Math final practice 1

What theorem can prove a triangle with side lengths 5, 12, and 13 is a right triangle?

Pythagorean Theorem

What happens to the point (4, -2) when reflected across the y-axis?

(-4, -2)

If two similar triangles have a scale factor of 2, and the longest side of the smaller triangle is 5, what is the longest side of the larger triangle?

10

Which transformation preserves both size and shape?

Reflection

Find the slope of the line through (2, 3) and (8, 15).

2

Find the distance between (1, 2) and (7, 10).

10

What is the area of a rectangle that is 8 units long and 5 units wide?

40 square units

What is the volume of a rectangular prism measuring 4 cm × 3 cm × 6 cm?

72 cubic centimeters

What is the difference between congruent figures and similar figures?

Congruent figures have the same shape and size; similar figures have the same shape but may have different sizes.

What is the third angle in a triangle with angles measuring 40° and 65°?

75°

Do the points (1,1), (3,5), and (5,9) lie on the same line?

Yes

What happens when the point (-2, 4) is translated by (+5, -3)?

(3, 1)

What is the result of rotating the point (3, 2) 180° about the origin?

(-3, -2)

What is the midpoint of the segment connecting (2, 6) and (8, 10)?

(5, 8)

How does slope determine if two lines are parallel?

Parallel lines have equal slopes.

What is the formula for slope?

Rise over run or (y₂ − y₁)/(x₂ − x₁)

What is the formula for distance between two points?

$$\text{Distance} = \\sqrt{(x₂ − x₁)² + (y₂ − y₁)²}$$

What is the formula for finding the midpoint?

Midpoint = $\left(\frac{x₁+x₂}{2}, \frac{y₁+y₂}{2}\right)$

What is the sum of the interior angles of a triangle?

180°

What is the sum of the interior angles of a quadrilateral?

360°

What happens to coordinates when reflected across the x-axis?

(x, y) becomes (x, -y)

What happens to coordinates when reflected across the y-axis?

(x, y) becomes (-x, y)

What happens to coordinates after a 180° rotation about the origin?

(x, y) becomes (-x, -y)

What is the mean of the class scores: 72, 75, 78, 80, 80, 85, and 90?

80

What is the median of the class scores: 72, 75, 78, 80, 80, 85, and 90?

80

What is the mode of the class scores: 72, 75, 78, 80, 80, 85, and 90?

80

Which graph is best for comparing categories?

Bar graph

Which graph is best for showing trends over time?

Line graph

Which graph is best for displaying relationships between two numerical variables?

Scatter plot

If a bag contains 5 red marbles and 3 blue marbles, what is the probability of drawing a red marble?

5/8

If a coin is flipped twice, what is the probability of getting two heads?

1/4

If a standard die is rolled, what is the probability of rolling a number greater than 4?

1/3

What is the probability of rolling an even number on a six-sided die?

1/2

What is the probability of drawing a heart from a standard deck of cards?

1/4

What does a positive correlation mean?

As one variable increases, the other tends to increase.

What does a negative correlation mean?

As one variable increases, the other tends to decrease.

What does no correlation mean?

There is no clear relationship between the variables.

What is an outlier?

A data value that is much higher or lower than the rest of the data.

Why is the mean sensitive to outliers?

Extreme values can significantly change the average.

When is the median often a better measure than the mean?

When there are outliers in the data.

What does a trend line do on a scatter plot?

Shows the overall pattern or relationship in the data.

What type of relationship exists when a student studies more hours and their scores increase?

Positive correlation.

What is the area formula for a triangle?

1/2 × base × height

What is the area formula for a circle?

$$\pi r^2$$

What is the circumference formula for a circle?

2$\pi r$

What is the volume formula for a rectangular prism?

length × width × height

If two lines have slopes of 3 and 3, what is their relationship?

Parallel

If two lines have slopes of 2 and -1/2, what is their relationship?

Perpendicular

What is the scale factor if a side length changes from 4 to 12?

3

If a triangle is enlarged by a scale factor of 2, what happens to its side lengths?

They double.

What property do similar figures always share?

The same shape.

What property do congruent figures always share?

The same shape and size.