IGCSE, Edexcel, IB and AP Science Courses | Dr Dabour Hub Academy

1.

Plane: 3x + 2y + -2z = 5; the line passes through P(3, 2, 1) with direction (1, 0, 1). Which option is correct?

angle between line and plane ≈ 4.9°, distance of P from the plane = 6

angle between line and plane ≈ 9.9°, distance of P from the plane = 1.46

angle between line and plane ≈ 4.9°, distance of P from the plane = 1.46

angle between line and plane ≈ 4.9°, distance of P from the plane = 3.88

2.

Find the length of AB.

136

11.66

7.211

16

3.

Find angle BAC in degrees.

122.3 °

28.84 °

32.32 °

57.68 °

4.

Find angle BAC in degrees.

70.53 °

109.5 °

19.47 °

35.26 °

5.

Find the length of AB.

7

13

81

9

6.

Find the length of AB.

10.05

101

5.745

15

7.

Find the length of AB.

10

9.274

6.164

38

8.

Find the perpendicular distance from the origin to the plane through A, B, C.

72

6.928

1.504

0.973

9.

Find the perpendicular distance from the origin to the plane through A, B, C.

3

4.583

0.1474

0.1

10.

Find angle BAC in degrees.

37.59 °

52.41 °

18.79 °

142.4 °

11.

Find the length of AB.

7.348

7.071

12

50

12.

Find angle BAC in degrees.

155.9 °

24.12 °

12.06 °

65.88 °

13.

Find the length of AB.

8.307

69

7.28

13

14.

Find angle BAC in degrees.

74.58 °

105.4 °

52.71 °

15.42 °

15.

Find the length of AB.

11

5

45

6.708

16.

Find angle BAC in degrees.

70.57 °

19.43 °

35.29 °

109.4 °

17.

Find angle BAC in degrees.

116.7 °

58.34 °

63.32 °

26.68 °

18.

Find the perpendicular distance from the origin to the plane through A, B, C.

28

2

0.9333

1.484

19.

Find the length of AB.

3.606

5

8.544

13

20.

Find the perpendicular distance from the origin to the plane through A, B, C.

45

1.225

0.75

3.742

21.

Find the length of AB.

9.11

7.141

51

11

22.

Find angle BAC in degrees.

87.79 °

46.11 °

92.21 °

2.212 °

23.

Find angle BAC in degrees.

14.09 °

151.8 °

28.19 °

61.81 °

24.

Find angle BAC in degrees.

168 °

12 °

78 °

5.999 °

25.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.07692

6

0.1275

5.099

26.

Find the perpendicular distance from the origin to the plane through A, B, C.

83

5

2.515

3.657

27.

Find the length of AB.

50

8

7.071

9.695

28.

Find the length of AB.

6.633

10

11.54

44

29.

Find angle BAC in degrees.

35.56 °

108.9 °

18.88 °

71.12 °

30.

Find the length of AB.

6.164

38

7.071

8

31.

Find the perpendicular distance from the origin to the plane through A, B, C.

6

5.099

0.07692

0.128

32.

Find angle BAC in degrees.

110.4 °

34.79 °

20.41 °

69.59 °

33.

Find angle BAC in degrees.

42 °

21 °

138 °

48 °

34.

Find the length of AB.

2

4

10.2

3.48

35.

Find angle BAC in degrees.

35.43 °

54.57 °

17.72 °

144.6 °

36.

Find the length of AB.

7.874

6.481

62

12

37.

Find angle BAC in degrees.

13.15 °

103.1 °

38.43 °

76.85 °

38.

Find the perpendicular distance from the origin to the plane through A, B, C.

2.857

5.745

80

3.288

39.

Find angle BAC in degrees.

26.58 °

58.29 °

63.42 °

116.6 °

40.

Find the length of AB.

41

12.69

6.403

9

41.

Find angle BAC in degrees.

99.69 °

9.685 °

40.16 °

80.31 °

42.

Find angle BAC in degrees.

24.27 °

32.87 °

114.3 °

65.73 °

43.

Find the length of AB.

4.583

11

7.28

53

44.

Find the perpendicular distance from the origin to the plane through A, B, C.

7.071

1.974

77

3.013

45.

Find the length of AB.

84

4.899

9.165

14

46.

Find angle BAC in degrees.

123.6 °

28.19 °

56.38 °

33.62 °

47.

Find the length of AB.

5.099

11.92

8

26

48.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.6438

5

40

0.3922

49.

Find the length of AB.

5.831

16

9.274

86

50.

Find the perpendicular distance from the origin to the plane through A, B, C.

8.124

1.294

176

1.922

51.

Find the length of AB.

8.602

8.124

14

74

52.

Find the length of AB.

46

10

7.616

6.782

53.

Find angle BAC in degrees.

148.8 °

15.6 °

31.2 °

58.8 °

54.

Find the perpendicular distance from the origin to the plane through A, B, C.

5.196

200

4.642

2.778

55.

Find the perpendicular distance from the origin to the plane through A, B, C.

1.974

2.933

5.099

77

56.

Find the length of AB.

8.602

74

12

10.49

57.

Find angle BAC in degrees.

5.558 °

47.78 °

95.56 °

84.44 °

58.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.8387

3.162

1.412

52

59.

Find the length of AB.

21

4.583

7

6.403

60.

Find angle BAC in degrees.

100.5 °

50.26 °

79.48 °

10.52 °

61.

Find the perpendicular distance from the origin to the plane through A, B, C.

3.016

233

8.124

2.219

62.

Find the perpendicular distance from the origin to the plane through A, B, C.

92

6.481

2.875

3.707

63.

Find the length of AB.

7.55

57

11

8.307

64.

Find the length of AB.

9.487

14

4.243

90

65.

Find the perpendicular distance from the origin to the plane through A, B, C.

2.373

178

5.831

2.854

66.

Find angle BAC in degrees.

93.8 °

46.9 °

3.797 °

86.2 °

67.

Find angle BAC in degrees.

28.71 °

32.58 °

57.42 °

122.6 °

68.

Find angle BAC in degrees.

156.6 °

45 °

0 °

90 °

69.

Find angle BAC in degrees.

33.61 °

56.39 °

16.81 °

146.4 °

70.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.1037

2

7.071

0.06667

71.

Find the length of AB.

12.69

161

21

3

72.

Find the length of AB.

8.775

6.708

77

13

73.

Find the perpendicular distance from the origin to the plane through A, B, C.

187

4.16

2.791

7.681

74.

Find the length of AB.

69

14.45

13

8.307

75.

Find the length of AB.

8.062

7

37

6.083

76.

Find the length of AB.

22

7.071

8

4.69

77.

Find angle BAC in degrees.

48.99 °

20.51 °

139 °

41.01 °

78.

Find the length of AB.

21

7

6.708

4.583

79.

Find angle BAC in degrees.

40.7 °

49.3 °

24.65 °

130.7 °

80.

Find the length of AB.

9

11

7.55

57

81.

Find the perpendicular distance from the origin to the plane through A, B, C.

1.411

0.88

6.164

132

82.

Find the length of AB.

11.05

4

3.162

10

83.

Find the length of AB.

50

10

6.481

7.071

84.

Find the length of AB.

66

8.124

10

7.348

85.

Find the length of AB.

9.487

14

6

3.742

86.

Find angle BAC in degrees.

68.8 °

42.39 °

137.6 °

47.61 °

87.

Find angle BAC in degrees.

54.47 °

71.07 °

108.9 °

18.93 °

88.

Find the length of AB.

98

16

9.899

7.616

89.

Find angle BAC in degrees.

21.14 °

68.86 °

55.57 °

111.1 °

90.

Find angle BAC in degrees.

117.5 °

62.52 °

27.48 °

31.26 °

91.

Find angle BAC in degrees.

26.14 °

153.9 °

63.86 °

13.07 °

92.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.4989

4.359

34

0.2982

93.

Find the perpendicular distance from the origin to the plane through A, B, C.

3.742

67

1.426

2.232

94.

Find angle BAC in degrees.

65.33 °

114.7 °

24.67 °

32.66 °

95.

Find the perpendicular distance from the origin to the plane through A, B, C.

45

5.831

0.7106

0.4412

96.

Find the perpendicular distance from the origin to the plane through A, B, C.

4.472

40

0.6349

0.8412

97.

Find angle BAC in degrees.

51.18 °

102.4 °

77.64 °

12.36 °

98.

Find angle BAC in degrees.

63.6 °

116.4 °

31.8 °

26.4 °

99.

Find angle BAC in degrees.

61.75 °

28.25 °

118.3 °

30.87 °

100.

Find angle BAC in degrees.

5.333 °

10.67 °

169.3 °

79.33 °

101.

Find angle BAC in degrees.

8.92 °

162.2 °

72.16 °

17.84 °

102.

Find angle BAC in degrees.

33.06 °

56.94 °

16.53 °

146.9 °

103.

Find the length of AB.

101

10.05

15

7.28

104.

Find the perpendicular distance from the origin to the plane through A, B, C.

4

6.403

0.1185

0.07407

105.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.25

2.236

9

0.4049

106.

Find the perpendicular distance from the origin to the plane through A, B, C.

2.484

231

3.319

4.243

107.

Find the length of AB.

2.236

3

7

5

108.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.05

6.403

5

0.07762

109.

Find the perpendicular distance from the origin to the plane through A, B, C.

20

3.742

1.006

0.6061

110.

Find the length of AB.

7.483

104

10.2

16

111.

Find the perpendicular distance from the origin to the plane through A, B, C.

5.477

109

4.909

3.114

112.

Find angle BAC in degrees.

38.59 °

77.18 °

12.82 °

102.8 °

113.

Find the perpendicular distance from the origin to the plane through A, B, C.

3.317

55

1.774

3.032

114.

Find the length of AB.

9.539

13

7.681

91

115.

Find the perpendicular distance from the origin to the plane through A, B, C.

3.529

2.151

157

4.583

116.

Find the length of AB.

8.124

6.164

10

38

117.

Find the perpendicular distance from the origin to the plane through A, B, C.

35

0.5833

7.071

0.8329

118.

Find angle BAC in degrees.

67.62 °

22.38 °

33.81 °

112.4 °

119.

Find the perpendicular distance from the origin to the plane through A, B, C.

5.099

0.8462

1.193

66

120.

Find the perpendicular distance from the origin to the plane through A, B, C.

72

2.057

5.385

2.947

121.

Find the length of AB.

20

138

4.69

11.75

122.

Find angle BAC in degrees.

120.1 °

29.95 °

59.89 °

30.11 °

123.

Find the perpendicular distance from the origin to the plane through A, B, C.

50

1.385

0.8333

4.123

124.

Find the length of AB.

144

12

6.633

20

125.

Find the perpendicular distance from the origin to the plane through A, B, C.

1.746

48

6

1.143

126.

Find the length of AB.

8.062

9

12.21

65

127.

Find the length of AB.

7

27

6.557

5.196

128.

Find the length of AB.

6.708

45

9

11

129.

Find the length of AB.

8.062

13

6.083

65

130.

Find the perpendicular distance from the origin to the plane through A, B, C.

64

4.69

1.333

1.651

131.

Find angle BAC in degrees.

123.2 °

33.21 °

56.79 °

28.39 °

132.

Find the perpendicular distance from the origin to the plane through A, B, C.

147

5.196

1.4

2.333

133.

Find the length of AB.

10

6.782

46

4.243

134.

Find the perpendicular distance from the origin to the plane through A, B, C.

7.681

0.6

0.9931

12

135.

Find the perpendicular distance from the origin to the plane through A, B, C.

1.609

111

2.72

6.403

136.

Find the length of AB.

125

11.18

17

6.083

137.

Find the length of AB.

10

5.477

46

6.782

138.

Find the length of AB.

11

49

10.63

7

139.

Find angle BAC in degrees.

121.7 °

31.65 °

29.17 °

58.35 °

140.

Find the perpendicular distance from the origin to the plane through A, B, C.

32

7.348

0.5161

0.784

141.

Find angle BAC in degrees.

137.3 °

21.36 °

42.72 °

47.28 °

142.

Find the perpendicular distance from the origin to the plane through A, B, C.

92

3

1.853

1.438

143.

Find angle BAC in degrees.

106.9 °

73.14 °

16.86 °

53.43 °

144.

Find angle BAC in degrees.

62.07 °

13.96 °

152.1 °

27.93 °

145.

Find the perpendicular distance from the origin to the plane through A, B, C.

6.481

2.616

1.652

38

146.

Find angle BAC in degrees.

64.36 °

25.64 °

12.82 °

154.4 °

147.

Find the perpendicular distance from the origin to the plane through A, B, C.

30

1.448

1.111

5.385

148.

Find the perpendicular distance from the origin to the plane through A, B, C.

4.583

3.28

1.909

42

149.

Find angle BAC in degrees.

41.05 °

24.47 °

131.1 °

48.95 °

150.

Find angle BAC in degrees.

20.48 °

40.95 °

49.05 °

139 °

151.

Find angle BAC in degrees.

122.6 °

28.71 °

57.43 °

32.57 °

152.

Find the length of AB.

93

15

6.708

9.644

153.

Find the perpendicular distance from the origin to the plane through A, B, C.

2.995

106

6

1.738

154.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.9341

0.6338

45

5.385

155.

Find the perpendicular distance from the origin to the plane through A, B, C.

100

5

1.042

1.648

156.

Find angle BAC in degrees.

91.95 °

88.05 °

44.02 °

1.954 °

157.

Find the perpendicular distance from the origin to the plane through A, B, C.

120

2.143

3

5.099

158.

Find the perpendicular distance from the origin to the plane through A, B, C.

66

0.7333

1.254

4.123

159.

Find the length of AB.

2.449

114

18

10.68

160.

Find the perpendicular distance from the origin to the plane through A, B, C.

3.996

6.481

3.1

279

161.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.9623

0.72

6.708

54

162.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.0303

0.04192

4.359

2

163.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.2277

4.123

23

0.3676

164.

Find the length of AB.

50

7.071

8

9.487

165.

Find the length of AB.

15

9.539

9.95

99

166.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.5122

6.481

0.3051

36

167.

Find the length of AB.

7.348

10

10.86

54

168.

Find the length of AB.

13

81

5.745

9

169.

Find the length of AB.

9.274

16

86

4.243

170.

Find angle BAC in degrees.

70.71 °

19.29 °

35.36 °

109.3 °

171.

Find the perpendicular distance from the origin to the plane through A, B, C.

0.8274

78

0.4875

6.481

Curriculum

Mathematics

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Lesson 1: Three-Dimensional Cartesian Coordinates and Vector Operations — Picture questions (exam style)

Quiz finished, well done