Equations Questions

1.  Solve the simultaneous equation (3 mks)

2.  A photograph is mounted on a frame that it leaves a uniform border at the bottom and at the top.  At each side a uniform border which is half the border at the bottom is left.

If the side of the square photograph is 5cm and area of frame is 75cm2.

(a) Write down an equation for the area of the frame (simplified)  (2mks)

(b) What are the dimensions of the frame?  (4mks)

(c) What is the percentage area of the frame that is not covered by the photograph?  (4mks)

3.  Solve the equation (3mks)

4.  Factorize completely: 75x2 – 27y2  (2mks)

5.  Solve for x given that  (3mks)

6.  Solve for x and y in. (4mks)

7.  The attendance at a party consisted of 35 men, a number of women and some children. The number of women was one and a half times that of the children present.

1. If there were a total of 65 participants, how many women attended the party?   (2mks)
2. During the party, each child took one bottle of soda, the men took two bottles each while some women took two and others three. Given that five crates each containing 24 bottles of soda were consumed, how many women took two bottles of soda?   (6mks)
3. Each crate of soda was bought for sh.432 plus a deposit of sh.10 per bottle incase it broke. How much money did the party organizers pay at the soda depot?   (2mks)

8.  Simplify the expression (3 marks)

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p2 – 4m2

2m2 – 7mp + 3p2

9.  During a certain ceremony goats and chicken were slaughtered. The number of heads (for both chicken and goats) was 45. The total number of legs was 100. Determine the exact number of goats and chicken slaughtered. (3 marks)

10.  A tailor bought a number of suits at a cost of Sh. 57,600 from Ken-suit wholesalers. Had he bought the same number of suits from Umoja wholesalers, it would have cost him Sh. 480 less per suit. This would have enabled him to buy 4 extra suits for the same amount of money.

(a)  Find the number of suits the tailor bought (4 marks)

(b)  The tailor later sold each suit for Sh. 720 more than he had paid for it. Determine the percentage profit he made? (4 marks)

11.  Use factor method to evaluate the following expression leaving your answer as a product of prime factors in power form.

(3mks)

12.  Solve for x in the given equation. (3mks)

64x – 121 = 7 – 43x

13.  Given the 4x = 3y, evaluate  (4mks)

14.  Find the value of y in the equation

(4mks)

15.  Factorise completely the expression

45a2 – 20b2

and hence or otherwise find its value when a = 5 and b = 3 (3mks)

16. Simply (3mks)

17.  Find the value of M in the following equation.  (3 mks)

1 M   -1

27   X 81  = 243

18.  Rotich bough 4 pencils and 6 pens for kshs. 184 and Kamau bought 3 pencils and 8 pens of the same type at kshs 222. Find the price of each item. (3 mks)

19.  A 60m by80m parking lot is torn up to install a side walk of uniform width around its perimeter. The new area of the parking lot is two thirds of the old area. How wide is the side walk?  (4 mks)

20.  Mukku bought 4 text books and 3 novels at total cost of sh. 4250. if he had bought 2 text books more and one novel less, he would have spent sh. 250 less. On another occasion makku bought 3 text books and 3 novel at the same prices, find how much he spent in the second occasion.  (4 marks)

21.  A Kenyan businessman US\$100 to a company in the United States of America. The Kenyan

can either pay through his account in Kenya or through his account in the United Kingdom.

Which method is cheaper and by how much? Give your answer in Kenya shillings given that;

1 US dollar = 76.84 Kenya shillings

1 Sterling Pound = 1.53 US dollars

1 Sterling pound = 115.70 Kenya shillings

22.  Foreign exchange on 27/5/2010 was given as follows:.

 Currency Buying (Kshs) Selling (Kshs) 1 Euro 84.15 84.26 1 Sterling pound 118.35 121.47

A tourist came to Kenya from London with 6000 Euros which he converted to Kenya shillings

at a bank. While in Kenya he spent a total of Kshs.300,000 then converted the balance into sterling pounds at the Same bank. Calculate the amount in sterling pounds he received.

23.  A Kenyan football fan visited South Africa from Kenya. He changed his currency from

Kenya shillings to South African rand. The exchange rates in Kenya were as per the table below:-

9.9399 10.0166

He has a total of shs.2, 8000,265 and must spend 13 days. During his stay, he spent 8900

Rands on food and accommodation, 97,000 Rands on a return air ticket and 53689

Rands on entertainment. On his return, he converted the remaining amount into Kshs.

How much did he receive to the nearest cents?

24.  A French tourist changes 3000 Francs into Kenyan shillings at 1 Franc = Kshs.1.89.

He spends shs.4695, then exchanges the remaining shillings back into Francs at 1 Franc =1.95.

How many Francs does he receive?

25.  Hamisi arrived in Nairobi from USA with 40 travelers cheques each with 75 US dollars. How

much does she receive in Kshs from the bank on a day when 1 US dollar was equivalent to Kshs

81.40 and the bank charges commission at the rate of Kshs.100 per travelers cheque

26.  A Kenya bank buys and sells foreign currencies as shown below  Buying in Kshs. Selling in Kshs.

1 Hong Kong dollar 9.74 9.77

1 South African rand 12.03 12.11

A tourist arrived in Kenya with 105,000 Hong Kong dollars and changed the amount to

Kenya shillings. While in Kenya, she spent Shs.403,879 and changed the balance to South

African rand before leaving for South Africa. Calculate the amount, in South African rand

27.  A Japanese tourist entered Kenya with Kshs.500,000 Japanese Yen which he converted

to Kenya currency. While in Kenya, he spend Kshs.16200 in all. He then converted all the

remaining money into Euros before leaving for Italy. If he carried out all his transactions

at the Stanbic bank using rates shown below, calculate to the nearest Euro, how much money

he left Kenya with.   (Do not use mathematical tables for this question)

 Selling (Kshs Buying Kshs 100 Japanese Yen 66.35 66.05 1 Euro 78.15 77.85

28.  Do not use mathematical tables in this question. Equity bank buys and sells foreign currencies

as shown:-

1 US dollar 77.43 78.10

I South African Rand 9.03 9.51

A tourist arrived in Kenya with 5,600 US dollars and changed the whole amount to Kenya

shillings while in Kenya he spend shs.201,367 and changed the balance to South African rand

before leaving to S. Africa . Calculate the amount in S. African rand that she received

29.  A tourist arriving from Britain had UK ₤ 9000. He converted the pounds to Kenyan shillings at a

commission of 5%. While in Kenya he spent ¾ of his money. He exchanged the remaining to US

dollars with no commission. Calculate to the nearest US dollars the amount using the exchange

rate below.

 Currency Buying Kshs. Selling Kshs. 1 US Dollar1 UK Dollar 63.00125.30 63.20125.95

30.  A company was to import goods worth Kshs.100,000 from U.K and changed the money to

Sterling pounds. The company later realized that it was cheaper to import the same goods

from U.S.A and changed the sterling pounds to dollar. Unfortunately the transaction failed

and the money was converted to Kenya shillings. How much money did the company end-up

with, given that;

1 US dollar = Kshs.78

1 Sterling pound = Kshs.120

1 Sterling pound = 1.79 U.S dollar

31.  A tourist arrives in Kenya from England with S.£ 50,000 and uses the money to buy Kenya

shillings. He quickly changes his mind and sells the Kenya shillings to get back his s£.

How much money in S.£ did he get? Use the table below

1 Sterling pound 120.7131 120.9294

32.  A Kenyan bank buys and sells foreign currencies at the exchange rates shown below:

(Kshs.)  (Kshs.)

1 Euro 147.86 148.00

1 US Dollar   74.22 74.50

An American arrived in Kenya with 20000 Euros. He converted all the Euros to Kenya

shillings at the bank. He spent Kshs.25100 200 while in Kenya and converted the remaining

Kenya shillings into US Dollars at the bank. Find the amount in dollars that he received

33.  Simplify;

(a) 6a – 2b + 7a – 4b + 2

(b) 2x – 2   3x + 2

2x   4x

 1 2x – 3 = y When M1     M1 A1 B1 partial fact or equivalentboth answers of x or yboth answers 4 2. Length of the frame (x + x + 5) = (2x + 5)Width of the frame ( ½ x + ½ x + 5) = (x + 5)Area = (2x + 5)(x + 5)(a) 75 = 2×2 + 10x + 5x + 252×2 + 15x – 50 = 0(b) 2×2 + 15x – 50 = 02×2 + 5x + 20x – 50 = 0x(2x – 5) + 10(2x – 5) = 0(x + 10)(2x – 5) = 0x = -10 or 2 ½length (2 x 5/2 + 5) = 10cmwidth (5/2 + 5) = 7.5cm(c) Area not covered = area of frame – area of photo  = 75 – 25  = 50cm2% area = 50/75 x 100  = 66.67%/66 2/3% B1 M1A1  M1 A1B1B1 M1 M1A1 Dimension with unknowns     Factorization     Difference in area 10 3. M1 M1   A1 Multiplication by LC. 4 3(25×2 – 9y2)3(5x – 3y) (5x + 3y) M1A12 For 3 out 5. 2(x – 3) = 10(4) – 5(x – 2)2x – 6 = 40 – 5x + 10 7x = 56 x = 8 M1 M1   A1 03

8.  (p + 2m) (p – 2m) B1  factors for numerator

2m – p m – 3p B1  factors for denominator

= – p + 2m  B1

m – 3p

3

9.  Let of goats be a

.” .” chicken be b

a + b = 45  B1  for both equations

4a + 2b = 100

a + b = 45

-2a + b = 50  M1  method for solving

any of the unknown

-a = -5

a = 5

b = 40

Goats were 5

Chicken were 40 A1

3

10.  Ken – suit;

Let the number of suits bought be x and the cost

per suit be y

Then xy = 57600

y = 57600

x  M1 Eq

Umoja

No. of suits bought is (x + 4)

Cost per suit is (y – 480)

= P(x + 4) (y – 480) = 57600 M1 Eq

y = (x + 4) (57600 – 480 M1 Sub of y

x

– 480x2 – 1920 + 230400 = 0

x2 + 4x – 480 = 0 M1 formation of quadratic eq

(x – 20) (x + 24) = M1 fact

No of suits = 20 A1

(b) Cost per suit = 57600 M1 exp of cost

20

Sh. 2880 A1

Profit per suit = Sh. 720

 % profit = 720 x 100 M1 exp

2880

= 25%  A1

10

 11. 13824 = 29 x 330.000125 = 1 = 1  8000 26x53 M1    M1   A1 Reciprocal   Prime products 03 12. 64x+43x = 128(43)x + 43x = 12843x + 43x = 1282(43x) = 12843x= 64 = 433x = 3 X = 1 M1 M1 A1 03 13. 4x = 3y  y = 4/3 x M1        M1M1A1 x = ¾ y    For subst        For  numFor  den 04 14. 35 x 32y = 3436 x 3y-2y+135+2y = 3437-yy = 2 M1 M1 A1 For  factorization For  simplification 03 15. B1   M1  A1 For  simplied factorization    substitutes and simplification 03 16. M1   M1     A1 Condone 0.667 03 17. 27-m x 1 = 243 81 (33)-m x 1 = 35 34 3 -3m – 4 = 35 – 3m – 4 = 5 – 3m = 9  m = -3 M1   M1    A1 3 Exp. in powers of 3   Equating powers of 3 18. 4p + 6q = 184….x33p + 8q = 222….x4 12p + 18q = 55212p + 32q = 888 14q = 33614 14q = 24 4p + 144 = 184 4p = 40 P = 10 M1  M1          A1 3 Formation of Equation  Elimination of p or q or equivalent         In both

 19. Old area = 80 x 60 = 4800m2New area = (80 – 2x)(60 – 2x) = 24x2 – 280x + 4800 = 2/3 x 48004x2 – 280 + 1600 = 0X = 6.28m M1 M1M1A1 old area  expsolvingCAO 04 20 5t =350n=2000-1050 = 950 B1  M1        A1   B1 2 equations  solving        For t and n

21.  Through A/C in Kenya

1000000 X 76.84 = Shs.7684000

through A/C in UK

1000000 X 115.70 = Shs.7,562,091.15

1.53

Through UK less by

768400 – 7562091.85 = 121,908.85

22.  6000 turn ______ 6000 X 84.15

= Kshs.504900

Balance = 504900 – 300000

= 204900

჻ sterling pound = 204900/121.47

= 1686.8

23.  In Rand = 2800265 = 279562.4264

10.0166

Expenses = (115,700 + 97000 + 53689)

= 266389 Rand

Remainder = 279562.4264

266,389.000

13, 174.4264

Amount in Kshs. = 13174.4264 x 9.9399

= 130,942.50

24.  Kshs. (3000 x 1.89) = 5670

Remain = 5670 – 4695 = 75

Francs =(975) = 500

1.95

25.  Amount in dollars = 75 x 40 = 3,000

Amount in Ksh = 3000 x 81.40 = 244,200/=

Less commission 4,000

26.  Hong Kong 8105,000 x 9.74 = ksh.1022700

Amount spent in Kenya = 403879

Balance = 1,022,600 – 403,879 = 618,821

Amount in South Africa = 618821

12.11= 51100rands

27.  500000 J yen into Kshs.= (500000 x 66.5)

100

= Kshs. 330,250

Amount spend in Kenya= Kshs. 16200

Remained with Kshs. (330250 – 16200)

= Kshs. 314,040

Kshs. 314040 into Euros:

= (314040)

78.15

= 4,018.554063Euros

He left Kenya with = 4,019 Euros (nearest Euro

28.  1 \$ Kshs. 77.43

5600\$ = (5600 x 77.43)

= 433608

Spent 201,367

Remainder = (433608 – 201367)

= 232241

1SR shs.9.51

Shs.232241

1 x 232241

9.51

= shs.24420.715

29.   1UK ₤ = 125.30

9000 UK ₤ = 125.30 x 9000

= 1,127,700

Commission = 5/100 x 1,127,700 = 56,385

He got 1,071,315

Expenditure = ¾ of 1,071,315 = 803,486.25

Amt. left = 267,828.75

In US \$ = 267,828.75

63.20

= 4237.7966 ≃ 4237 US \$

30.  1 sterling pound = Kshs.120

? = Kshs.100000

100000/120 = 833.3 sterling pounds

1 sterling pound = 1.79 U.S dollars

833.3 = ?

= 833.3 x 1.79 = 1491.7 dollars

1 U.S dollar = Kshs.78

1491.7 dollars = Kshs?

1491.7 x 78 = 116350 Kenya shillings

31.  Amount received in Kenya shillings

= 50,000 x Shs.120.7131

 = Kshs.6035655

= 1 x Kshs.6035655

120.9294 =  49910.568

32.  Sh(20000 x 147.86) = sh.2957200

To US Dollars = 44700

74.5  = 6000

33.  a) 6a + 7a – 2b – 4b + 2

= 13a – 6b + 2

b) 2x – 2 – 3x + 2 = 2(2x – 2) – (3x + 2)

2x 4x 4x

= 4x – 3x – 4 – 2

4x

= x – 6

4x

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1 Comment

• powel Ochieng, May 23, 2024 @ 10:47 amReply

We’re are notes

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