3472
MATEMATIK
TAMBAHAN
JAN/FEB/MAC
2010
SEKOLAH MENENGAH KEBANGSAAN GURUN
UJIAN BULANAN PERTAMA
2010
MATEMATIK TAMBAHAN
TINGKATAN 5
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU.
1. Answer all questions.
2. Give only one answer/solution for each question.
3. Show your working. It may help you to get marks.
4. The diagrams in the questions provided are not drawn to scale unless stated.
5. The marks allocated for each question and sub-part of a question are shown in brackets.
6. A list of formulae is provided in page 2.
7. You may use a non-programmabel scientific calculator.
Prepared by: ……….…….. Proved by: …………… Verified by : ……………...
(EN. MAZLAN ABU BAKAR) (PN. KEE HOOI MENG) (PN. SALMAH BT. ALI)
1
The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.
2
Answer all questions.
1. Calculate the 25 term of the arithmetic progression 5, 8, 11, …..
(4 marks)
2. Calculate the number of terms of the arithmetic progression 7, 11, 15, …, 163.
(3 marks)
3. Given the progression -7, -2, 3, …, calculate the sum of the first 15 terms
(3 marks)
3
4. Given a geometric progression 18, x, 32, …, find the value(s) of x.
(3 marks)
5. Calculate the sum to infinity of each of the following geometric progressions:
a. 75, 30, 12, … b. 6, -3,
(4 marks)
6. The sum of the first n terms of the geometric progression 3, 12, 48, … is 65 535. Find
a. the common ratio of the progression,
b. the value of n.
a) b)
(4 marks)
4
7. Express each of the recurring decimals as a fraction in its lowest terms.
a. b.
(4 marks)
8. x and y are related by the equation where a and b are constants. Reduce the non-
linear relation to linear form Y = mX + c where m and c are constants.
(3 marks)
9. The variables x and y are related by the equation , where a and b are constants.
When a graph of is plotted against x, the resulting line has a gradient of 5 and the intercept
on the -axis is 0.25. Calculate the values of a and b.
(4 marks)
5
10. Find the following indefinite integrals
a.
(4 marks)
11. Evaluate the following definite integrals:
a.
(4 marks)
6
12. Use the graph paper to answer this question.
Table shows the values of two variables, x and y, obtained from an experiment. Variables x
and y are related by the equation where p and k are constants.
x 1 2 3 4 5 6
y 4.0 5.7 8.7 13.2 20.0 28.8
a) Plot log y against (x + 1), using a scale of 2 cm to 1 unit on the (x + 1)-axis and 2 cm to
0.2 unit on the log y-axis.
Hence, draw the line of best fit.
b) Use your graph from 3(a) to find the value of
i. P
ii. k
(10 marks)
13. Diagram shows the straight line y = x + 4 intersecting the curve at the points A
and B.
y
y = (x - 2) 2
y = x+ 4
B
A P
O k x
Find
a) the value of k,
b) the area of the shaded region P.
(10 marks)
7
8
