## Mathematics Form 1 End Term 2 Exams 2021 with Marking Schemes

- Write in words 437 308 041. (2mks)
- Test whether the number 24831 is divisible by 3. (3mks)
- Three tanks are capable of holding 361, 841 and 901 of milk. Determine the capacity of the greatest vessel which can be used to fill each one of them on exact number of times. (3mks)
- Write the following in standard form. (2mks)
- 0.001576
- 325.87

- Use tables to find the:
- Square of 36.21 (2mks)
- Square root of 0.0293 (2mks)

- Find the perimeter of the figure below. (3mks)
- If x = -2, y =-6 and z=4, find the value of: (2mks)

3YZ

X - Express the following numbers as a product of prime factors.
- 472 (2mks)
- 1078 (2mks)

- Arrange the following fractions in ascending order. (2mks)
^{11}/_{12},^{5}/_{6},^{2}/_{3},^{5}/_{6} - The sum of three consecutive whole numbers is 84. Find the numbers. (3mks)
- Express the following as a fraction.

0.67˙ (3mks)

2.8˙3˙ (3mks) - Maureen spent sh. 207 to buy 7 exercise books and 4 pens while Sharon spent sh. 165 to buy 5 exercise books and 5 pens of same type. Find the cost of each item. (3mks)
- The sum of interior angles of a regular polygon is 720O. Find the number of sides of the polygon and give its name. (3mks)
- A lady bought US £ 5000. From this, she spent US£ 1000 on a return ticket and US£ 1750 while in USA. Upon her return, she sold the remaining dollars. Using the following exchange rate:

Currency buying selling 1US Dollar (£) 78.4133 78.4744 - How much did she pay to the bank in Kenya shillings to yet the US £ 5000? (2mks)
- How much in Kenya shilling did she get after selling the remaining amount to the bank? (2mks)

- Solve the following pair of simultaneous equations graphically. (6mks)

2x – y = 3

X + 2y = 14

**SECTION II (20MKS)****Answer all questions.**

- The travel timetable below shows the departure and arrival times for a bus plying between two towns M and R, 300km apart.

Town Arrival Departure M 0830h N 1000h 1020h P 1310h 1340h Q 1510h 1520h R 1600h - How long does the bus take to travel from town M to N? (2mks)
- What time does it take at town P? (2mks)
- At what time does it arrive at town R in 12hr clock system? (2mks)
- What is its average speed for the whole journey? (4mks)

- Daniela spent ¼ of her net January salary on school fees. She spent ¼ of the remainder on electricity and water bills. She then spent 1/9 of what was left on transport. If she finally had sh. 3400.
- What fraction of her January salary was spent on electricity and water bill? (2mks)
- What fraction remained after she spent on fees, electricity and water bills? (2mks)
- What fraction was spent on transport? (2mks)
- Calculate her net January salary. (4mks)

## Marking Scheme

- Write in words 437 308 041. (2mks)
**Four hundred and thirty seven million three hundred and eight thousand and fourty one.** - Test whether the number 24831 is divisible by 3. (3mks)
**24831****2+4+8+3+1=**^{18}/_{3}= 6 it is divisible by 3 - Three tanks are capable of holding 361, 841 and 901 of milk. Determine the capacity of the greatest vessel which can be used to fill each one of them on exact number of times. (3mks)

2 36 84 90 3 18 42 45 6 14 15 - 001576
**1.576 x 10**^{-3} - 325.87

3.2587 x 10^{2}

- 001576
- Use tables to find the:
- Square of 36.21 (2mks)
**36.21**^{2}= (3.621 x 10^{1})^{2}**3.621**^{2}x 10^{2}**13.111 x 10**^{2}= 1311.1 - Square root of 0.0293 (2mks)
**0.0293**^{ ½ }= (2.93 x 10^{-2})^{½}**2.93**^{ ½ }x 10^{-1}**1.7117 x 10**^{-1}**0.17117**

- Square of 36.21 (2mks)
- Find the perimeter of the figure below. (3mks)
^{300}**/**_{360}x 2 x^{22}/_{7}x 12 = 62.8571**Perimeter = 62.8571 + 12 + 12 = 86.8571 cm** - If x = -2, y =-6 and z=4, find the value of: (2mks)

3YZ

X**3YZ = 3X – 6 X 4 = -72 = 36****X -2 -2** - Express the following numbers as a product of prime factors.
- 472 (2mks)
**2[472****2[236****2[118****[59****472 = 2**^{3}x 59 **2[1078****7[539****7[77****1[11****1078= 2 X 7**^{2}x 11

- 472 (2mks)
- Arrange the following fractions in ascending order. (2mks)
^{11}/_{12},^{5}/_{6},^{2}/_{3},^{5}/_{6}^{11}**/**_{12}x 2,^{5}/_{6}x12,^{2}/_{3}x 12,^{5}/_{6}x 12**11, 10, 8,10****Ascending order:**^{2}/_{3},^{5}/_{6},^{5}/_{6},^{11}/_{12} - The sum of three consecutive whole numbers is 84. Find the numbers. (3mks)
**x + x + 1 + x + 2 = 84****3x + 3 = 84**^{3x }**/**_{3}=^{81}/_{3}**X= 27, the numbers are : 27, 28 and 29** - Express the following as a fraction.
- 0.67˙ (3mks)
**Let r = 0.6777****10r = 6.777****100r = 67.777****100r – 10r = 67.777 – 6.777****90r =**^{61}/_{90}**90r****r =**^{61}/_{90} - 2.8˙3˙ (3mks)
**Let r = 2.838383****10r = 28.383838****100r = 283.838383****100r – r = 283.838383 – 2.838383**^{99}**/**_{99}r =^{281}/_{99}**R=**^{281}/_{99}or 2^{83}/_{99}

- 0.67˙ (3mks)
- Maureen spent sh. 207 to buy 7 exercise books and 4 pens while Sharon spent sh. 165 to buy 5 exercise books and 5 pens of same type. Find the cost of each item. (3mks)
**7e + 4p = 207 …. X 5****5e + 5p = 165 …. X 4****35e + 20p = 1035****20e + 20p = 660**^{15}**/**_{15}e^{375}/_{15}**e = 25****7 (25) + 4p = 207****175 + 4p = 207**^{4}**/**_{4}p =^{32}/_{4}**P = 8****The cost of 1 exercise book = shs. 25 and the cost of a pen sh. 8.** - The sum of interior angles of a regular polygon is 720
^{O}. Find the number of sides of the polygon and give its name. (3mks)**(22n – 4) 90 =**^{720}/_{90}**90****2n – 4 = 8**^{2}**/**_{2}n =^{12}/_{2}**n = 6****number of sides = 6. hexagon** - A lady bought US £ 5000. From this, she spent US£ 1000 on a return ticket and US£ 1750 while in USA. Upon her return, she sold the remaining dollars. Using the following exchange rate:

Currency buying selling

1US Dollar (£) 78.4133 78.4744- How much did she pay to the bank in Kenya shillings to yet the US 5000? (2mks)
**1 US dollar = sh. 78.4744****5000 dollar = 5000 x 78.4744****1****= sh. 392 372** - How much in Kenya shilling did she get after selling the remaining amount to the bank? (2mks)
**5000 – 1000 – 1750 = 2250 dollars****1 US dollar = sh. 78.4133****2250 dollars = 2250 x 78.4133****1****= sh. 176 429.90**

- How much did she pay to the bank in Kenya shillings to yet the US 5000? (2mks)

- Solve the following pair of simultaneous equations graphically. (6mks)

2x – y = 3**2x – y = 3****x 0 3****y -3 3**X + 2y = 14**x + 2y = 14****x 0 4****y 7 5**

**SECTION II (20MKS)**

**Answer all questions.**

- The travel timetable below shows the departure and arrival times for a bus plying between two towns M and R, 300km apart.
- How long does the bus take to travel from town M to N? (2mks)
**1000****0830****130 = 1hr 30mins** - What time does it take at town P? (2mks)
**1340****1310****30 = 30 mins** - At what time does it arrive at town R in 12hr clock system? (2mks)
**1600****1200****400 = 4.00 pm** - What is its average speed for the whole journey? (4mks)
**1600****0830****7 30 = 7 ½ hrs or**^{15}/_{2}hrs**Average speed = total distance covered****Total time taken****=**^{300}/^{15/}_{2}**= 40km/h**

- How long does the bus take to travel from town M to N? (2mks)
- Daniela spent ¼ of her net January salary on school fees. She spent ¼ of the remainder on electricity and water bills. She then spent
^{1}/_{9}of what was left on transport. If she finally had sh. 3400.- What fraction of her January salary was spent on electricity and water bill? (2mks)
**¼ x ¾ =**^{3}/_{16} - What fraction remained after she spent on fees, electricity and water bills? (2mks)
**¼ +**^{3}/_{16}=^{ 7}/_{16}**Remaining =**^{16}/_{16}–^{7}/_{16}=^{9}/_{16} - What fraction was spent on transport? (2mks)
^{1}**/**_{9}x^{9}/_{16}=^{1}/_{16} - Calculate her net January salary. (4mks)
^{7}**/**_{16}+^{1}/_{16}= ½**½ --> 3400****1 --> 1 x 3400**½

**= sh. 6800**

- What fraction of her January salary was spent on electricity and water bill? (2mks)

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