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Grade 7 Mathematics Online Lessons on Algebra: Questions and Answers
Illustrate each of the following inequalities on a number line.
a)
0
<
x
<
3
b)
14
<
x
<
17
(2m 24s)
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1.
Form algebraic expressions from the following statements. a) How many centimetres are there in x metres? b) Sam is 10 years older than Ali. What is the sum of their ages?
2.
During a sports day, Njenga, Musomba and Awiti received x, y and z medals respectively. How many medals did they receive altogether?
3.
A school has c teachers. The number of female teachers is b. Write an expression for the number of male teachers in the school.
4.
Chebet bought n avocados and shared them equally among her four children. Form an expression to represent the number of avocados each child received.
5.
A farmer has z cows. Each cow produces 25 litres of milk every day. His family drinks 8 litres and sells the rest. Form an expression to represent the capacity of milk that she sells.
6.
A bus charges sh m to travel from Nakuru to Nairobi. A matatu charges 40 shillings more than the bus. To travel from Nakuru to Nairobi using a matatu, Gatwiri paid fare using a 500-shillings note. Write an expression to represent the balance that she got.
7.
A company hired b cleaners and c security guards. The cleaners earn 850 shillings per day and the security guards earn 900 shillings per day. The company also gives each of them 150 shillings for lunch per day. Form an expression to represent the company’s total expenditure on cleaners and security guards in a day.
8.
A bag has a mass of n kilograms when empty. When full of clothes its mass is 15 kilograms. Write an expression to represent the mass of the clothes.
9.
A school had r computers. The school leadership bought twice as many computers. The school then received a donation of 6 more computers from the Constituency Development Fund office. Write an expression to represent the number of computers the school has altogether.
10.
Simpify the following algebraic expressions. a)
1
3
(9x - 12y) b) 6p + 3q – 5 – 2p c) 2(3b – 2c + d)
11.
Mueni and Muchira bought milk from a dairy farm to donate to a community event. Mueni bought n litres of milk and Muchira bought (n + 2) litres of milk. The cost of a litres of milk was sh 60. Form and simplify an expression to represent the total cost of milk they donated to the event.
12.
A group of learners from Werevu Junior Secondary School visited Nakuru County to view Menengai Crater. The learners were transported in m buses. Two buses carried 33 learners each. The remaining buses carried 25 learners each. Form and simplify an expression to represent the number of learners that visited Menengai Crater.
13.
Abdala bought n tree seedlings to plant in his farm. His friend Kokwaro bought twice as many seedlings as Abdala. Another friend Melda bought two thirds of the total number of seedlings that Abdala and Kokwaro bought. Form and simplify an expression to represent the total number of tree seedlings that they bought?
14.
Simplify the following algebraic expressions. a) 6(2r + 3s) + 3(r – 5s) b) 15y × 2 + 12y ÷ 2
15.
Three friends, Kanyoni, Lesit and Auma bought masks to donate to learners in a certain school. Kanyoni bought n masks and Lesit bought twice as many masks as Kanyoni. Auma bought m more masks than Lesit. Form and simplify an expression to represent the total number of masks they bought.
16.
A factory manufactures and distributes vaccines for the Coronavirus disease to different countries as shown in the table below. Country Number of vaccines distributed A z + p B 2z C p - z Write a simplified expression for the total number of vaccines distributed to the countries.
17.
Omari’s wife is x years old. Omari is 5 years older than his wife. The age of their daughter is half the age of his wife. The sum of their ages is 75 years. Form an equation to represent their total ages.
18.
During a vaccination exercise against Polio, a hospital received y vaccines from the government. The health officer vaccinated 50 children with one vaccine per child. If 25 vaccines remained, form an equation to represent the number of vaccines that the government gave the hospital.
19.
A trader had n oranges. She bought 25 more oranges. Later in the day, she sold 45 oranges. At the end of the day, she still had 28 oranges. Form an equation to represent the number of oranges she had by the end of the day.
20.
A school bought 15 story books for Grade 7 learners. Five of the story books cost 90 shillings each while the other story books cost b shillings each. The school spent 950 shillings to buy the books. Form an equation to represent the total expenditure.
21.
Three times Olekoren’s age added to 36 is 90 years. Form an equation from this information.
22.
Karuri’s age is two times that of his brother. The sum of their ages is 45 years. Form an equation to represent their ages.
23.
A number x is doubled, and the result added to 120. When we subtract 20 from the answer, the difference is 200. Form an equation that can be used to determine the value of x.
24.
A school received n packets of face masks from a donor. Two fifth of the packets were distributed to the learners. If 120 packets remained, form an equation to represent the number of face masks that remained.
25.
Solve the following equations. a) 6 + a = 21 b) 7y – 4y = 24 c) 12 + 4x = 62 – x d) 14w – 21 = 7
26.
Ondimu is two times as old as his sister. In three years, the sum of their ages will be 30 years. How old is Ondimu’s sister?
27.
Solve the following equations. a) 6n – 25 = 5n + 25 b) 8(y + 7) – 6y = 66 c) 6(z + 3) = 2(2z + 12)
28.
Kibe is a Grade 7 learner. Every time he is give money to spend, he ensures he saves some of the money. After saving for three months, he found that he had ten 20-shilling coins and x 10-shilling coins. In total he had saved sh 600. How many 10-shilling coins did he have in his savings?
29.
Fatuma had sh x. She spent half of the money to buy food for her children and was still left with 500 shillings. How much money did she save?
30.
Korir donated pens and books to a certain school. The total number of books and pens he donated was 400. Each learner received three pens and one book. The number of learners in the school was x. Work out the value of x.
31.
The cost of a book is 25 shillings more than the cost of a pen. The cost of 4 books and 5 pens is 334 shillings. Work out the cost of each item.
32.
A number is five times another number. The sum of the two numbers is 180. Determine the two numbers.
33.
The length of a rectangle is 5 cm more than its width. The perimeter of the rectangle is 90 cm. Work out the dimensions of the sides of the rectangle.
34.
Abadan is a fruit farmer. She planted 408 seedlings comprising of orange, mango and apple seedlings on her farm. The number of orange seedlings was
2
3
of the seedlings and that of mango seedlings was
1
6
of the seedlings. She planted 68 apple seedlings in the farm. Work out the number of orange and mango seedlings she planted.
35.
Achieng spent 350 shillings to buy 2 books and a pen. The cost of a book is 100 shillings more than that of a pen. What is the cost of a pen and a book?
36.
Marete gave his daughter n oranges to share equally with her three friends. After sharing, one of the friends gave 2 oranges to her sister and was left with 7 oranges. How many oranges did Marete give his daughter?
37.
The cost of a mango at Ngara Market is x shillings, while at Muthurwa Market the cost is 5 shillings less than at Ngara. On his way to work, Waswa bought 8 mangoes at Ngara Market. While at work, he bought the same number of mangoes at Muthurwa Market. He spent 200 shillings in total. What is the cost of a mango at Muthurwa Market?
38.
Njambi and Kyalo are teachers. They live in Upesi town. One day, they attended a training in Usawa Town. Njambi took m hours to travel to Usawa Town while Kyalo took 30 minutes more than Njambi. The total time they took was 5 hours 30 minutes. How long did Njambi take to travel to Usawa Town?
39.
Fill in the gaps using the correct inequality symbol. a) 8 ______ 4 b) 154 l ______ 72 l c) 10 cm ______ 0.5 m
40.
The mass m of a packet of maize seeds is less than 10 kg. Form an inequality to represent this statement.
41.
Amandi had b bananas. The bananas were not enough for her 5 children. Form an inequality to represent the number of bananas Amandi had.
42.
When a number x is multiplied by 8, the result is more than 100. Form an inequality to represent this statement.
43.
Linda visited a hospital to seek medication. The doctor prescribed a few tablets for a certain drug. She was told to take less than 4 tablets per day for 5 days. If she took t tablets for the 5 days, form an inequality for the total number of tablets Linda took.
44.
Three times a number added to 8 is less than 25. Form an inequality to represent this statement.
45.
If a number is divided by 6 and subtract 8 from the quotient, the result is less than 5. Form an inequality to represent this statement.
46.
The number of girls in a certain school is x + 4 and that of boys is x. The number of teachers and workers is 22. If the total population of the school is more than 300, form an inequality to represent the school population.
47.
Wangila and Kibuchi are brothers. Wangila has two sons and Kibuchi has a daughter. Each of Wangila’s sons has m children. Kibuchi’s daughter has 4 children. The total number of their grandchildren is less than 10. Form an inequality to represent the number of children Wangila’s son has.
48.
Mwaniki bought y fish to feed his family. The number of fish he bought were more than 5. Form an inequality and illustrate it on a number line.
49.
Illustrate each of the following on a number line. a)
x
>
3
b)
y
>
1
2
c)
p
<
11
d)
d
<
5
50.
Form compound inequalities from each of the following pairs of inequalities. a)
x
>
4
,
x
<
9
b)
j
<
2
5
,
j
>
0.3
c)
s
<
5
,
s
>
0
51.
Gikunju works in a certain company. In a week, he earns more than 1200 shillings and less than 2500 shillings. Form an inequality to represent Gikunju’s weekly salary.
52.
The fare from Nyeri to Nairobi is more than 200 shillings but less than 400 shillings. Museti travelled from Nyeri to Nairobi. Form an inequality to represent the fare he paid.
53.
The length of a football pitch should be less than 106 m and more than 89 m. Form an inequality to represent the length of a football pitch.
54.
The daily temperature of a certain town ranges above 20 °C to less than 36 °C in a month. Form an inequality to represent the daily temperature of the town.
55.
Illustrate each of the following inequalities on a number line. a)
0
<
x
<
3
b)
14
<
x
<
17
56.
Deng was expecting some visitors in his house. He needed to buy more than 4 kg of meat but less than 7 kg to feed his visitors. Illustrate the mass of the meat he bought on a number line.
57.
To raise funds to sponsor needy learners, Kilele Junior Secondary School learners participated in a walk. Some learners could not walk far. They covered over 5 km. Those who walked the farthest covered less than 10 km. Form an inequality from the information and represent it on a number line.
58.
The life expectancy of a dog is less than 13 years. Kasim bought a dog that was 2 years old. If the dog is m years old, form an inequality from the information and illustrate it on a number line.
59.
To travel from Nairobi City to Thika Town, public service vehicles charge less than 150 shillings but more than 100 shillings. Rudisha travelled from Nairobi to Thika. Form an inequality to illustrate the fare he paid and represent it on a number line.
60.
Juhudi Junior Secondary School has 325 learners. A few learners toured Aberdare Ranges. The number of learners who went for the tour was more than 50. Form an inequality to represent this information.
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