# A-AS Level (CIE) Mathematics Paper-5: Specimen Questions with Answers 1 - 5 of 20

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## Question 1

### Question

MCQ▾### Choices

Choice (4) | |
---|---|

a. | |

b. | 0 |

c. | |

d. | Question does not provide sufficient data or is vague |

### Answer

b.### Explanation

**Integral powers of**

To compute for , we divide by and write it in the form , where is quotient and is remainder

Hence

This is G. P with first term and common ratio

Sum of terms in G. P is given by

## Question 2

### Question

MCQ▾If , where then is ________

### Choices

Choice (4) | |
---|---|

a. | |

b. | |

c. | 0 |

d. | 2 |

### Answer

d.### Explanation

**Definite Integral by Parts**:

, if is an odd function, i.e.. , if

is an odd function

## Question 3

### Question

MCQ▾he value of the integral is ________

### Choices

Choice (4) | |
---|---|

a. | |

b. | |

c. | π |

d. | 0 |

### Answer

a.### Explanation

**Some Properties of Definite Integrals**:

## Question 4

### Question

MCQ▾The area of the region bounded by the circle and parabola is

### Choices

Choice (4) | |
---|---|

a. | Sq. unit |

b. | Sq. unit |

c. | Sq. unit |

d. | Sq. unit |

### Answer

a.### Explanation

The area of the region enclosed between two curves and the lines is given by the formula,

Area where in

If in and in , then

Area

and

and

Intersection points

Consider

Put

From (1) ,

Sq. unit

## Question 5

### Question

MCQ▾The minimum value of will be at equal to

### Choices

Choice (4) | |
---|---|

a. | |

b. | |

c. | |

d. |

### Answer

c.### Explanation

Way 1:

Let

Coefficient of

Minimum value of will be at

i.e.. ,

OR

Way 2:

For minimum value, by differentiating we get,