Sample of Basic Algebra Test

Author: Matthew David

Sample of Basic Algebra Test

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. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. (Source: Wikipedia)

In this topic we are discuss about Sample of Basic Algebra Test  introduction and Sample of Basic Algebra Test examples

Sample of Basic Algebra Test Questions:

1) Solve the add sum of 4x4 – x2 + 2x + 1 and x + 3x3 – 3x2 – 1.
2) Solve this problems Subtract 5x3 – 2x2 – 2 from x3 + 4x2 – 3x – 5
3) Find the product of 2x3 – 3x2 – 5 and 3x2 + 4x – 2 .
4) Solve the following system:x + y + z  = 4; x - 2y - z = 1; 2x - y - 2z = -1
5) Find the coefficients of a4, a3, a2 and a term in the product of 7a3 – 6a2 – 9a + 8 and 5a2 – 3a + 5 without doing actual multiplication.
6) Solve the equation by completing the square (2x - 3)2.
7) Solve the equation by completing the square x2 + 6x – 7 = 0.
8) What should be added with x2 + 12x to get a perfect square? What is that square?
9) Express (5 – 3i) 3 in the form a + ib.
10) Express (v3 + v2) (2 v3 -i) in the form of a + ib
11) Multiply (3AB + 2A)(A2 + 2AB2).
12) Multiply (X + Y)3
13) Find the statement is equal or not equal: 7(-4x - 3) - (x - 4) = -8(2x + 6) + 11
14) To find the equation of the line through the points (-8, -6) and (-5, 8), we first use the slope m.
15) Solve: 8x - 2y = 3
16) Solve the equation 2x4 -x4 -8x2 + 4x2 + 8x = 0x3 - 35, if one of its roots is 2 + v3 i
17) Solve the quadratic equation x2  + 7 = -x2
18) Solve the equation x4 - 4x2 + 8x = 0x3 - 35, if one of its roots is 2 + v3 i

Sample of Basic Algebra Test Answers:

1) 4x4 + 3x3 – 4x2 +3x + 0
2) –4x3 + 6x2 – x – 3.
3) 6x5 – 3x4 – 16x3 – 9x2 – 20x + 10.
4) The answer is (2, -1, 3).
5) So the coefficient of a term in X × Y is– 69; So the coefficient of a2 in X × Y is 37; So the coefficient of a3 in X × Y is 8; So the coefficient of a4 in the product of X × Y is –51.
6) 4x² - 12x + 9
7) The solution set = {1, –7}
8) 36.
9) – 10 – 198i.
10) (-6 + v2) +v3 (1+ 2 v2) i
11) 3A3B + 6A2B3 + 2A3 + 4A2B2
12) X3 + 3X2Y + 3XY2 + Y3
13) Not Equal.
14) Slope m =3/14
15) The x intercept is at the point (3/8 , 0).
16) Thus the roots are 2 ± iv 3 and - 2 ± i
17) (- 1 +v 3 i)/2 and (- 1 -v 3i)/2 are conjugate to each other.
18) Thus the roots are 2 ± iv 3 and - 2 ± i

Example problems for search answer to the algebra

Search algebra example problem 1:

Simplify the given [removed]13x + 23) + 50x = 10 - 43x

Solution:

Given expression is (13x + 23) + 50x = 10 - 43x

Expand the above expression, we get

13x + 23 + 50x = 10 - 43x

63x + 23 = 10 - 43x

Subtract (10 - 43x) on both the side of the equation, we get

106x + 13 = 0

Subtract 13 on both the sides, we get

106x = - 13

Divide the above equation by 106, we get

x = `(- 13 / 106)`

Answer:

The final answer is x = `(- 13 / 106)`

Search algebra example problem 2:

Find the x intercept of the given polynomial equation f (x) = 2x2 - 72

Solution:

The given polynomial equation is f (x) = 2x2 - 72

Plug f (x) = 0, for finding x intercept

0 = 2x2 - 72

Rearrange the above equation, we get

2x2 - 72 = 0

Add 72 on both the sides of the equation, we get

2x2 = 72

Divide the above equation by 2 on both the sides, we get

x2 = 36

Take square root on both the sides, we get

x = ± 6

x intercepts are ± 6

Answer:

The final answer is x = ± 6

Search algebra example problem 3:

Find the slope the line which passes through the (2, 8) and (0, 16).

Solution:

Given points are (2, 8) and (0, 16)

Here, x1 = 2, y1 = 8, x2 = 0 and y2 = 16

Slope formula:

Slope (m) = `((y_2 - y_1) / (x_2 - x_1))`

Substitute the given values in the above fomula, we get

Slope (m) = `((16 - 8) / (0 - 2))`

=` ((8 / - 2))`

= - 4

Slope of the line is m = - 4

Answer:

The final answer is m = - 4

Practice problems for search answer to the algebra

Search algebra practice problem 1:

Find the slope of the given straight line equation y = 5.3x - 17

Answer:

The final answer is slope (m) = 5.3

Search algebra practice problem 2:

Find the factors of the given quadratic equation x2 - 17x + 60 = 0

Answer:

The factors are (x - 12) and(x - 5)

Search algebra practice problem 3:

Simplify the expression 5x + 28 = 108

Answer:

The final answer is 16

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