ILTS 305 EXAM QUESTIONS AND
CORRECT REVISED ANSWERS
WITH EXPLANATIONS
A student was confused as to where to place the decimal points in the result of the
product 24.5 X 0.02. Which of the following activities would best help the student
understand decimal point placements when finding the product of two decimal
numbers?
A. Practicing counting decimal places in decimal numerals
B. Converting decimals to fraction equivalents and finding the fraction products
C. Finding decimal products on a calculator and recording the results
D. Adding zeros to decimal numerals so that they have the same number of decimal
places. - Answer- B. Converting decimals to fraction equivalents and finding the fraction
products
A student consistently simplifies algebraic expressions as shown below
2x + 3x +5 = 20
10x = 20
x=2
This work provides the most direct evidence that the student does not understand which
of the following mathematical concepts?
A. Commutative property of multiplication
B. Distributive property of multiplication over addition
C. Division has the inverse of multiplication
D. Associative property of multiplication and addition. - Answer- B. Distributive property
of multiplication over addition(Factorization)
Students are given the following problem to simplify.
2x + 5 - 3(x-1)
,Student work:
Step 1: 2x + 5 - 3(x-1) = 2x + 5 - 3x + 3
Step 2: 2x + 5 - 3x + 3 = 2x - 3x + 5 + 3
Step 3: 2x - 3x + 5 + 3 = (2-3)x + 5 + 3
Step 4: (2-3)x + 5 + 3 = -x + 8
Which of the following properties justifies Step 2 in the student's work?
A. Associative property
B. Closure Property
C. Commutative Property
D. Distributive Property - Answer- C. Commutative Property
Use the table to answer the question
# of lbs of Potatoes(X) # of lbs of carrots(Y)
0 37
10 32
20 27
30 22
40 17
The table above showed the relationships between x and y, a chef can purchase for
$18.50 at a local vegetable markets. Which of the following equations best models the
data in the table?
A. y =37 - 5x
B. x + 2y = 74
C. x + 10 = y - 5
D. 10x - 5y = 37 - Answer- B. x + 2y = 74
A rectangular garden is to be enclosed with 48 feet of fencing. The ratio of length to
width of the garden needs to be 5:3. What is the area of the garden if all the fencing
must be used?
A. 90 square feet
B. 135 square feet
C. 215 square feet
, D. 540 square feet. - Answer- B. 135 square feet
A circular cylinder is 12 cm tall. It is closed at both ends and is 3/4 full. Contains 144(pi)
cubic centimeters of liquid. What is the surface area of the cylinder?
A. 90(pi)
B. 112(pi)
C. 128(pi)
D. 208(pi) - Answer- C. 128(pi)
A television station's logo is made up of a circle inscribed in a square, as shown in the
diagram above What is the area of the shaded region of the logo if the circle's
circumference is 16(pi)?
A. 64 - 8(pi)
B. 64 - 16(pi)
C. 256 - 16(pi)
D. 256 - 64(pi) - Answer- D. 256 - 64(pi)
To find the height of a tree, a student placed a 3 ft stick 6 in vertically into the ground
and measured the shadow to be 1 ft long. The shadow of the tree measures 66 in long.
Which of the following is closest to the height of the tree?
A. 14 ft
B. 17 ft
C. 19 ft
D. 26 ft - Answer- A. 14 ft
A 12 ft ladder and a 8 ft ladder are leaning against the side of a house such that each of
the ladders forms the same angle with the ground. The 12 ft ladder reachers 9 ft up and
the side of the house. Which of the following expressions can be used to find how high
up the side of the house the 8 ft ladder reachers?
A. 12/(9X8)
B. 9/(8X12)
CORRECT REVISED ANSWERS
WITH EXPLANATIONS
A student was confused as to where to place the decimal points in the result of the
product 24.5 X 0.02. Which of the following activities would best help the student
understand decimal point placements when finding the product of two decimal
numbers?
A. Practicing counting decimal places in decimal numerals
B. Converting decimals to fraction equivalents and finding the fraction products
C. Finding decimal products on a calculator and recording the results
D. Adding zeros to decimal numerals so that they have the same number of decimal
places. - Answer- B. Converting decimals to fraction equivalents and finding the fraction
products
A student consistently simplifies algebraic expressions as shown below
2x + 3x +5 = 20
10x = 20
x=2
This work provides the most direct evidence that the student does not understand which
of the following mathematical concepts?
A. Commutative property of multiplication
B. Distributive property of multiplication over addition
C. Division has the inverse of multiplication
D. Associative property of multiplication and addition. - Answer- B. Distributive property
of multiplication over addition(Factorization)
Students are given the following problem to simplify.
2x + 5 - 3(x-1)
,Student work:
Step 1: 2x + 5 - 3(x-1) = 2x + 5 - 3x + 3
Step 2: 2x + 5 - 3x + 3 = 2x - 3x + 5 + 3
Step 3: 2x - 3x + 5 + 3 = (2-3)x + 5 + 3
Step 4: (2-3)x + 5 + 3 = -x + 8
Which of the following properties justifies Step 2 in the student's work?
A. Associative property
B. Closure Property
C. Commutative Property
D. Distributive Property - Answer- C. Commutative Property
Use the table to answer the question
# of lbs of Potatoes(X) # of lbs of carrots(Y)
0 37
10 32
20 27
30 22
40 17
The table above showed the relationships between x and y, a chef can purchase for
$18.50 at a local vegetable markets. Which of the following equations best models the
data in the table?
A. y =37 - 5x
B. x + 2y = 74
C. x + 10 = y - 5
D. 10x - 5y = 37 - Answer- B. x + 2y = 74
A rectangular garden is to be enclosed with 48 feet of fencing. The ratio of length to
width of the garden needs to be 5:3. What is the area of the garden if all the fencing
must be used?
A. 90 square feet
B. 135 square feet
C. 215 square feet
, D. 540 square feet. - Answer- B. 135 square feet
A circular cylinder is 12 cm tall. It is closed at both ends and is 3/4 full. Contains 144(pi)
cubic centimeters of liquid. What is the surface area of the cylinder?
A. 90(pi)
B. 112(pi)
C. 128(pi)
D. 208(pi) - Answer- C. 128(pi)
A television station's logo is made up of a circle inscribed in a square, as shown in the
diagram above What is the area of the shaded region of the logo if the circle's
circumference is 16(pi)?
A. 64 - 8(pi)
B. 64 - 16(pi)
C. 256 - 16(pi)
D. 256 - 64(pi) - Answer- D. 256 - 64(pi)
To find the height of a tree, a student placed a 3 ft stick 6 in vertically into the ground
and measured the shadow to be 1 ft long. The shadow of the tree measures 66 in long.
Which of the following is closest to the height of the tree?
A. 14 ft
B. 17 ft
C. 19 ft
D. 26 ft - Answer- A. 14 ft
A 12 ft ladder and a 8 ft ladder are leaning against the side of a house such that each of
the ladders forms the same angle with the ground. The 12 ft ladder reachers 9 ft up and
the side of the house. Which of the following expressions can be used to find how high
up the side of the house the 8 ft ladder reachers?
A. 12/(9X8)
B. 9/(8X12)
