T-Leng Tuition · mugcornersg.com
Total: 30 marksSuggested time: 45 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
1(a)Solve −5−5x<−5. Answer (a)[1]
(b)Solve −x+8<2x−3. Answer (b)[1]
2Solve the simultaneous equations 3x+5y=18 and y=−4x+7 by substitution. Answer[3]
3(a)Find the largest integer value of x that satisfies 4x+7<−9. Answer (a)[2]
(b)Solve the inequality 2x+8<4x+9. Hence write down the smallest perfect square that satisfies the inequality. Answer (b)[2]
Section B
4(a)Write down the inequality shown on the number line.
Answer (a)[1]
(b)(i)Write down all the integer values of x such that −1<x<1. Answer (b)(i)[1]
(b)(ii)Write down all the integer values of x such that 1≤x≤5. Answer (b)(ii)[1]
(c)(i)Solve 3x−4≥11. Answer (c)(i)[1]
(c)(ii)Solve 4x−1≥32x+3. Answer (c)(ii)[2]
5(a)Write down the inequality shown on the number line.
Answer (a)[1]
(b)Solve the simultaneous equations 4x−2y=−2 and 3x−2y=−3. Answer (b)[3]
(c)Mrs Lim is 3 times as old as her daughter. In 8 years' time, Mrs Lim will be 2 times as old as her daughter. Find their present ages.
Answer (c)[3]
6(a)Solve the inequality 52x+5>22x−4. Hence write down the largest prime number that satisfies the inequality. Answer (a)[2]
(b)(i)The sum of the digits of a two-digit number is 5. When the digits are reversed, the new number is 27 more than the original number. Find the original number.
Answer (b)(i)[3]
(b)(ii)The sum of the digits of a two-digit number is 9. When the digits are reversed, the new number is 45 less than the original number. Find the original number.
Answer (b)(ii)[3]
END OF PAPER
Question 1
(a)Answer: x>0 (dividing by a negative number reverses the sign)[1] −5x<0x>0 (dividing by a negative number reverses the sign) (b)Answer: x>311 (dividing by a negative number reverses the sign)[1] −3x<−11x>311 (dividing by a negative number reverses the sign) Question 2
Answer: =18, the right-hand side of (1).[3] 3x+5y=18 ... (1)y=−4x+7 ... (2)3x+5(−4x+7)=183x−20x+35=18−17x=−17x=−17−17=1y=−4(1)+7=3Check in (1): 3(1)+5(3)=18, the right-hand side of (1). Question 3
(a)Answer: In x<−4, the largest integer is −5.[2] 4x<−16x<−4In x<−4, the largest integer is −5. (b)Answer: In x>−21: 0, 1, and only 1 is a perfect square.[2] −2x<1x>−21 (dividing by a negative number reverses the sign)In x>−21: 0, 1, and only 1 is a perfect square. Question 4
(a)Answer: −2≤x≤2[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).−2≤x≤2 −1<x<1: leave out the left end, leave out the right end.0 (b)(ii)Answer: 1, 2, 3, 4, 5[1] 1≤x≤5: include the left end, include the right end.1, 2, 3, 4, 5 (c)(i)Answer: x≥5[1] 3x≥15x≥5 (c)(ii)Answer: x≤−3 (dividing by a negative number reverses the sign)[2] 3(x−1)≥4(2x+3)3x−3≥8x+12−5x≥15x≤−3 (dividing by a negative number reverses the sign) Question 5
(a)Answer: x<−4[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x<−4 (b)Answer: =−3, the right-hand side of (2).[3] 4x−2y=−2 ... (1)3x−2y=−3 ... (2)(1)×3:12x−6y=−6 ... (3)(2)×4:12x−8y=−12 ... (4)The x-terms have the same sign, so subtract.(3)−(4):2y=6y=26=34x−2(3)=−24x=4x=44=1Check in (2): 3(1)−2(3)=−3, the right-hand side of (2). (c)Answer: =8, the right-hand side of (2).[3] x=3yx−3y=0 ... (1)x+8=2(y+8)x+8=2y+16x−2y=8 ... (2)The x-terms have the same sign, so subtract.(2)−(1):y=8x−3(8)=0x=24Check in (2): (24)−2(8)=8, the right-hand side of (2).Mrs Lim is 24 years old and her daughter is 8 years old. Question 6
(a)Answer: In x<5: 4, 3, and only 3 is a prime number.[2] 2(2x+5)>5(2x−4)4x+10>10x−20−6x>−30x<5 (dividing by a negative number reverses the sign)In x<5: 4, 3, and only 3 is a prime number. (b)(i)Answer: The original number is 14.[3] x+y=5 ... (1)Original number: 10x+y. Reversed number: 10y+x.(10y+x)−(10x+y)=27−9x+9y=27 ... (2)(1)×9:9x+9y=45 ... (3)The y-terms have the same sign, so subtract.(3)−(2):18x=18x=1818=11+y=5y=4Check in (2): −9(1)+9(4)=27, the right-hand side of (2).10(1)+4=14The original number is 14. (b)(ii)Answer: The original number is 72.[3] x+y=9 ... (1)Original number: 10x+y. Reversed number: 10y+x.(10y+x)−(10x+y)=−45−9x+9y=−45 ... (2)(1)×9:9x+9y=81 ... (3)The y-terms have the same sign, so subtract.(3)−(2):18x=126x=18126=77+y=9y=2Check in (2): −9(7)+9(2)=−45, the right-hand side of (2).10(7)+2=72The original number is 72.