End Of Term 2 Revision Sheet

Transcription

1 Egyptian British International School Math Department Name:. Year (8..) End Of Term 2 Revision Sheet

2 * Answer The following questions after revising your classwork copybook, course book, homework book and worksheets : 1] Work out the first three terms and the 100 th term of the sequence 9n + 9 First three terms..,., 100 th term =.. 2] Look at these numbers : Using only the numbers above, write down a) a prime number, b) a square number, c) a factor of 24, d) 144, e) a cube number. Page 1 of 27

3 3] Mariam and Farida share $ 8940 in the ratio 5 : 7. Find the share of each of them. 4] Simplify these ratios : a) 500 m : 2 km : 20 m b) $1.09 : 99 cents : $ 4 5] Find the nth. Term and the 30 th term of the following sequence : 23, 20, 17, 14, 11,. n th. Term =.. 30 th. term =.. Page 2 of 27

4 6] Here are the first five terms of a number sequence i) Write down the next two numbers in the sequence. ii) Find the nth. Term of this sequence. 7] Here are the first four terms of another number sequence i ) Write down the next two numbers in the sequence. ii) Find the nth. Term of this sequence. Page 3 of 27

5 8] In a school the students ratio of girls : boys is 11 : 9. There are 880 girls Work out the total number of students in the school. 9] ABC is a right-angled triangle. AB = 15 m and BC = 12 m. Calculate the length of AC. 10] Write down the number of each special quadrilateral that is described. a) I have order 2 rotational symmetry and two lines of symmetry. I also have four right angles.. b) I have all sides the same length. My diagonals bisect each other at 90. I have 4 lines of symmetry. c) Parallelogram has lines of symmetry and order of rotational symmetry. d) Rectangle has lines of symmetry and order of rotational symmetry. Page 4 of 27

6 11] Draw all lines of symmetry. 12] These two triangles are congruent. A X a) Write down the length of the side : 41 i. AC = ii. XY = iii. BC =.. 4 cm B 49 C Y 90 Z b) Write down the size of : i. <ABC = ii. <YXZ = iii. <XZY =.. Page 5 of 27

7 13] If A ( -3, 5 ) and B ( 1, -1 ) then the midpoint of AB =.. 14] In this cuboid Find : Volume = cm 3 Total surface area =. Cm 2 5 cm 4 cm 15] Simplify : a) m 2 x m 5 = 12 cm b) P 9 P 4 = c) m 3 P 2 P = d) ( 2 m 3 ) 2 = e) C 5 x C 10 = f) (3x 3 ) 4 = g) 8x 6. 3x = h) m 11 m 3 = i) (n 6 ) 3 j) 25b 8 = k) k6 k² = Page 6 of 27

8 16] The triangle ABC is shown on the grid : Y 4 B 3 2 A 1 C X Y = a) write down the co-ordinates of the point A. (,. ) b) Plot the point ( -3, 2 ) on the grid. Label point P. c) Triangle ABC is reflected in the line Y= -1. Plot the point B after this reflection.label the new point Q. d) Triangle ABC is rotated 90 º anti clockwise about the point ( 0, 0 ). Plot the new point C after this rotation. Label the new point R. Page 7 of 27

9 17] A letter from the word CHECKPOINT is chosen at random. * Write down the probability of : a) choosing a letter T = b) choosing either a letter N or a letter H = c) not choosing a letter C = d) choosing a letter S = 18] In a box there are 6 red balls, 5 green balls and 2 white balls. on drawing a ball randomly.find the probability of : a) getting a red ball = b) not getting a white ball = c) getting a red and white balls = d) getting a yellow ball = 19] Ali is building a window frame. The internal measurements of the frame are 1.5m by 2m. * Use Pythagoras theorem to work out the length of the diagonal. [ 2 marks ] 1.5 m 2 m Page 8 of 27

10 20] Tania has drawn a plan of her school. 7.5 m Classroom 18 m 8 m Playground 21 m Work out the area of the playground. 21] The school has a circular sandpit. It has a radius of 3 meters. Work out the area and the circumference of the sandpit. Use π = 3.14 or your calculator value. 22] Enlarge this triangle with scale factor 2 from the center marked in the grid. Page 9 of 27

11 23] Look at the diagram which is drawn on a 1cm² grid. X = A B C The points A ( 2, 4 ), B ( 4, 4 ) and C ( 4, 2 ) are marked. a) the triangle ABC is reflected in the line x = 5. Plot the point A after reflection label the new point R. b) The triangle ABC is rotated about the point ( 5, 5 ) with angle 90 clockwise.plot the point B after rotation. label the new point Q. c) The triangle ABC is translated with translation ( 5, 2 ).Plot the point C after translation.label the new point S. d) Enlarge this triangle with scale factor 2 from the center ( 2, 2 ). Page 10 of 27

12 24] A is the point with coordinates ( 15, -9 ), B is the point with coordinates ( 3, 9 ). Find the gradient of the line AB. 25]Find the midpoint of the line segment joining the points. ( 7, 5 ), ( 2, 3 ) 26] Find the area of each figure. a) 5.9 cm b) 45.3 m 6 cm 7.1 cm 29 m 27.6 m 11.1 cm c) 1.8 m Page 11 of 27

13 27] A straight line L is shown on the grid. Work out the equation of line L. 28] Find the circumference of the following circle. 29] Find the area and perimeter of the following shape Page 12 of 27

14 30] Find the area of the following shape 31] Find the area of the shaded part. Page 13 of 27

15 32] From the graph above answer the following questions. a. How far has he run after 3.5 seconds? b. How long has it taken Usain to run 110 metres? Page 14 of 27

16 33] The ages, in years, of seven passengers are shown below Find : a. The range of the ages of the passengers. b. The median age of the passengers. c. The modal age of the passengers. d. (i) The total age of the passengers. (ii) The mean age of the passengers. Page 15 of 27

17 34] Ronaldo rolls a six-sided die thirty times. He recorded his results a) Complete the frequency column for his results. Number Frequency Total = 30 b) i. Write down the mode. ii. Write down the median. iii. Write down the mean Page 16 of 27

18 35] a) Complete the table of the values for y = 5x 2. X Y -7 3 b) Use your results to plot the graph of y = 5x 2 on the axes below. C) The graph of y = 3x 4 has already been drawn on the grid above. Use the graph you have drawn to solve the simultaneous equations. y = 3x 4 x =. y = 5x 2 y =. Page 17 of 27

19 36] a = 5, b = 6 and c = -2. Find the value of each of the following: (i) 3a - 2c (ii) (b - 2c) 2 37] Work out the following a) HCF of 12 and 16. b) LCM of 10 and 15 38] Work out the following: a) = b) = c) = Page 18 of 27

20 d) = e) 2 5 of 65 = h) = i) x 8 27 = 39] Find the value of X in these equations. a) 3X 2 = 19 b ) 5 X + 2 = 3 X + 14 Page 19 of 27

21 c ) X³ = 125 d) X² = 16 e) X³ = 64 40] Look at these numbers Using only the numbers above, write down a) a prime number b) a square number c) a factor of 48. e) a cube number.. 41] Work out the sizes of the angles a, b ( State the reasons ) 60 a 40 b * m(<a)= because * m(<b)= because Page 20 of 27

22 42] Look at the diagram below, made from four straight lines. The lines marked with arrows are parallel. Work out the sizes of the angles marked with letters. Not drawn accurately a =.. b b =.. a 80 c =.. c d 50 d =.. 43] In triangle PQR, PQ is drawn for you, QR = PQ and PR = 4 cm. Construct triangle PQR accurately. P Q Page 21 of 27

23 44] Solve the following equations : 1. 3x 4 = x = 15 x x + 13 = 2(x + 9) 4. 5x - 2 = 3x x 5. 2(2x + 3) = x = 4 3 9x = k + 1 = 17 4 Page 22 of 27

24 45] Solve the following simultaneous equations : 1. 3p + q = p + q = 3 x + 2y = 4 3x 4y = x + 2y = 1 x y = a + 3b = 9 2a 3b = 12 Page 23 of 27

25 46] Construct the bisector of angle y. 47] Construct a perpendicular bisector for the following line segment. Page 24 of 27

26 48] One day, at noon, in Maseru, the temperature was 17 C. At midnight the temperature was 20 C lower. Work out the temperature at midnight. 49] A taxi journey costs $4.50, plus 80 cents for each kilometre travelled. Julianna travels 7 km. Work out the cost of her journey. 50] Calculate the size of one interior angle of a regular 12-sided polygon. 51] Make m the subject of the formula n = mt q. 52] Mariam has a box with 8 balls numbered from 1 to 8. on drawing a ball randomly.find the probability of : a) an even number = b) a multiple of 3 = c) a prime number = d) number 18 = Page 25 of 27

27 53] (a) Martha makes hats. Each week she makes 160 hats. (i) Work out how many hats she makes in 5 weeks. (ii) The hats are made in the ratio small : medium : large = 2 : 5 : 3. Work out how many of the 160 hats are large. (iii) She sells 3 of the 160 hats. Work out how many hats she sells. 8 (b) Nina sells T-shirts. The prices are shown in the table. (i) Sam buys 3 plain T-shirts and 2 logo T-shirts. Work out how much she pays altogether. (ii) One day, Nina reduces all prices by 20%. Work out the new price of a striped T-shirt. Page 26 of 27

28 54] (i) On the grid, reflect triangle A in the line x = 1. (ii) On the grid, enlarge triangle A by scale factor 2, centre (0, 0). (iii) Describe fully the single transformation that maps triangle A onto triangle B Good luck Page 27 of 27