Practice test

Basic algebra - Test Set 1

Review 20 exam-focused questions with detailed explanations, then start the interactive test when you are ready.

20 questions

Questions and explanations

Question 1
What is valid for (a + b)²=a² + b²?
1. Can be true only for a finite number of (a, b)
2. Cannot be true for any set of (a, b)
3. Can be true for exactly one pair (a, b)
4. Can be true for infinite number of (a, b)
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Question 2
If ab = 10 and a² + b² = 29 then (a-b)² = ?
1. 9
2. 3
3. 19
4. 39
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Question 3
If a = 0.1 + $\sqrt{0.9}$ and b = 0.1 - $\sqrt{0.9}$ then find value of a² + b².
1. 2.82
2. 1.82
3. 1.9
4. 2
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Question 4
Simplify: (4x - 5y)² + (5x + 4y)² + (4x + 5y) (4x - 5y)
1. 57x² + 16y²
2. -57x² - 16y²
3. -58x² + 16y²
4. 58x² + 16y²
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Question 5
If x² + y² - 4x + 8y + 20 = 0 then find the value of x² + y².
1. 30
2. 20
3. 10
4. 40
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Question 6
If a² +b² + c² + 3 = 2(a + b + c) then what will be the value of (a + b + c)?
1. 2
2. 3
3. 5
4. 4
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Question 7
If x = b + c, y = c - a, z = a - b, then find the value of x² + y² + z² - 2xy - 2xz + 2yz.
1. 4b²
2. 4a²
3. 4c²
4. 2b
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Question 8
If a = x + y, b = x - y and c = 2x - 1 then find the value a² + b² + c² - 2ab + 2ac - 2bc?
1. 0
2. (2x + 2y - 1)²
3. (2x - 2y - 1)²
4. (x - y -1)²
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Question 9
If x = $\sqrt{3} + \sqrt{2}$ then what is the value of $x^{2} + \frac{1}{x^{2}}$ ?
1. 12
2. 14
3. 13
4. 10
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Question 10
If x > 1, and $x + \frac{1}{x} = \sqrt{29}$ , then find value of $x - \frac{1}{x}$ ?
1. 4
2. 2
3. 5
4. 3
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Question 11
If $x^{2} y^{2} + \frac{1}{x^{2} y^{2}} = 83$ the find the value of $x y - \frac{1}{x y}$ ?
1. 10
2. 85
3. 9
4. 81
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Question 12
If x² + 1 = 2x, then find the value of $x - (\frac{1}{x})$ ?
1. 0
2. 2
3. 4
4. 12
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Question 13
If x² - 3x + 1 = 0 then what is the value of $x^{2} + x + (\frac{1}{x}) + (\frac{1}{x^{2}})$ ?
1. 2
2. 10
3. 6
4. 8
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Question 14
If $x = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} and y = \frac{1}{x}$ then find value of x² + y²?
1. 4
2. 6
3. 7
4. 5
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Question 15
If $x = \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} and y = \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}$ then find the value of (x + y)².
1. 36
2. 100
3. 25
4. 225
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Question 16
If a = 2b = 3c and a + b + c = 121 then what is the value of $\sqrt{a^{2} + b^{2} + c^{2}}$ ?
1. 75
2. 77
3. 73
4. 72
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Question 17
If x⁴ + x^-4 = 1154, then find the value of x + x^-1.
1. 8
2. 6
3. 5
4. 12
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Question 18
If $x^{4} + \frac{1}{x^{4}}$ = 194 then find the value of $x^{3} + \frac{1}{x^{3}}$ ?
1. 56
2. 52
3. 54
4. 62
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Question 19
If a² + b² = 82 and ab = 9, find the value of a³ + b³?
1. 750
2. 730
3. 720
4. 830
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Question 20
If , a + b = 10 and a² + b² = 68, then find the value of a³ + b³?
1. 520
2. 560
3. 620
4. 540
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Questions and explanations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20