The City School - · PDF fileMathematics Class – 8 Worksheets for ... The answers are...

The City School

PAF Chapter

Prep Section

Mathematics

Class – 8

Worksheets for Intervention Classes

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math /Class – 8 of 27

Task#1

Q1 Given a function , Find the values of y when

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Q2 Find the gradient of the following linear functions

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Q3) Find the gradient of the straight line determined by each of the following pair of points:

a)

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Task#2

Q1 Write down the co-ordinates of the points of intersections of the graphs of the following equation

with y-axis

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Q2 Find the y intercepts

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Q3 Given the linear function

, Calculate the value of y when

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Task#3

Q1 Find the co ordinates of the point at which the given lines cuts the y-axis

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Q2 Find any 4 points that satisfy the linear function, calculate and display these points in a table,

also find the gradient

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Q3 Write down the co-ordinates of 4 points of each of the following lines

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Task # 4

Q1 Thirty students were asked how many foreign countries they had visited. The answers are given

below.

1 0 0 2 3 1 1 0 2 4

5 1 2 0 2 0 1 3 2 4

3 0 1 1 2 3 2 1 0 1

a) Construct a frequency table of the above result.

b) Represent the frequency distribution using a histogram.

c) Find the percentage of pupil who visited 1 country.

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Task # 5

Q1 The marks out of ten scored by a class in a test are as given in the following table.

Marks 6 7 8 9 10

No. of students 2 5 10 12 6

a) How many students sat for the test?

b) Calculate the mean, median and modal marks.

c) Find the percentage of students who scored more than the median marks.

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Task # 6

Q1 Find the mean, median and mode of the following set of numbers.

a) 1.8, 1.9, 2.0, 1.7, 1.8, 1.9, 1.6, 2.0, 1.8, 1.9, 1.8

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b) 12, 18, 24, 20, 18, 11, 20, 29, 41, 20

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Task # 7

Q1 The table below shows the number of fillings a class of 40 students had at the time of a dental

inspection.

No. of fillings 0 1 2 3 4 5 6

No. of students 1 4 8 10 9 6 2

Find the mean, median and mode of the given distribution.

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TASK # 8

Q1) Factorize each if the following. Where there are no factors, state so

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TASK # 9

Q1) Use algebraic identities to evaluate the following

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Practice Questions

Q1 Simplify each of the following.

t)

v)

Q2 Expand:

Q3 Factorize:

Q4 Use Algebraic identities to evaluate the following:


Q5. Find two consecutive positive odd numbers which are such that the square of their sum exceeds the

sum of their square by 126.

Q6. The area of a rectangular field is and the difference between the lengths of the two adjacent

sides is 7m. Find the length of the shorter side and the perimeter of the rectangle.

Q7. Given that x =3 is one solution of the equation , calculate the the value of p and

hence find the other solution.

Q8. The product of two numbers is 154. If the difference between the two numbers is 3, find the

numbers.

Q9. The sum of a number and twice its square is 36. Find the number.

Q10. The sum of the squares of two consecutive even integers is 340.find the two numbers.

Q11. The sum of the squares of three consecutive positive numbers is 245. Find the largest number.

Q12. Fatimah is 5 years older than Dollah. If the product of their ages is 234, how old is Dollah.

Q13.5x articles cost dollars while 2x similar articles cost dollars. Find x.

Q14. The length and the width of a rectangle are cm and cm respectively. If the area of

the rectangle is 209 cm2, find

a) the value of . b)the perimeter of the rectangle.

Q15. When x2 is divided by – the quotient is 12 and the remainder is 1. Find the possible values of

x.

Q16. The sides of a rectangle are of lengths and . The area of the rectangle is

Find x and the perimeter of the rectangle.

Q17. If and , calculate the value of .

Q18. Factorize . Hence evaluate the value of .

Q19. If – and – , find the value of .

Q20. If and , calculate the value of

a) , b) –

.

Q21. Evaluate the following by using algebraic method.

a) 102 – 92 + 82 – 72 + 62 – 52 + 42 – 32 + 22 – 12 .

b) – – – .


Q22. The marks out of ten scored by a class in a test are given in the following table:

Q23) The contents of 114 boxes of screws are examined. The

diagram shows a histogram for the number of defective

screws in each box.

a) How many boxes contain no defective screw?

b) What is the most common number of defective screw per

box?

c) How many boxes contain at least 2 defective screws?

d) Calculate the fraction of boxes containing less than 4

defective screws per box.

Q24) At a telephone exchange, the number of calls received in a

minute interval was recorded for ach of one hundred

chosen intervals.

The results are illustrated by the histogram.

a) What is the most common number of calls per interval?

b) In how many intervals were 2 calls received per minute?

c) What fraction of the intervals chosen were there more

than 3 calls per minute?

d) What percentage of the interval were there not more than

2 per minute?

Q25) Each pupil in a class of 40 pupils was asked to measure

the length of the pencil he was using. The results are

shown in the histogram.

a) What is the shortest length? How many pupils are using

pencils of this length?

b) What is the most common length?

c) What fraction of the class is using pencils of at least 11 cm

long?

d) Find the percentage of pupils using pencils shorter than

10 cm.


Q26) A record was kept of the number of packets of potato chips sold each day in a store and

the results are as follows:

No. of packets 32 57 82 107 132 157 182 No. of days 3 5 8 7 10 6 1

a) On how many days was a record kept of the number of packets of chips sold?

b) Calculate the mean number of packets sold.

c) Find the difference between the mode and the median.

Q27) The table below shows the number of errors made by Peter in typing a report.

No. of errors 0 1 2 3 4 5 6 No. of pages 1 3 10 7 4 3 2

a) How many pages are there in Peters’ report ?

b) What was the percentage of pages with less than 3 errors?

c) What was the mode of the distribution?

d) Calculate the mean number of errors made by Peter.

Q28) In a Mathematics test, the mean score of 30 students was 12.4. Mary, one of the 30

students, scored 8 marks. It later transpired that her score was recorded wrongly. After

correcting Mary’s score the new mean score of the students became what was

Mary’s actual score ?

Q29) The following are the heights (in meters) of a group of basket ball players:

1.8, 1.9, 2.0, 1.7, 1.8, 1.9, 1.6, 2.0, 1.8, 1.9 1.8

a) Find

i. The model height of the group

ii. The median height of the group

iii. The mean height of the group, correct to one decimal place

b) When the 12th member joined the group, the mean height became 1.9 m exactly. What

was the height of the 12th member?

Q30) Find the mean, median and mode of the following set of numbers.

a) 12, 11, 13, 11, 15, 16

b) 12, 18, 24, 20, 18, 11, 20, 29, 41, 20

c) 14.3, 13.5, 10.5, 12.6, 15.3, 16.4, 12.6, 16.0

d) 10.5, 9.6, 7, 11, 9.4, 8.1, 10.4, 11.7, 8.1, 9.4, 8.1


Q31) The mean, the median and the mode of 4 numbers are 54, 56 and 60 respectively. Find

the mean of the largest and the smallest numbers.

Q32) The table shows the number of fillings a class of 40 pupils had at the time of a dental

inspection.

No. of fillings 0 1 2 3 4 5 6 No. of pupils 1 4 8 9 2

a) If the mean number of the fillings per pupil is 3.2, find the values of and .

b) If the mode is 4, find the largest possible value of and calculate the mean

number of fillings per pupil with taking the largest value.

Q33) (a) The median of the set of eight numbers is 4.5. Given that seven of the numbers are

7, 2, 13, 4, 8, 2 and 1. Find the eighth number and write down the mode of the eight

numbers.

(b) The mean of a set of twelve numbers is 5 and the mean of a different set of eight

numbers is . Given that the mean of the combined set of twenty numbers is

8, calculate .

Q34) Find the gradient of the straight line determined by each of the following pair of points:

a)

b)

Q35) Solve the following simultaneous equations using the graphical method.

a) – –

– –

–

Q36) Write down the coordinates of the points of intersection of the graphs of the following

equations with the Y-axis

a) y = -9x b) y = 5x + 3

Q37) Simplify the following:


Q38) Solve:


Q48. Evaluate:


Q49. Calculate the value of the unknown in the following figures.


FACTS TO REMEMBER

FORMULAE

Linear Graphs

The graph is a drawing which shows the relationship between number of quantities.

The co ordinates are always written in ordered pair as not as

: Where, m is the co efficient of , c is the constant and co efficient of

must be 1.

Gradient: The measure of the steepness is called the gradient. The gradient of a straight

line is the measure of the ratio of the vertical change to the horizontal change. In an

equation , m is called the gradient of the line.

– intercept: In the equation , c is the y-intercept it’s a point where a line

cuts the y-axis i.e. in the equation , y-intercept is 0.

The co ordinates of the point where the line cuts the y-axis is

and are two points of a line and the gradient of the line is

or

Equation of y axis is .

Equation of x axis is .

Line of the equation is always parallel to x axis.

Line of the equation is always parallel to y axis.

If m>0, then the line will pass from 1st quadrant to 3rd quadrant.

If m<0, then the line will pass from 2nd quadrant to 4th quadrant.

The solution of simultaneous linear equations is the point of intersection of the two

lines on their graph.

There is no solution of simultaneous linear equations if their graph drawn are two

parallel lines in the same plane.


Statistics

Frequency Table :

A set of raw data can be organized and then arranged in an orderly way in the form of a frequency table.

Histogram / Bar Graph :

A frequency table can be represented graphically by a histogram or Bar graph.

The area of each bar is proportional to the frequency it represents.

There is no gap between the bars of a histogram

UnGrouped Data :

Mean =

Median :

Arrange the data in ascending or descending order.

For an odd number of data, Median is the middle value.

For an even number of data, Median is the SUM OF TWO MID VALUES / 2

Mode :

It is the most occurring value.

Grouped Data :

Mean =

where is the sum

and

Median :

CF is the cumulative frequency

1. If is even then calculate

2. If is odd then calculate


Now search the calculated answer in the CF column

1) If the exact calculated answer is present in the C.F column, then

Sum of the of that place and next place divided by 2 is the median.

2) If the calculated answer is not present in the C.F. column, then choose the nearest but greater value

in the C.F. column of that C.F. is the median

Mode :

of the highest frequency


ALGEBRA

Laws of Indices

Where m and n are integers and a 0, b 0.

Algebraic Identities


BREAKING OF THE MIDDLE TERM

co efficient of ( is the 1st term)

co efficient of ( is the 2nd term)

constant ( c is the 3rd term )

Find the product of 1st and the 3rd. (a

X c)

Product is positive and the middle

term is also positive.

Find two such factors of the product

that their sum will be equal to the

middle term.

Both the factors must have positive

signs.

Find the product of 1st and the 3rd. (

a x -c)

Product is negative and the middle

term is positive.


that their difference is equal to the

middle term.

Sign of the greater factor is positive

and smaller factor is negative.

Find the product of 1st and the 3rd.

(a X c)

Product is positive and the middle

term is also negative.


that their sum will be equal to the

middle term.

Both the factors must have negative

signs.

Find the product of 1st and the 3rd. (a

x -c)

Product is negative and the middle

term is also negative.


that their difference is equal to the

middle term.

Sign of the greater factor is negative

and smaller factor is positive.

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