Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 1. There are 112 balls in a bag. If 84 of them are yellow and the rest are blue, what percentage of the balls are blue? A. 25% B. 28% C. 75% □ D. 84% (1 mark) 2. There are 14 boys in S1B, which makes up 40% of all students in this class. How many students are there in S1B? A. 21 B. 35 C. 56 □ D. 60 (1 mark) 3. Among 80 MP3 files stored in a smartphone, 35% of them are pop music and there are 32 piano solos. If the rest of the MP3 files are guitar solos, what percentage of the files are guitar solos? A. 13% B. 20% C. 25% □ D. 33% (1 mark) 2015 Chung Tai Educational Press. All rights reserved. 1 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 4. Find the following unknowns. (a) a % of 75 is 18. (1 mark) (b) 25% of 112 is b. (1 mark) (c) 24% of c is 30. (1 mark) 2015 Chung Tai Educational Press. All rights reserved. 2 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 5. There are 900 students in a school, where 55% are boys. 40% of the boys and 60% of the girls have reading habits. What percentage of students have reading habits? (4 marks) 2015 Chung Tai Educational Press. All rights reserved. 3 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 6. The ticket prices of a stand-up comedy show are $120, $180 and $250. 60% of the tickets are $120-tickets, 30% of the tickets are $180-tickets, and there are 800 $250-tickets. If all of the tickets are sold, find the income obtained. (5 marks) END OF PAPER 2015 Chung Tai Educational Press. All rights reserved. 4 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 1. Benjamin obtained 50 Halloween candies last year and he obtained 80 this year. What is the percentage increase in the number of Halloween candies obtained? A. 30% B. 37.5% C. 60% □ D. 62.5% (1 mark) 2. Which of the following is the greatest? A. Increase from 90 by 20%. B. Increase from 100 by 6. C. Decrease from 110 by 5. □ D. Decrease from 120 by 15%. (1 mark) 3. In a group of students, there are 275 boys, which makes up 55% of all students. If the number of boys increases by 8% and the number of girls decreases by 72, then the total number of students A. decreases by 10%. 1 B. decreases by 11 % . 9 C. increases by 10%. 1 D. increases by 11 % . 9 □ (1 mark) 2015 Chung Tai Educational Press. All rights reserved. 5 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 4. The weight of Scott was 60 kg last year. If his weight increases by 5% this year, find his weight this year. (2 marks) 5. The length of a square decreases from 4 cm to 2 cm. Find the percentage decrease in the area of the square. (2 marks) 6. After increasing A by 10%, it is equal to B. If B decreases by 10%, is it equal to A? Explain your answer. (2 marks) 2015 Chung Tai Educational Press. All rights reserved. 6 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 7. The number of red envelopes sold in February was 30% more than that in January. The number of red envelopes sold in March was 80% less than that in February. It is given that 3 445 red envelopes were sold in February. (a) How many red envelopes were sold in January? (2 marks) (b) How many red envelopes were sold in March? (2 marks) (c) What was the percentage increase / decrease in the number of red envelopes sold from January to March? (2 marks) Solution: (a) (b) 2015 Chung Tai Educational Press. All rights reserved. 7 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A (c) END OF PAPER 2015 Chung Tai Educational Press. All rights reserved. 8 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 1. Amy bought a book for $120. She sold it to Betty at a profit of 20%. Betty then sold the book to Coey and lost $30. How much did Coey pay for the book? A. $100.8 B. $108 C. $110 □ D. $114 (1 mark) 2. Dave sells a watch for $1 725 at a loss of 8%. Find the cost of the watch. A. $1 587 B. $1 597 C. $1 863 □ D. $1 875 (1 mark) 3. Which of the following cases will give a profit of more than $9? I. Cost $50, percentage profit 18% II. Cost $100, selling price $110 III. Selling price $92, percentage profit 15% A. II only B. III only C. II and III only □ D. I, II and III (1 mark) 2015 Chung Tai Educational Press. All rights reserved. 9 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 4. Jimmy bought 2 dozens of energy bars for $96. If he sold all the energy bars for $5 each, find the percentage profit. (2 marks) 5. A sports shop sold a soccer for $88 at a loss of 20%, and a badminton racket for $206 at a profit of $16. (a) Find the cost of the soccer. (2 marks) (b) Find the cost of the badminton racket. (1 mark) (c) Did the shop make an overall profit or loss for selling these two items? Explain your answer. (2 marks) (d) Find the overall percentage profit / loss for selling these two items. (2 marks) Solution: (a) (b) (c) 2015 Chung Tai Educational Press. All rights reserved. 10 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A (d) 6. A cafe owner sold two items as follows. Item Cost Selling price Percentage profit A lemon tart $20 $22 10% A cup of green tea $10 $11 10% The owner claims that an overall profit of 20% is made from selling a lemon tart and a cup of green tea. Do you agree? Explain your answer. (3 marks) END OF PAPER 2015 Chung Tai Educational Press. All rights reserved. 11 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 1. The marked price of a suit is $888. If it is sold at a discount of 25% on its marked price, find the selling price of the suit. A. $222 B. $444 C. $666 □ D. $1 110 (1 mark) 2. A battery charger is $39 cheaper if it is sold at a discount of 12%. Find the marked price of the battery charger. A. $44 B. $286 C. $325 □ D. $364 (1 mark) 3. Which of the following gives the least percentage discount? A. Marked price $120, selling price $114 B. Marked price $125, discount $10 C. Selling price $117, discount $13 □ D. 7% off (1 mark) 2015 Chung Tai Educational Press. All rights reserved. 12 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 4. The original marked price of a headset is $x. The shop owner raises the marked price by 12% and then sells it at a discount of 5% on the new marked price. If the headset is sold for $266, find x. A. 222 B. 250 C. 273 □ D. 283 (1 mark) 5. Vanessa buys a soft toy for $129 with a marked price of $150. Find the percentage discount. (2 marks) 6. Jayden buys a cap for $23 at a discount of 8% on its marked price. (a) Find the marked price of the cap. (b) Find the discount. (2 marks) (1 mark) Solution: (a) 2015 Chung Tai Educational Press. All rights reserved. 13 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A (b) 7. A department store is holding a seasonal sale and all items are sold at a discount of 10%. If the total purchase after discount exceeds $1 000, an extra discount of 5% will be offered. (a) Miss Yam is going to buy an item with a marked price of $800. How much should she pay? (2 marks) (b) If Miss Yam decides to buy an additional item with a marked price of $400, how much more should she pay? (4 marks) Solution: (a) (b) END OF PAPER 2015 Chung Tai Educational Press. All rights reserved. 14 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A Stage Quiz § 6.1 1. Number of blue balls 112 84 28 28 100% 112 25% Required percentage The answer is A. 1A (1) 2. Let n be the number of students in S1B. n 40% 14 n 14 40% 35 There are 35 students in S1B. The answer is B. 1A (1) 32 100% 80 40% 3. Percentage of the files which are piano solos Percentage of the files which are guitar solos 100% 35% 40% 25% The answer is C. 1A (1) 4. (a) 75 a % 18 18 a 100 75 24 1A (1) (b) 112 25% b b 28 1A (1) (c) c 24% 30 c 30 24% 125 1A (1) 2015 Chung Tai Educational Press. All rights reserved. 15 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 5. Number of boys 900 55% 495 Number of girls 900 495 405 Number of boys with reading habits 495 40% 198 1A Number of girls with reading habits 405 60% 243 1A Percentage of students with reading habits 1M 198 243 100% 900 441 100% 900 49% 1A (4) 6. Percentage of the tickets which are $250-tickets 100% 60% 30% 10% Let n be the total number of tickets. n 10% 800 n 800 10% 8 000 There are 8 000 tickets in total. 1A Number of the $120-tickets 8 000 60% 4 800 1A Number of the $180-tickets 8 000 30% 2 400 1A Income obtained $(4 800 120 2 400 180 800 250) $(576 000 432 000 200 000) $1 208 000 1M 1A (5) Stage Quiz § 6.2 1. Increase in number 80 50 30 30 100% Percentage increase 50 60% The answer is C. 1A (1) 2015 Chung Tai Educational Press. All rights reserved. 16 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 2. A. 90 (1 20%) 90 1.2 108 B. 100 6 106 C. 110 5 105 D. 120 (1 15%) 120 0.85 102 The answer is A. 1A (1) 3. Let n be the original number of students in the group. n 55% 275 n 275 55% 500 New number of boys 275 (1 8%) 2751.08 297 New number of girls (500 275) 72 153 New total number of students 297 153 450 Decrease in the total number of students 500 450 50 50 100% Percentage decrease 500 10% The answer is A. 1A (1) 4. Increase in weight 60 5% kg 3 kg 1A His weight this year (60 3) kg 63 kg 1A (2) Alternative method: His weight this year 60 (1 5%) kg 60 1.05 kg 1M 63 kg 1A (2) 2015 Chung Tai Educational Press. All rights reserved. 17 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 5. Decrease in the area (42 22 ) cm 2 (16 4) cm2 12 cm 2 1A 12 100% 16 75% Percentage decrease 1A (2) 6. A(1 10%) B If B decreases by 10%, B(1 10%) A(1 10%)(1 10%) A(1.1)(0.9) 0.99 A 1A A It is not equal to A. 1A (2) 7. (a) Let x be the number of red envelopes sold in January. x(1 30%) 3 445 1M x 3 445 (1 30%) 3 445 1.3 2 650 The number of red envelopes sold in January was 2 650. 1A (2) (b) Number of red envelopes sold in March 3 445 (1 80%) 3 445 0.2 689 1M 1A (2) (c) Decrease in the number of red envelopes sold from January to March 2 650 689 1 961 1A Percentage decrease 1 961 100% 2 650 74% 1A (2) 2015 Chung Tai Educational Press. All rights reserved. 18 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A Stage Quiz § 6.3 1. Amount paid by Betty $120 (1 20%) $120 1.2 $144 Amount paid by Coey $144 $30 $114 The answer is D. 1A (1) 2. Let $C be the cost of the watch. C (1 8%) 1 725 C 1 725 (1 8%) 1 725 0.92 1 875 The cost of the watch is $1 875. The answer is D. 1A (1) 3. I. Profit $50 18% $9 II. Profit $110 $100 $10 III. Cost $92 (1 15%) $92 1.15 $80 Profit $92 $80 $12 The answer is C. 1A (1) 4. Number of energy bars 2 12 24 Selling price of 24 energy bars $5 24 $120 Profit $120 $96 $24 24 100% Percentage profit 96 25% 1A 1A (2) 2015 Chung Tai Educational Press. All rights reserved. 19 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 5. (a) Let $C be the cost of the soccer. C (1 20%) 88 1M C 88 (1 20%) 88 0.8 110 The cost of the soccer is $110. 1A (2) (b) Cost of the badminton racket $206 $16 $190 1A (1) (c) Total amount obtained from selling the two items $88 $206 $294 Total cost of the two items $110 $190 $300 $294 A loss is made. 1M 1A (2) (d) Loss $300 $294 $6 1A 6 100% Overall percentage loss 300 2% 1A (2) 6. Total cost $20 $10 $30 Total selling price $22 $11 $33 Overall profit $33 $30 $3 1A 3 100% 30 10% 20% Overall percentage profit 1A The claim is disagreed. 1A (3) 2015 Chung Tai Educational Press. All rights reserved. 20 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A Stage Quiz § 6.4 1. Discount $888 25% $222 Selling price $888 $222 $666 The answer is C. 1A (1) 2. Let $m be the marked price of the battery charger. m 12% 39 m 39 12% 325 The marked price of the battery charger is $325. The answer is C. 1A (1) 3. A. Discount $120 $114 $6 6 100% 120 5% Percentage discount 10 100% 125 8% B. Percentage discount C. Marked price $117 $13 $130 13 100% Percentage discount 130 10% D. Percentage discount 7% The answer is A. 1A (1) 4. x(1 12%)(1 5%) 266 x 266 (1 12%) (1 5%) 266 1.12 0.95 250 The answer is B. 1A (1) 2015 Chung Tai Educational Press. All rights reserved. 21 Chapter 6 Effective Learning Mathematics Stage Quiz | S1A 5. Discount $150 $129 $21 1A 21 100% Percentage discount 150 14% 1A (2) 6. (a) Let $m be the marked price of the cap. m(1 8%) 23 1M m 23 (1 8%) 23 0.92 25 The marked price of the cap is $25. 1A (2) (b) Discount $25 $23 $2 1A (1) 7. (a) Required amount $800 (1 10%) 1M $800 0.9 $720 1A (2) (b) Overall marked price $800 $400 $1 200 1A Amount to be paid after 10% off $1 200 (1 10%) $1 200 0.9 $1 080 $1 000 1A Miss Yam can enjoy the extra discount of 5%. Amount to be paid after 5% off $1 080 (1 5%) $1 080 0.95 $1 026 Extra amount should be paid $1 026 $720 $306 1A 1A (4) 2015 Chung Tai Educational Press. All rights reserved. 22