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Quadratic Equations Practice 3: Word Problems and Error Analysis

Section A: Model and Solve

Question 1mcq
The product of two consecutive positive integers is 5656. If the smaller integer is xx, which equation is formed?
A.x(x+1)=56x(x+1)=56
B.x+(x+1)=56x+(x+1)=56
C.x(x−1)=56x(x-1)=56
D.2x+1=562x+1=56
Question 2mcq
A rectangular field has length x+8x+8 m and breadth xx m. Its area is 240240 m². Which equation is correct?
A.x2+8x−240=0x^2+8x-240=0
B.x2+8x+240=0x^2+8x+240=0
C.2x+8=2402x+8=240
D.x2−8x−240=0x^2-8x-240=0
Question 3mcq
The product of two consecutive positive integers is 7272. What are the integers?
A.88 and 99
B.77 and 88
C.99 and 1010
D.66 and 1212
Question 4mcq
A garden is 66 m longer than it is wide and has area 135135 m². What is its width?
A.99 m
B.1515 m
C.66 m
D.1212 m
Question 5mcq
Solving a length problem gives roots x=8x=8 and x=−5x=-5. Which root should be used?
A.88 only
B.−5-5 only
C.Both roots
D.Neither root

Section B: Validate and Analyse

Question 6mcq
A time problem leads to t2−9t+20=0t^2-9t+20=0, so t=4t=4 or t=5t=5. The condition says the faster machine takes less time. If the slower machine takes 55 hours, what is the valid faster-machine time?
A.44 hours
B.55 hours
C.99 hours
D.2020 hours
Question 7mcq
Which value checks correctly as a root of x2−5x+6=0x^2-5x+6=0?
A.x=2x=2 because 4−10+6=04-10+6=0
B.x=1x=1 because 1−5+6=01-5+6=0
C.x=5x=5 because 25−5+6=025-5+6=0
D.x=6x=6 because 36−30+6=036-30+6=0
Question 8mcq
Which method is usually most efficient for x2−11x+30=0x^2-11x+30=0?
A.Factorisation
B.Quadratic formula only
C.Graphing only
D.Trial without factors
Question 9mcq
A student calculates DD for x2−4x+7=0x^2-4x+7=0 as (−4)2+4(1)(7)=44(-4)^2+4(1)(7)=44. What is the error?
A.They used ++ instead of −- in b2−4acb^2-4ac.
B.They squared −4-4 incorrectly.
C.They should divide by 2a2a first.
D.There is no error.
Question 10mcq
Assertion: 3x2=12x3x^2=12x has roots 00 and 44. Reason: We should first write 3x2−12x=03x^2-12x=0 and factorise as 3x(x−4)=03x(x-4)=0. Choose the correct option.
A.Both assertion and reason are true, and the reason explains the assertion.
B.Both are true, but the reason does not explain the assertion.
C.Assertion is true, but reason is false.
D.Assertion is false, but reason is true.