**SPM Mathematics (Model Test Paper)**

*Section***B**

[48 marks]

Answer any

**four**questions from this section.

**14.**The data in Diagram 9 shows the weight of meat, in kg, sold each day over 40 days.

36 | 63 | 43 | 47 | 67 | 71 | 68 | 79 | 92 | 49 |

41 | 52 | 66 | 78 | 84 | 55 | 77 | 86 | 58 | 94 |

60 | 74 | 73 | 62 | 56 | 68 | 46 | 35 | 72 | 68 |

80 | 40 | 57 | 59 | 71 | 81 | 92 | 60 | 63 | 53 |

(a) Based on the data in Diagram 9, complete Table 14 in the answer space. [ 4 marks]

(b) Based on Table 2, calculate the estimated mean of the weight of meat sold over 40 days. [3 marks]

(c) For this part of question, use the graph paper provided on page. By using the scale of 2 cm to 10 kg on the horizontal axis and 2 cm to 1 day on the vertical axis, draw a histogram for the data. [4 marks]

(d) Based on the histogram in 14(c), state one information about the weight of meat sold each day. [1 mark]

Answer:

(a)

Weight (kg) |
Mid point |
Frequency |

30 – 39 |
||

Table 2

Answer and solution:Answer and solution:

**(a)**

Weight (kg) |
Mid point (x) |
Frequency (f) |

30 – 39 |
34.5 |
2 |

40 – 49 |
44.5 |
6 |

50 – 59 |
54.5 |
7 |

60 – 69 |
64.5 |
10 |

70 – 79 |
74.5 |
8 |

80 – 89 |
84.5 |
4 |

90 – 99 |
94.5 |
3 |

(b)

(b)

$\begin{array}{l}\text{Mean}=\frac{\Sigma xf}{\Sigma f}\\ =\frac{34.5(2)+44.5(6)+54.5(7)+64.5(10)+74.5(8)+84.5(4)+94.5(3)}{40}\\ =\frac{2580}{40}\\ =64.50\text{kg}\end{array}$

**(c)**

(d)

(d)

Modal class is 60 – 69.

**15.**You are

**not**allowed to use graph paper to answer this question.

(a) Diagram 10.1 shows a solid right prism with rectangular base

*EFGH*on a horizontal table. The surface*EFRJKL*is the uniform cross-section of the prism. Rectangle*KLMN*and*JPQR*are horizontal planes. Rectangle*JKNP*is an inclined plane.*RF*and*LE*are vertical edges.Diagram 10.1

Draw full scale, the elevation of the solid on a vertical plane parallel to

*EF*as viewed from*X*[3*marks*](b) A solid cuboid is removed from the solid in Diagram 10.1. The remaining solid is as shown in Diagram 10.2. Rectangle

*TUVW*is a horizontal plane.*JT*and*BW*are vertical edges.*UF*= 4 cm and*UV*= 3 cm.Diagram 10.2

Draw to full scale,

(i) the plan of the remaining solid. [4 marks]

(ii) the elevation of the remaining solid on a vertical plane parallel to

*FG*as viewed from*Y.*[5 marks]

*Answer and solution:***(a)**

**(b)(i)**

**(b)(ii)**