AHSGE Math Items - Standard VII



AHSGE Math Items - Standard VII

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

1. Apply properties of angles and relationships between angles. (4 items)

ELIGIBLE CONTENT

• The following properties and relationships may be included:

- vertical angles

- adjacent angles

- supplementary angles

- complementary angles

- linear pair (adjacent supplementary angles)

- relationships among the measures of angles formed by two parallel lines

and a transversal

• Word problems may be used.

• The knowledge of the sum of measures of angles may be used.

• Determining measurements of angles when the measurements of angles are expressed as algebraic expressions may be required.

A convex polygon has 8 sides. What is the The measure of an angle in degrees is

sum of the measures of the interior angles? 4x. Which of these represents the measure

of its complement?

A. 720 ° A. 180 - 4x

B. 360° B. 90 - 4x

C. 1080° C. 180 + 4x

D. 960° D. 90 + 4x

Given: that v║w, [pic]°.

What would be the [pic]

1 3 5 7

2 4 6 8

V W

A. 120°

B. 30°

C. 180°

D. 100°

What is the value of x?

A. 90°

B. 60°

C. 100°

D. 120°

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

2. Apply Pythagorean Theorem. (4 items)

ELIGIBLE CONTENT

• The Pythagorean Theorem will be given on the reference page.

• Diagrams will be included.

• Word problems will be used.

• Radicals may be included in options.

• All radicals will be simplified.

• Drawings will be to scale.

George was working on the roof of Which of these sets of numbers could be

his house. He used a 13 ft ladder. The the lengths of the side of a right triangle?

ladder was 5 ft from his house. What was the

height of the side of the house?

13 ft. x

5 ft

A. 16 ft A.{3,6,9}

B. 10 ft B.{5,10,12}

C. 12 ft C.{7,11,13}

D. 8 ft D. {3,4,5}

What is the value of x in the right What is the value of x in the right

triangle below? triangle below?

15 35 37

6

x

x

A. [pic] A. 14

B. [pic] B. 12

C. [pic] C. 20

D. [pic] D. 18

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

3. Apply properties of similar polygons. (4 items)

ELIGIBLE CONTENT

• Diagrams may be included.

• Drawings will be to scale.

• The word similar or the symbol “~” may be used.

• Use of the scale factor will be required.

If ΔCDE~ΔABC, what is the length of In the figure below ΔJKL ~ ΔJFG.

segment DE? What is the length of line segment KL?

A. 7.8 cm A. 8.3 cm

B. 8.4 cm B. 9.2 cm

C.6.2 cm C. 6 cm

D.10 cm D. 7.5 cm

In the figure below, GHKL and MNPQ

are similar rectangles. What is the length

Which of these dimensions form a of line segment LK?

rectangle similar to a rectangle with a width

of 2 centimeters and a length of 9 centimeters?

G H

A. 4 centimeters by 25 centimeters.

B. 4 centimeters by 24 centimeters.

C.6 centimeters by 27 centimeters.

D. 8 centimeters by 16 centimeters.

M N

9.6 in.

4 in.

L ? K Q 1.5 in. P

A. 4.5 inches

B. 3.6 inches

C. 5.5 inches

D. 6 inches

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

4. Apply properties of plane and solid geometric figures. (4 items)

ELIGIBLE CONTENT

• Diagrams may be included.

• Word problems may be used.

• The following content may be included:

- area and perimeter of triangles, rectangles, and squares

- area and circumference of a circle, given radius or diameter

- perimeter of a regular polygon, given one side

- volume of rectangular prism or cylinder

- sum of the measures of the angles in a triangle

- sum of the measures of the angles in a rectangle

• Determining any dimension of a figure may be required.

• Determining any dimension of a figure when the dimension is expressed as an algebraic

expression may be required.

What is the area of a circle with a If the perimeter of the figure shown diameter of 4x + 4? Below is 74 inches, what is the value of x?

2x + 1 2x + 1

4x + 4

2x 2x

A. [pic] 3x + 6

B.[pic] A. 6

C. [pic] B. 10

D. [pic] C. 8

D. 4

What is the area of the ΔFGH? What is the measure of [pic] in the figure below?

G Q

3x°

x

F H P x° R

[pic]

A.[pic] A. 48°

B. [pic] B. 36°

C. [pic] C. 108°

D. [pic] D. 72°

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

5. Determine measures of central tendency. (4 items)

ELIGIBLE CONTENT

• The word “mean” will be used for the arithmetic average.

• The set of numbers used to assess the range will not be in numerical order.

• Decimals up to hundredths may be used.

• Decimals with different numbers of decimal digits may be used in the same item.

• Frequency diagrams may be used.

Nine students took a 10 point quiz in The monthly rainfall in inches for a city

Mrs. Jones’s science class. The nine in New Mexico is listed below.

scores are shown in the chart below.

Science Quiz Scores

Student 1 2 3 4 5 6 7 8 9 10 Month J F M A M J J A S O N D

inches 2 1 1 1 0 0 0 1 1 1 2 3

Scores 6 8 7 9 8 10 8 10 7 9 of

rainfall

What is the median score of the quiz scores? What is the mean annual monthly rainfall?

A. 6 A.1.42 inches

B. 9 B. 2 inches

C.10 C. 1.5 inches

D. 8 D. 1.08 inches

What is the mode of the data in What is the median in this set of data?

question # 1 ? 17, 14, 15, 21, 19, 24, 28, 31, 12

A. 8 A. 14

B. 7 B. 28

C. 9 C. 19

D. 10 D. 2

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

6. Determine probabilities. (4 items)

ELIGIBLE CONTENT

• Both AND and OR situations may be included.

A teacher’s homeroom consisted of 8 boys A bag contains 26 candy bars. 8 were

and 6 girls. If members were chosen to chocolate, 12 were caramel, and 6 were

participate in a play, what is the probability that coconut. If one candy bar is drawn at

the first member selected is a boy and the second random, what is the probability that it

member is a girl? is chocolate?

A. [pic] A.[pic]

B. [pic][pic] B. [pic]

C. [pic] C.[pic]

D. [pic] D. [pic]

On the high school basketball team, What is the probability of spinning a 6

5 players were guards, 3 were centers, on the spinner pictured below?

4 were forwards. If two were chosen as

captains, what is the probability that they

would be guards or centers?

A. [pic] A.[pic]

B. [pic] B. [pic]

C. [pic] C [pic]

D.[pic] D [pic]

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

7. Solve problems involving direct variation. (4 items)

ELIGIBLE CONTENT

• Diagrams may be used.

• Verbal descriptions of proportions may be used.

If y varies directly as x, and y = 12 A model battleship is built to a scale

when x = 16, find y when x = 48. of 1:75. If the length of the model is

18 inches, what is the length of the

A. 48 actual battleship?

B. 36

C. 72 A. 1350 ft.

D. 24 B. 112.5 ft

C. 96 ft.

D. 16200 ft.

A painter can paint 96 square feet in

Karen can type 60 words per minute. 60 minutes. At this rate, how long would

Her essay has 900 words. How long take to paint a barn that is 240 square feet?

will it take her to type her paper?

A. 12 minutes A. 150 minutes

B. 50 minutes B. 120 minutes

C. 8.5 minutes C. 90 minutes

D. 15 minutes D. 6 hours

STANDARD VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

OBJECTIVE

8. Solve problems involving algebraic concepts. (4 items)

ELIGIBLE CONTENT

• Word problems will be used.

• Interpretation of figures may be required.

• The following content may be included:

- distance-rate-time problems

- money problems, which may require a system of equations

- numbers (sum, difference, product, quotient)

- simple age problems referring only to the present

- consecutive integers

- area, volume, dimension problems

- quantity problems

- cost problems

- wage problems

Grandpa Mike is three times as old as A beauty salon has a senior citizen’s

Jerry. The sum of their ages 96. discount of 15% on Wednesday. If

How old is GrandpaMike? Jessie Lee wants a perm that is originally

$60, how much will it cost if she has it

A. 58 done on Wednesday?

B. 104

C. 72 A. $ 57

D. 24 B. $ 45

C. $ 51

D. $ 9

If a family is going on a vacation that

The sum of 3 consecutive integers is 75. will require travel of 950 miles at an

What is the value of the middle integer? average speed of 50 mph, how many hours will it take to reach their

A. 24 destination?

B. 25

C. 26 A. 19 hours

D. 27 B. 24 hours

C. 16 hours

D. 45 hours

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