Secondary 1 Mathematics Practice Paper 5

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TuitionGoWhere Practice Paper - Mathematics Secondary 1

TuitionGoWhere Practice Paper (AI) — Version 5

Subject: Mathematics
Level: Secondary 1
Paper: Practice Paper (Topic: Numbers, Ratio & Proportion)
Duration: 60 minutes
Total Marks: 50
Name: ___________________________
Class: _________
Date: ___________

Instructions:

1. Answer all questions in this paper.
2. Show your working clearly where required.
3. Use the spaces provided for your answers.
4. Calculators may be used.

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Section A (Questions 1–10) — Short Answer [20 marks]

(2 marks each)

1. Express the ratio $12 : 18$ in its simplest form.

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2. A recipe uses flour and sugar in the ratio $3 : 2$. If $240\text{ g}$ of flour is used, how many grams of sugar are needed?

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3. Calculate $35\%$ of $420$.

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4. The price of a book increased from \24$to$$30$. Find the percentage increase.

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5. A car travels $150\text{ km}$ in $3$ hours. Find its average speed in $\text{km/h}$.

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6. Write $0.375$ as a fraction in its simplest form.

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7. The ratio of boys to girls in a class is $5 : 4$. If there are $36$ students altogether, how many boys are there?

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8. A shirt originally priced at \80$is sold at a$15%$ discount. Find the sale price.

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9. $x$ is inversely proportional to $y$. When $y = 6$, $x = 4$. Find $x$ when $y = 8$.

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10. A worker is paid \15$per hour. How much does he earn in$7.5$ hours?

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Section B (Questions 11–15) — Structured Response [15 marks]

11. [3 marks] A bag contains red and blue marbles in the ratio $4 : 7$. There are $44$ red marbles. (a) How many blue marbles are there? (b) Find the total number of marbles.

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12. [3 marks] The number of students in a club increased from $80$ to $100$. (a) Find the percentage increase. (b) If the club then decreased by $10\%$ from $100$, what is the new number?

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13. [3 marks] A machine packs $500\text{ g}$ of rice per second. How many $2\text{ kg}$ bags can it fill in $4$ minutes?

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14. [3 marks] The ratio of $A$ to $B$ is $2 : 5$ and the ratio of $B$ to $C$ is $5 : 3$. Find the ratio $A : B : C$.

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15. [3 marks] A price is increased by $20\%$ then decreased by $10\%$. What is the overall percentage change?

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Section C (Questions 16–20) — Problem Solving [15 marks]

16. [3 marks] Ali and Ben share \210$in the ratio$3 : 4$. How much does each receive?

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17. [3 marks] A shop has $120$ customers. $45\%$ are male. How many female customers are there?

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18. [3 marks] The time to paint a fence is inversely proportional to the number of painters. With $3$ painters it takes $12$ hours. How long with $4$ painters?

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19. [3 marks] A mixture is made from juice and water in the ratio $2 : 5$. If $1.4\text{ L}$ of juice is used, find the total volume of mixture.

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20. [3 marks] A population grew from $5000$ to $5750$. Find the percentage increase, then state if it is more or less than $15\%$.

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TuitionGoWhere Practice Paper — Answer Key (Version 5)

Subject: Mathematics
Level: Secondary 1
Topic: Numbers, Ratio & Proportion
Total Marks: 50

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Section A Answers (Q1–10)

Q1. [2 marks]
Ratio $12 : 18$ → divide both by HCF $6$ → $2 : 3$.
Answer: $2 : 3$
Teaching note: Simplify by dividing both terms by the same number until no common factor remains.

Q2. [2 marks]
Flour : Sugar = $3 : 2$. $3$ units = $240\text{ g}$ → $1$ unit = $80\text{ g}$. Sugar = $2$ units = $160\text{ g}$.
Answer: $160\text{ g}$

Q3. [2 marks]
$35\% \times 420 = \frac{35}{100} \times 420 = 147$.
Answer: $147$

Q4. [2 marks]
Increase = $30 - 24 = 6$. $\frac{6}{24} \times 100\% = 25\%$.
Answer: $25\%$

Q5. [2 marks]
Speed = $\frac{150}{3} = 50\text{ km/h}$.
Answer: $50\text{ km/h}$

Q6. [2 marks]
$0.375 = \frac{375}{1000} = \frac{3}{8}$.
Answer: $\frac{3}{8}$

Q7. [2 marks]
Boys : Girls = $5 : 4$, total $9$ units = $36$ → $1$ unit = $4$. Boys = $5 \times 4 = 20$.
Answer: $20$

Q8. [2 marks]
Discount = $15\% \times 80 = 12$. Sale price = $80 - 12 = 68$.
Answer: \68$

Q9. [2 marks]
$x = \frac{k}{y}$. $4 = \frac{k}{6} \Rightarrow k = 24$. When $y=8$, $x = \frac{24}{8} = 3$.
Answer: $3$

Q10. [2 marks]
Earnings = $15 \times 7.5 = 112.5$.
Answer: \112.50$

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Section B Answers (Q11–15)

Q11. [3 marks]
(a) $4$ units = $44$ → $1$ unit = $11$. Blue = $7$ units = $77$. [2 marks]
(b) Total = $11$ units = $121$. [1 mark]
Answer: (a) $77$ marbles (b) $121$ marbles

Q12. [3 marks]
(a) Increase = $20$ from $80$ → $\frac{20}{80}\times100\% = 25\%$. [2 marks]
(b) Decrease $10\%$ of $100 = 10$ → $90$. [1 mark]
Answer: (a) $25\%$ (b) $90$

Q13. [3 marks]
Rate = $500\text{ g/s}$. $4$ min = $240\text{ s}$. Total = $500 \times 240 = 120000\text{ g} = 120\text{ kg}$. Bags = $\frac{120}{2} = 60$.
Answer: $60$ bags [3 marks]

Q14. [3 marks]
$A:B = 2:5$, $B:C = 5:3$ → common $B=5$ → $A:B:C = 2:5:3$.
Answer: $2 : 5 : 3$ [3 marks]

Q15. [3 marks]
Start $100$. After $+20\% = 120$. After $-10\% = 120 \times 0.9 = 108$. Change = $+8\%$.
Answer: $8\%$ increase [3 marks]

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Section C Answers (Q16–20)

Q16. [3 marks]
$3+4=7$ units = $210$ → $1$ unit = $30$. Ali = $90$, Ben = $120$.
Answer: Ali \90$, Ben$$120$

Q17. [3 marks]
Male = $45\% \times 120 = 54$. Female = $120 - 54 = 66$.
Answer: $66$ females

Q18. [3 marks]
$t = \frac{k}{n}$. $12 = \frac{k}{3} \Rightarrow k=36$. With $4$: $t = \frac{36}{4}=9$ hours.
Answer: $9$ hours

Q19. [3 marks]
Juice : Water = $2:5$. $2$ units = $1.4\text{ L}$ → $1$ unit = $0.7\text{ L}$. Total = $7$ units = $4.9\text{ L}$.
Answer: $4.9\text{ L}$

Q20. [3 marks]
Increase = $750$ from $5000$ → $\frac{750}{5000}\times100\% = 15\%$. It is exactly $15\%$, not more or less.
Answer: $15\%$, equal to $15\%$