Year 8 Term 2 Homework
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1 Yimin Math Centre Year 8 Term 2 Homework Student Name: Grade: Date: Score: Table of contents 10 Year 8 Term 2 Week 10 Homework Geometric Constructions Constructing regular polygons in a circle Constructing triangles Problem solving Miscellaneous Exercises This edition was printed on March 23, 2018 with worked solutions. Camera ready copy was prepared with the L A TEX2e typesetting system. Copyright Yimin Math Centre Year 8 Homework
2 Year 8 Term 2 Week 10 Homework Page 1 of Year 8 Term 2 Week 10 Homework 10.1 Geometric Constructions Constructing regular polygons in a circle A regular polygon has all its sides equal and all its angles equal. Regular polygons are named according to the number of sides. Polygon names: Polygon Name Edges henagon (or monogon) 1 digon 2 triangle (or trigon) 3 quadrilateral (or tetragon) 4 pentagon 5 hexagon 6 heptagon 7 octagon 8 enneagon (or nonagon) 9 decagon 10 hendecagon 11 dodecagon 12 tridecagon 13 tetradecagon 14 pentadecagon (or quindecagon or pentakaidecagon) 15 Exercise Draw a circle with centre O and a radius OA of 3 cm. 1. Use a protractor to construct OB and OC so that AOB = AOC = Joint the points A, B and C to from ABC. 3. Measure the side lengths of ABC. What kind of triangle is it?
3 Year 8 Term 2 Week 10 Homework Page 2 of 10 Exercise Draw a circle of radius of 3 cm with centre O, without changing the radius of your compass, mark 6 equally spaced points around the circle. 2. Joint the points to form a regular hexagon. 3. Do the axes of symmetry pass through centre O? Exercise Construct each of the following regular polygon in a circle of radius of 3 cm. (1) octagon (2) nonagon (3) decagon (4) dodecagon
4 Year 8 Term 2 Week 10 Homework Page 3 of Constructing triangles Exercise Construct an equilateral triangle with sides: 1. 3 cm 2. 5 cm Exercise Construct isosceles triangles: 1. with a base of 4 cm and its equal sides of 3 cm. 2. with a base of 5 cm and its equal sides of 4 cm.
5 Year 8 Term 2 Week 10 Homework Page 4 of 10 Exercise Construct these scalene triangles: 1. with sides 3 cm, 5 cm and 7 cm. 2. with sides 3 cm, 4 cm and 5 cm. 3. with sides 5 cm, 3 cm and 6 cm. Exercise Construct a triangle with sides 3 cm, 3.5 cm and 4 cm. 2. measure the 3 angles. 3. Is the largest angle opposite the longest side? 4. Is the smallest angle opposite the shortest side?
6 Year 8 Term 2 Week 10 Homework Page 5 of 10 Exercise Consolidation 1. Construct an isosceles triangle JKL with a base of 7 cm and equal sides of 5 cm. 2. Find the midpoint M of the base JK and join LM. 3. Verify by measurement that: (a) the base angles are equal (b) LM bisects the base JK (c) LM bisects the apex angle, JLK (d) LM JK 4. Is LM an axis of symmetry of JKL 5. Are there any other axes of symmetry? Exercise Construct a triangle with sides 7.5 cm, 6 cm and 4.5 cm. 2. Measure each angle of the triangle 3. Is the triangle right-angled?
7 Year 8 Term 2 Week 10 Homework Page 6 of 10 Exercise Construct full size drawing of these triangles, using a ruler and protractor.
8 Year 8 Term 2 Week 10 Homework Page 7 of 10 Exercise Further applications 1. Construct ABC with sides 3 cm, 4, cm and 5 cm. What type of triangle is this? (a) Join A to D, the midpoint of BC. (b) Measure AD, BD and CD. What property do you notice? (c) Would this property also hold for a triangle with sides 9 cm, 12 cm and 15 cm? 2. Show that it is not possible to construct triangle with sides: (a) 3 cm, 4 cm and 8 cm. (b) 4 cm, 4 cm and 9 cm. (c) How would you determine whether the construction of a certain triangle was possible given the length of its sides?
9 Year 8 Term 2 Week 10 Homework Page 8 of Problem solving Exercise Yesterday Roy and Ken each had an average of 44 marbles. Each of them bought 22 more marbles today. Now Roy has 20% more marbles than Ken. Find the ratio of Roy s marbles to the number of marbles Ken had yesterday. 2. The length of a rectangle is 120% of its breath. The perimeter of the rectangle is 88 cm. Find the area of the rectangle. 3. The breath of a rectangle is 20% of its perimeter. If the length of the rectangle is 24 cm longer than its breath, find the area of the rectangle. 4. The ratio of the number of girls to the number of boys at a party was 7:3. Each girl was given 5 sweets and each boy was given 3 sweets. A total of 352 sweets were given to these children. How many sweets were given to the boys?
10 Year 8 Term 2 Week 10 Homework Page 9 of Miscellaneous Exercises Exercise Which sampling method would be appropriate for each situation: (a) A school principal wants to take a sample of students in her school to find out whether they are satisfied with the level of library resource. (b) A farmer needs to know whether a disease has infected any of the horses, cattle and sheep on his property. (c) A sample of plates produced in factory is to be inspected to check the quality of the plate s shape and colour. 2. A bag contains 81 black marbles and a number of white marbles. Graham chose 30 marbles from the bag without replacement. 12 were white. How many marbles were originally in the bag? 3. Find the mean of the given data set, correct to 1 decimal place. Score Frequency How many 3 digit numbers can be formed from the first five numbers 1 to 5 if each is used only once? 5. In how many ways can 5 boys line up?
11 Year 8 Term 2 Week 10 Homework Page 10 of 10 Exercise Patterns and sequences 1. In each of the following find the first three terms if the nth terms is: (a) 2n + 5 (b) 3n 2n 2 (c) ( 2) n+1 2. For the following sequences: find the next two terms. write down the nth term of each of the sequences hence find the sum of the first 20th terms. (a) 5, 13, 21, 29,... (b) 31, 24, 17, 10,... (c) -7, 2, 11, 20, For the following sequences: by first writing each term in index form then find the 20th term write down the nth of each of the sequences. (a) 6, 18, 54, 162,... (b) 1 24, 1 6, 2 3, 8 3,...
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