1001_Math_Problems__LearningExpress_

–ALGEBRA–

808. When estimating distances from aerial photo-				812. A rain barrel contained 4 gallons of water just
graphs, the formula is (A × l) ÷ f = D, where A				before a thunderstorm. It rained steadily for 8
is the altitude, l is the measured length on the				hours, filling the barrel at a rate of 6 gallons
photograph, f is the focal length of the camera,				per day. How many gallons of water did the
and D is the actual distance. If the focal length				barrel have after the thunderstorm?
is 6 inches, the measured length across a lake				a.	4 gallons
on a photograph is 3 inches, and the lake is				b.	6 gallons
3000 feet across, at what altitude was the				c.	7 gallons
photograph taken?				d.	9 gallons
a.	1500 feet
b.	3000 feet			813. Find three consecutive odd integers whose sum
c.	4500 feet			is 117.
d.	6000 feet			a.	39,39,39
				b.	38,39,40
	2	3	11	c.	37,39,41
809. Solve for x: x – 5		+ x + 3	= x2 – 2x – 15 .
a.	3			d.	39,41,43
b.	4
c.	6			814. Three species of songbirds live in a certain plot
d.	11			of trees, totaling 120 birds. If species A has 3
				times as many birds as species B, which has half
810. A new telephone directory with 596 pages has				as many birds as C, how many birds are belong
114 less than twice as many pages as last year’s				to species C?
edition. How many pages were in last year’s				a.	20
directory?				b.	30
a.	298 pages			c.	40
b.	355 pages			d.	60
c.	412 pages
d.	482 pages			815. The base of a rectangle is seven times the
				height. If the perimeter is 32 meters, what is
811. A vacationing family travels 300 miles on their				the area?
			2	a.	28 m	2
first day. The second day they travel only 3 as
far. But on the third day they are able to travel				b.	24 m2
3				c.	16 m	2
4 as many miles as the first two days combined.
How many miles have they traveled altogether?				d.	14 m2

a.375 miles

b.875 miles

c.525 miles

d.500 miles

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–ALGEBRA–

816.Which equation is represented by the graph below?

y

x

a.y = –x2 – 1

b.y = –x2

c.y = –x2 + 1

d.y = x2 + 1

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S E C T I O N

6 Geometry

The 12 sets of basic geometry problems in this section involve lines, angles, triangles, rectangles, squares, and circles. For example, you may be asked to find the area or perimeter of a shape, the length of a line, or the circumference of a circle. In addition, the word problems

will illustrate how closely geometry is related to the real world and to everyday life.

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–GEOMETRY–

Set 52 (Answers begin on page 209.)

817.Each of the following figures has exactly two pairs of parallel sides EXCEPT a

a.parallelogram.

b.rhombus.

c.trapezoid.

d.square.

818.How many faces does a cube have?

a.4 faces

b.6 faces

c.8 faces

d.12 faces

819.A polygon is a plane figure composed of connected lines. How many connected lines must there be to make a polygon?

a.3 or more

b.4 or more

c.5 or more

d.6 or more

820.An acute angle is

a.180 degrees.

b.greater than 90 degrees.

c.90 degrees.

d.less than 90 degrees.

821.A straight angle is

a.exactly 180 degrees.

b.between 90 and 180 degrees.

c.90 degrees.

d.less than 90 degrees.

822.A right angle is

a.180 degrees.

b.greater than 90 degrees.

c.exactly 90 degrees.

d.less than 90 degrees.

823.Which of the following statements is true?

a.Parallel lines intersect at right angles.

b.Parallel lines never intersect.

c.Perpendicular lines never intersect.

d.Intersecting lines have two points in common.

824.A triangle has two congruent sides, and the measure of one angle is 40 degrees. Which of the following types of triangles is it?

a.isosceles

b.equilateral

c.right

d.scalene

825.A triangle has one 30-degree angle and one 60degree angle. Which of the following types of triangles is it?

a.isosceles

b.equilateral

c.right

d.scalene

826.A triangle has angles of 71 degrees and 62 degrees. Which of the following best describes the triangle?

a.acute scalene

b.obtuse scalene

c.acute isosceles

d.obtuse isosceles

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–GEOMETRY–

827. In which of the following are the diagonals of		831. What is the greatest area possible enclosed by a
the figure always congruent and perpendicular?		quadrilateral with a perimeter of 24 feet?
a.	isosceles trapezoid	a.	6 square feet
b.	square	b.	24 square feet
c.	isosceles triangle	c.	36 square feet
d.	rhombus	d.	48 square feet
828. In a triangle, angle A is 70 degrees and angle B		832. What is the difference in area between a square
is 30 degrees. What is the measure of angle C?		with a base of 4 feet and a circle with a diame-
a.	90 degrees	ter of 4 feet?
b.	70 degrees	a.	16 − 2π square feet
c.	80 degrees	b.	16 − 4π square feet
d.	100 degrees	c.	8π − 16 square feet
		d.	16π − 16 square feet

829.Which of the following could describe a quadrilateral with two pairs of parallel sides and two interior angles that measure 65 degrees?

a.square

b.triangle

c.rectangle

d.rhombus

830.If pentagon ABCDE is similar to pentagon

FGHIJ, and AB = 10, CD = 5, and FG = 30,

what is IH?

5

a.

3

b. 5

c. 15

d. 30

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–GEOMETRY–

Set 53 (Answers begin on page 209.)

833.What is the difference in perimeter between a square with a base of 4 feet and a circle with a diameter of 4 feet?

a.8 − 2π square feet

b.16 − 2π square feet

c.16 − 4π square feet

d.16 − 8π square feet

834.A rectangle’s topmost side is 3 times that of the leftmost side. If the leftmost side is A inches long, what is the area of the rectangle?

a.3A

b.6A

c.3A2

d.6A2

835.What is the perimeter of the triangle shown below?

3

4

a.12 units

b.9 units

c.8 units

d.7 units

836.What is the perimeter of the polygon shown below?

8

4

a.12

b.16

c.24

d.32

837.What is the perimeter of the following figure?

a

a

a.a2 ÷ 2

b.2a + 2a2

c.2a + 2a2

d.4a

838.The perimeter of a rectangle is 148 feet. Its two longest sides add up to 86 feet. What is the length of each of its two shortest sides?

a.31 feet

b.42 feet

c.62 feet

d.72 feet

839.How many feet of ribbon will a theatrical company need to tie off a performance area that is 34 feet long and 20 feet wide?

a.54

b.68

c.88

d.108

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–GEOMETRY–

840.What is the outer perimeter of the doorway shown below?

2

10

a.12

b.24

c.20 + 2π

d.24 + 2π

841.What is the perimeter of the triangle below?

7

9

10

a.90

b.70

c.26

d.19

842.What is the perimeter of the parallelogram shown below?

8

6 12

a.26

b.32

c.48

d.56

843.What is the perimeter of the shaded area, if the shape is a quarter circle with a radius of 8?

a.2π

b.4π

c.2π + 16

d.4π + 16

844.What is the perimeter of the triangle below?

4

13

7

a.11

b.13

c.24

d.28

845.What is the length of the side labeled x of the polygon shown below if the perimeter is 40

inches?
	x
6			6
6	6

a.6 inches

b.8 inches

c.10 inches

d.16 inches

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–GEOMETRY–

846. What is the perimeter of the rectangle below?

4

9

a.13

b.22

c.26

d.36

847.What lines must be parallel in the following diagram?

a

b

848.What is the measure of angle F in the following diagram?

60°

F

a.15 degrees

b.45 degrees

c.30 degrees

d.90 degrees

130º

60º

c

120º

120º

d

a.a and b

b.a and d

c.b and c

d.c and d

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–GEOMETRY–

Set 54 (Answers begin on page 210.)

849.In the figure below, which of the following pairs of angles must be congruent?

1

4 2

3

a.1 and 2

b.1 and 3

c.3 and 4

d.1 and 4

850.Which of the following lengths could form the sides of a triangle?

a.1, 2, 3

b.2, 2, 5

c.2, 3, 6

d.2, 3, 2

851.Which side of the right triangle shown below is the shortest, if angle ACB is 46 degrees?

B

46°

A C

a.AB

b.AC

c.BC

d.All sides are equal

852.Which side of the triangle shown below is the shortest, if angles BAC and ABC are 60

degrees?

B

A C

a.AB

b.AC

c.BC

d.All sides are equal

853.Which of the angles in the figure must be con-

gruent if lines l and m are parallel?

l

m

1	2	5	6
3	4	7	8

a.1 and 2

b.1 and 8

c.2 and 8

d.4 and 7

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–GEOMETRY–

854. What is the measure of angle ABC?

B

A	42°	61°	C

a.42 degrees

b.61 degrees

c.77 degrees

d.103 degrees

855.Plattville is 80 miles west and 60 miles north of Quincy. How long is a direct route from Plattville to Quincy?

a.100 miles

b.110 miles

c.120 miles

d.140 miles

856.Which is the longest side of the triangle shown

below? (Note: not drawn to scale.)

C

100°

A	38°	42°	B

a.AB

b.AC

c.BC

d.AC and BC

857.An angle has twice the measure of its complement. What is its measure?

a.120 degrees

b.60 degrees

c.45 degrees

d.30 degrees

858.What is the complement of a 34-degree angle?

a.34 degrees

b.56 degrees

c.66 degrees

d.146 degrees

859.What is the supplement of a 75-degree angle?

a.15 degrees

b.25 degrees

c.105 degrees

d.115 degrees

860.Three times an angle is equal to two times its complement. What is the angle?

a.180 degrees

b.120 degrees

c.36 degrees

d.30 degrees

861.The supplement of an angle is equal to three times the complement. What is the angle?

a.90 degrees

b.60 degrees

c.45 degrees

d.30 degrees

862.Which of these angle measures form a right triangle?

a.40 degrees, 40 degrees, 100 degrees

b.20 degrees, 30 degrees, 130 degrees

c.40 degrees, 40 degrees, 40 degrees

d.40 degrees, 50 degrees, 90 degrees

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