The City School PAF Chapter Prep Section Class 6 Worksheets for Intervention Workbook (2 nd Term) M A T H E M A T I C S
Algebra Q1. Simplify the following expressions using the correct order of operations. 1) 2a + 3a -4a 2) 2b 5b + 7b b 3) 3c + 2b + 2c 4b 4) 5d 4f + 3e 2d + f -2e 5) 4g + 2(3g-4h) +2h 6) 3(2j-k) 4(j-2k) 7) 4m + 5(2n+3p) 4(n-m-p) 8) 8q + 6(4q-3r+5t) + 2(r-7t) 9) 5u 8v +9(2u-3v) 4(2v-5u) 10) 7(4w+x+2y) -5(w-x+3y) Q2. Evaluate the following expression. a) 15x + ( 7y) + ( 18x) + 4y b) 7x ( 15y) ( 2x) + ( 6y) c) 5(2x + 4) 3( 6 x) d) x + y 2(3x 4y + 3) e) 9(2a + 4b 7c) 4(b c) 7( c 4b) f) 2{3a 4[a (2 + a)]} g) 1 [2x + 2(x 3)] 2 h) 2 [12p (5 + 2p)] 5 i) 3y 1 4 2y 3 6 j) 2h 7 + h+1 5 k) 3 z 2 4 4 2z 3 5 Q3. a) Write the following expression for the distance around the edges of each of these shapes. b) Simplify your expression where possible. a) b) c) d) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 2 of 20
Q3. Write the expressions for the area of these shapes. 1. 2. 3. 4. 5. 6. 7. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 3 of 20
Linear Equations & Simple inequality 1. 3x + 4 = x 10 2. 2x 5 = 5x 12 3. 2(x 3) = 3x + 4 4. 2(y 1) + 3(y 1) = 4 2y 5. 8 2x 3 = 4 6. x 2 + 9 = 5 7. 5 7 y + 2 = 1 2 y + 3 1 4 8. 3z 1 2 = z 4 3 9. 5(2d + 7) = 11(d + 14) 10. 2y 1 5 y+3 7 = 0 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 4 of 20
Coordinates Q1. Draw a grid with centre (0,0), the origin, and mark the x and y axes with scales from -8 to 8. Marks these points on your grid. 1) A = (5,2) 2) B = (7.,3) 3) C = (-8,5) 4) D = (-6,-8) 5) E = (7,-3) 6) F = (6,-6) 7) G = (2,4) 8) H = (2,4) 9) I = (3,-7) 10) J = (3,-9) Q2. Draw a grid with the x and y axes with scales from -10 to 10. Mark these points on your grid. Q3. plot the P= (6,4), Q= (6,4), and R= (6,-2). Plot point S such that PQRS is a rectangle. a) Write down the coordinates of S. b) Draw diagonals PR and QS. What are the coordinates of their point of intersection? c) What is the area of PQRS? Q4.On the same grid plot points M = (-8,4) and N = (4,4). a) joint points MNRS. What shape have you drawn? b) What is the area of MNRS? c) Explain your answer to parts b). Q5. On the same grid plot point J where point J has y coordinate +10 and JRS forms an isosceles triangle. a) Write down the coordinates of J. b) What is the x coordinate of all the points on the line of symmetry of triangles JRS? Q6.(a) Draw a grid with both the axes running from -10 to + 10, as in the diagram above. (b) Plot and label the following points. (i) A (6,1) (ii) B (-5,-3) (iii) C (4,-6) (iv) D (-8,5) Q7. (a) Draw another grid as on question 1. (b) Plot and label the following points. (i) A (3,1) (ii) B, (6,2) (iii) C, (3,7) (iv) D (-6,2) (v) E (-3,2) (vi) F (-3,7) (c) Join A, B and C to form a triangle. (d) Join D, E and F to form another triangle. (e) In what way are the two triangles the same? (f) In what way are they different The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 5 of 20
Number Sequence Q1. Find the next two terms and nth term of the following sequence. i. 2,9,16,23,30,, ii. iii. iv. 7,13,19,25,31,, 23,27,31,35,39,, 11,19,27,35,43,, Q2. 4,5,6,7 for the given sequence shown. Find the 50 th term Q3. 7, 8,9,10 for the given sequence shown. Find the 50 th term Q4. -6, -3, 0, 3, 6, 9,..., Find: (a) the next two terms Q5.16, 25, 36, 49 Find (a) the next two terms Q6. 3, 6, 11, 18, 27, 38, Find (a) the next two terms Q7. Consider the pattern: 1 = 1 2 1+3 = 2 2 1+3+5 = 3 2 1+3+5+7 = 4 2... 1+3+5+ + (2k-1) = 144 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 6 of 20
a) Write down the eighth line of the pattern b) Find the value of k. Q8. (a) Write down the next four terms of the sequence 1, 3, 6, 10, 15,.. Similarly, write down the next four terms of the sequence 0, 1, 4, 10, 20, 35,. (b) Consider the following pattern: 1 3 1 = 0 = 6 x 0 2 3 2 = 6 = 6 x 1 3 3 3 = 24 = 6 x 4 4 3 4 = 60 = 6 x 10 5 3 5 = 120 = 6 x 20 6 3 6 = 210 = 6 x 35.... m 3 m = n = k x 84 Using the result in (a): i) Write down the ninth and tenth lines in the pattern. ii) Find the value of m and of n. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 7 of 20
Q9) These diagrams show the first three patterns in a sequence of growing tile patterns. a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white 1 2 3 4 5 tiles Number of red tiles c) Describe the pattern linking the number of white files and the number of red tiles. d) Use your rule in part c) to predict the number of red tiles in a pattern with 100 white files. Q10) a) Draw the next two diagrams in the sequence. b) Copy and complete this table. Number of white 1 2 3 4 5 tiles Number of green tiles c) Describe the pattern linking the number of white tiles and the number of green tiles. d) Use your rule in part e) to predict the number of green tiles in a pattern with 100 white tiles. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 2 of 20
Q11) a) Draw the next two diagrams in the sequence. b) Copy and complete this table Q12) Number of white 1 2 3 4 5 Tiles Number of orange Tiles a) Draw the next two diagrams in the sequence. b) Copy and complete this table Q13) Number of white 1 2 3 4 5 tiles Number of blue tiles a) Draw the next two diagrams in the sequence. b) Copy and complete this table Number of white 1 2 3 4 5 tiles Number of yellow tiles The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 3 of 20
Q14. Shape Number 1 2 3 4 5 6 Number of sides Number of diagonals 3 4 5 6 7 0 2 5 9 (a) Copy the diagram above and fill in the blank spaces (b) How many sides would there be in the 50 th shape? The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 4 of 20
Percentage Q1. Calculate the following. a. 50% of 300 b. 75% of 400 c. 40% of 600 d. 25% of 360 e. 80% of 250 f. 37% of 240 g. 87.5 of 880 h. 12.5% of 320 i. 75% of 40 j. 40% of 75 Q2. In a survey of 100, 47 were white, 23 were blue and 30 were red. Express each of these numbers as a percentage of totals. Q3. 7 Of the surface of the earth is water. Express this as a percentage. 2 Q4. 15% of students in a school of 720 students are left- handed. What numbers of student are right handed? Q5. At Cambridge college, 65% of the math students came from England. If there are 240 math students, how many are not from England. Q6. A survey showed that 75% of vehicles passing schools were cars. If 4200 vehicles passed the school in one day, how many were cars? Q7. In a village of 3500 people, 12% are left-handed, and 15% of left handed people have blonde hair. How many people in the village are blonde and left-handed? Q8. There are 200 birds in a flock. 120 of them are female. What percentage of the flock is? a) Female b) male Q9. Write these percentages as fractions of 100. a) 73% b) 28% c) 10% d) 25% Q10. Write these fractions as percentages. a) 27 100 b) 3 10 c) 7 50 d) 1 4 Q11. Convert the following percentages to decimals. a) 39% b) 47% c) 83% d) 7% e) 2% f) 20% Q12. Convert the following decimals to percentages. a) 0.31 b) 0.67 c) 0.09 d) 0.05 e) 0.2 f) 0.75 Q13. Write the first quantity as a percentage of the second. a. 36 out of 72 b. 18 out of 90 c. 6 out of 60 d. 36 out of 60 e. 7% of 70 f. 21 out of 70 g. 45 out of 900 h. 135 out of 900 i. 11 of 44 j. 11 out of 440 The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 5 of 20
RATIO Q1. Copy these set equivalent ratios and fill in the blanks. 1) 4:5 = 8: = :50 =12: 2) 7:2 = 14: = :10 = 49: 3) 8:4 = = :50 = 32: = 4: Q2. a) A heater used 3 units of electricity in 40minutes. How many units does it use in 2 hours? b) A machine prints 1500 newspaper in 45 minutes. How many does it print in 12 hours? c) A bricklayer lays 12 bricks in an average 8-hour day. How many bricks dos he lay in 40- hour week? d) A combine harvester produces 9 tonnes of grain in 6 hours. How many tonnes does it produce in 54 hours? e) A machine put tar on a road at the rate of 4 metres in 5 minutes. i) How long does it take to cover 1 km of road? ii) How many metres of road does it cover in 8 hours? Q3. Simplify these ratios. 1) 27:36 2) 45:75 3) 28:70 4) 20 minutes:1 hour 5) 3kg:750g 6) 8m:75cm 7) 7 litres to 750ml 8) $2 to 20 cents 9) 3 hours to 1 day 10) 8 weeks to 1 year The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 6 of 20
Q4. Copy and complete this table. Fraction Ratio Percentage 1 2 1 4 3 4 1 8 3 8 5 8 7 8 1 10 2 10 or 1 5 3 10 4 10 or 2 5 6 10 or 3 5 7 10 8 10 or 4 5 9 10 1 to 2 50% 1 to 25% To 4 1 to 12.5% To 8 5 to 87.5% 1 to 10% To 5 20% 3 to To 5 To 5 9 to 10 70% The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 7 of 20
Triangle Q1. Find the area of the given triangles: a) b) c) d) Q2. Find the height of the given triangle: Q3 Calculate the area of each of these triangles. Q4 Use the formula for the area of a triangle to work out the missing values in this table. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 8 of 20
Time Q1.Maureen started her homework at 7.20 p.m. She finished it at 8.05 p.m. How long did she take to do her homework? Q2. A chess game started at 10.20 a.m. and ended at 12.30 p.m. How long did the game last? Q3. Peter opens his shop at 9.30 a.m. and closes it at 8.00 pm. every day. How long is the shop open? Q4. It takes 1 h 5 min for Bob to travel from home to his office. If he wants to reach the office by 8.30 a.m. what time should he leave his house? Q5. Susan spent 1 h 15 min washing her car and 1 h 50 min cleaning her house. How long did she take to complete both these tasks? Q6. Alison took 54 minutes to walk to school. Her brother took 18 minutes less to walk to the same school. How long did it take Alison s brother to walk to school? Convert 1) Oliver spent 2 hours and 55 minutes playing video games. If he stopped to eat dinner at 7:55, what time did he originally start playing? 2) Robin spent 1 hour and 50 minutes cleaning her room. If it was 6:45 when she finished, what time was it when she started? 3) Mike spent 1 hour and 5 minutes working on homework. If it was 5:35 when he finished, what time was it when he started? 4) Will took a nap for 2 hours and 40 minutes. If he woke up at 5:05, what time was it when he started his nap? 5) The school football game ended at 8:20. If the game lasted 3 hours and 30 minutes, what time did it start? 6) John's father spent 2 hours and 55 minutes working on his truck. If it was 4:55 when he stopped working, what time was it when he originally started? 7) Cody spent 3 hours and 5 minutes looking for his missing cat. If he finally found it at 7:25 what time did was it when he originally started looking? 8) Katie took a train from her house to the state capitol. The train ride lasted 2 hours and 55 minutes. If Katie arrived at 8:35, what time did her train leave? 9) Edward finished jogging at 5:30. If he had been jogging for 1 hour and 50 minutes, what time was it when he started? 10) Janet went to the town carnival. She ended up staying for 2 hours and 50 minutes. If Janet left the carnival at 4:10, what time did she originally get there? Q11. Determine the hours and minutes. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 9 of 20
1) 81 minutes = hour(s) and minutes. 2) 195 minutes = 3 hour(s) and 15 minutes. 3) 183 minutes = 3 hour(s) and minutes. 4) 167 minutes = 2 hour(s) and 4 7 minutes. 5) 216 minutes = 3 hour(s) and 3 6 minutes. 6) 197 minutes = 3 hour(s) and 17 minutes. 7) 125 minutes = 2 hour(s) and 5 minutes. 8) 267 minutes = 4 hour(s) and 7 minutes. 9) 111 minutes = 1 hour(s) and 51 minutes. 10) 210 minutes = 3 hour(s) and 30 minutes. Q12. Determine the minutes 1) minutes = 5 hours and 10 minutes. 2) 291 minutes = 4 hours and 51 minutes. 3) 158 minutes = 2 hours and 38 minutes. 4) 270 minutes = 4 hours and 30 minutes. 5) 160 minutes = 2 hours and 40 minutes. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 10 of 20
Area and perimeter Q1. Calculate the area of each of these triangles. a) b) c) Q2. Draw a triangle similar to this one. i) measure the length of side of AB and let be the base of the triangle. ii) Draw on your diagram a line which represents the height of the triangle. iii) Calculate the area of your triangle. iv) Calculate the area of your triangle. b) Draw another triangle identical to the one you drew in part a) i) measure the length of side of BC and let be the base of the triangle. ii) Draw on your diagram a line which represents the height of the triangle. iii) Calculate the area of your triangle. iv) Calculate the area of your triangle. The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 11 of 20
c) Draw another triangle identical to the one you drew in part a) i) Measure the length of side of AC and let be the base of the triangle. ii) Draw on your diagram a line which represents the height of the triangle. iii) Calculate the area of your triangle. iv) Calculate the area of your triangle. d) What do you notice about the areas of the three triangles you drew? Comment carefully on the reasons for any differences or similarities in your answers. Q3. Use the formula for the area of a triangle to work out the missing values in this value. Base length Perpendicular height Area a 7.2cm 4.8cm b 20cm 100cm 3 c 15cm 15cm 3 d 11cm 55cm 3 Q4. Calculate the area of of each of these shapes. a) b) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 12 of 20
Q5. Calculate the area of the coloured region of each of these shapes. a) b) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 13 of 20
PERIMETER Q1. Calculate the perimeters of the following shapes. (a) (b) (c) (d) (e) (f) The City School /PAF Chapter / Prep + Senior I Section / Worksheet for Intervention Class /Math /Class 6 Page 14 of 20