End of Year

Topic: Sequence and Patterns

Q1: Fill in the missing number in the following sequence and state a rule for each:

a) -20, 80, -320, ________, ________. Rule: _________________

b) 256, 128, 64, 32, ________, ________. Rule: _________________

c) 729, 243, 81, ________, ________. Rule: _________________

d) 420, 470, 520, ________, ________. Rule: _________________

e) -409, -399, -389, ________, ________. Rule: _________________

f) 6, 36, 216, ________, ________. Rule: _________________

g) -99, -91, -83, ________, ________. Rule: _________________

h) 202, 204, 207, 209,________, ________. Rule: _________________

i) -27, -18, -9, ________, ________. Rule: _________________

j) 321, 324, 329, 332, 337, ________, ________. Rule: _________________

k) 4, 0, -4, -8, ________, ________. Rule: _________________

Q2: Given: 𝑻𝒏 = 𝟓𝒏 − 𝟏. Find: Q3: Given: 𝑻𝒏 = 𝟐𝒏 + 𝟑. Find:

(i) 7th term (i) 11th term

(ii) 10th term (ii) 19th term

(iii) Sum of 5th and 7th term

Q4: Use the arithmetic sequence to find the nth term formula

Q5: Consider the sequence -4, -1, 2, 5, 8,…

a) Write the next two terms of the sequence.

b) Find in terms of n, a formula for nth term of the sequence.
c) Hence find the 87th term.

Q6: Consider the sequence 60, 67, 74, 81, 88,…

a) Write the next two terms of the sequence.

b) Find in terms of n, a formula for nth term of the sequence.
c) Hence find the 109th term.
Real life examples:
1.

2.

3.

4.
2.
5.
 Algebraic expressions
Question 1: Do as directed:
1.

2.

Question 2: Expand and/ or simplify the following:

Question 3: Expand and/ or simplify the following:

Question 4: Expand and/ or simplify the following:

Question 5: Factorize the following:

Factorization
Question 1: Factorize the following algebraic expressions. Use identities, mid-term breaking,
taking common factors, or grouping as appropriate.
 Algebraic Equations
Inequalities:
Question 1: Solve each of the following inequalities, illustrating each solution on a number
line.

Question 2: Find the smallest integer value of 𝒙/𝒚 which satisfies each of the following
inequalities.

Question 3: Find the largest integer value of 𝒚 which satisfies each of the following
inequalities.

Question 4: Given the inequality 3(𝑥 + 2) ≥ 5( 𝑥 – 1), find the greatest possible value of 𝑥 if
it is
(a) a rational number,
(b) an integer,
(c) a prime number.
Question 5:
Given the inequality 2𝑥 – 5 ≤ 7, find the greatest possible value of x if it is:
(a) a rational number,
(b) a whole number,
(c) a multiple of 2.

Question 6:
Given the inequality 3𝑥 + 4 > 10, find the greatest possible value of x if it is:
(a) a composite number,
(b) a multiple of 5,
(c) a prime number.

Question 7: A rectangle’s length is 5 cm more than its width. If the perimeter of the rectangle is at
most 60 cm, find the maximum possible width.

Question 8: Samantha wants to buy several shirts that cost $25 each. If she has at most $150 to
spend, what is the greatest number of shirts she can buy?

Question 9: Jack earns $15 per hour at his job. If he needs to earn at least $300 this week, what is
the minimum number of hours he must work?
Question 10: The speed limit on a road is 60 mph. If a driver goes faster than the speed limit, they
receive a fine. What is the minimum speed at which a driver will get fined?

Question 11: To pass a test, students must score at least 40 marks. If Mia scored x marks, what is
the minimum value x can be for her to pass?

Question 12: A water bottle holds less than 2 liters. If it currently contains x liters of water, what
is the greatest possible value of x?

Question 13: Amy’s internet plan allows up to 100 GB of usage per month. If she has already
used dd GB, how much more can she use without exceeding her limit?

Question 14: Ali is 3 years younger than Bilal. If the sum of their ages is no more than 50 years,
find the maximum possible age of Ali.

Question 15: Amina is twice as old as her cousin. If the sum of their ages is no more than 36
years, what is the greatest age Amina can be?
Simultaneous Equations:
Question 1: Solve the following simultaneous equations.

Question 2: Solve the following simultaneous.

Word problems:
1. Two friends bought movie tickets. One adult ticket and one child ticket cost $22. Two adult
tickets and three child tickets cost $58. What is the price of each adult and child ticket?

2. Sarah bought 3 apples and 2 bananas for $4.40. Tom bought 2 apples and 4 bananas for
$5.20. How much does one apple and one banana cost?

3. A car rental company charges a fixed fee plus a per-mile cost. John drove 100 miles and
paid $70. Lisa drove 150 miles and paid $90. What is the fixed fee and the cost per mile?

4. Two books and five pens cost $25. Three books and two pens cost $24. Find the cost of one
book and one pen.
5. Emma bought 2 VIP and 3 regular concert tickets for $210. Liam bought 3 VIP and 2
regular tickets for $230. What is the cost of each type of ticket?

6. The sum of Alice and Bob's ages is 40. Four years ago, Alice was three times as old as Bob.
How old are they now?

7. A 10-ride subway card for adults and a 5-ride card for children cost $35. A 6-ride adult card
and 7-ride child card cost $33. What is the cost per ride for adults and children?

8. At a café, two lattes and one muffin cost $11. Three lattes and two muffins cost $17. Find
the cost of one latte and one muffin.
 Fractions, Decimals and Percentages
Fractions and decimals

Simplify each expression using the correct order of operations.

18.

19.

20.

Word Problems:
3 1 1
1. A bakery received an order for kg of flour. Later, they used kg for baking cakes and kg for
4 2 4
making bread. How much flour is left?

1 1
2. A pizza shop made 2 pizzas. They cut each pizza into -sized slices. How many slices are
2 4
there in total?
 2 1 1
3. Liam mixed 2 liter of orange juice and 1 liter of apple juice in a jug. Later, he drank 1
3 4 6
liter of the mixture. How much juice is left in the jug?

1 1
4. Emma read of a book on Monday and of it on Tuesday. What fraction of the book has she
3 4
read in total?

5 1
5. A rope is meters long. It is cut into meter pieces. How many pieces can be made?
6 3

3 1 1
6. Ryan runs 2 km in the morning, km during the day and 1 km in the evening. How much
5 3 2
total distance does he run in a day?

5 1
7. A water tank is filled with 5 liters of water. If 2 of the water is used for watering plants, and
6 3
1
1 liters is used for washing, how much water remains?
2

1 1
8. A box contains 2 kg of chocolates. Each packet holds kg of chocolates. How many packets
4 4
can be made from the box?

9. A baker used 3.75 liters of milk for a cake recipe. He then added 2.4 liters more but spilled 1.25
liters while mixing. How much milk remains?

10. Emma bought 2.5 kg of apples and 1.75 kg of oranges. She later used 0.8 kg of apples to make
a fruit salad. How much fruit does she have left?
Percentages
Question 1: Do as directed:

1. Express 90 km as a percentage of 450 km.

2. What is 25% of 200?

3. Express 500 g as a percentage of 5 kg.

4. Express 8 mm as a percentage of 4 cm.

5. Express 250 ml as a percentage of 2 liters.

6. Express 40 cm as a percentage of 2 meters.

7. If 40% of a number is 80, what is the number?

8. What is 12% of 300?

9. If a student scores 45 marks out of 60, what is their percentage?

10. What percentage is 25 out of 125?

Question 2: Complete the table:

Fraction Decimal Percentages

0.265

12
25

61.5%

0.085

5
8
3
2 %
5

0.24

7
3
8

145%

0.07

6
1
25
Question 3: Complete the given table:

Question 4: Solve the given word problems:

1) A shopkeeper makes a 40% profit on the cost price of a book. If the profit is PKR 320, find:
(i) The cost price of the book.
(ii) The selling price of the book.

2) A seller buys a laptop for PKR 50,000 and sells it at a loss of 12%. Find:
(i) The loss in PKR.
(ii) The selling price of the laptop.

3) A vendor buys a set of 10 notebooks for PKR 350. He sells each notebook for PKR 30.
Express his loss as a percentage of the cost price.

4) A shopkeeper mixes 4 kg of rice costing PKR 100 per kg with 6 kg of rice costing PKR 80 per
kg. He sells the mixture at PKR 95 per kg. Calculate his profit as a percentage of the cost
price.
5) A trader mixes 5 liters of petrol costing PKR 250 per liter with 5 liters of kerosene costing
PKR 150 per liter. He sells the mixture at PKR 200 per liter. Calculate his loss as a percentage
of the cost price.

6) A shopkeeper gains 28% on the cost price by selling a chair for PKR 1540. Find the cost price
of the chair.

7) A smartphone costs PKR 78400 and is sold at a loss of 6% on the cost price. Find its selling
price.

8) By selling a book for PKR 225, Ali loses 15% on the cost price. Find the cost price of the
book.

9) During a clearance sale, a shirt has a discount of 10%. If the discount amount is PKR 75, find
(i) the marked price and
(ii) the sale price of the shirt

10) A book priced at PKR 250 is sold for PKR 225. Find the percentage discount.
11) The marked price of a toaster is PKR 1200. A discount of 8% is given during a sale. Find
the sale price of the toaster.

12) A laptop is sold for PKR 17100 after a discount of 11%. (i) Find the marked price of the
laptop. (ii) If a 6% discount is given on the marked price of the laptop before it is sold at a
further discount of 5%, would the sale price still be PKR 17100?

13) A television is sold for PKR 27720 after a discount of 12%.

(i) Find the marked price of the television.
(ii) If a 7% discount is given on the marked price of the television before it is sold at a further
discount of 5%, would the sale price still be PKR 27720?

Simple interest:
1. Ali invested $1,000 in a savings account at an annual interest rate of 5%. How much
interest will he earn in 3 years?

2. A bank offers a 6% annual simple interest rate. If Sarah deposits $2,500, how much interest
will she earn after 4 years?

3. Ahmed earned $480 in interest from a $2,000 investment. If the interest rate was 8% per
year, for how many years did he invest the money?
4. Ayesha took a loan of $3,600 at a simple interest rate of 10% per annum. How much
interest will she have to pay after 2.5 years?

5. A student borrowed $1,200 at 4% simple interest for 3 years. What is the total amount to be
repaid at the end of the period?

6. Bilal invested a sum of money at 7% annual simple interest. After 5 years, he earned $875
as interest. What was the original amount he invested?

7. A sum of money earns $600 as simple interest in 4 years at 5% per annum. Find the
principal.

8. If an amount of $900 is invested at a 6% annual interest rate, how long will it take to earn
$324 in simple interest?

Exchange rate:
1. The exchange rate is 1 USD = 285 PKR. If Ahmed wants to buy a product costing 15,000
PKR, how much will it cost him in USD?

2. If the exchange rate is 1 EUR = 310 PKR, how many euros will you get for 10,000 PKR?
3. The exchange rate is 1 GBP = 340 PKR. If Zara has 500 GBP, how much will she get in
Pakistani Rupees?

4. The exchange rate is 1 SAR = 75 PKR. If Bilal has 10,000 PKR, how many Saudi Riyals
will he receive in exchange?

5. The exchange rate is 1 USD = 285 PKR. If you want to convert 50,000 PKR into USD,
how many USD will you receive?

6. The exchange rate is 1 EUR = 310 PKR. If you have 2,500 EUR, how much will you get in
Pakistani Rupees?

7. A businessman in Pakistan is purchasing a list of items for his store. The prices of the items
in Pakistani Rupees (PKR) are as follows:
1,500 PKR for a refrigerator
3,200 PKR for a television
4,000 PKR for a washing machine
850 PKR for a microwave
The current exchange rate is 1 USD = 285 PKR. What is the total cost of all the items in
Pakistani Rupees? Then, convert that total cost into US Dollars.
8. A traveler is planning a trip to Pakistan and needs to convert his money to Pakistani Rupees
for various expenses. The traveler is bringing US Dollars (USD) and needs to budget for the
following:
Hotel stay for 5 nights at 100 USD per night
Daily meals for 7 days, costing 20 USD per day
A tour package that costs 150 USD
Souvenirs costing 80 USD
The current exchange rate is 1 USD = 285 PKR. First, calculate the total cost in USD for all
the expenses. Then, convert that total into Pakistani Rupees to determine how much the
traveler will need.

9. A woman is shopping in a store in Paris and purchasing the following items:

A designer handbag costing 250 EUR
A pair of shoes costing 120 EUR
A coat costing 180 EUR
A scarf costing 30 EUR
The store allows payments in Pakistani Rupees, and the current exchange rate is
1 EUR = 310 PKR.
First, calculate the total cost of the items in Euros. Then, convert the total into Pakistani
Rupees. How much will the woman spend in Pakistani Rupees?
Inheritance:
1. A man passes away, leaving behind one son and two daughters. According to Islamic
inheritance laws, the son will receive twice the amount of the daughters. If the total estate is
worth 900,000, how much will the son and each daughter receive?

2. A woman dies, leaving behind three sons and one daughter. The sons will receive twice the
share of the daughter. If the total estate is worth PKR1200,000, how much will each son
and the daughter receive?

3. A man passes away, leaving behind a wife and two sons. The wife will receive a portion of
the estate, while the remaining estate is divided between the two sons. Each son will receive
an equal share of the remaining estate. If the total estate is worth PKR 64,000,000, how
much will the wife and each son receive?

4. A man dies, leaving behind a wife, two sons and one daughter. The wife will inherit a
portion of the estate, and the daughter will inherit the rest. If the total estate is PKR
48,000,000 how much will the wife and the daughter receive?
5. A man dies, leaving behind a wife, a son and two daughters. The wife will receive a portion
of the estate, and the daughters will share the rest equally, with each daughter receiving the
same amount. If the estate is worth $80,000, how much will the wife and each daughter
receive?

6. A man passes away, leaving behind a wife, one son, and one daughter. The wife will inherit
a portion of the estate, while the son will inherit twice the amount of the daughter. If the
estate is worth $40,000, how much will each heir receive?
 Coordinate Geometry
Question 1: Identify the gradient and y-intercept from the given equation of a straight
line:

Question 2: Calculate the gradient and y-intercept of a straight line from the given
graph:

a. b.

c. d.
Question 3:
Question 4: Write an equations for given lines

Question 5: Draw the following equations on a graph paper

a) 𝑥 = −3
b) 𝑥 = 4 ½
c) 𝑦 = −5.5
d) 𝑦 = 2
Question 6: On a sheet of graph paper, using a scale of 1 cm to represent 1 unit on the x-axis
and 1 cm to represent 2 units on the y-axis, draw the graph of 𝒚 = 𝟐𝒙 − 𝟏 for values of x as
−2 ≥ 𝑥 ≤ 2.
Question 7: On a sheet of graph paper, using a scale of 1 cm to represent 1 unit on the x-axis
and 1 cm to represent 1 units on the y-axis, draw the graph of 𝒚 = 𝟑𝒙 + 𝟏 for values of x as
−3 > 𝑥 < 3.
Question 8: On a sheet of graph paper, using a scale of 1 cm to represent 1 unit on the x-axis
and 1 cm to represent 2 units on the y-axis, draw the graph of 𝒚 = −𝟐𝒙 + 𝟑 for values of x
from -1 to 3.
Question9: Find the slope of the line through each pair of points.

Question 10: Tell whether each slope is positive, negative, zero, or undefined.

Question 11: From the given graph find the value:

a) 𝑦 𝑤ℎ𝑒𝑛 𝑥 𝑖𝑠 2 b) 𝑥 𝑤ℎ𝑒𝑛 𝑦 𝑖𝑠 − 4

c) 𝑦 𝑤ℎ𝑒𝑛 𝑥 𝑖𝑠 − 2 d) 𝑥 𝑤ℎ𝑒𝑛 𝑦 𝑖𝑠 1
 Volume and surface area
Question 1: Find the unknowns:

Question 2: Find the unknowns:

Question 3: Find the volume of the following:

Question 4: Find the surface area of the following:

 3) 4)

5)

Word Problems:
1. A basketball has a radius of 12 cm. Calculate the volume of the basketball. Use π=3.14\pi =
3.14.

2. A glass marble has a diameter of 10 cm. Find the total surface area of the marble. Use
π=3.14\pi = 3.14.

3. An ice cream cone has a radius of 4 cm and a height of 12 cm. Find the volume of the cone.
Use π=3.14\pi = 3.14.
4. A party hat is in the shape of a cone with a radius of 6 cm and slant height of 10 cm. Find
the total surface area of the hat. Use π=3.14\pi = 3.14.

5. A square-based pyramid has a base of 10 meters on each side and a height of 15 meters.
Calculate the volume of the pyramid.

6. A square pyramid has a base side of 8 cm and a slant height of 10 cm. Find the total surface
area of the pyramid.

7. A rectangular pyramid has a base measuring 5 meters by 3 meters and a vertical height of 9
meters. Find the volume of the pyramid.

8. A rectangular pyramid has a base of 6 m by 4 m. The slant heights of the triangular faces
are 5 m and 6 m, respectively. Find the total surface area of the pyramid.
9. A triangular pyramid has a base area of 24 square cm and a height of 10 cm. Calculate the
volume of the pyramid.

10.A triangular pyramid has three sides at the base measuring 6 cm each. Each triangular face
has a height of 5 cm, and the base is equilateral. Find the total surface area of the pyramid.

11.The volume of a cone is 376.8 cm³ and its radius is 6 cm. Find the height of the cone.

12.A spherical balloon has a volume of 904.32 cm³. Find the radius of the balloon.

13.A square pyramid has a base side of 10 m and a volume of 1,500 m³. Find the vertical
height of the pyramid.

14.A cone has a surface area of 452.16 cm² and a slant height of 12 cm. Find the radius of the
cone.
15.The radius of a globe is 14 cm. Find the surface area of the globe. Use π=3.14\pi = 3.14.

16.The surface area of a rectangular pyramid is 336 cm². Its base is 8 cm by 6 cm, and its slant
heights are 10 cm and 9 cm. What is the volume of the pyramid?

17.A triangular pyramid has a base area of 50 cm² and a volume of 200 cm³. Find the height of
the pyramid.

18.A spherical tank has a surface area of 1,131.6 m². What is the radius of the tank?

19.A cone has a surface area of 706.86 cm² and a radius of 9 cm. Find its slant height.

20.A square pyramid has a surface area of 484 cm². Its base side is 11 cm. Find the slant height
of the pyramid.
 Sets
Question 1: Match the correct word to the definition.

1. Set The objects of a set

2. Finite set If a set has no elements

3. Infinite Set A set with identical members

4. Equal set A well-defined collection of distinct objects

5. Elements A set whose members can be counted

6. Empty set Sets having same number of elements

7. Equivalent A set with members that cannot be counted

8. Proper sets Sets not having common elements at all

9. Improper sets Set which is not equal to original set

10. Overalpping Set which is exactly equal to original set

11. Disjoint Sets having at least one common element

Question 2: Describe the following sets.

a. {hearing, tasting, feeling, seeing, smelling} _________________________________________

b. {1,2,3,4,5} __________________________________________________________________

c. { 1, 4, 9, 16, 25}______________________________________________________________

d. {1, 3, 5, 7….}____________________________________________________________

e. {triangle, square, rectangle, circle}________________________________________________

Question 3: List the elements or members of the following sets in set notation:

i. Days of the week that do not contain the letter ‘’ s’’

ii. The odd numbers between 5 and 15
iii. All the prime numbers less than 50
iv. The vowels in the word ‘’ parishes ‘’
v. A = {x : x is a primary colour}
vi. C = {x : x is prime number such that 2 < x ≤ 10}
vii. S = {x : x is a 2-digit number less than 15}
viii. U = {x: x is a positive integer less than 5},
ix. A = {x: x is an odd number}, and
x. B = {x: x is divisible by 4}.

Question 4: Write down the elements in the following sets.

Let U = {0,1,2,3,4,5,6,7,8,9,10}; A = {0,1,2,3,5,8}; B = {0,2,4,6}; C = {1,3,5,7}

i) A  B =
ii) B’ =
iii) B  C =
iv) (B  C)’ =
v) A  C =
vi) A  (C  B) =
vii) (A  C)  B =
viii) (A  C)  B =
Question 5: Find B, when:
i) A = {2, 4, 6, 8}
A  B = {1, 2, 3, 4, 5, 6, 7, 8}

ii) C = {5, 10, 15, 20, 25}

C  B = {15}
C  B = {3, 5, 6, 9, 10, 12, 15, 20, 25}
Question 6: U = {5,10,15,20,25,30,35,40,45,50} E = {5,10,25,40,50} F = {5,10,15,30}
G = {5,15,25,35,45}
a) Find
i. E  (F  G) =
ii. (E  F)  G =
iii. (E  F)  G =

b) Draw Venn Diagram for each:

Question 7: Complete the statements and name the property:

i) A  B =_______________________________________________________________
ii) B  C = _______________________________________________________________
iii) A  (C  B) =
_______________________________________________________________
iv) (A  C)  B =
_______________________________________________________________
Probability
4.

5.5.
6.

7.

8.

9.