11 - 20 of 48 Questions
# | Question | Ans |
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11. |
Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place. A. 6.8% B. 7.3% C. 9.6% D. 14.4% E. 15.4% Detailed Solution% error = errorexact x 1001 =
0.091.23 x
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12. |
In the diagram above, ∠SPR = P and ∠SQR = 2x. Find x in terms of P A. x = p + 2 B. x = p - 2 C. x = p2 D. x = p/2 E. x = 2p Detailed SolutionP = 2x (angle in the same segment);x = p/2 |
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13. |
In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE. A. 3.05cm2 B. 8.20cm2 C. 16.20cm2 D. 24.40cm2 E. 48.8cm2 Detailed SolutionArea of ABDE = b x h12.2 x 4 = 48.8cm 2 |
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14. |
Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x? A. 0o B. 20o C. 30o D. 45o E. 50o Detailed SolutionFrom the graph; when sin x = cos xx = 45 0 |
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15. |
The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects? A. 165 B. 160 C. 155 D. 135 E. 85 Detailed SolutionAt least 2 subjects = 30 + 45 + 75 + 10 = 160 students |
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16. |
An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle? A. 25.7o B. 44o C. 51.43o D. 98o E. 114.55o Detailed SolutionL = 14cm, r = 7cm; \(\theta\)= ?L = \(\frac{\theta}{360}\) x 2πr 14= \(\frac{\theta\}{360}\) x 2π(7) \(\theta = \frac{360 \times 14}{44}\) =114.55° |
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17. |
If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer. A. 21 B. 9 C. 7 D. 4 E. 3 Detailed SolutionLet the integer = y\(\therefore\) 5y - 2y = 63 3y = 63 \(\implies\) y = 21 |
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18. |
If 3\(^y\) = 243, find the value of y. A. 2 B. 3 C. 4 D. 5 E. 6 Detailed Solution3\(^y\) = 243;3\(^y\) = 3\(^5\) y = 5 |
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19. |
Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree A. 024o B. 114o C. 156o D. 204o E. 336o Detailed Solutiontan\(\theta\) = 9/20 = 0.45\(\theta\) = tan\(^{-1}\) 0.45 = 24.2° the bearing of y from x = 180 0 - 0 = 180° - 24.2° the bearing = 155.8° \(\approxeq\) 156° |
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20. |
In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD A. 3cm B. 4cm C. 5cm D. 8cm E. 15cm Detailed SolutionIn \(\Delta DOB\), let < DOB = \(\alpha\)In \(\Delta DOB\), \(5^2 = 3^2 + s^2\) \(s^2 = 25 - 9 = 16\) \(s = 4cm\) \(\sin \alpha = \frac{4}{5}\) \(\alpha = \frac{< AOB}{2}\) Length of chord = \(2r \sin (\frac{\theta}{2})\) |OB| = r = 5cm L = \(2(5)(\frac{4}{5})\) = 8 cm |
11. |
Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place. A. 6.8% B. 7.3% C. 9.6% D. 14.4% E. 15.4% Detailed Solution% error = errorexact x 1001 =
0.091.23 x
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12. |
In the diagram above, ∠SPR = P and ∠SQR = 2x. Find x in terms of P A. x = p + 2 B. x = p - 2 C. x = p2 D. x = p/2 E. x = 2p Detailed SolutionP = 2x (angle in the same segment);x = p/2 |
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13. |
In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE. A. 3.05cm2 B. 8.20cm2 C. 16.20cm2 D. 24.40cm2 E. 48.8cm2 Detailed SolutionArea of ABDE = b x h12.2 x 4 = 48.8cm 2 |
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14. |
Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x? A. 0o B. 20o C. 30o D. 45o E. 50o Detailed SolutionFrom the graph; when sin x = cos xx = 45 0 |
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15. |
The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects? A. 165 B. 160 C. 155 D. 135 E. 85 Detailed SolutionAt least 2 subjects = 30 + 45 + 75 + 10 = 160 students |
16. |
An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle? A. 25.7o B. 44o C. 51.43o D. 98o E. 114.55o Detailed SolutionL = 14cm, r = 7cm; \(\theta\)= ?L = \(\frac{\theta}{360}\) x 2πr 14= \(\frac{\theta\}{360}\) x 2π(7) \(\theta = \frac{360 \times 14}{44}\) =114.55° |
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17. |
If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer. A. 21 B. 9 C. 7 D. 4 E. 3 Detailed SolutionLet the integer = y\(\therefore\) 5y - 2y = 63 3y = 63 \(\implies\) y = 21 |
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18. |
If 3\(^y\) = 243, find the value of y. A. 2 B. 3 C. 4 D. 5 E. 6 Detailed Solution3\(^y\) = 243;3\(^y\) = 3\(^5\) y = 5 |
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19. |
Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree A. 024o B. 114o C. 156o D. 204o E. 336o Detailed Solutiontan\(\theta\) = 9/20 = 0.45\(\theta\) = tan\(^{-1}\) 0.45 = 24.2° the bearing of y from x = 180 0 - 0 = 180° - 24.2° the bearing = 155.8° \(\approxeq\) 156° |
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20. |
In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD A. 3cm B. 4cm C. 5cm D. 8cm E. 15cm Detailed SolutionIn \(\Delta DOB\), let < DOB = \(\alpha\)In \(\Delta DOB\), \(5^2 = 3^2 + s^2\) \(s^2 = 25 - 9 = 16\) \(s = 4cm\) \(\sin \alpha = \frac{4}{5}\) \(\alpha = \frac{< AOB}{2}\) Length of chord = \(2r \sin (\frac{\theta}{2})\) |OB| = r = 5cm L = \(2(5)(\frac{4}{5})\) = 8 cm |