Download - Mathematics* · PDF fileMathematics* St.BonaventureCollegeandHighSchool Form4,Quiz4(Ch1&2:QuadraticEquationI&II) ! 3! 3. HKCEE!MATH!1993Q6!! !

Mathematics St. Bonaventure College and High School

Form 4, Quiz 4 (Ch1&2: Quadratic Equation I & II)

1

Name: Class: ( ) Date: Mark: /29

Time: 40min, Full Marks: 29 SECTION A: Structure Questions 1. HKCEE MATH 1988 Q4



2

2. HKCEE A.MATH 1998 Q2



3

3. HKCEE MATH 1993 Q6



4

SECTION B: Multiple Choices (Correct answer 2M, Wrong answer -1M) Each question carry one CORRECT answer only. 4. HKCEE MATH 2008 II Q7

5. HKCEE MATH 2007 II Q4

Let x be the smaller one of two consecutive integers. If the sum of the squares of the two integers is less than three times the product of the two integers by 1, then

A. x2 + (x + 1)2 = 3x(x + 1) – 1 B. x2 + (x + 1)2 = 3x(x + 1) + 1 C. 3[x2 + (x + 1)2] = x(x + 1) - 1 D. 3[x2 + (x + 1)2] = x(x + 1) + 1






5




6

Solution: 1. (a) 9𝑥! − 𝑘 + 1 𝑥 + 1 = 0… ∗ ℎ𝑎𝑠 𝑒𝑞𝑢𝑎𝑙 𝑟𝑜𝑜𝑡, 𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒,∆= 0 …1M

(𝑘 + 1)! − 4 9 1 = 0 …1M 𝑘! + 2𝑘 + 1− 36 = 0 𝑘! + 2𝑘 − 35 = 0 𝑘 − 5 𝑘 + 7 = 0 𝑘 = 5 𝑜𝑟 𝑘 = −7 …1A (b) If k takes the negative value obtained in part (a), that means take k=-‐7, then we have 9𝑥! − −7+ 1 𝑥 + 1 = 0… ∗ …1M 9𝑥! − −6 𝑥 + 1 = 0 9𝑥! + 6𝑥 + 1 = 0 (3𝑥 + 1)! = 0 …1M 3𝑥 + 1 = 0 𝑥 = − !

! …1A



7

2.



8

3.

4. C 5. A 6. D 7. A 8. B (85) 9. D (47)

Download - Mathematics* · PDF fileMathematics* St.*Bonaventure*College*and*High*School* Form*4,*Quiz4*(Ch1&2:QuadraticEquationI&II) *! 3! 3. HKCEE!MATH!1993Q6!! !

Download - Mathematics* · PDF fileMathematics* St.BonaventureCollegeandHighSchool Form4,Quiz4(Ch1&2:QuadraticEquationI&II) ! 3! 3. HKCEE!MATH!1993Q6!! !