is 6 more than 3 times his age. How old is his cousin?

1. 3t + 5
2. 3t + 6
3. 4t + 5
4. 5t + 3

Q. Ben keeps 4 apples in a carton. How many apples are there in p cartons?

1. 4m
2. 5n
3. 8p
4. 4p

Q. Bob's brother is $y$ years old. If Bob is $4$ years younger than his brother, what is Bob's age?

1. $(4-y)\text{years}$
2. $(y-4)\text{years}$
3. $(y+4)\text{years}$
4. $(y\times 4)\text{years}$

Q.

Solve each equation using trial and error method

$5b+6=11$

Q.

Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

1. $4n$
2. $2n$
3. $5n$
4. $9n$

Q. Find the perimeter of a pentagonal photo frame having side length a units.

1. 5a
2. 6a
3. 4a
4. 3a

Q.

What is the number of matchsticks you need to make n number of 2's?

1. 2n

2. 5n

3. 5+n

4. Cannot tell without knowing the value of n.

Q.

Subtract by horizontal method : $(2\mathrm{a}+3\mathrm{b})$from $(5\mathrm{a}-7\mathrm{b})$

Q.

Multiple Choice Questions. Tick Only One Option.

A variable

1. can vary its value

2. Has fixed value

3. Is called constant

4. None of these

Q. If Ben is x years old today, how old can he be in the future?

1. x + 4
2. x - 3
3. x - 1/2
4. x - 2

Q.

Which of the following is a mathematical phrase that can contain numbers, variables and operators?

1. Algebraic Variable

2. Algebraic expression

3. Algebraic coefficient

4. Algebraic inverse

Q. is not an equation.

1. 5y-2 = 13
2. -p+11 = 2
3. t+6 < 9

Q. If the cost of one apple in Ben's shop is d rupees , what is the cost of 5 apples in rupees?

1. 3d
2. 5d
3. 4p
4. 5n

Q.

The branch of mathematics in which we study the use of letters to write rules and formulae in a general way is known as _______.

1. Arithmetic

2. Algebra

3. Statistics

4. None of these

Q. Which value of q satisfies the equation 4q/3 > 13?

1. 12
2. 9
3. 3
4. 6

Q. Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b, c 1 x=3y

Q.

Solve each equation using trial and error method

$4z+2=10$

Q.

I want to know that if in simplification of algebra the values are in different orders will the answer be correct .eg-3a²+4b²-8ab+6 as

4b²+3a²-8ab+6

Q. Which of the following is the default operation in algebra, if no operation is specified between two variables?

1. Addition
2. Subtraction
3. Multiplication
4. Division

Q. Which of the following is the default operation in algebra, if no operation is specified between two variables?

1. Addition
2. Multiplication
3. Subtraction
4. Division

Q.

Which out of the following are expressions with numbers only?

(a) y + 3 (b) (7 × 20) − 8z

(c) 5 (21 − 7) + 7 × 2 (d) 5

(e) 3x (f) 5 − 5n

(g) (7 × 20) − (5 × 10) − 45 + p

Q. What is the simple way of doing algebra ???