Question

1. kirsten rides her bike at the speed of \\(15\text{ km/hr}\\) from \\(1:00\text{pm}\\) to \\(1:20\text{pm}\\), rests until \\(1:30\text{pm}\\), then jogs at a speed of \\(2\text{m/s}\\) from \\(1:30\text{pm}\\) to \\(2:00\text{pm}\\). what is her average speed over the time interval \\(1:00\text{pm}\\) to \\(2:00\text{pm}\\)?

a. \\(8.0\text{km/hr}\\)
b. \\(9.2\text{km/hr}\\)
c. \\(8.6\text{km/hr}\\)
d. \\(8.8\text{km/hr}\\)
e. \\(9.0\text{km/hr}\\)

1. out of \\(200\\) tennis balls tested for the australian open, \\(10\\) were defective. if a tennis ball was chosen at random from this batch of tennis balls what is the probability that it is not defective?

a. \\(0.1\\)
b. \\(0.05\\)
c. \\(0.95\\)
d. \\(0.9\\)
e. none of these

1. what is \\(\\$350\\) divided in the ratio \\(9 : 5\\)?

a. \\(\\$250, \\$100\\)
b. \\(\\$225, \\$125\\)
c. \\(\\$125, \\$225\\)
d. \\(\\$100, \\$250\\)
e. none of these

1. the value of the angle which is complementary to \\(27^{\circ}\\) is:

a. \\(72^{\circ}\\)
b. \\(63^{\circ}\\)
c. \\(153^{\circ}\\)
d. \\(163^{\circ}\\)
e. none of these

1. the value of the angle, \\(a\\), in the figure below is:

a. \\(69^{\circ}\\)
b. \\(111^{\circ}\\)
c. \\(79^{\circ}\\)
d. \\(89^{\circ}\\)
e. none of these

1. the three angles in a triangle add up to:

a. \\(90^{\circ}\\)
b. \\(120^{\circ}\\)
c. \\(360^{\circ}\\)
d. \\(180^{\circ}\\)
e. none of these

Explanation:

Calculate average speed for Question 29

Find total distance and total time.
First interval: \(20\text{ min} = \frac{1}{3}\text{ hr}\) at \(15\text{ km/hr}\).

$$d_1 = 15 \times \frac{1}{3} = 5\text{ km}$$

Second interval: rest for \(10\text{ min}\), \(d_2 = 0\text{ km}\).
Third interval: \(30\text{ min} = 1800\text{ s}\) at \(2\text{ m/s}\).

$$d_3 = 2 \times 1800 = 3600\text{ m} = 3.6\text{ km}$$

Total distance: \(5 + 0 + 3.6 = 8.6\text{ km}\).
Total time: \(1\text{ hour}\).
Average speed: \(8.6\text{ km/hr}\).

Calculate probability for Question 30

Using the Probability knowledge point.
Total balls: \(200\). Defective: \(10\).
Not defective: \(200 - 10 = 190\).

$$P(\text{not defective}) = \frac{190}{200} = 0.95$$

Divide amount in ratio for Question 31

Total parts: \(9 + 5 = 14\).
Value per part: \(\frac{\$350}{14} = \$25\).
First share: \(9 \times \$25 = \$225\).
Second share: \(5 \times \$25 = \$125\).

Find complementary angle for Question 32

Complementary angles sum to \(90^\circ\).

$$\text{Angle} = 90^\circ - 27^\circ = 63^\circ$$

Find angle a in parallel lines for Question 33

The diagram shows parallel lines cut by a transversal.
The given interior angle is \(111^\circ\).
Angle \(a\) and \(111^\circ\) are consecutive interior angles, which are supplementary.

$$a = 180^\circ - 111^\circ = 69^\circ$$

Find sum of angles in a triangle for Question 34

The interior angles of any triangle always add up to \(180^\circ\).

Answer:

Question 29

• A. 8.0Km/hr
• B. 9.2Km/hr
• C. 8.6Km/hr (Correct answer)
• D. 8.8Km/hr
• E. 9.0Km/hr

Question 30

• A. 0.1
• B. 0.05
• C. 0.95 (Correct answer)
• D. 0.9
• E. none of these

Question 31

• A. $250, $100
• B. $225, $125 (Correct answer)
• C. $125, $225
• D. $100, $250
• E. none of these

Question 32

• A. 72°
• B. 63° (Correct answer)
• C. 153°
• D. 163°
• E. none of these

Question 33

• A. 69° (Correct answer)
• B. 111°
• C. 79°
• D. 89°
• E. none of these

Question 34

• A. 90°
• B. 120°
• C. 360°
• D. 180° (Correct answer)
• E. none of these