GRADE 7 MATHEMATICS WORK SHEET

GRADE 7 MATHEMATICS WORK SHEET

AMHARA EDUCATION BUREAU

CURRICLUM DEVELOPMENT AND IMPLIMENTATION DIRECTORATE

AUGUST, 2020 BAHIR DAR.

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GRADE 7 MATHEMATICS WORK SHEET

UNIT FOUR 4. DATA HANDLING 4.1 Ways of collecting data Note:- How can we collect data:  By using a questionnaire  By making observations and recording the results  By carrying out an experiment  From records or data base  From the internet Exercise 1. Which one is not correct when we are writing questions for a questionnaire? A. Be clear what we want to find out and what data we need. B. Ask short and simple questions. C. Provide tick boxes with possible answers D. Writing vague questions and questions which may influence the answer. 4.2 Some ways of presenting data Note:- A. Collecting data using Tally marks:  Tally mark is one way of presenting data by line segments. Example:- //// represents 5 members of the sample. Example: In a survey, 20 pupils were asked how many of their friends they got last Sunday. Here are the results: 3 2 4 1 4 2 5 5 7 6 4 6 3 4 2 6 4 2 8 5 Number of friends Tally Frequency 1 / 1 2 //// 4 3 // 2 4 //// 5

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GRADE 7 MATHEMATICS WORK SHEET

5 /// 3 6 /// 3 7 / 1 8 / 1 Total 20 Exercise 2. The age of students in a class were recorded as follows: 13 12 13 14 14 13 14 16 14 13 14 13 14 14 14 15 15 14 15 15 15 14 15 14 13 12 15 15 16 15 16 14 16 16 15 16 15 14 16 16 14 16 13 14 14 15 14 15 16 15 13 14 15 14 14 17 17 16 13 14 Show this information more clearly by drawing a tally chart. Note:- B. Line graphs:  The line graph is most commonly used to represent two related facts. To plot a line graph, you can take two lines at right to each other. These lines are called the axes of reference. Their intersection is called the origin. The number of units represented by a unit length along an axis is called a scale. A line graph is drawn based on pairs of measurements of two quantities. To plot a line graph the following points are important: A. Draw the horizontal and vertical lines (axes) and label them by using appropriate scale so that it should be enough to represent the data to be used. B. Make a table of data arranged in pairs. The first number of each pair is read from the horizontal scale( axis) and the other number is from the vertical scale(axis). Use these numbers to locate points on the graph. C. connects the points by a straight line or a smooth . Exercise 3. Draw a line graph to represent each of the following sets of data. a. The temperature in Bahir Dar at midday during the Second week in July Day Sun Mon Tue Wed Thur Fri Sat Temprature(c)•• 13 12 15 14 13 16 12

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GRADE 7 MATHEMATICS WORK SHEET

Note:- C. Pie Chart:  Pie chart is a very common and accurate way of representing data especially useful for showing the relations of one item with another and one item with the whole items. The portion of a circular region enclosed between two radii and part of the circumference (an arc) is called a sector of the . The size of the sector is determined by the size of the formed by the two radii. Exercise 4. Ato Alemayehu family’s had an income of Birr 12,000 per. In month his family expenditure is; Food – 6000 Travel- 800 Rent- 4000 Entertainment-200 Saving- 1000 Construct a pie chart representing the above information? 5. The following pie chart shows a family budget based on a net income of Birr 2400 per month A. Determine the amount spent on rent B. Determine the amount spent on car payments. C. Determine the amount spent on utilities D. How much more money is spent than saving.

30% rent 25% Saving

8% Utilize 10% Others 12% Car 15% payment Grocery

4.3 The mean, Mode, Median and Range of Data Note:- The mean, Mode, Median and Range  The mean of a set of data is the sum of all values divided by the number of values.  The Mode of a set of data is the value which occurs most frequently.  The Median is the middle value when the data is arranged in order of size from the smallest to the largest or from the largest to the smallest.

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GRADE 7 MATHEMATICS WORK SHEET

 The range of a set of data is the difference between the highest value and the lowest value.

Exercise 6. What number should be included in the data 2,8,7,4 and 9 so that the mean is 6. A. 7 B. 5 C. 6 D. 8 7. Find the range of data , -5 ,-10, 8, -92 A. 100 B. 87 C. 92 D. 97 8. The middle value in an arrangement of data in a sending or descending order is called? A. Mean B. mode C. median D. Range 9. Which of the following is measure of dispersion ? A. Mode B. Range C. median D. mean 10. What is the mode of the data: 8, 4, 6, 8, 7, 4, 9? A. 6 B. 7 C. 4 and 8 D. 9 UNIT FIVE 5. GEOMETRIC FIGURES AND MEASUREMENT OF Note:- Quadrilateral :  Is a four sided geometric figure bounded by line segments?  The point at which the sides are connected are vertices.  Adjacent sides of a quadrilateral are sides that have a common end point.  Opposite sides are sides that have no common points.  A diagonal is a that connects two opposite vertices. Note:- A Trapezium :  Is a special type of quadrilateral in which exactly one pair of opposite sides are parallel.  The parallel sides are called the bases of the trapezium.  The distance between the bases is known as the height ( altitude) of the trapezium. Exercise 11. Which of the following is not a special ? A. Trapezium B. C. D. 12. Diagonals of any quadrilateral are equal. A. True B. False

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GRADE 7 MATHEMATICS WORK SHEET

13. A having four sides is called------A. B. Quadrilateral C. D. 14. DEFG is a quadrilateral D A. Name all its vertices E B. Name all its sides G C. Name all pairs of opposite sides F D. Name all pairs of opposite sides E. Name adjacent sides of a quadrilateral. Note:- parallelogram:  A parallelogram is a quadrilateral in which each side is parallel to the side opposite to it.  Opposite sides of a parallelogram are congruent and parallel.  The diagonals of a parallelogram bisect each other  Opposite angles of a parallelogram are congruent and consecutive angles of a parallelogram are supplementary. Note:- Special :  Rectangle , Rhombus and Square are special parallelograms. Exercise 15. Write the properties of A. Rectangle ------B. Rhombus ------C. Square------16. A special type of quadrilateral in which exactly one pair of opposite sides are parallel is---- A. Parallelogram B. Rectangle C. Trapezium D. Rhombus 17. ABCD is a parallelogram, if measure of angle A is 110°, then what is measure of angle D? A D A. 110° B. 70° C. 350° D, 250°

B C 18. In rectangle ABCD the length of diagonal AC is given by (20× +2) cm and diagonal BD is ( 14× +14) cm. what is the length of AC? A B A. 52 cm B. 32 cm C. 42 cm D. 2cm

D C

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GRADE 7 MATHEMATICS WORK SHEET

19. Find the length of the side of a rhombus whose diagonals are length of 12cm and 16cm.

A. 5cm B. 10 cm C. 6 cm D. 8 cm

20. ABCD is a square. Find the measuring < ADB ? A B A. 90° B. 60° C. 45° D. 35°

D C

Match column A with column B with the appropriate property more than once. A B 21. All diagonals are equal in length A. Rectangle 22. All angles are equal B. Parallelogram 23. All sides are equal C. Rhombus 24. The diagonals bisect the angle at the vertices D. Trapezium 25. The diagonals bisect each other at right angle E. Quadrilateral

Note:- POLYGON:  Is a simple closed figure formed by three or more line segments joined end to end. A. A is a simple polygon in which all of its interior angles measures less than 180° each. B. A is a simple polygon which has at least one interior angle of measures greater than 180°  A diagonal of a convex polygon is a line segment whose end points are non- consecutive vertices of the polygon.  If the number of sides of a polygon is ‘’n” , then, Number of diagonals drawn from one vertex is n-3.  Number of all possible diagonals is n(n-3)/2 Exercise 26. How many possible diagonals are there in a polygon of 8 sides? A. 20 B. 40 C. 35 D. 15 27. A simple polygon which has at least one interior angle of measures greater than 180° is------A. Convex B. Concave C. Square D. Rectangle

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GRADE 7 MATHEMATICS WORK SHEET

Match column A with column B with the appropriate name and number of sides. A B 28. Hexagon A. 9 sides 29. Quadrilateral B. 5 sides 30. C. 8 sides 31. D. 7 sides 32. E. 6 sides 33. G. 4 sides 34. Pentagon H. 11 sides I. 10 sides Note:- :  A circle is the set of all points in a plane that are equidistant from a fixed point called the center of the circle. C C D - Chord CD and AB

A O B - Radius OA , OB and OE - Diameter AB E - Arc ACD , DBE, AEB Exercise 35. The longest chord in the circle is------36. Complete path of a circle is------A. Arc B. Circumference C. chord D. radius Note:- Theorems of :  The sum of the degree measure of the interior angles of a is equal to 180°.  If two parallel lines are cut by a transversal line, then alternate interior angles are equal.  If two parallel lines are cut by a transversal line, then interior angles on the same sides of the transversal line are supplementary.  If two parallel lines are cut by transversal line, then corresponding angles are equal.  The measure of an exterior angle of a triangle is equal to the sum of the measure of the two remote (non-adjacent interior) angles.  The formula for the sum (S) of the measures of all the interior angles of polygon of n sides is given by S= (n-2)180.

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GRADE 7 MATHEMATICS WORK SHEET

 The measures of each interior angle of an n-sided is

 A polygon whose all sides are congruent is called an . Example; Rhombus.  A polygon whose all angles are congruent is called an . Example; Rectangle  A polygon which is both equilateral and equiangular is called a regular polygon. Example; , Square Exercise 37. In the figure AB //CD, m (

39. Find the degree measures of marked angle

40. What is the degree measure of each interior angles of a regular 6 sided polygon A. 540º B. 720º C. 60º D. 120º 41. The interior angles of a polygon is 100º, the other interior angles are all equal to 110º. How many sides has a polygon A. 4 B. 5 C. 6 D. 7

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GRADE 7 MATHEMATICS WORK SHEET

42. which one of the following is an example of regular polygon A. Square B. Rectangle C. Rhombus D. Trapezium 43. Which one of the following an example of equiangular polygon A. Rhombus B. Parallelogram C. Trapezium D. Rectangle Measurement Note:- Perimeter and of a Triangle: The area of a triangle whose base is b and altitude to this base is h is given by A= If the length of the sides of a triangle are a, b, and c, then the perimeter p of the triangle is p= a+b+c Note :- Perimeter and Area of Trapezium. If the lengths of the bases of a trapezium are denoted by

and and its altitude is denoted by h, then the area A of the trapezium is given by; A= ( + )

or A= ( + )h or A=( + )h/2 The perimeter of the trapezium is given by P= AB +BC+ CD+ DA

Note :- Perimeter and Area of parallelogram. The Area A of a parallelogram with length of base and corresponding height is given by A= bh. If the length of the sides of a parallelogram ABCD are a and b , then the perimeter p of the parallelogram is given by: p = AB +BC+CD+DA, P= b+a+b+a, P= 2a+2b, P= 2(a+b) Exercise 44. The Area of a trapezium is 276 , the altitude is 12cm and one base is 14cm long. Find the other base A. 16 cm B. 18cm C. 32cm D. 8cm 45. ABCD is a parallelogram. If AQ=4cm , AB=6cm, then find the Area of ABCD. A 6cm B 4cm D Q C A. 24 B. 36 C. D. 48 46. In the figure below NFE is a straight line. Find the area of DEF. A. 15 B. 60 C. D. 12 D D 10cm

N x F 6cm E

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GRADE 7 MATHEMATICS WORK SHEET

47. In the figure below CD AB with AB= 16cm and if the vertex is C moved to E by 2cm, then what is the area of shaded region A. 32 B. 8 C. D. 16

48. In the figure below parallelogram ABCD the length of AB= 10cm and BC=8cm. Find the perimeter of a parallelogram. A B

A. 18cm B. 80cm C. D. D C 49. In the figure below what is the perimeter of DEF A. 18cm B. 80cm C. D. D 5cm

E 12cm F Note:- Circumference of a circle:  The perimeter of a circle is called its circumference.  The circumference of a circle is related its radius or diameter.  The circumference of a circle whose diameter d is given by : C= or C

 ( pi) = = 3.14

Area of a circle The area of a circle whose radius r unit long is given by or ( )2

Exercise 50. The circumference of a semi- circle with radius 10cn is A.20 cm B. 5 cm C. 25 cm D. 10 cm 51. Two concentric circles have radii 8cm and 3cm respectively. Find the area of annulus (shaded region). A.64 B. 9 C. 55 D. 73

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GRADE 7 MATHEMATICS WORK SHEET

Note:- A prism:  Is a solid figure that has two parallel and congruent bases. Depending on the of its base a prism can be triangular, rectangular, and pentagonal and so on.  A rectangular prism has six faces; two bases and four lateral faces.EH ,HG GC=h B C

A D F G F E l H  A prism has two bases upper base and lower base. The edge of a prism is the line segments that bound

the prism. Area of base (AB)= a(ABCD)+ a( EFGH),= LW+LW= 2LW  Total surface Area(AT)= Area of two bases + Area of four lateral faces.

AT = a(ABCD) +a (EFGH) +a (BCGF) +A (CDHG)+ a(ADHE)+ a(ABFE)

AT = lw+lw+wh+lh+wh+lh = 2lw+2wh+2lh = 2(lw+wh+lh) Exercise 52. if A rectangular prism with a base of 6cm and 5cm and height 4cm then, calculate the total surface area of the prism.

 A cylinder is a solid figure whose upper and lower bases are congruent simple closed lying on parallel planes.  A right circular cylinder is a cylinder in which the bases are circles and the planes of the bases are perpendicular to the line join the corresponding points of the bases.

Upper base Area of the bases (AB): 2AB=2

Lateral surface Area of lateral surface (AL)=2 , =ph,p-perimeter Lower base A = 2A +A =2 +2 rh = 2 r(r+h) T B L

Exercise 53. The lateral surface Area of a right circular cylinder is 60 and the circumference of the base is 6cm. Find the altitude of the cylinder. A. 20 cm B. 10 cm C. 15 cm D. 12cm

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GRADE 7 MATHEMATICS WORK SHEET

Note:-volume (v) of a rectangular prism equals the product of its length (l), width (w) and height(h): V= length × width × height , v= l × w × h Volume of a cube can be calculated by v = l× l× l = A circular cylinder is a special prism where the base is a circle. The area of the base with radius r is , so its volume (v) = Area of the base ×height , v= ABH , v= The volume of any prism (cylinder) equals the product of its base area and altitude.

Volume = Base Area × height , v= AB × h

Exercise 54. A right triangular prism has height 12 cm and volume 60 . What is the area of triangular base A. 20 B. 720 C. D. 5 55. The volume of a triangular prism is 204 , if its base area is 17 , then find the height of the prism A. 17cm B. 24cm C. D. 56. The volume of a circular cylinder is Find the height of this cylinder , if its base radius is 4cm. A. 3 cm B. 12 cm C. 6 cm D. 8cm

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