Algebra preparation test questions
Introduction to algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.In mathematics, a quadratic equation is a polynomial equation of the second degree. The way of generalizing arithmetic is called algebra. The letters are used in algebra. This letters are called variables. It represents any value in a formula and it becomes a general formula applied to all numbers.(source:wikipedia)
Algebra preparation test questions:
Algebra preparation test question 1:
Simplify the expression and find the x value 5( - 6 - 4) + 3 = x
(1) - 47 (2) 18
(3) -2 (4) 53
Solution:
The given expression 5( - 6 - 4) + 3 = x
5(- 10) + 3 = x
- 50 + 3 = x
- 47 = x
Answer: (1) - 47
Algebra preparation test question 2:
Simplifying Radical Expressions `4 sqrt2 + 2 sqrt 2 - (sqrt2)^2`
(1) `5sqrt2` (2) `sqrt2`
(3) `6sqrt2 - 2` (4)` 4 sqrt2`
Solution:
The given radical expression ` 4 sqrt2 + 2 sqrt 2 - (sqrt2)^2`
` 4 sqrt2 + 2 sqrt 2 - 2`
` sqrt2 (4 + 2) - 2`
` 6sqrt2 - 2`
Answer: (3) `6sqrt2 - 2`
Algebra preparation test question 3:
Which one of the expression is equal to the given expression - 3 (2x - 4y) = ?
(1) - 6x + 12y (2) - 6x - 12y
(3) 18xy (4) - 6xy
Solution:
The Given algebraic expression is - 3 (2x - 4y)
= (- 3 * 2x) - ((- 3) * ( 4y))
= - 6x - (12y)
= - 6x + 12y
Answer: (1) - 6x + 12y
Algebra preparation test question 4:
If x = 3, Find the - 4x2 + 6x - 1 = ?
(1) 19 (2) -19
(3) - 55 (4) 55
Solution:
Substitute the x = 3 in the given equation - 4x2 + 6x - 1
= - 4(3)2 + 6(3) - 1
= - 4(9) + 18 -1
= - 36 + 18 - 1
= - 19
Answer: (2) -19
Algebra preparation test question 5:
Which one of the number is largest?
(1) `(-6)/5` (2) 4
(3) (-2)(-3) (4) | - 1 - 2|
Solution:
Option (1) is `(-6)/5 ` = - 1.2
Option (2) is 4 = 4
Option (3) is (-2)(-3) = 6
Option (4) is | - 1 - 2| = 3
So, The largest value is 6
Answer: (3). (-2)(-3)
Algebra preparation test question 6:
Simplify 8 - 4z - w - 8 - w
(1) 16 - 2w - 4z (2) 16 - 4z
(3) - 4z (4) - 4z - 2w
Solution:
The given expression is 8 - 4z - w - 8 - w
Arrange the same variables - 4z - w - w - 8 + 8
- 4z - 2w + 0
- 4z - 2w
Answer: (4) - 4z - 2w
Algebra preparation test question 7:
Simplify (- 6x6y)(4x4y5)
(1) - 24x10y6 (2) 2x10y6
(3) - 24x24y5 (4) 10x24y5
Solution:
The expression is (- 6x6y)(4x4y5)
(- 6)(4) (x6) (x4) (y) (y5) = - 24 (x6+4y1+5) = - 24x10y6
Answer: (1) - 24x10y6
Algebra preparation test question 8:
Which represents 8 subtracted from the sum of a number and 9?
(1) 9x - 8 (2) 8 - (x + 9)
(3) (x + 9) - 8 (4) `(x - 8)/9`
Answer: (3) (x + 9) - 8
Algebra preparation test question 9:
Find ` (n + 4)/(n^2 + 4n)`
(1) `1/(3n)` (2) `4/(n + 5)`
(3) n2 (4)` 1/n`
Solution:
` (n + 4)/(n^2 + 4n)`
Take n outside in the denominator term, `(n + 4)/(n(n + 4))`
= `1/n` .
Answer: (4) `1/n`
Algebra preparation test question 10:
Which one of the following is equals 12x.
(1) (6x)(6x) (2) 132 - x
(3) - 7x + 19x (4) 12 + x
Answer: (3) - 7x + 19x
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.In mathematics, a quadratic equation is a polynomial equation of the second degree. The way of generalizing arithmetic is called algebra. The letters are used in algebra. This letters are called variables. It represents any value in a formula and it becomes a general formula applied to all numbers.(source:wikipedia)
Algebra preparation test questions:
Algebra preparation test question 1:
Simplify the expression and find the x value 5( - 6 - 4) + 3 = x
(1) - 47 (2) 18
(3) -2 (4) 53
Solution:
The given expression 5( - 6 - 4) + 3 = x
5(- 10) + 3 = x
- 50 + 3 = x
- 47 = x
Answer: (1) - 47
Algebra preparation test question 2:
Simplifying Radical Expressions `4 sqrt2 + 2 sqrt 2 - (sqrt2)^2`
(1) `5sqrt2` (2) `sqrt2`
(3) `6sqrt2 - 2` (4)` 4 sqrt2`
Solution:
The given radical expression ` 4 sqrt2 + 2 sqrt 2 - (sqrt2)^2`
` 4 sqrt2 + 2 sqrt 2 - 2`
` sqrt2 (4 + 2) - 2`
` 6sqrt2 - 2`
Answer: (3) `6sqrt2 - 2`
Algebra preparation test question 3:
Which one of the expression is equal to the given expression - 3 (2x - 4y) = ?
(1) - 6x + 12y (2) - 6x - 12y
(3) 18xy (4) - 6xy
Solution:
The Given algebraic expression is - 3 (2x - 4y)
= (- 3 * 2x) - ((- 3) * ( 4y))
= - 6x - (12y)
= - 6x + 12y
Answer: (1) - 6x + 12y
Algebra preparation test question 4:
If x = 3, Find the - 4x2 + 6x - 1 = ?
(1) 19 (2) -19
(3) - 55 (4) 55
Solution:
Substitute the x = 3 in the given equation - 4x2 + 6x - 1
= - 4(3)2 + 6(3) - 1
= - 4(9) + 18 -1
= - 36 + 18 - 1
= - 19
Answer: (2) -19
Algebra preparation test question 5:
Which one of the number is largest?
(1) `(-6)/5` (2) 4
(3) (-2)(-3) (4) | - 1 - 2|
Solution:
Option (1) is `(-6)/5 ` = - 1.2
Option (2) is 4 = 4
Option (3) is (-2)(-3) = 6
Option (4) is | - 1 - 2| = 3
So, The largest value is 6
Answer: (3). (-2)(-3)
Algebra preparation test question 6:
Simplify 8 - 4z - w - 8 - w
(1) 16 - 2w - 4z (2) 16 - 4z
(3) - 4z (4) - 4z - 2w
Solution:
The given expression is 8 - 4z - w - 8 - w
Arrange the same variables - 4z - w - w - 8 + 8
- 4z - 2w + 0
- 4z - 2w
Answer: (4) - 4z - 2w
Algebra preparation test question 7:
Simplify (- 6x6y)(4x4y5)
(1) - 24x10y6 (2) 2x10y6
(3) - 24x24y5 (4) 10x24y5
Solution:
The expression is (- 6x6y)(4x4y5)
(- 6)(4) (x6) (x4) (y) (y5) = - 24 (x6+4y1+5) = - 24x10y6
Answer: (1) - 24x10y6
Algebra preparation test question 8:
Which represents 8 subtracted from the sum of a number and 9?
(1) 9x - 8 (2) 8 - (x + 9)
(3) (x + 9) - 8 (4) `(x - 8)/9`
Answer: (3) (x + 9) - 8
Algebra preparation test question 9:
Find ` (n + 4)/(n^2 + 4n)`
(1) `1/(3n)` (2) `4/(n + 5)`
(3) n2 (4)` 1/n`
Solution:
` (n + 4)/(n^2 + 4n)`
Take n outside in the denominator term, `(n + 4)/(n(n + 4))`
= `1/n` .
Answer: (4) `1/n`
Algebra preparation test question 10:
Which one of the following is equals 12x.
(1) (6x)(6x) (2) 132 - x
(3) - 7x + 19x (4) 12 + x
Answer: (3) - 7x + 19x