T-Leng Tuition · mugcornersg.com
Total: 30 marksSuggested time: 50 minutes
Name: ______________________________Class: ____________ Date: ____________
Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1Solve the simultaneous equations 3x−3y=18 and −4x+y=−21 by substitution. Answer[3]
2Solve the simultaneous equations 3x+5y=19 and 6x+7y=32. Answer[3]
3(a)At a funfair, 205 tickets were sold. Adult tickets cost $18 each and child tickets cost $5 each. The tickets sold for $1,805 altogether. Find the number of adult tickets and the number of child tickets sold.
Answer (a)[3]
(b)1 notebook and 2 rulers cost $3.10. 4 notebooks and 2 rulers cost $10. Find the cost of one notebook and the cost of one ruler.
Answer (b)$[3]
4(a)Solve the simultaneous equations −5x−y=19 and −5x+5y=−5. Answer (a)[3]
(b)Solve the simultaneous equations x+9y=27 and 4x+3y=42. Answer (b)[3]
Section B
5(a)A box contains 12 coins. All the coins are 10-cent coins or 50-cent coins. The total value of the coins is $4. Find the number of 10-cent coins and the number of 50-cent coins.
Answer (a)[3]
(b)Solve the simultaneous equations 4x−4y=0 and y=−4x+30 by substitution. Answer (b)[3]
6(a)Solve the simultaneous equations 3x−4y=3 and 3x+y=33. Answer (a)[3]
(b)Solve the simultaneous equations 2x+4y=−22 and x−4y=7 by substitution. Answer (b)[3]
END OF PAPER
Question 1
Answer: =18, the right-hand side of (1).[3] 3x−3y=18 ... (1)−4x+y=−21 ... (2)y=4x−21 ... (3)3x−3(4x−21)=183x−12x+63=18−9x=−45x=−9−45=5y=4(5)−21=−1Check in (1): 3(5)−3(−1)=18, the right-hand side of (1). Question 2
Answer: =32, the right-hand side of (2).[3] 3x+5y=19 ... (1)6x+7y=32 ... (2)(1)×2:6x+10y=38 ... (3)The x-terms have the same sign, so subtract.(3)−(2):3y=6y=36=23x+5(2)=193x=9x=39=3Check in (2): 6(3)+7(2)=32, the right-hand side of (2). Question 3
(a)Answer: =1805, the right-hand side of (2).[3] x+y=205 ... (1)18x+5y=1805 ... (2)(1)×5:5x+5y=1025 ... (3)The y-terms have the same sign, so subtract.(2)−(3):13x=780x=13780=6060+y=205y=145Check in (2): 18(60)+5(145)=1805, the right-hand side of (2).60 adult tickets and 145 child tickets were sold. (b)Answer: One notebook costs $2.30 and one ruler costs $0.40.[3]
x+2y=3.1 ... (1)4x+2y=10 ... (2)The y-terms have the same sign, so subtract.(2)−(1):3x=6.9x=36.9=2.32.3+2y=3.12y=0.8y=20.8=0.4Check in (2): 4(2.3)+2(0.4)=10, the right-hand side of (2).One notebook costs $2.30 and one ruler costs $0.40. Question 4
(a)Answer: =−5, the right-hand side of (2).[3] −5x−y=19 ... (1)−5x+5y=−5 ... (2)The x-terms have the same sign, so subtract.(2)−(1):6y=−24y=6−24=−4−5x−(−4)=19−5x=15x=−515=−3Check in (2): −5(−3)+5(−4)=−5, the right-hand side of (2). (b)Answer: =42, the right-hand side of (2).[3] x+9y=27 ... (1)4x+3y=42 ... (2)(2)×3:12x+9y=126 ... (3)The y-terms have the same sign, so subtract.(3)−(1):11x=99x=1199=99+9y=279y=18y=918=2Check in (2): 4(9)+3(2)=42, the right-hand side of (2). Question 5
(a)Answer: =400, the right-hand side of (2).[3] x+y=12 ... (1)10x+50y=400 ... (2)(1)×50:50x+50y=600 ... (3)The y-terms have the same sign, so subtract.(3)−(2):40x=200x=40200=55+y=12y=7Check in (2): 10(5)+50(7)=400, the right-hand side of (2).There are 5 10-cent coins and 7 50-cent coins. (b)Answer: =0, the right-hand side of (1).[3] 4x−4y=0 ... (1)y=−4x+30 ... (2)4x−4(−4x+30)=04x+16x−120=020x=120x=20120=6y=−4(6)+30=6Check in (1): 4(6)−4(6)=0, the right-hand side of (1). Question 6
(a)Answer: =33, the right-hand side of (2).[3] 3x−4y=3 ... (1)3x+y=33 ... (2)The x-terms have the same sign, so subtract.(2)−(1):5y=30y=530=63x−4(6)=33x=27x=327=9Check in (2): 3(9)+(6)=33, the right-hand side of (2). (b)Answer: =−22, the right-hand side of (1).[3] 2x+4y=−22 ... (1)x−4y=7 ... (2)x=4y+7 ... (3)2(4y+7)+4y=−228y+14+4y=−2212y=−36y=12−36=−3x=4(−3)+7=−5Check in (1): 2(−5)+4(−3)=−22, the right-hand side of (1).