TCAP Review Questions

What is the combined mass of Earth and the Moon? Express your answer in scientific notation. Show your work.

• 6.0434 × 10^24 kilograms

• 5.972 × 10^24 kilograms

• 7.348 × 10^22 kilograms

• 1.989 × 10^30 kilograms

Answer explanation

The mass of Earth is approximately 5.972 × 10^24 kg and the Moon is about 7.348 × 10^22 kg. Adding these gives 6.0434 × 10^24 kg, which is the combined mass of Earth and the Moon.

How many more kilograms is the mass of Earth than the mass of the Moon? Express your answer in scientific notation.

• 5.8966 × 10^24 kilograms

• 4.5678 × 10^23 kilograms

• 3.4567 × 10^25 kilograms

• 2.3456 × 10^22 kilograms

Answer explanation

The mass of Earth is approximately 5.972 × 10^24 kg, and the mass of the Moon is about 7.342 × 10^22 kg. The difference is 5.972 × 10^24 kg - 7.342 × 10^22 kg = 5.8966 × 10^24 kg, which is the correct answer.

About how many times as great is the mass of Earth as the mass of the Moon? Express your answer in scientific notation.

• 81.34

• 10.34

• 50.12

• 100.45

Answer explanation

The mass of Earth is approximately 81.34 times greater than the mass of the Moon. This ratio is derived from their respective masses, with Earth being about 5.97 x 10^24 kg and the Moon about 7.35 x 10^22 kg.

Which sequence of transformations is performed so that Figure 1 is congruent to Figure 2?

Answer explanation

To make Figure 1 congruent to Figure 2, a sequence of transformations including rotation and translation is performed. This aligns the corresponding sides and angles of both figures.

Based on the equations above, which statements are true? Mark all that apply.

• A. Stan’s equation suggests that a person’s height is approximately 7.5 times his or her head length.

• B. Olivia’s equation suggests that a person’s height is approximately 2.2 times his or her head length.

• C. Olivia’s equation indicates that a person with a head length of 8 inches would likely be about 63.4 inches tall.

• D. Stan’s equation indicates that a person 69 inches tall would likely have a head length of about 9 inches.

• E. The y-intercept in Stan’s equation indicates that a person with a head length of 0 would likely be about 7.5 inches tall.

Answer explanation

A is true as Stan's equation shows height is 7.5 times head length. C is true since 8 inches head length gives 63.4 inches height. D is true as 69 inches tall corresponds to about 9 inches head length. E is also true for the y-intercept.

Answer explanation

The equation y = x^2 + 3 is a function because for every x-value, there is exactly one corresponding y-value. This satisfies the definition of a function, confirming the correct answer.

Line XY is parallel to line segment AC as shown in the figure below. Name two similar triangles shown in the figure.

• △ABX and △ACX

• △ABC and △AXY

• △BXY and △BAC

• △AXY and △BCA

Answer explanation

Triangles △ABX and △ACX are similar because line XY is parallel to line AC, creating corresponding angles that are equal. This similarity is a result of the Angle-Angle (AA) similarity criterion.

Line XY is parallel to line segment AC as shown in the figure below. Explain why the triangles are similar.

• The triangles are similar because they have two pairs of corresponding angles that are equal.

• The triangles are similar because they have two pairs of corresponding sides that are proportional.

• The triangles are similar because they have the same area.

• The triangles are similar because they are congruent.

Answer explanation

The triangles are similar because line XY is parallel to line AC, creating two pairs of corresponding angles that are equal. This satisfies the Angle-Angle (AA) similarity criterion.

Consider the interior angles of triangles ABC and BXY: angle A, angle B, angle C, angle X, and angle Y. What is the sum of these 5 angles in terms of angle B?

• 540° - 2B

• 360° - B

• 720° - 3B

• 180° + B

Answer explanation

The sum of the interior angles of triangle ABC is 180°. For triangle BXY, the sum is also 180°. Therefore, the total sum of angles A, B, C, X, and Y is 180° + 180° = 360°. Since angle B is included twice, the sum is 540° - 2B.

Consider the numbers 1.4 × 10³ and 5.6 × 10². In scientific notation, what is the sum of the numbers?

• 1.96 × 2

• 1.96 × 10³

• 1.96 × 4

• 1.969 × 5

Answer explanation

To sum 1.4 × 10³ and 5.6 × 10², convert 5.6 × 10² to 0.56 × 10³. Now, add: 1.4 × 10³ + 0.56 × 10³ = 1.96 × 10³. Thus, the correct answer is 1.96 × 10³.