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
2 8 + 24 .
x 2 − 5x − 6 , x 3 − 27 .
(4 marks) (4 marks)
Write FB116 in the expanded form and convert it to a decimal number.
&& Express 0.8964 in the form
a where a and b are positive integers. b
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)
Expand ( x + 5)( x − 3) . Solve the inequality ( x + 5)( x − 3) ≤ x 2 − 2 x + 5 and represent the solution graphically. (6 marks)
6 3+ 2
and express the answers with the simplest surd form.
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
F.3 First Term Exam, 2009-2010
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)
− x −1 y
(x − y )
11. Solve x 3 + 3.4 × 101000 = 2.5 × 101001 and express the answer in scientific notation. A
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 < BD, find BE. D B Figure 1 C
13. In Figure 2, ED is a perpendicular bisector of ∆ABC. It is given that BD = 5, AB = 6 and ∠BAC = 90°. (a) (b) Find AC and ED. Find the area and the perimeter of the quadrilateral ABDE. B 6
A E Figure 2
(10 marks) 14. The mean of a, b, c, d and x is 2009. (a) (b) Find a + b + c + d + x. If x is unchanged while each of a, b, c and d is increased by 20%, the mean will be increased by 10%. Find the value of x. (6 marks) 15. In Figure 3, CD and BE are medians of ∆ABC. F is a point on ED produced such that FB // AC.
Prove that AEBF is a parallelogram. If ∠FDB = 90° and ∠DBE = 20°, find ∠ACB. A
E Figure 3 A
16. In Figure 4a, G is the in-centre of ∆ABC and GB = GC. (a) (b) Show that ∆ABH ≅ ∆ACH. Hence, show that AH ⊥ BC.
H is a
point on BC such that A, G and H lie on the same straight line.
In Figure 4b, K is a point on AC such that GK ⊥ AC. (i) Show that GH = GK and HC = KC. B
G H Figure 4a C B
G H Figure 4b
(ii) If GH = 3 and HC = 4, find the perimeter of ∆ABC.
(12 marks) END OF PAPER
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