Maths Paper
Sing Yin Secondary School First Term Examination, 2009 – 2010 Mathematics 1 Form 3 Full marks: 100 Answer ALL questions. Unless otherwise specified, all working must be clearly shown. The diagrams in this paper are not necessarily drawn to scale. Unless otherwise specified, numerical answers should either be exact or correct to 3 significant figures. 1.
2.
Time allowed: 1.5 hours
Simplify
2 8 + 24 . x 2 − 5x − 6 , x 3 − 27 .
(
)
(4 marks)
Factorize (a)
(b)
(4 marks) (4 marks)
3.
Write FB116 in the expanded form and convert it to a decimal number.
4.
&& Express 0.8964 in the form
a where a and b are positive integers. b
(4 marks)
5.
Peter deposits $P in a bank at a rate of 2% p.a. compounded monthly. 2 years is $208964, find, correct to the nearest integer, the value of P.
If the expected amount after (4 marks)
6.
(a) (b)
Expand ( x + 5)( x − 3) . Solve the inequality ( x + 5)( x − 3) ≤ x 2 − 2 x + 5 and represent the solution graphically. (6 marks)
7.
Rationalize
6 3+ 2
and express the answers with the simplest surd form.
(5 marks)
8. 9.
Solve 27 2 x −1 = 9 x . In a class, there are 20 boys and n girls. are 71, 62 and 67 respectively. (a) (b) Find the value of n. After mark adjustment, each of the mark of x students is increased by 1. If the new mean mark is 67.25, find the value of x.
(5 marks) In a test, the mean mark of boys, girls and the whole class
(7 marks)
F.3 First Term Exam, 2009-2010
Mathematics 1
p.2 of 2
10. Simplify the following expressions and express the answers with positive indices. (a) (−2a 3 b −2 ) 3 4a −1b (b)
(xy
−1
− x −1 y
)
−1
(x − y )
(8 marks)
11. Solve x 3 + 3.4 × 101000 = 2.5 × 101001 and express the answer in scientific notation.
A
(5 marks)
12. In Figure 1, AC intersects DE at B and ∠DAB = ∠CEB. (a) (b) Prove that ∆ABD ~ ∆EBC. Hence, prove that AB × BC = EB × BD . If AB = 8, BC = 12, DE = 22 and BE <
2.
Time allowed: 1.5 hours
Simplify
2 8 + 24 . x 2 − 5x − 6 , x 3 − 27 .
(
)
(4 marks)
Factorize (a)
(b)
(4 marks) (4 marks)
3.
Write FB116 in the expanded form and convert it to a decimal number.
4.
&& Express 0.8964 in the form
a where a and b are positive integers. b
(4 marks)
5.
Peter deposits $P in a bank at a rate of 2% p.a. compounded monthly. 2 years is $208964, find, correct to the nearest integer, the value of P.
If the expected amount after (4 marks)
6.
(a) (b)
Expand ( x + 5)( x − 3) . Solve the inequality ( x + 5)( x − 3) ≤ x 2 − 2 x + 5 and represent the solution graphically. (6 marks)
7.
Rationalize
6 3+ 2
and express the answers with the simplest surd form.
(5 marks)
8. 9.
Solve 27 2 x −1 = 9 x . In a class, there are 20 boys and n girls. are 71, 62 and 67 respectively. (a) (b) Find the value of n. After mark adjustment, each of the mark of x students is increased by 1. If the new mean mark is 67.25, find the value of x.
(5 marks) In a test, the mean mark of boys, girls and the whole class
(7 marks)
F.3 First Term Exam, 2009-2010
Mathematics 1
p.2 of 2
10. Simplify the following expressions and express the answers with positive indices. (a) (−2a 3 b −2 ) 3 4a −1b (b)
(xy
−1
− x −1 y
)
−1
(x − y )
(8 marks)
11. Solve x 3 + 3.4 × 101000 = 2.5 × 101001 and express the answer in scientific notation.
A
(5 marks)
12. In Figure 1, AC intersects DE at B and ∠DAB = ∠CEB. (a) (b) Prove that ∆ABD ~ ∆EBC. Hence, prove that AB × BC = EB × BD . If AB = 8, BC = 12, DE = 22 and BE <