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## Algebra Level 1 Test 6

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*Algebra Level 1 Test 6*. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

Find the value of p

^{3}+ q^{3}, given pq = 900, (p+ q) = 6036000 | |

54000 | |

48000 | |

60000 |

Question 1 Explanation:

p + q = 60

Cubing both sides

p

p

(Replacing the variables by two values given)

p

Cubing both sides

p

^{3}+ q^{3}+ 3pq (p + q) = 216000p

^{3}+ q^{3}+ 3 ´ 900(60) = 216000.(Replacing the variables by two values given)

p

^{3}+ q^{3}= 216000 – 162000 = 54000.Question 2 |

If x

^{2}+ 1/x^{2}= 66, what is the value of x - 1/x?8 | |

+ 8 , -8 | |

-8 | |

9 |

Question 2 Explanation:

x

Subtract 2 from both sides

x

(x - 1/x)

Hence x - 1/x = +8,-8

^{2}+ 1/x^{2}= 66,Subtract 2 from both sides

x

^{2}+ 1/x^{2}-2 = 66 – 2(x - 1/x)

^{2}= 64Hence x - 1/x = +8,-8

Question 3 |

Find the range of : x

^{2}– 7x – 8 < 0-1 < x < 8. | |

-8 < x < 1 | |

-1 < x < 1 | |

-8 < x < 8 |

Question 3 Explanation:

x

(x-8)(x+1) < 0

x <8 ,x > -1

Hence answer = -1 < x < 8

^{2}– 7x – 8 < 0(x-8)(x+1) < 0

x <8 ,x > -1

Hence answer = -1 < x < 8

Question 4 |

If P+Q = 54 and PQ = 9, find 1/P+ 1/Q.

9 | |

6 | |

18 | |

12 |

Question 4 Explanation:

1/P+1/Q = P+Q/ PQ = 54/9 = 6

Question 5 |

Find the value of (0.512 + 0.216) /(0.64+ 0.36+0.48)

1.4 | |

0.8 | |

0.2 | |

2 |

Question 5 Explanation:

The equation is: a

(a

Hence the value should be = 1.4

^{3}+b^{3}= (a+b)(a

^{2}−ab+b^{2})Hence the value should be = 1.4

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