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The City School/ PAF Chapter/ Comprehensive Worksheet/ December 2019/ Mathematics / Class 8 of 12

The City School PAF Chapter

Comprehensive Worksheet

December 2019

MATHEMATICS

Class – 8

INSTRUCTIONS:

Write your name, index number, section, branch/campus and date clearly in the space provided.

Read and follow the instructions of the given questions.

Answer all the questions in the space provided.

Select only one answers when made to choose, otherwise no marks will be given.

Check your answers before handing your paper in.

Marks for each section are shown below.

This paper consists of 12printed pages including the cover page.

……………………For Examiner’s use only……………………

Question 1 2 3 4 5 6 7 8 9 10

Max. Marks 10 10 10 10 10 10 10 10 10 10 100

Marks

Obtained

Percentage

Grade

_________________ _____________ _____________________

INVIGILATED BY MARKED BY MARKS TALLIED BY

Candidate Name: _________________________________________________________________

Index Number: _____________________________________________ Section: _____________

Branch/Campus: ____________________________________________ Date: _____________

Maximum Marks: 100 Time Allowed: 2 hours


Q.1Encircle the correct answer: [ /10]

1) By using algebraic identity, the value of 𝟏𝟎𝟏𝟐 is

a. 10200

b. 10201

c. 10202

2) Square of a+5 is

a. 𝑎2 + 10𝑎 + 25

b. 𝑎2 + 25

c. 𝑎2 + 5𝑎 + 25

3) The value which occurs maximum number of times is called

a. Mean

b. Median

c. Mode

4) 752 − 252 = _______________

a. 15000

b. 500

c. 5000

5) Mean of 7, 5, 1, 0, 3, 8, 6, 2, 4 is

a. 3

b. 4

c. 5

6) Factorize 𝑥2 − 5𝑥 + 6

a. (𝑥 + 2)(𝑥 + 3)

b. (𝑥 − 6)(𝑥 + 1)

c. (𝑥 − 2)(𝑥 − 3)

7) A helicopter travels 425 miles in 5hours. The average speed of the helicopter

is

a. 75km/h

b. 85km/h

c. 95km/h


8) A journey started at 07:44 and finished at 11:32. How long, in hours and

minutes, did the journey take

a. 3hrs 12mins

b. 3hrs 48mins

c. 4hrs 12mins

9) Estimate 58.8 ×20.9

101.4correct to 2 significant figures

a. 12

b. 120

c. 1200

10) The general term of the sequence 2, 5, 8, …. is ______________

a. n + 1

b. 2n - 0

c. 3n - 1

Q.2 Fill in the blanks: [/10]

1) Speed and time is an example of _______________ proportion.

2) If the formula for the nth

term of the sequence is 3n2+1, then 12

th term will be

______________

3) Factors of 121𝑥2-169𝑦2are __________________

4) Expanded form of (a-b)(3a+b) ___________________

5) If 5 − 𝑥 < 3, then𝑥__________________2

6) A car took 2 hours to cover a distance of _____________ km with a speed of

60kms/hour.

7) Median of 3,0,8,0,5 is ____________________

8) (7a-5𝑏)2=________________

9) 101 x 99 = __________________

10) If the diagonals of a parallelogram bisect each other perpendicularly then the

shape is a __________________________


Q.3 (a) Consider the following pattern [ /04]

13-1 = 0 = (1-1) x 1 x (1+1)

23–2 = 6 = (2-1) x 2 x(2+1)

33-3 = 24 = (3-1) x 3 x (3+1)

43 -1 = 60 = (4-1) x 4 x (4+1)

:

n3-n = 2184 = (n-1) x n x (n+1)

:

i. Write down the 8th line of the pattern

ii. Find the value of n

Q.3 (b) Sum of the ages of Ahmad and his mother is 40, two years ago Ahmad’s

mother was 5 times as old as Ahmad. Calculate Ahmad’s age [ /06]


Q.4 (a) Sana, Zara and Sara have birthdays in the same month. They were given a

sum of money to be divided in proportion according to their ages, which are 8years,

7years and 5years. Given that Sana and Zara together obtained a total of $270. Find

the sum of money to be divided. [/04]

(b) Razi pays $6 for parking a car in a shopping center for 2.5hours. [ /04]

i. Calculate the parking charges per minute.

ii. The amount he will have to pay if he parks his car for 𝟏𝟑

𝟒 hours

(c) A driver travels the first 120km of a 200km journey at an average speed of

40km/hr. He travels the remaining journey at the speed of 60kms/hr. Find the time

taken for the whole journey. [ /02]


Q.5 Factorize the following:

(i) 𝟏𝟖𝒙𝟐 − 𝟑𝒙 − 𝟔 [ /03]

(ii) 𝟐𝒙𝟒𝒚 − 𝟏𝟖𝒙𝟐𝒚𝟑 [ /02]

(iii) 𝒂𝟐 + 𝟏𝟐𝒂 + 𝟑𝟔 [ /02]

(iv) If𝒙𝟐 − 𝒚𝟐 = 𝟔and𝒙 − 𝒚 = 𝟐, find the value of (𝒙 + 𝒚)𝟐 [ /03]


Q.6 Solve

(i) 𝟐𝒄𝟐 + 𝟕𝒄 − 𝟒 = 𝟎 [ /03]

(ii) The product of two numbers is 154. If the difference between the numbers is 3

find the numbers. [ /05]

(iii) Expand and simplify 𝒙 + 𝟕 𝒙 − 𝟑 − 𝟓(𝒙 − 𝟑) [ /02]


Q.7 (a) A contractor undertook a contract to complete a part of a stadium in 9 months

with a team of 560 workers. Later on, it was required to complete the job in 5

months. How many extra workers should he employ to complete the work?

[ /04]

(b) Given that 𝒚 is inversely proportional to𝒙, when 𝒚 = 𝟏𝟐𝟓 and 𝒙 = 𝟓

i. Find the equation connecting 𝒚 and 𝒙 [ /03]

ii. Find the value of 𝒙 when 𝒚 = 𝟐𝟓 [ /03]


Q.8. (a). Find the area and perimeter of the shaded region [ /06]

(b). Solve the following inequality and illustrate your answer on a number line

[ /04] 4𝑥 − 3

2≥

5𝑥 + 2

4


Q.9. (a). Life span of bees (in days) in a certain colony is given below [ /06]

Class interval Frequency

8

9

10

13

Calculate the mean life span of the bees.

(b) Draw a histogram to illustrate the distribution. [ /04]


Q.10 (a) Construct a rhombus PQRS such that PQ=60mm and the diagonal

PR=9mm. measure and write down the size of ∠QPS [ /05]


(b) Construct a trapezium ABCD such that angle ∠ABC=85⁰, ∠BCD=75⁰,

AB=6.5cm and BC=9.4cm

Measure and write down the length of AD and CD [ /05]

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