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
1Write down the inequality shown on the number line.
Answer[1]
2(a)Solve 4x+3>−9. Answer (a)[1]
(b)Solve 3x−2≥4. Answer (b)[1]
3Solve 6x−2=4x+2. Answer[2]
4(a)Solve the simultaneous equations 5x−5y=5 and 2x+5y=23. Answer (a)[3]
(b)Solve the simultaneous equations 5x+2y=33 and 5x−2y=37. Answer (b)[3]
Section B
5(a)Write down the inequality shown on the number line.
Answer (a)[1]
(b)A box contains 55 coins. All the coins are 50-cent coins or one-dollar coins. The total value of the coins is $47.50. Find the number of 50-cent coins and the number of one-dollar coins.
Answer (b)[3]
6(a)Write down the inequality shown on the number line.
Answer (a)[1]
(b)(i)Solve the simultaneous equations x−6y=−50 and −x+4y=34 by substitution. Answer (b)(i)[3]
(b)(ii)Solve the simultaneous equations −3x−y=−14 and x+2y=13 by substitution. Answer (b)(ii)[3]
7(a)(i)Solve 3x−1<−1. Answer (a)(i)[1]
(a)(ii)Solve 4x−3≤5. Answer (a)(ii)[1]
(b)(i)Solve the simultaneous equations x+4y=20 and −4x+y=22 by substitution. Answer (b)(i)[3]
(b)(ii)Solve the simultaneous equations 5x−2y=39 and x+y=5 by substitution. Answer (b)(ii)[3]
END OF PAPER
Question 1
A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x<3 Question 2
(a)Answer: x>−3[1] 4x>−12x>−3 (b)Answer: x≥2[1] 3x≥6x≥2 Question 3
Answer: x=−10[2] 4(x−2)=6(x+2)4x−8=6x+124x−6x=12+8−2x=20x=−10 Question 4
(a)Answer: =23, the right-hand side of (2).[3] 5x−5y=5 ... (1)2x+5y=23 ... (2)The y-terms have opposite signs, so add.(1)+(2):7x=28x=728=45(4)−5y=5−5y=−15y=−5−15=3Check in (2): 2(4)+5(3)=23, the right-hand side of (2). (b)Answer: =37, the right-hand side of (2).[3] 5x+2y=33 ... (1)5x−2y=37 ... (2)The y-terms have opposite signs, so add.(1)+(2):10x=70x=1070=75(7)+2y=332y=−2y=2−2=−1Check in (2): 5(7)−2(−1)=37, the right-hand side of (2). Question 5
(a)Answer: x<−5[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x<−5 (b)Answer: =4750, the right-hand side of (2).[3] x+y=55 ... (1)50x+100y=4750 ... (2)(1)×100:100x+100y=5500 ... (3)The y-terms have the same sign, so subtract.(3)−(2):50x=750x=50750=1515+y=55y=40Check in (2): 50(15)+100(40)=4750, the right-hand side of (2).There are 15 50-cent coins and 40 one-dollar coins. Question 6
(a)Answer: x<0[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x<0 (b)(i)Answer: =−50, the right-hand side of (1).[3] x−6y=−50 ... (1)−x+4y=34 ... (2)x=4y−34 ... (3)(4y−34)−6y=−504y−34−6y=−50−2y=−16y=−2−16=8x=4(8)−34=−2Check in (1): (−2)−6(8)=−50, the right-hand side of (1). (b)(ii)Answer: =−14, the right-hand side of (1).[3] −3x−y=−14 ... (1)x+2y=13 ... (2)x=−2y+13 ... (3)−3(−2y+13)−y=−146y−39−y=−145y=25y=525=5x=−2(5)+13=3Check in (1): −3(3)−(5)=−14, the right-hand side of (1). Question 7
(a)(i)Answer: x<0[1] 3x<0x<0 (a)(ii)Answer: x≤2[1] 4x≤8x≤2 (b)(i)Answer: =20, the right-hand side of (1).[3] x+4y=20 ... (1)−4x+y=22 ... (2)y=4x+22 ... (3)x+4(4x+22)=20x+16x+88=2017x=−68x=17−68=−4y=4(−4)+22=6Check in (1): (−4)+4(6)=20, the right-hand side of (1). (b)(ii)Answer: =39, the right-hand side of (1).[3] 5x−2y=39 ... (1)x+y=5 ... (2)x=−y+5 ... (3)5(−y+5)−2y=39−5y+25−2y=39−7y=14y=−714=−2x=−(−2)+5=7Check in (1): 5(7)−2(−2)=39, the right-hand side of (1).