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