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]
2Write down the inequality shown on the number line.
Answer[1]
3Write down the inequality shown on the number line.
Answer[1]
4(a)Solve 2x+9>11. Answer (a)[1]
(b)Solve 3x−2>7. Answer (b)[1]
5(a)Solve 2x+8≥−2. Answer (a)[1]
(b)Solve 5−3x≤−1. Answer (b)[1]
6Find the largest integer value of x that satisfies 3x+8≤−1. Answer[2]
7(a)Solve 2x+1≥5. Answer (a)[1]
(b)Solve 2x+2≤−6. Answer (b)[1]
8Find the largest integer value of x that satisfies 3x+7<−2. Answer[2]
9(a)Find the smallest integer value of x that satisfies 2x+5>−3. Answer (a)[2]
(b)Find the largest integer value of x that satisfies −4−4x>−12. Answer (b)[2]
Section B
10(a)Solve the inequality −5x−4>5x+10. Answer (a)[2]
(b)Hence write down the largest integer value of x that satisfies the inequality. Answer (b)[1]
11(a)Solve the inequality −4x−1>4x+5. Answer (a)[2]
(b)Hence write down the largest integer value of x that satisfies the inequality. Answer (b)[1]
12A taxi charges a flag-down fare of $3.20, plus $0.60 for every kilometre travelled. Ali has $19 and takes the taxi for x km.(a)Write down an inequality in x. [1]
(b)Solve your inequality, and hence find the greatest number of whole kilometres Ali can travel.
Answer (b)km[2]
13Mei buys x pens at $1.20 each and (x+3) notebooks at $2.50 each. She spends at most $40, and she buys at least 5 pens.(a)Show that 37x≤325. [2]
(b)Find all the possible numbers of pens Mei could buy.
Answer (b)[2]
END OF PAPER
Question 1
Answer: x<−5[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x<−5 Question 2
Answer: x≥−3[1] A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x≥−3 Question 3
A filled circle means the value is included (≤ or ≥); an open circle means it is not (< or >).x>2 Question 4
(a)Answer: x>1[1] 2x>2x>1 (b)Answer: x>3[1] 3x>9x>3 Question 5
(a)Answer: x≥−5[1] 2x≥−10x≥−5 (b)Answer: x≥2 (dividing by a negative number reverses the sign)[1] −3x≤−6x≥2 (dividing by a negative number reverses the sign) Question 6
Answer: In x≤−3, the largest integer is −3.[2] 3x≤−9x≤−3In x≤−3, the largest integer is −3. Question 7
(a)Answer: x≥2[1] 2x≥4x≥2 (b)Answer: x≤−4[1] 2x≤−8x≤−4 Question 8
Answer: In x<−3, the largest integer is −4.[2] 3x<−9x<−3In x<−3, the largest integer is −4. Question 9
(a)Answer: In x>−4, the smallest integer is −3.[2] 2x>−8x>−4In x>−4, the smallest integer is −3. (b)Answer: In x<2, the largest integer is 1.[2] −4x>−8x<2 (dividing by a negative number reverses the sign)In x<2, the largest integer is 1. Question 10
(a)Answer: x<−57[2] −5x−4>5x+10−10x>14Divide by −10, a negative number, so the sign reverses: x<−57 x<−57The largest integer is −2. Question 11
(a)Answer: x<−43[2] −4x−1>4x+5−8x>6Divide by −8, a negative number, so the sign reverses: x<−43 x<−43The largest integer is −1. Question 12
(a)[1]
Total fare =3.20+0.60x, and it must be at most $19:3.20+0.60x≤19 0.60x≤15.80x≤26.33…The greatest whole number of kilometres is 26. Question 13
(a)[2]
1.20x+2.50(x+3)≤403.7x+7.5≤403.7x≤32.537x≤325 (shown) (b)Answer: 5,6,7,8[2] x≤37325=8.78…x≥5, and x is a whole numberx=5,6,7 or 8