latihan matematik t3_scheme answers
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UNIT 1: WHOLE NUMBERS
Find the value of each of the following
1. 10 + 3 – 4 =
2. 14 - 6 + 2 =
3. 2 – 5 + 8 =
4. -3 + 7 – 1 =
5. -2 – 5 +13 =
6. 15 – 3 + 8 =
7. 2 – 6 + 17 =
8. 8 – 3 + 4 =
9. 21 + 5 – 12=
10. 3 – 5 + 7 =
11. 3( 6 + 2 ) =
12. 4(7 – 3 ) =
13. (20 – 6) + 8 =
14. 30 – 2(4+5) =
15. 40 – 3(7-2) =
16. 2 ( 11 + 17) =
17. 3 ( 25 - 4) =
18. 3 (14 + 8 ) =
19. 58 – 3(10+2) =
20. 32 + 2 ( 11 + 17) =
21. 6 + 4 ÷ 2 =
22. 4 + 6 ÷ 3 =
23. 4 + 10 ÷ 2=
24. 6 + 8 ÷ 4 =
25. 7 + 10 ÷ 5=
26. 10 – 4 ÷ 2 =
27. 8 – 6 ÷ 2 =
28. 15 –12 ÷ 4 =
29. 12 – 15 ÷3 =
30. 9 – 8 ÷ 4 =
9
10
5
3
6
20
13
9
14
5
24
16
22
12
25
Nama : …………………………………………. Form : ………………. Date: ………………….
1
31. 5 + 2 × 4 =
32. 6 + 3 × 3 =
33. 8 + 3 × 2 =
34. 10 + 4 × 2 =
35. 7 + 5 × 2 =
36. 10 – 2 × 2 =
37. 9 – 3 × 2 =
38. 8 – 2 × 2 =
39. 12 – 5 × 2 =
40. 14 – 3 × 3 =
41. 20 – 2( 4 + 10 ÷ 2) =
42. 15 – 2( 4 + 6 ÷ 3 ) =
43. 30 – 3(10 – 4 ÷ 2)=
44. 18 – 3( 8 – 6 ÷ 2)=
45. 16 – 4( 5 – 12 ÷ 4)=
46. 23 + 4 (5 – 12 ÷ 4)=
47. 2( 15 + 3) ÷ (10-6)=
48. (20 – 2 × 4) ÷ 3 =
49. 3 ( 12 – 4) ÷ ( 5 – 2 )=
50. 40 ÷ 5 × 2 – 3(4)=51. 58 – 3(10+2)=
52. 32 + 2 ( 11 + 14)=
53. (18 – 6) + 8 =
54. 30 – 2(4+7)=
55. 21 + 5 – 12=
56. 2( 15 + 3) ÷ (6-4)=
57. 3 ( 12 – 4) ÷ ( 5 – 2 )=
58. 40 ÷ 5 × 2 – 3(4)=
59. 32 + 2 ( 11 + 17)=
60. 2 ( 14 + 17)=
61. 3 ( 25 - 4) =
62. 58 – 3(10+2)=
63. 10 + 10 ÷ 2=
64. 8 + 10 ÷ 5=
2
UNIT 2: FRACTIONSReduce the following to the lowest terms
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Name :…………………………………….. Form :…………… Date : ……………………..
3
UNIT 3 : FRACTIONS (Equivalent Fractions)
Copy and complete each of the following pairs of equivalent fractions
1. =
2.
3.
4.
5.
6.
7.
8.
9.
11.
12.
13.
14.
15.
16.
17.
18.
19.
21.
22.
23.
24.
25.
26.
27.
28.
29.
Name :…………………………………….. Form :…………… Date : ……………………..
4
10. 20. 30.
UNIT 4 : FRACTIONS (Improper Fractions)
Express the following mixed numbers as improper fractions
1. 1
2. 1
3. 2
4. 2
5. 3
6. 1
7. 3
8. 6
9. 7
11. 5
12. 2
13. 1
14. 2
15. 4
16. 10
17. 9
18. 4
19. 5
21. 4
22. 3
23. 12
24. 5
25. 1
26. 2
27. 8
28. 6
29. 3
Name :…………………………………….. Form :…………… Date : ……………………..
5
10. 4 20. 8 30. 7
UNIT 5 : FRACTIONS (Lowest Common Multiples (LCM))
Find the LCM for the following pairs of numbers.
1. 2 and 4 24. 7 and 8
2. 2 and 8 25. 9 and 10
3. 2 and 12 26. 10 and 11
4. 3 and 6 27. 11 and 12
5. 3 and 12 28. 12 and 13
6. 3 and 18 29. 13 and 14
7. 4 and 8 30. 6 and 7
8. 4 and 16
9. 4 and 24
10. 5 and 10
11. 4 and 6
12. 8 and 12
13. 12 and 15
14. 15 and 20
15. 6 and 15
16. 10 and 15
17. 8 and 10
18. 6 and 9
19. 12 and 16
Name :…………………………………….. Form :…………… Date : ……………………..
6
20. 8 and 6
21. 2 and 3
22. 3 and 4
23. 4 and 5
UNIT 6: ADDITION OF FRACTIONS
Simplify
1.
2.
3.
4.
5.
6.
7.
8.
11. 1+
12. 2+
13. 3+
14. 3+2
15. 10+4
16. 18+6
17. 6
18. 7
21. 4
22. 1
23. 3
24. 5
25. 3
26. 4
27. 5
28. 3
Name :…………………………………….. Form :…………… Date : ……………………..
7
9.
10.
19. 13
20. 2
29. 3
30. 1
UNIT 7: SUBTRACTION OF FRACTIONS
Simplify the following
1.
2.
3.
4.
5.
6.
7.
8.
11.
12.
13.
14.
15.
16.
17.
21. 2
22. 1
23. 5
24. 1
25. 3
26. 7
27. 12
28. =
Name :…………………………………….. Form :…………… Date : ……………………..
8
9.
10.
18.
19.
20.
29. 18
30. 23
31. 4
32. .2
33. 5
34. 3
35. 1
36. 3
37. 5
40.
41. 3
42.
43. 1
44.
45.
48.
49.
50.
9
38. 2
39. 4
46.
47.
UNIT 8: MULTIPLICATION OF FRACTIONSSimplify the following.
1.
2.
3.
4.
5.
6.
11.
12.
13.
14.
15.
16.
21.
22.
23.
24.
25.
26. 12
Name :…………………………………….. Form :…………… Date : ……………………..
10
7.
8.
9.
10.
17.
18.
19.
20.
27. 2
28. 4
29. 5
30. 8
31.
32.
33.
34.
35.
40.2
41.1
42.2
43.1
44.2
11
36. 1
37. 2
38. 1
39. 3
45.1
46.2
47.1
48.2
UNIT 9: DIVISION OF FRACTIONSSimplify the following
1.
2.
3.
4.
5.
11.
12. 1
13. 2
14.
15. 10
21.
22. 4
23.
24. 4
25. 1
Name :…………………………………….. Form :…………… Date : ……………………..
12
6.
7.
8. 6
9. 1
10. 1
16. 2
17.
18. 1
19.
20.
26. 1
27. 1
28. 1
29. 1
30. 1
UNIT 10: DECIMALS (Addition , Subtraction , Multiplication and Division of Decimals )
Examples : 1) 0.9 + 3.5 = 4.4 2) 4.5 – 2.3 = 2.2 3)3.3 10 = 33 4) 4.5 10 = 0.45
1) 0.5 + 9.8 =
2) 4.5 + 3.2 =
3) 5.5 + 2.3 =
4) 3.3 + 3 =
5) 6.7 + 5.9 =
6) 7.71 + 3.5 =
7) 0.06 + 1.2 =
8) 8.9 + 2.6 =
9) 6 + 3.7 =
1) 4.8 – 3.2 =
2) 4.6 –2 =
3) 9.9 – 3.2 =
4) 12 - 0.3 =
5) 3.9 –1.2 =
6) 6.9 – 1.2 =
7) 9.7 – 2 =
8) 9.4 – 3.8 =
9) 12.9 – 1 =
1) 1.2 2 =
2) 0.3 6 =
3) 0.9 3 =
4) 4.8 2 =
5) 2.5 2 =
6) 0.9 9 =
7) 8.9 3 =
8) 3.9 3 =
9) 3.3 4 =
1) 21.2 0.1 =
2) 9.1 2 =
3) 2.2 5 =
4) 8.6 2 =
5) 9.5 5 =
6) 12.9 0.3 =
7) 14.7 7 =
8) 15.5 0.5 =
9) 30.6 6 =
Nama : …………………………………………. Form : ………………. Date: ………………….
Exercises: Evaluate the following
13
10) 4.6 + 1.2 =
11) 8 + 1.56 =
12) 9.8 + 1.5 =
13) 5.7 + 1.3 =
14) 6.7 + 3.9 =
15) 9 + 5.9 =
16) 7 + 6.8 =
17) 0.7 + 3.4 =
18) 0.8 + 3.7 =
10) 15 – 0.5 =
11) 34.9 – 1.2 =
12) 23.8 – 1.2 =
13) 5.6 – 1.2 =
14) 9.7 –1.3 =
15) 7.7 – 3.3 =
16) 12.6 – 1.4 =
17) 33.5 – 1.2 =
18) 5.6 – 3.4 =
10) 3.4 5 =
11)4.6 0.3 =
12) 3.7 0.8 =
13) 6.6 0.9 =
14)3.4 0.2 =
15) 7.6 0.5=
16) 9.5 100 =
17) 6.3 100 =
18) 3.5 1000 =
10) 23.4 2 =
11) 11.3 10 =
12) 4.45 10 =
13)2 5.5 10 =
14) 30.5 100=
15) 23.4 100 =
16) 1.3 100=
17) 4.45 1000 =
18) 555.67 1000=
Express each of the following fractions as a decimal.
1) =
2) =
3) =
4) =
5) =
6) =
7) =
15) =
16) =
17) =
18) =
19) =
20) =
21) =
28) =
29) =
30) =
31) =
32) =
33) =
34) =
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 11: DECIMALS
14
8) =
9) =
10) 1 =
11) 2 =
12) 2 =
13) 5 =
14) 3 =
22) =
23) =
24) =
25) =
26) =
27) =
35) =
36) =
37) =
38) =
39) =
40) =
UNIT 12: INTEGERS
Arrange each of the following sets of integers in increasing order.
1. -5,-3,0,-1,2,-4
2. 8,-7,-5,6,-9,3
3. -10,-1,1,3,4,-2
4. -7,-3,5,-2,7,4
5. 6,-4,0,1,-3,-9
6. 8,-6,4,2,-8,-1
7. -7,-6,0,3,4,1
8. 6,-5,-1,3,4,-5
9. 9,-12,-6,3,7,-10
10. -11,-4,8,-3,5,-6
21. 0,-1,-8,4,7,8
22. -8,-11,13,15,16,-4
23. 15,17,-18,-11,-12,-1
24. -7,-12,4,7,9,8
25. 3,4,-5,-6,7,8
26. -4,-3,-7,-1,-10,4
27. 9,11,-7,-12,-14,-17
28. -9,-1,0,3,7,10
29. 1,-2,3,0,-5,4
30. 11,-14,-17,-18,4,5
Nama : …………………………………………. Form : ………………. Date: ………………….
15
11. -7,5,-9,3,0,-2
12. 8,-12,13,-15,7,11
13. -20,-15,16,7,11,1
14. 5,-15,-20,15,10,-5
15. 4,-12,-11,1,4,-10
16. 7,3,-4,-7,-8,-5
17. 16,-17,-20,9,0,1
18. -1,3,-4,-5,10,12
19. 17,4,-3,-11,-20,-1
20. 17,4,-3,-11,-20,-1
31. 10,-10,-9,9,-7,7
32. -1,-2,-3,-4,-5,-6
33. -20,-18,-16,-14,-12,1
34. 1,4,-3,4,-11,-17
35. -4,0,7,9,-16,-15
36. 9,-1,-7,-9,0,1
37. 11,13,-14,19,-20,-12
38. -3,1,7,-9,-11,-15
39. -12,-14,-1,2,3,8
40. 10,20,-12,-17,4,-4
UNIT 13: INTEGERS
Complete each of the following with symbol `<` or `>`
1. -4 ______ +2
2. +8 ______ -9
3. -3 ______ -7
4. -5 ______ +6
5. +9 ______ -20
6. +3 ______ -2
7. -7 ______ -6
8. -1 ______ -2
9. +10 ______ -9
21. -1 ______ -3
22. +3 ______ -2
23. +9 ______ -1
24. -10 ______ -1
25. 0 ______ +8
26. -7 ______ +7
27. +3 ______ -8
28. +7 ______ -1
29. -9 ______ +8
Nama : …………………………………………. Form : ………………. Date: ………………….
16
10. -2 ______ -1
11. +6 ______ -5
12. +7 ______ -7
13. -3 ______ +3
14. 0 ______ -2
15. -6 ______ +5
16. -9 ______ -7
17. +4 ______ -7
18. +5 ______ -2
19. -3 ______ -5
20. -2 ______ +3
30. -4 ______ -8
31. +1 ______ -4
32. +7 ______ -6
33. -9 ______ +9
34. +2 ______ -1
35. +9 ______ -8
36. +2 ______ -3
37. -5 ______ -6
38. -8 ______ -7
39. +6 ______ -9
40. +7 ______ -10
UNIT 14: INTEGERS
Calculate each of the following
1. 6 + (-4) + (-5) =
2. -2 + (-3) + 7 =
3. 8 – (-4) – 3 =
4. 5 + (-7) + 10 =
5. -7 + 1 + 2 =
6. -6 + (-4) + (-3) =
7. 3 + 6 + (-10) =
8. -4 + 9 + (-5) =
9. -8 + (-7) + 10 =
25. 6 + (-6) – 4 =
26. 5 + (-13) + 4 =
27. -4 - 8 -7 =
28. -7 + 1 - (-4) =
29. 1 – (-1) + 4 =
30. 7 – 4 + (-1) =
31. 10 – (-1) – (-4) =
32. 7 + 8 + (-9) =
33. -4 - 6 – (-3) =
Nama : …………………………………………. Form : ………………. Date: ………………….
17
10. 4 – (-4) – 12 =
11. 8 – 15 – (-2) =
12. -6 – (-7) – (-2) =
13. 6 – (-3) – (-1) =
14. -2 – 5 – (-6) =
15. -9 – (-5) – 8 =
16. 20 – (-7) – (-2) =
17. 3 + (-4) + 3 =
18. 4 + (-4) – 7 =
19. 3 + (-1) +7 =
20. -6 + (-11) + 9 =
21. -10 – 2 - 3 =
22. 7 – (-1) – (-14) =
23. -4 + 7 – 3 =
24. -7 + (-2) – 1 =
34. -1 - 4 + 5 + =
35. 10 + (-4) – (-6) =
36. 4 – (-4) + 4 =
37. -8 – (-1) + 6 =
38. -4 + (-1) + 6 =
39. -10 – 12 + (-1) =
40. 7 – (-1) + 2 =
41. -4 + (-7) – 8 =
42. -9 – (-1) – (-4) =
43. 11 – 1 + (-4) =
44. 5 – (-4) + 3 =
45. -10 – (-1) + 4 =
46. 13 + 2 – (-1) =
47. -17 + (-2) – 1 =
48. -14 - 5 - 4 =
UNIT 15: DIRECTED NUMBER Find the value of each of the following
1. 0.1 × 2 =
2. 0.04 × 2 =
3. 0.02 × 3 =
4. 2.2 × 3 =
5. 1.4 × 2 =
6. 3.2 × 4 =
7. 1.8 × 3 =
8. 5 × 1.3 =
9. 7 × 0.5 =
19. -0.3 + 0.6 =
20. -0.9 + 1.3 =
21. 0.8 – ( - 0.2) =
22. 0.5 – (- 0.3) =
23. 2.5 – (-0.5) =
24. 0.6 – (-1.5) =
25. 1.2 – ( -0.8) =
26. 0.5 + (-1.5) =
27. 0.3 + (-1.5) =
Nama : …………………………………………. Form : ………………. Date: ………………….
18
10. 1.1 + 0.5 =
11. -0.8 + 1.0 =
12. -0.5 + 0.7=
13. -0.3 + 0.5 =
14. -0.6 + 0.9 =
15. -0.4 + 0.5 =
16. -0.7 + 1.1 =
17. -0.8 + 1.2 =
18. -0.4 + 0.8 =
28. 0.4 + ( - 0.5)
29. 0.8 + ( -0.4) =
30. 1.2 + ( -0.2) =
31. 0.8 ÷ ( -0.2) =
32. 0.8 ÷ ( -0.4)=
33. 0.9 ÷ ( -0.3) =
34. 0.6 ÷ ( -0.2) =
35. 0.4 ÷ ( -0.2) =
UNIT 16: DIRECTED NUMBERExpress the following mixed numbers as a decimal.
1.
2.
3.
4.
5.
13.
45÷1
3=
14.
37÷ 6
11=
15.
56+ 2
8=
16.
36−4
8=
Nama : …………………………………………. Form : ………………. Date: ………………….
19
6.
7.
8.
9.
Find the value of each of the following
10.
78×2
6=
11.
47×3
6=
12.
58×3
6=
17.
12+ 2
4=
18.
48+ 2
7=
19.
12−1
6=
20.
21.
27−(−1
3 )=
22.−1
2−(−1
5 )=
23.− 2
5− 1
4=
24.−1
3+(−2
3 )=
25.−5
6+ 3
4=
26.1 2
3−(−1
6 )=
27.9 3
5−1
2=
28.4 2
3+7 2
3=
29.1 1
2+2 2
3=
39.−3
4−2
6=
40.−3
8+ 3
4=
41.
56−(−5 1
4 )=
Calculate each of the following and express the answer as a decimal
20
30.7 1
5−4 1
3=
31.7 3
4+8 2
3=
32.4 3
4×1 1
2=
33.2 1
2×1 2
3=
34.5 2
3×4 3
4=
35.3 1
4÷1 2
3=
36.1 1
2÷2 2
3=
37.
25−(− 7
10 )=
38.
79+(−1
3 )=
42.0 . 7+ 3
5=
43.0 .06+ 2
5=
44.0 .08+(−4
5 )=
45.−0 .5−1
5=
46.−0 . 04+(−1
4 )=47. 3 . 4×0 . 2+0. 31=
48.3 . 6×0 . 2+ 1
5=
49.4 .2×0 .3+1 1
2=
50.4 .21×0 .3+(−1 1
5 )=
51.4 .21×0 .3−(−1 1
2 )=
52.0 .1×2−(−1 1
2 )=
53.0 . 04×2−(−1 1
2 )=
54.0 . 02×3−(−1 1
4 )=
64.−0 .08+(− 3
10 )=
65.−1
4+ 1
5=
67.
25+(−1
5 )=
68. 1 .2×0 .7+ (−1. 6 )=
21
55.2 .2×3−(−1 1
2 )=
56.1 . 4×2−(−1 1
4 )=
57.1 .8×3+(−1 1
2 )=
58.1 .5×3+(−1 1
4 )=
59.3 .26×0 . 4−(−1 1
2 )=
60.2 . 48×0 . 2−(−1 1
4 )=
61.1 .24×0 . 3−(−1 1
2 )=
62.−0 . 5+1
5=
63.−0 .05+ 1
2=
69.3 .12×0 .6+(−1 1
4 )=
70.
71.2 .14×0 .5+(−1
2 )=
72.5 .21×0 . 4−(−1
5 )=
73.3 .22 × 0. 2- (−1
2 )=
74.2 .32 × 0 . 04 -(−1
5 )=
75.1 .24 × 0 .2 -(−1
2 )=
UNIT 17: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
Squares Of NumbersWrite the following numbers in the form of a
2.
Examples1) 1×1=12
2)
3) 4)
34×3
4=( 3
4 )2
Exercises : Write the following numbers in the form of a
2
Nama : …………………………………………. Form : ………………. Date: ………………….
22
1)
2)
3)
4)
5)
6)
1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
6)
1)
2)
3)
4)
Express each of the following as a form of multiplication.examples
1) 2) 3) 4)
1)
2)
3)
4)
5)
6)
7)
1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
6)
7)
Estimating the squares of the following numbers
Examples
1) 2) 3) 4)
Exercises
1) 6) 11) 16)
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 18: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
23
2)
3)
4)
5)
7)
8)
9)
10)
12)
13)
14)
15)
17)
18)
19)
20)
Examples 1
Examples 2
Exercises
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
Perfect Squares Complete the table below
Whole Numbers Squares Perfect Squares1 12 43456789
10111213
SQUARESFind the square roots of the following.Example 1
Therefore
Example 2 Example 3
Therefore
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 19: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
24
Therefore Exercise 1)
2)
3) 4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
19)
20)
21)
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
Find the value of the following.Examples Examples
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 20: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
25
1)
2) 1)
2) Exercise
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
Exercise
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
26
CUBES
Complete the table belowWhole Numbers Cubes Whole Numbers Cubes
1
2
3
4
5
= 1 1 1 6
7
8
9
10
Write the following numbers in the form of a3.Example :
7 7 7 =
Exercises:Write the following numbers
in the form of .
Express each of the following as a form of multiplication
= 2 2 2
Exercises: Express each of the following as a form of multiplication
Find the following value.
= 4 4 4 = 64
=5 5 5 = 125
Exercises: Find the following value.
1) 2 2 2 =
2) 4 4 4 =
3) 8 8 8 =
4) 12 12 12 =
5) 3.5 3.5 3.5 =
6) 4.5 4.5 4.5 =
7) 7.6 7.6 7.6
8) =
9) =
10) ( ) ( ) ( ) =
1) =
2) =
3) =
4) =
5) =
6) =
7) =
8) =
9)( ) =
1) =
2) =
3) =
4) =
5) ( ) =
6) ( ) =
7) ( ) =
8) ( 9)3 =
9) ( 4)3 =
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 21: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
27
10) ( ) = 10) ( )3 =
CUBE ROOTS
Examples : Find the following value.
1. = = 2 2. = = 4
Exercises : Find the following value. 1).
=
2). =
3) =
4). =
5) =
6) =
7). =
8) =
9). =
11) =
12) =
13) =
14) =
15) =
16) =
17) =
18) =
19) =
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 22: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
28
10). =20) =
UNIT 23: GEOMETRICAL CONSTRUCTIONS
1. Construct line segments with the measurements given below by using a ruler and pair of compasses.
a) RS = 3 cm
b) AB = 5.7 cm
c) LM = 8.3 cm
d) ST = 3.2
2. Using a ruler and a pair of compasses only, construct the following triangles.a) AB = 5cm, BC = 4cm and AC = 5 cm.
A
B) AB = 6 CM, BC = 6.5 cm and AC = 7 cm
Name :…………………………………….. Form :…………… Date : ……………………..
29
B
c) AB = 4 cm , BC = 6 cm and AC = 9 cm
A
d) An equilateral triangle ABC of sides 7 cm
A
e) AB = 7cm , BC = 7 cm and AC = 5.8 cm
30
X
A
3) By using a ruler and a pair of compasses and a ruler, construct the perpendicular bisector for each of the following line segments.
a) b)
c) d) e)
4) Construct the perpendicular to each line segment given below that passes through X. a) b)
X X
c) d) e) X
5) Construct the perpendicular from M to line given. a) b )
c) d)
X
* M
* M
* M
31
e) g)
6. Construct the bisector for each of the following angles.
7. Using ruler and a pair of compasses only, construct the following angles.
a ) Angle PQR = 90º b) Angle ABC = 45º
Q R B C
c ) Angle XYZ = 60º d) Angle LMN = 30º
* M
* M
* M
32
Y Z M N
e) Angle EFG = 120º f ) Angle RST = 60º
S
F G
T
8. Using ruler and a pair of compasses only, construct the following.
a) Rectangle ABCD, with AB 4cm and BC 2cm.
A
b) Parallelogram PQRS, based on the figure shown. S R
2cm 60º P Q 3cm
33
P c) Triangle DEF, based on the figure shown. F 6cm
45º D E
D E
UNIT 24: LOCI IN TWO DIMENSIONS ( Constant distance from one point)
1. Construct the locus of Y such that it is 2 cm from point X.
X
2. Construct the locus of W such that it is 3 cm from Point A
A
3. Construct the locus of Z such that it is 4 cm from point B
Name :…………………………………….. Form :…………… Date : ……………………..
34
B
4. Construct the locus of M such that it is always 3 cm from point P
P
5. Construct the locus of X such that EX = 2 cm
● E
● F
6. Construct the loocus of Y such that AY = 3 cm.
● ● B A
7. Construct the locus of W such that BW = 4 cm
35
● B
● C
8. Construct the locus of Q such that PQ = 2.5 cm
● ● P Q
9. Construct the locus of Y such that EY = EH
E F
H G
10. Construct the locus of X such that AX = 3 cm
36
A 6 cm B
3 cm
D C
11. Construct the locus of Z such that PZ = PQ
P
Q RUNIT 25: LOCI IN TWO DIMENSIONS (equidistant from two points)
1. Construct the locus of M such that M is equidistant from K and L
● ● K L
2. Construct the locus of Y such that Y is equidistant from A and B
● B
A ●
3. Construct the locus of W such that W is equidistant from P and Q
Name :…………………………………….. Form :…………… Date : ……………………..
37
P ●
● Q
4. Construct the locus of X such that AX = XB
B ●
● A
5. Construct the locus of P such that MP = PN
● ● M N
6. Construct the locus of Q such that AQ = QX
● A
● X
7. Construct the locus of A such that it is equidistant from P and Q
P Q
38
S R
8. Construct the locus of X such that it is equidistant from A and B
A
B C
9. Construct the locus of Y such that MY = YN
Q P
M N
10. Construct the locus of Z such that PZ = ZR
P Q
S R
11. Construct the locus of K such that its distance from point A and point B are the same.
39
A
E B
D C
UNIT 26: LOCI IN TWO DIMENSIONS ( Constant distance from one straight line )
1. Construct the locus of X such that it is 2 cm from the line AB
A B
2. Construct the locus of Y such that it is 3 cm from the line PQ.
P
Name :…………………………………….. Form :…………… Date : ……………………..
40
Q
3. Construct the locus of Z such that it is 2 cm from the line SR
R
S
4. Construct the locus of X such that it is 2 cm from the line PQ
P
Q
5. Construct the locus of X such that it is 3 units from the y-axis.
y
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
654321
41
6. Construct the locus of y such that it is 4 units from the x-axis y
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
7. Construct the locus of Z such that it is 3 units from the line x = 2
y x = 2
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
8. Construct the locus of P such that it is 2 units from the line y = 3
y
654321
654
654321
42
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
9. Construct the locus of R such that it is 3 units from the line x = - 2.
y x = - 2
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
10. Construct the locus of S such that it is 2 units from the line y = - 3
y
321
y = 3
654321
65432
43
x - 6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-2-3-4-5
UNIT 27: LOCI IN TWO DIMENSIONS ( Equidistant from two straight lines)
1. Construct the locus of Z such that its equidistant from line FG and GH.
G
F
H
2. Construct the locus of Y such that its equidistant from line AB and BC.
A
B
1
y = - 3
Name :…………………………………….. Form :…………… Date : ……………………..
44
C
3. Construct the locus of X such that it is equidistant from line EF and FG. G
E
F
4. Construct the locus of X such that its equidistant from line AB and BC.
D C
A B
5. Construct the locus of Y such that its equidistant from line FG and FH.
F G
H I
6. Construct the locus of Z such that it is equidistant from line PS and SR.
45
S R
P Q
7. Construct the locus of X such that its equidistant from line AD and DC.
D C
A B
8. Construct the locus of Z such that it’s equidistant from line EH and GH.
H G
E F
9. Construct the locus of Y such that it is equidistant from line PQ and QR
S R
P Q
10. Construct the locus of X such that it’s equidistant from line AB and AD.
46
D C
A B
11. Construct the locus of Y such that it is equidistant from line QR and RS
S R
P Q
12. Construct the locus of Z such that it’s equidistant from line CH and HG.
G F
H E
C D
13. Construct the locus of X such that it is equidistant from line AB and AF.
A B
F C
47
11
1
11
2
E D
14. Construct the locus of Y such that it’s equidistant from line AB and AC
C
D E
UNIT 28: SOLID GEOMETRYInstruction : On the grid of squares in the answer space, draw a net for each of the following solids, base on the measurements given.
1. 2.
Nama : …………………………………………. Form : ………………. Date: ………………….
48
2
11
2
1
1
2
31
1 3
2
3. 4.
5. 6.
49
2
1
21
21
21
21
21
1
1
7. 8.
9.
50
21
21
21
11
2
4
2
21
2
1
1
10.
UNIT 29: SOLID GEOMETRYInstruction : On the grid of squares in the answer space, draw a net for each of the following solids, base on the measurements given.1. 2.
Nama : …………………………………………. Form : ………………. Date: ………………….
51
3
4
5
3
5
64
10
10
8
6
3
3. 4.
5.
52
3 4
15
6.
53
5
UNIT 30: STATISTICS (Mode)
Find the mode for each of the following.1. 1, 2, 3, 2, 4, 2, 3, 5 Mode =2. 3, 4, 7, 4, 5, 4, 7 Mode = 3. 50, 60, 60, 70, 50, 40, 50 Mode =4. 100, 104, 106, 104, 100, 105, 100 Mode =5. 0.1, 0.2, 0.3, 0.1, 0.2, 0.1 Mode =6. 15m, 18m, 20m, 15m, 18m, 21m, 15m
Answer: a) Marks 1 2 3 4 5 6Frequency
b) Mode :
12. The data in the table below shows marks obtained by participants in a quiz.
1 2 3 4 2 3 2 4
Name : …………………………………………. Form : ………………. Date: ………………….
54
Mode =
State the mode for each of the following frequency table (Question 7 to Question 10)7.
Size of shirt
S M L XL XXL
Frequency
33 40 48 25 18
Mode = 8.
Score 1 2 3 4 5 6 7Frequenc
y4 1 6 3 7 2 4
Mode = 9.
Score 1 2 3 4 5 6Frequenc
y2 8 7 4 3 1
Mode = 10.
Score 1 2 3 4 5Frequenc
y3 4 8 6 5
Mode =
11. The data in diagram below shows marks obtained by participants in a quiz.
1 3 4 3 2 5 1 2 3 1 1 4 4 3 3 5 6 4 6 3
a) Using the data above, complete the following frequency table below.
b) State the mode.
2 1 3 2 1 2 4 5
a) Using the data above, complete the frequency table in the answer space.
b) State the mode.
Answer: a)
Marks 1 2 3 4 5Frequency
b) Mode :
13. The data in the table below shows the grades obtained by participants in a quiz.
A B C A C B A AB B C A B C C A
a) Using the data, complete the frequency table in the answer space.
b) State the mode.
Answer: a)
Grade A B CFrequency
b) Mode:
.
UNIT 31: STATISTICS (Pictogram)
1. The diagram below shows the number of cassettes produced by a factory over three months.
July Δ Δ Δ Δ Δ Δ Δ Δ Δ
3. The diagram below shows the number of magazines produced by a company over three days.
Wednesday
Δ Δ Δ
Name : …………………………………………. Form : ………………. Date: ………………….
55
August Δ Δ Δ
September Δ Δ Δ Δ Represents 20 cassettes
Find the total number of cassettes produced in three month.
2. The diagram below shows the number of car produced by a factory over four months
Jan █ █ █ █ █ █
Feb █ █ █ █
March █ █ █ █ █
April █ █
█ Represents 5 car
Find the total number of car produced in March.
Thursday Δ Δ Δ Δ Δ Δ
Friday Δ Δ Δ Δ
Δ Represents 10 magazines
Find the total number of magazines produced in three days.
4. The diagram below shows the number of badges collected by a Maznah, Norliah and Ziana
Maznah О О О О
Norliah О О
Liana О О О О О
О Represents 40 badges
Find the total number of badges collected by these three girls.
5. Diagram below shows the number of books in three classes, A, B and C.
Class Number of books A
B
C
56
Given that the total number of books of the 3 classes is 180. Each represents ……………… books.
6. Diagram below shows the number of computers sold by Mr. Tan over three months.
Month Number of computers sold
Jan
Feb
March
Given that the total number of computers sold in three months was 96. Each represents …………………. computers.
7. Diagram below shows the number of tyres manufactured over four years.
Year Number of tyres manufactured
2002
2003
2004
2005
Given that the total number of tyres manufactured over the past four years was
48,000. Each represents …………………. tyres.
UNIT 32: STATISTICS (BAR CHART) 1.
Grade Number of students
A 25B 40C 20D 15E 10
Name : …………………………………………. Form : ………………. Date: ………………….
57
Table 1 Table 1 shows the grade obtained by a group of students in a test. On the square grid provided, construct a bar chart to represent all the information given in the table.
2. Month Number of lorries
January 10February 8
March 12April 6
Table 2 Table 2 shows the productions of lorries by an automobile factory in the first four months of 2004. On the square grid provided, construct a bar chart to represent all the information given in the table.
3.Month Number of lorries
January 800February 1000
March 750April 500
Table 3 Table 3 shows the productions of lorries by an automobile factory in the first four months of 2005. On the square grid provided, construct a bar chart to represent all the information given in the table.
4.Grade Number of students
A 12B 18C 20D 10
Table 4 Table 4 shows the grade obtained by a group of students in a test. On the
6. Plantation Number of trees
A 20B 5C 15D 10E 35
Table 6 Table 6 shows the number of trees in 5
58
square grid provided, construct a bar chart to represent all the information given in the table
5.Club Number of students
Science 2Geography 6
History 5Mathematics 8
English 10 Table 5 Table 5 shows the number of members in the five clubs. On the square grid provided, construct a bar chart to represent all the information given in the table.
plantations. On the square grid provided, construct a bar chart to represent all the information given in the table
7. School Number of teachers
A 16B 4C 8D 20E 10
Table 7 Table 7 shows the number of teachers of 5 schools in Kulim. On the square grid provided, construct a bar chart to represent all the information given in the table.
UNIT 33: STATISTICS (PIE CHART)
Solve the following
1.
Tables in Question 11 to 14 show the scores for five players in one competition. Answer the question according to the given table.
11. Score 1 2 3 4 5
Name : …………………………………………. Form : ………………. Date: ………………….
59
2.
3.
4.
5.
6.
7.
8. 50% X 360° =
9. 70% X 360° =
10. 80% X 360° =
Frequency 3 8 15 6 3 a) Find the total frequency.
b) Find the fraction of score 3.
12. Score 1 2 3 4 5Frequency 10 15 5 12 8
a) Find the total frequency.
b) Find the fraction of score 2. 13
Score 1 2 3 4 5Frequency 2 7 6 3 12
a) Find the total frequency.
b) Find the fraction of score 4.
14. Score 1 2 3 4 5Frequency 8 6 7 9 13
a) Find the total frequency.
b) Find the fraction of score 4.
UNIT 34: STATISTICS (PIE CHART)
Complete each of the following table.
1. a) Table 1Type of games
Number of students
Angles of the sector
b) Complete the pie chart to represent all the information in Table 2.
Hand ball600
Name : …………………………………………. Form : ………………. Date: ………………….
60
Badmin
Protein 108°
Table tennis 8
Badminton 15
Hockey 25
Hand ball 12
b) Complete the pie chart to represent all the information in Table 1.
2. a) Table 2 Type of games
Number of students
Angles of the sector
Table tennis 12
Badminton 20
Hockey 18
Hand ball 10
3. a) Table 3
Nutrients Mass (g)Angles of the sector
Carbohydrate 140
Protein 90
Fat 50
Mineral 20
c) Complete the pie chart to represent all the information in Table 3.
Name : ………………………………………. Form ……….. Date: ……………….
UNIT 35 : INDICES (Multiplication)
Simplify each of the following.
1. a2 x a3 = 16. 2k2 x 3k2 =
Badminton 90°
61
2. b4 x b2 = 17. 3p2 x 2p2 =
3. c3 x c5 = 18. 4m x 5m2 =
4. d2 x d2 = 19. 3n4 x 4n =
5. e x e4 = 20. 6p5 x 3p2 =
6. 25 x 28 = 21.8q2 x2q7 =
7. 37 x 39 = 22. 4r2 x 3r8 =
8. 48 x 410 = 23. 9s2 x 2s =
9. 107 x 109 = 24. 5t2 x 3t5 =
10. 76 x 73 = 25.7u x 3u9 =
11. 3g2 x g5 = 26.4v5 x 4v5 =
12. 4h3 x h3 = 27. 9w6 x 2w7 =
13. 5i4 x i5 = 28. 8x7 x 3x2 =
14. 7j6 x j3 = 29. 10y5 x 3y =
15. 2f2 x f3 = 30. 4z x 2z7 =
Name : ………………………………………. Form ……….. Date: ……………….
UNIT 36 : INDICES (Division)Simplify each of the following.
1. a4 ÷ a2 =
2. b5 ÷ b2 =
24. 4t 8 ÷ 5t 3 =
25. 2u 10 ÷ 5u =
62
3. c8 ÷ c6 =
4. d10 ÷ d4 =
5. e12 ÷ e5 =
6. f15 ÷ f3 =
7. g9 ÷ g =
8. h16 h 8 =
9. i 14 ÷ i 3 =
10. j 17 ÷ j 9 =
11. 2 8 ÷ 25 =
12. 3 9 ÷ 3 7 =
13. 4 8 ÷ 4 4 =
14. 7 12 ÷ 7 =
15. 9 18 ÷ 9 =
16. 3k 6 ÷ k 2 =
17. 4h 8 ÷ h5 =
18. 7m10 ÷ m 8 =
19. 8n9 ÷ n =
20. 12p 12 ÷ p =
21. 9q 16 ÷ q 7 =
22. 2r4 ÷ 3r 2 =
23. 3s 7 ÷ 4s 2 =
26. 4v 8 ÷ 2v 3 =
27. 6w 11 ÷ 3w 7 =
28. 8x 12 ÷ 2x 3 =
29. 12y 15 ÷ 4y 7 =
30. 15z 8 ÷ 5z =
31. 24 a 6 ÷ 2 2 a 3 =
32. 36 b8 ÷ 32 b2 =
33. 45 c 7 ÷ 4c 2 =
34. 5 6 d 15 ÷ 5 2 d 9 =
35. 8 9 e 7 ÷ 8e =
UNIT 37: INDICES (Numbers and algebraic terms expressed in index notation raised to a power)
Simplify the following
1. ( 2 2 ) 3 =
2. ( 33 ) 4 =
21. ( 53 x 23 ) 2 =
Name :…………………………………….. Form :…………… Date : ……………………..
63
3. ( 65 ) 2 =
4. ( 72 ) 3 =
5. ( 84 ) 3 =
6. ( a2 ) 3 =
7. ( b3 ) 3 =
8. ( c2 ) 4 =
9. ( x3 ) 5 =
10.( y4 ) 6 =
11. ( 2a ) 2 =
12. ( 3x2 ) 2 =
13. ( 4y3 ) 2 =
14. ( 5p4 ) 2 =
15. ( 3q3 ) 3 =
16. ( g2h ) 3 =
17. ( m2n3 ) 5 =
18. ( 2 x 32 ) 2 =
19. ( 32 x 5 ) 6 =
20. ( 42 x 32 )3 =
22. ( 72 x 34 ) 3 =
23. ( 32 ) 2 x ( 33 ) 2 =
24. ( 23 ) 2 x ( 24 ) 3 =
25. ( 52 ) 2 x ( 52 ) 2 =
26. ( 32 ) 3 x ( 42 ) 3 =
27. ( 53 ) 2 x ( 23 ) 4 =
28. ( 73 ) 3 x ( 53 ) 2 =
29. ( 23 ÷ 7 ) 2 =
30. =
31. =
32. =
33. =
34. =
35. ( 33 ÷ 22 )3 =
36. ( 42 ÷ 33 )2 =
UNIT 38: INDICES ( Fractional Indices)
Find the value of each of the following
1. = 16. =
Name :…………………………………….. Form :…………… Date : ……………………..
64
2. = 17. =
3. = 18. =
4. = 19. =
5. = 20. =
6. = 21. x =
7. = 22. x =
8. = 23. x =
9. = 24. x =
10. = 25. x =
11. = 26. x =
12. = 27. x =
13. = 28. x . =
14. = 29. x =
15. = 30. x =
31. x = 41. ÷ =
32. x . = 42. ÷ =
65
33. x = 43. ÷ =
34. x = 44. ÷ =
35. x = 45. ÷ =
36. x = 46. ÷ =
37. x = 47. ÷ =
38. x = 48. ÷ =
39. x = 49. ÷ =
40. x = 50. ÷ =
UNIT 39 : NEGATIVE INDICES
Name :…………………………………….. Form :…………… Date : ……………………..
66
State each of the following in the form of fraction.
1. a -1 = 11. r -10 = 21. s -12 =
2. a -2 = 12. 3 -r = 22. q -1 =
3. a -3 = 13. 4 -k = 23. k -2 =
4. p -4 = 14. 10 -n = 24. z -7 =
5. x -2 = 15. 2 -r = 25. y -4 =
6. r -5 = 16. m -10 = 26. y -5 =
7. 2 -n = 17. r -12 = 27. 100 -2 =
8. 3 -k = 18. c -11 = 28. 2 -3 =
9. 2 -p = 19. a -10 = 29. 4 -6 =
10. s -3 = 20. b -13 = 30. 20 -5 =
UNIT 40: NEGATIVE INDICES
Name :…………………………………….. Form :…………… Date : ……………………..
67
Find the value of each of the following
1. 2-1 = 11. 4-3 = 21. 2-5 =
2. 3-1 = 12. 10-3 = 22. 2-4 =
3. 4-1 = 13. 5-3 = 23. 9-2 =
4. 10-1 = 14. 6-3 = 24. 2-4 =
5. 4-2 = 15. 3-4 = 25. 5-4 =
6. 5-2 = 16. 10-4 = 26. 4-4 =
7. 6-2 = 17. 3 -2 = 27. 2-2 =
8. 10-2 = 18. 8-2 = 28. 2-8 =
9. 2-3 = 19. 7-2 = 29. 2-7 =
10. 3-3 = 20. 1-2 = 30. 3-5 =
Name : ………………………………………. Form ……….. Date: ……………….
68
UNIT 41: INDICES (Fractional Indices)
State each of the following in the form of
1. = 13. = 25. =
2. = 14. = 26. =
3. = 15. = 27.
4. = 16. = 28. =
5. = 17. = 29. =
6. = 18. = 30. =
7. = 19. = 31. =
8. = 20. = 32. =
9. = 21. = 33. =
10. = 22. = 34. =
11. = 23. = 35. =
12. = 24. = 36. =
Name : ………………………………………. Form ……….. Date: ……………….
69
UNIT 42: INDICES
Evaluate each of the following.
1. = 6. =
2. = 7. =
3. = 8. =
4. = 9. =
5. = 10. =
70
Name : ………………………………………. Form ……….. Date: ……………….
UNIT 43: INDICES
Calculate the value of x.
1. 2 x-2 = 16
2. 2 x-2 = 8
3. 2 x-3 = 32
4. 3 x-2 = 27
5. 3 x-1 = 9
6. 2 x+2 = 32
7. 2 x+1 = 16
8. 2 x+2 = 8
9. 3 x+1 = 9
10. 3 x+1 = 27
11. 2 5+x = 16
12. 2 x+3 = 8
13. 2 3+x = 32
14. 3 2+x = 27
15. 3 x+1 = 9
16. 2 x-2 = 32
17. 2 x-1 = 16
18. 4 x+1 = 16
19. 2 x-1 = 8
20. 3 x-2 = 9
71
Name : ……………………………………….Form ……….. Date: ……………….
UNIT 44: ALGEBRAIC EXPRESSIONSSimplify each of the following 1. p + p = 27. 3p – p =
2. 2b + b = 28. 6x – 6x =
3. a + 3a = 29. 20y – 13y =
4. 3y + y = 30. 7p – 3p =
5. 6m + 5m = 31. –x + 3x =
6. 3c + 2c = 32. –x + 5x =
7. 6x + 4x = 33. x + 10x =
8. y + 10y = 34. -2x + 5x =
9. 3r + 7r = 35. -7p + p =
10. 5m + 2m = 36. -10y + 3y =
11. m + 10m = 37. 3p + _____ = 10p
12. 2c + 13c = 38. 6c + _____ = 10c
13. 7c + 7c = 39. -6x + 3x =
14. p + 12p = 40. -2x + 3x =
1. 6r + 3r = 41. 3xy + 2xy =
2. 3k + 10k = 42. 4ab + 3ab =
3. r + 16r = 43. 2mn + mn =
4. 7k + 9k = 44. 4pq + pq =
5. 6b + 7b = 45. 3pqr + 6pqr =
6. 8a – 2a = 46. 2ab – ab =
7. 6y – 3y= 47. 3pq – pq =
8. 7k – 2k = 48. 10cd – 3cd =
9. 10k – k = 49. _____ + 2cd = 4cd
10. 7m – m = 50. 3ab + _____ = 8a
72
UNIT 45: ALGEBRAIC EXPRESSIONS (Algebraic Fraction)Simplify each of the following to a single fraction in its lowest term
1. + = 14. - =
2. + = 15. + =
3. + = 16. + =
4. + = 17. + =
5. + = 18. + =
6. - = 19. + =
7. - = 20. - =
8. - = 21. - =
9. - = 22. +
10. - = 23. + =
11. + = 24. + =
12. + = 25. - =
13. + = 26. - =
Name :…………………………………….. Form :…………… Date : ……………………..
73
27. - = 34. + =
28. - = 35. - =
29. + = 36. - =
30. + = 37. + =
31. - = 38. - =
32. + = 39. - =
33. + = 40. + =
74
UNIT 46 : ALGEBRAIC EXPRESSIONSExpand each of the following
1. 2 ( a b ) 16. 3 ( a – b ) 31. -2 ( a + b )
2. 5 ( x y ) 17. 2 ( x – y ) 32. -3 ( x + y )
3. 7 ( c d ) 18. 2 ( 2a – b ) 33. -4 (( 2x + y )
4. 2 ( 2a b ) 19. 7 ( c – d ) 34. -5 ( 2a + b )
5. 5 ( x 3y ) 20. 5 ( 3y – x ) 35. -6 ( 3p + 2q )
6. 7( 4c d ) 21. 3 ( 4c – d ) 36. -2 ( a – b )
7. 3 ( 3p 2q ) 22. 7 ( 3p – 2q ) 37. -3 ( x – y )
8. 4 ( 2x 3y) 23. 5 ( 2x + 3y ) 38. -4 ( 2x – y )
9. 5 ( 4a 5b) 24. 4 ( 4a – 5b ) 39. -5 ( 2a – b )
10. 6 ( 5e 7f ) 25. 6 ( 7f – 5e ) 40. -6 ( 3p – 2q )
11. 2 ( a b c ) 26. 2 ( a + b – c )
12. 3 ( x + y + z ) 27. 3 (x – y –z )
13. 2 (2a + b + c ) 28. 2 ( 2a – b + c )
14. 3 (3x + 2y + z ) 29. 3 (3x – 2y – z )
15. 4 (p + 2q + r ) 30. 4 ( p – 2q – r )
Name :…………………………………….. Form :…………… Date : ……………………..
75
UNIT 47 : ALGEBRAIC EXPRESSIONS
Expand each of the following
1. (a + 1) (a + 2) = 21. (2v + 3) (v – 4) =
2. (b + 3) (b + !) = 22. (3w + 1) (w – 5) =
3. (c + 2) (c + 4) = 23. (4x + 3) (x – 6) =
4. (d + 3) (d + 5) = 24. (3y + 2) (2y – 1) =
5. (e + 6) (e + 2) = 25. (5z + 3) (2z – 3) =
6. (2f + 3) (f + 4) = 26. (2a + 3) (4a – 1) =
7. (3g + 2) (2g + 1) = 27. (6b + 1) (2b – 3) =
8. (4h + 3) (2h + 5) = 28. (8c + 3) (3c – 4) =
9. (5i + 2) (2i + 3) = 29. (2d + 5) (4d – 3) =
10. (3j + 2) (4j + 3) = 30. (3e + 8) (2e – 5) =
11. (2k – 3) (k + 4) = 31. (2f – 1) (3f – 2) =
12. (3l – 1) (l + 5) = 32. (3g – 4) (g – 5) =
13. (4m – 3) (m + 6) = 33. (4h – 1) (2h – 7) =
14. (3n – 2) (2n + 1) = 34. (6h – 1) (3h – 4) =
15. (5p – 3) (2p + 3) = 35. (2i – 7) (3i – 2) =
16. (2q – 3) (4q + 1) = 36. (3j – 8) (2j – 3) =
17. (6r – 1) (2r + 3) = 37. (5k – 2) (3k – 1) =
18. (8s – 3) (3s + 4) = 38. (2k – 7) (4k – 3) =
19. (2t – 5) (4t + 3) = 39. (6p – 5) (2p – 3) =
20. (3u – 8) (2u + 5) = 40. (3m – 2) (2m – 5) =
Name :…………………………………….. Form :…………… Date : ……………………..
76
UNIT 48 : ALGEBRAIC EXPRESSIONS . Expand each of the following
1. (a + 1)2 = 26. (2a – 5)2 = 51. (2v + 1) (2v – 1) =
2. (b + 2)2 = 27. (5b – 3)2 = 52. (3w + 2) (3w – 2) =
3. (c + 3)2 = 28. (3c – 10)2 = 53..(5x + 1) (5x – 1) =
4. (d + 4)2 = 29. (7d – 6)2 = 54. (2y + 3) (2y – 3) =
5. (e + 5)2 = 30. (4e – 5)2 = 55. (4z + 5) (4z – 5) =
6. (f + 6)2 = 31. (a + 1) (a – 1) = 56. (3a – 4) (3a + 4) =
7. (g – 1)2 = 32. (b + 2) (b – 2) = 57. (6a – 1) (6a + 1) =
8. (h – 2)2 = 33. (c + 3) (c – 3) = 58. (5b – 2) (5b + 2) =
9. (p – 3)2 = 34. (d + 4) (d – 4) = 59. (4c – 3) (4c + 3) =
10. (j – 3)2 = 35. (e + 5) (e – 5) = 60. (2d – 7) (2d + 7) =
11. (k – 5)2 = 36. (f + 6) (f – 6 ) =
12. (u – 6)2 = 37. (g + 7) (g – 7) =
13. (2m + 1)2 = 38. (h + 8) (h – 8) =
14. (3n + 1)2 = 39. (p + 9) (p – 9) =
15. (2p + 3)2 = 40. (j + 10) (j – 10) =
16. (4q + 1)2 = 41. (k – 2) (k + 2) =
17. (3r + 1)2 = 42. (w – 4) (w + 4) =
18. (2s + 5)2 = 43. (m – 6) (m + 6) =
19. (5t + 3)2 = 44. (n – 8) (n + 8) =
20. (3u + 4)2 = 45. (p – 10) (p – 10) =
21. (2v – 7)2 = 46. (q – 1) (q + 1) =
22. (3w – 8)2 = 47. (r – 3) (r + 3) =
23. (2x – 9)2 = 48. (s – 5) (s+ 5) =
Name :…………………………………….. Form :…………… Date : ……………………..
77
24. (4y – 1)2 = 49. (t – 7 ) (t + 7) =
25. (3z -1)2 = 50. (u – 9) (u + 9) =
UNIT 49 : ALGEBRAIC EXPRESSIONS
Find the LCM of the following pairs of algebraic terms
1. a and 2a = 23. 5x and 10x =
2. b and 3b = 24. 2y and 3y =
3. c and 4c = 25. 3z and 4z =
4. 5d and d = 26. 2a and 5a =
5. 6e and e = 27. 4b and 5b =
6. 10f and f = 28. 3c and 5c =
7. 2g and 4g = 29. 4d and 7d =
8. 3h and 6h = 30. 3e and 8e =
9. 2i and 8i = 31. a and ay =
10. 3j and 12j = 32. b and bx =
11. 4k and 2k = 33. c and cz =
12. 6k and 12k = 34. d and ed =
13. 3m and 15m = 35. f and af =
14. 9n and 3n = 36. gh and gk =
15. 12p and 4p = 37. mn and mp =
16. 4q and 6q = 38. qr and pqr =
17. 6r and 8r = 39. xy and ay =
18. 8s and 10s = 40. ax and ab =
19. 12t and 8t = 41. 3ab and 6a =
20. 9u and 12u = 42. 2mn and 4n =
21. 6v and 9v = 43. 9gh and 3h =
Name :…………………………………….. Form :…………… Date : ……………………..
78
22. 4w and 10w = 44. 6pq and 9q =
UNIT 50 : ALGEBRAIC EXPRESSIONS Factorise completely each of the following expressions.
1. 2a + 2b = _____ (a + b) 24. 3ab – a = a (___ - ___)
2. 3c + 3d = _____ (c + d) 25. 4c – 7cd = c (___ - ___)
3. 5p + 5q = _____ (p + q) 26. 2a + 4ab = 2a (___ + ___)
4. 7x – 7y = ______(x – y) 27. 3cd + 6d = 3d ( ___ + ___)
5. 9r – 9s = _______(r – s) 28. 4x + 8xy = 4x ( ____ + ___)
6. 4a + 4b =________(a + b) 29. 3ab – 9b = 3b (____ +____)
7. 6p + 6q = ________(p + q) 30. 6c – 8cd = 2c (____ + ____)
8. 8r + 8s = ________(r + s) 31. 2xy + 4y =
9. 10x – 10y=______(x – y) 32. 3cd + 9c =
10. 3c – 3d = _______(c – d) 33. 6f + 8fy =
11. 2x + 2y = _______( x + y) 34. 4ab + 6b =
12. 3a + 3b = _______(a + b) 35. 4e + 12ef =
13. 5x + 5y = _______( x + y ) 36. 6cd – 3c =
14. 7r – 7s = _______(r – s ) 37. 8xy – 2y =
15. 9p – 9g=_______( p – g ) 38. 2ef – 6e =
16. 2a + 4b = 2 (___ + ___) 39. 10pq – 4p =
17. 3c + 6d = 3 (___ +____) 40. 12gh – 4g =
18. 4x + 6y = 2 (___ + ____)
19. 3p – 9q = 3 (___ +____)
20. 6x + 8y = 2 (___ +____)
21. 2a + 3ab = a (___ +___)
79
22. 3cd + 4d = d (___ + ___)
23. 4x + 5xy = x (____ +____)
UNIT 51: ALGEBRAIC EXPRESSIONSFactorise completely each of the following.
1. a2 +2a + 1 = 25. v2 + 12v + 36 =
2. b2 + 2b + 1 = 26. a2 + 2ab + b2 =
3. x2 + 2x + 1 = 27. a2 – 2ab + b2 =
4. y2 + 2y + 1 = 28. e2 – 16e + 64 =
5. a2 – 2a + 1 = 29. k2 + 14k + 49 =
6. b2 - 2b + 1 = 30. u2 – 18u + 81 =
7. y2 -2y + 1 =
8. p2 + 4p + 4 =
9. m2 + 4m + 4 =
10. k2 + 6k + 9 =
11. r2 + 6r + 9 =
12. p2 – 4p + 4 =
13. m2 – 4m + 4 =
14. r2 – 6r + 9 =
15. s2 – 10s + 25
16. p2 + 6p + 9 =
17. r2 + 10r + 25 =
18. m2 – 10m + 25 =
19. p2 – 6p + 9 =
20. k2 + 20k + 100=
21. r2 + 8r + 16 =
22. 1 + 2t + t2 =
Name :…………………………………….. Form :…………… Date : ……………………..
80
23. 4 + 4a + a2 =
24. 1 + 2a + a2 =
UNIT 52: ALGEBRAIC EXPRESSIONS
Factorise completely the following expressions
1. a2 – b2 = 19. y2 – 64 =
2. c2 – d2 = 20. z2 – 121 =
3. e2 – f2 = 21. 4a2 – 9 =
4. g2 – h2 = 22. 9b2 – 16 =
5. 22 – j2 = 23. 25c2 – 9 =
6. k2 – 22 = 24. 16d2 – 25 =
7. f2 – 32 = 25. 4e2 – 1 =
8. m2 – 42 = 26. 36f2 – 49 =
9. n2 – 52 = 27. 9g2 – 25 =
10. p2 – 62 = 28. 4h2 - 49 =
11. q2 – 1 = 29. 9c2 – 100 =
12. r2 – 4 = 30. 64j2 – 81 =
13. s2 - 16= 31. 4k2 – 9p2 =
14. t2 – 25 = 32. 9m2 – 25n2 =
15. u2 – 49 = 33. 49 – 9b2 =
16. w2 – 100 = 34. w2 – 36p2 =
17. v2 – 81 = 35. 16x2 – 49y 2 =
18. x2 – 36 =
Name :…………………………………….. Form :…………… Date : ……………………..
81
UNIT 53: ALGEBRAIC EXPRESSIONS
Factorise completely each of the following expressions
1. 2x2 – 8 = 11. 4 – 100y2 =
2. 3x2 – 12 = 12. 100y2 – 4 =
3. 4x2 – 16 = 13. 2 – 50p2 =
4. 5 – 20x2= 14. 50p2 – 2 =
5. 2 – 8x2 = 15. 1000r2 – 10 =
6. 6 – 24x2 = 16. 10 – 1000r2 =
7. 7x2 – 28 = 17. 2 – 2t2 =
8. 8x2 – 32 = 18. 2t2 – 2 =
9. 2x2 – 72 = 19. 10t2 – 10 =
10. 3x2 – 75= 20. 10 – 10t2 =
Name :…………………………………….. Form :…………… Date : ……………………..
82
UNIT 54: ALGEBRAIC FORMULAE
Express x as the subject for each of the following formulae.
1) p + x = q
2) a – x = s
3) –x + b = t
4) w + x = -q
5) q = 3p + x
6) q = 3p – x
7) –p = x + 4s
8) 8a = x -10
9) 2r = x – 8
10 ) 4 y = x + 3
11) 2r = x -8
12) x + 4 = --2s
13) x – 6 = 3p
14) x- = 4y
15) x + = 8y
16) + x = z
17) - + x = -m
19) p =
20) r =
21) b =
22) –t =
23) m =
24) f =
25) m =
26) y = 3p –x
27) p =
28) = y
29) a = 3b – x
30) a = 3b – 2x
33) = b
34) a = 4 – 8x
35) = 3
36) a – x = 2t
37) v-2x = 5y
38) s (1-x) = g
39) 15 x + 2y = a
40) a - x =
41) x – u =
42) = y
43) 3x -2t = 2a
44) 2p -1 = 5x
Name :…………………………………….. Form :…………… Date : ……………………..
83
18) – (-x) + w = 0.6s31) p =
32) 12p = 2x -q
45) = 2x
91UNIT 55: SCALE DRAWING On the grid of squares in the answer space, draw each of the following figures based on the scale given.
1
Scale 1:1 3 units 4cm
7cmScale 1:1
2
6cmScale 1: 1
5
Scale 1:13
8 units
6cm Scale 1:1
Name :…………………………………….. Form :…………… Date : ……………………..
4 units
7 units
4 units
6 units
2cm2 units
6 units
84
UNIT 56: SCALE DRAWING On the grid of squares in the answer space, draw each of the following figures based on the scale given.
1
6 units
8cmScale 1:2
4
6cm
10cmScale 1:2
2
4 units
6 cm Scale 1: 2
5
Scale 1: 2
3
Scale 1: 2
Name :…………………………………….. Form :…………… Date : ……………………..
6 units
10 units
8 units
8 units
6 units
4 units
85
UNIT 57: SCALE DRAWING On the grid of squares in the answer space, draw each of the following figures based on the scale given.
1
Scale 1:½
3
Scale 1 : ½
2
2 units
3cmScale 1 : ¼
4
Scale 1: ¼
Name :…………………………………….. Form :…………… Date : ……………………..
4 units 3 units
4 units
3 units
86
UNIT 58: SCALE DRAWING On the grid of squares in the answer space, draw each of the following figures based on the scale given.
1
Scale : 1: 100
3
Scale 1 : 200
2
Scale 1 : 200
4
Scale 1: 200
Name :…………………………………….. Form :…………… Date : ……………………..
5 m
7 m 14 m
16 m
10 m
8 m 8 m
10 m
87
UNIT 59: SCALE DRAWING Draw the figure on each of the following scale given.
Scale 1: 1
Scale 1 : ½
Scale 1: 2
Scale 1: ¼
Scale 1 : 4
Name :…………………………………….. Form :…………… Date : ……………………..
88
C
UNIT 60: TRANSFORMATION (Translations)
State the translations vector of the following
Answer : Answer :
Answer : Answer :
Name :…………………………………….. Form :…………… Date : ……………………..
A
A'
B
B'
D'
D
C'
E F'
89
Answer : Answer :
UNIT 61: TRANSFORMATION : (Translations)
Determine the coordinates of the image of point P under a translation given below.
Translation of Translation of
Translation of
E'F
Translation of
-1-2-3-4 1-1-2-3
12•
•
-1-2-1-2-3
123
1 2 3 4 5
1 2 3 4 5-1-2-3-4
-1
123
-1
•
-1-2-3-4-5-6
-2-3-4
1
123
-1-2-3-4-5 1 2
12 •
-1-2
123
1 2 3 5 6
•
P
P
P P
P
Nama : …………………………………………. Form : ………………. Date: ………………….
90
-3
Answer : ________________
x-1-2-4
Translation of Translation of
UNIT 62: TRANSFORMATION (Reflections)
Determine the coordinates of P’, the image of point P under given reflections.a) x–axis b) y–axis
Answer : ________________ Answer : ________________
c) y–axis d) x–axis
Answer : ________________A
e) x = 3 f ) y = 4
•
-1-2-3
-1-2-3
•
•
•
•
•
•
-1-2-3
123
1 2 3 4 5 -1-2-3-4-1-2-3
123
1 2
y
xx
y
y
-1 1 2
123456
-1-2-3-4 -1-2-3
123
y
1 2 3
123
345yy
x
P
P
P
PP
PP
Nama : …………………………………………. Form : ………………. Date: ………………….
91
Answer : ________________ Answer : _______________
1. h + 6 = 9
2. s + 10 = 5
3. b + 7 = 4
4. c + 10 = 3
5. j + 12 = 24
6. k + 10 = 20
7. s + 8 = 2
8. d + 11 = 3
9. e + 12 = 14
10. m + 17 = 8
11. c – 3 = 8
12. d – 14 = 4
13. e – 5 = 4
14. f -3 = 10
15. g – 9 = 13
16. h – 12 = 4
17. b – 14 = 24
18. p – 10 = - 6
19. j – 18 = - 12
20. k – 10 = -18
21. m – 20 = -6
25. 14 + q = 25
26. 9 + s = 18
27. 12 + c = 25
28. 16 + g = 19
29. 15 + k = 20
30. 17 + m = 12
31. 28 + d = 12
32. 2 – m = 6
33. 8 – j = 12
34. 12 – k = 24
35. 5 – u = 12
36. 17 – s = 26
37. 16 – a = - 12
38. 18 – c = - 20
39. -4 – w = - 16
40. – 8 – k = - 16
41. – 20 – q = - 6
42. 20 = m -6
43. 30 = m + 3
44. 12 = m – 20
45. 25 = m – 5
50. 25 = m - 2
51. 8a + 10 = 26
52. 6k + 6 = 30
53. 2q + 3 = 25
54. 3a + 6 = 18
55. 9t + 9 = 36
56. 4p + 12 = - 60
57. 6w – 2 = 34
58. 6k – 4 = 56
59. 4t – 6 = 42
60. 2c – 3 = 17
61. 3n – 6 = 12
62. -10 + 2k = -20
63. - 10+ 2k = 20
64. 3s + s = 8
65. - 3s + s = 8
66. m + 5m = 30
67. – m + 5m = 20
68. 6u – u = 35
69. u – 6u = 35
70. 6u – u = - 35
-1 -1-2-3
1 2 3 4 5 6
-1-2 -1-2
12
1 2 3 4 x
x
Nama : …………………………………………. Form : ………………. Date: ………………….
UNIT 63: LINEAR EQUATIONS Solve each of the following equations
92
22. p – 18 = - 12
23. 7 + s = 10
24. 9 + p = 20
46. 30 = m + 10
47. 24 = m – 4
48. 8 = m – 4
49. 14 = m – 4
71. u – 6u = - 35
72. 5m – m = - 24
73. 2 ( 3 + m ) = 30
74. 2 ( 3 – m ) = 30
75. 2 ( 3 + m ) = -30
76. 2 ( 3 – m ) = - 30
77. 3b – 9 + 2b = 31
78. 7c – 4 = 41 – 2c
79. 4m – 3 = 47 – 6m
80. 2 ( 5k + 6 ) – 4 ( 3k ) = -2
81.
82.
83.
84.
85.
87.
88.
89.
90.
91.
92.
93.
97.
98.
99.
93
86.
87.
94.
95.
UNIT 64: LINEAR EQUATIONS Solve each of the following equations
1. a) 3y – 8 = y
b) 3x + 1 = 5x – 9
2. a) – m = - 8 2
b) 5c – 6 = 2(c + 6)
3. a) 6h = 4 3
b) 10x – 6 = 9x
4. a) x = - 8 3
b) n + 6 = n - 10 2
5. a) – 4x = 20
b) 4y – 8 = 2y - 3
6. a) m = - 6 4
b) 12 + 3p = 2p - 1
7. a) – 8a = -32
b) 2 (x – 6) = 4x + 12
8. a) 5p = 20
b) 5k – 2 (k + 1) = 7
9. a) 15 – n = 18
b) 2 (4x – 3) = 3x - 11
10. a) 2k = k – 6 2
b) 5m – (m – 7) = 15
11. a) m = 2 4
b) 2p – 3(p – 8) = 5p
12. a) x + 2 = -4 3
b) 3 (k + 5) = 2 (6 – k)
13. a) y + 3 = -5 2
b) 8p – 2 = 3p + 8
14. a) k = - 4 3
b) 1 + m = 7 – 2m
15. a) y – 6 = 10
b) 2 (y + 3) = 2 - y
16. a) 2k = 6 17. a) 6x = 48 18. a) 3x = 21
Nama : …………………………………………. Form : ………………. Date: ………………….
94
3
b) 5 (q – 3) = 9 - q
b) 2m + 3 = m + 4 b) 3e – 7 = -2(e – 4)
19. (a)
(b) 3k – 7 = - 2 ( k –4 )
20. (a)
(b) 2(k – 5) – 3 (4 – 2k) = 2
21. (a) y – 5 = 5
(b)
22. (a) (b) 5p - 2(p+1) = 7
23. (a) (b) 2 (4x-3) = 3x -11
24. (a) 2a = 10
(b) 10 = 3t – 2(4t – 3 )
25. (a)
(b) 15 = 4m – 3(2m – 3)
27. (a)
(b) 3 (2c+4) – 8(c-2) = 12
28. (a) -3x = -12
(b) 5n – 3(1-n) =13
29. (a)
(b) 4 (y - 3) = 2 (y + 1) – 6
30. (a)
(b) 5m – 2 ( 2 – m ) = 24
31. (a)
(b) 3y – 2 = 2 ( 3 + 2y)
32. (a)
(b) k = 10 – 3k
33. (a)
95
26. (a)
(b) 3 (x-4) – (x -5) = 7
(b)
34. (a)
(b) 4x – 3 = 3x + 7
UNIT 65: LINEAR INEQUALITIES Write each of the following sentences using the symbols >, < , , . Example : 10 is greater than 4
10 > 4
Exercises :
1. 11 is greater than 10
____________
2. 4 is less than 6
__________
3. -6 is less than 6
_________
4. 5 is greater than 2
__________
5. -5 is greater than -10
__________
6. 3 is less than 10
__________
7. 5 is less than 8
__________
8. 6 is greater than 3
__________
11. a is less than c
__________
12. k is greater than p
__________
13. m is greater than or equal to 15
__________
14. z is less than d
__________
15. 12 is less than 15
__________
16. 50 is greater than 40
__________
17. 8 is greater than 4
__________
18. 25 is greater than 20
__________
Nama : …………………………………………. Form : ………………. Date: ………………….
96
9. 4 is greater than -20
_________
10. 8 is less than 10
_________
19. d is less than or equal to 5
__________
20. u is greater than or equal to 4
__________
21. k is less than or equal to 20
__________
UNIT 66: LINEAR INEQUALITIES State True or False to each of the following inequalities. Example : 4 < 5 True.
1. 3 < 2 __________
2. 7 > 9 __________
3. 12 > 1 __________
4. 7 < 5 __________
5. 3 > 2 __________
6. 5 > 6 __________
7. 12 < 3 __________
8. 4 < 6 __________
9. 6 < 9 __________
10. 5 > 11 __________
11. 14 < 9 __________
12. 3 > 6 __________
13. 8 > 9 __________
14. 2 < 7 __________
15. 7 > 14 __________
16. 25 < 17 __________
17. 29 > 23 __________
18. 21 < 16 __________
22. 12 > 25 __________
23. -4 < 6 __________
24. -17 < -20 __________
25. 19 > -32 __________
26. -3 < -15 __________
27. -12 > 5 __________
28. + 6 < - 25 __________
29. - 24 < -- 4 __________
30. + 2 > - 26 __________
31. 9 > - 100 __________
32. - 33 < 4 __________
32. + 1 > - 25 __________
33. - 23 < - 3 __________
34. + 3 < - 8 __________
35. + 7 > - 43 __________
36. - 22 > 2 __________
37. + 3 > - 63 __________
38. - 4 < - 25 __________
Nama : …………………………………………. Form : ………………. Date: ………………….
97
19. 2 > 9 __________
20. 8 < 4 __________
21. 27 < 60 __________
39. + 6 < - 32 __________
40. - 9 > - 29 __________
UNIT 67: LINEAR INEQUALITIES Represent each of the following inequalities on a number line. Example x < 3
3 Exercises:
1. x 3
3
2. x > 7
3. x < 5
4. x -3
5. x 5
6. x - 4
7. x 4
9. x < 6
10. x 9
11. x 8
12. x > 3
13. x < 7
14. x 9
15. x > 9
16. x 4
Nama : …………………………………………. Form : ………………. Date: ………………….
98
8. x - 3 17. x > -7
UNIT 68: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. x + 5 8
2. x + 7 > 11
3. x + 5 12
4. x + 11 > 15
5. x + 34 < 44
6. x + 8 18
7. x + 7 > 15
10. x + 15 > 20
11. x + 14 35
12. x + 9 49
13. x + 27 > 30
14. x + 5 < 45
15. x + 10 37
16. x + 8 29
Nama : …………………………………………. Form : ………………. Date: ………………….
99
8. x + 20 40
9. x + 13 19
17. x + 55 > 65
18. x + 38 72
UNIT 69: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. 10 + x > 17
2. 34 + x 14
3. 18 + x > 28
4. 23 + x 33
5. 14 + x 12
6. 22 + x < 44
7. 25 + x > 50
11. 26 + x > 46
12. 14 + x 12
13. 9 + x 27
14. 17 + x < 25
15. 32 + x > 49
16. 19 + x 53
17. 15 + x 40
Nama : …………………………………………. Form : ………………. Date: ………………….
100
8. 13 + x 49
9. 15 + x 32
10. 36 + x 77
18. 28 + x > 37
19. 15 + x 55
20. 12 + x < 82
UNIT 70: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. x 6 < 4
2. x - 4 > 8
3. x - 1 10
4. x - 8 > 12
5. x - 12 9
6. x - 7 < 21
7. x - 9 19
11. x - 13 < 24
12. x - 4 20
13. x - 25 > 3
14. x - 12 36
15. x - 31 > 13
16. x - 12 30
17. x - 33 77
Nama : …………………………………………. Form : ………………. Date: ………………….
101
8. x - 12 > 36
9. x - 6 < 20
10. x - 31 33
18. x - 4 < 9
19. x - 8 19
20. x - 21 14
UNIT 71: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. 12 x - 4
2. 10 > x - 7
3. 6 x - 1
4. 15 > x - 22
5. 18 x - 15
6. 8 > x - 10
7. 32 x + 4
11. 10 = x + 3
12. 13 = x + 13
13. 8 < x - 7
14. 32 x + 10
15. 24 < x - 5
16. 9 x + 12
17. 23 > x - 11
Nama : …………………………………………. Form : ………………. Date: ………………….
102
8. 8 x - 8
9. 24 < x + 20
10. 17 = x + 7
18. 12 x + 7
19. 30 > x - 6
20. 37 x + 3
UNIT 72: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. 2x < 12
2. 3 x 9
3. 6 x > 18
4. 2 x < 20
5. 4 x 48
6. -8 x 32
7. 5x > 35
8. 3 x 30
13. 5 x < 50
14. 12 x 36
15. 7 x 56
16. -4 x < 44
17. 5 x 100
18. 11 x 132
19. -7 x < 7
20. 9 x 63
Nama : …………………………………………. Form : ………………. Date: ………………….
103
9. 6 x 42
10. 9 x > 81
11. 2 x 24
12. -9 x > 27
21. -12 x > 144
22. 9 x < 108
23. 6 x > 42
24. 8 x 56
UNIT 73: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. < 7
2. 4
3. < 4
4. 10
5. > 13
9. > 9
10. < 6
11. 3
12. < 5
13. 4
14. > 5
Nama : …………………………………………. Form : ………………. Date: ………………….
104
6. 3
7. 3
8. 5
15. < 20
16. 6
UNIT 74: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.
1. < 3
2. 3
3. < 10
4. 6
5. > 10
9. > 4
10. 7
11. 3
12. 5
13. < 7
Nama : …………………………………………. Form : ………………. Date: ………………….
105
6. 5
7. > 4
8. 5
14. 10
15. > 3
UNIT 75: LINEAR INEQUALITIES Operations on Inequalities.Solve each of the following inequalities.1. 3x + 2 < 11
2. 8 - 3x > 2
3. 2x + 1 7
4. - 1 < 2
5. 12 x + 3
6. x - 3 > 1
11. 3x + 1 7
12. X - 5 > 1
13. > 7
14. x + 3 8
15. 6 - x > 10
16. 2x + 3 15
Nama : …………………………………………. Form : ………………. Date: ………………….
106
7. 2x + 5 < 11
8. 3x - 6 12
9. 3 + 2x 7
10. 5
17. 3x - 2 13
18. - x > 10
19. 13 - 3x < 4
UNIT 76: GRAPH OF FUNCTIONS
(Use the graph paper to answer the following questions.)
a) Table A shows the values of two variables x and y, of a function, draw the graph of a function
x 0 1 2 3 4 5 6y 6 5 4 3 2 1 0
Table A By using a scale 2cm to 1 unit for both x-axis and y-axis.
b) Table B shows the values of two variables x and y, of a function.
x 0 1 2 3 4 5 6y 0 2 4 6 8 10 12
Table B By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 2 units on y-axis, draw the graph of the function.
c) Table C shows the values of two variables x and y, of a function.
x -2 -1 0 1 2 3 4 5y -10 -4 0 2 2 0 -4 -10
Table C By using a scale of 2 cm to 1 unit for both x-axis and y-axis. draw the graph of the function
Name : …………………………………………. Form : ………………. Date: ………………….
107
d) Table D shows the values of two variables x and y, of a function.
x -3 -2 -1 0 1 2 3y -5 -9 -10 -5 3 15 31
Table D By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.
e) Table E shows the values of two variables x and y, of a function.
x -3 -2 -1 0 1 2 3y -35 -16 -9 -8 -7 0 19
Table E By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.
f) Table F shows the values of two variables x and y, of a function.
x -3 -2 -1 0 1 2 3 4y 27 7 -7 -15 -17 -13 -3.5 13
Table F By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.
g) Table G shows the values of two variables x and y, of a function.
x -2 -1 0 1 2 3 4 4.5y 18 5 -1.5 -2 -1 -5.5 -17 -25
Table G By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.
h) Table H shows the values of two variables x and y, of a function.
x -3 -2 -1 0 1 2 3 3.5 4y 32 12 -2.5 -15 -21 -15 -9 -15 -45
Table H By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 10 units on y-axis, draw the graph of the function.
i) Table I shows the values of two variables x and y, of a function.
108
C
A
opposite sidehypotenuse
B adjacent side
R
x -3 -2 -1 0 1 2 3 3.5 4y -50 -25 -7 -5 11.5 12 12.5 19 37.5
Table I By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 10 units on y-axis, draw the graph of the function.
j) Table J shows the values of two variables x and y, of a function.
x -3 -2 -1 0 1 2 3 4 5y -7 0.5 2 0.5 -1 0.5 8 20 35
Table J By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on y-axis, draw the graph of the function.
UNIT 77: TRIGONOMETRY
Exercise1. Based on the right-angled triangle PQR, name;
a) the hypotenuse =______________________b) the opposite side to angle = ____________c) the adjacent side to angle =_____________
2. Find the value of .
Nama : …………………………………………. Form : ………………. Date: ………………….
Q
P
109
6cm
8cm
10cm
3
1cm
2cm
12cm
4cm
2.5cm
2cm
1.5cm
5cm
13cm
12cm
24
10 26
8
6
10
4
3 5
6.5 6
2.5
25 7
24
a)
= _________
b)
= __________
c)
= __________
d)
= __________
e)
= ___________
f)
= __________
3. Find the value of .
a)
= __________
b)
= __________
c)
= ___________
d)
= __________
e)
= ___________
f)
= ___________
4. Find the value of .
110
5
12
13
12
3.5
12.5
213
113 1
x
9
9
x
a)
= __________
b)
= ___________
c)
= ___________
d)
= __________
e)
= ____________
f)
= _________
UNIT 78: TRIGONOMETRY Find the unknowns
a) Given tan = , find the value of x
c) Given that tan = , find the value of x.
b) Given tan = , find the value of x.
d) Given sin = , find the value of x
Nama : …………………………………………. Form : ………………. Date: ………………….
x
111
8
e) Given sin = ,find the value of x
g) Given cos = , find the value of x.
f) Given sin = , find the value of x
24
h) Given cos = , find the value of x
x
x
14
8
x
112
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