Elementary Education (Grades K–6)
Subtest 2 Sample Items
1. A book store is having a sale. The table below shows the discount on selected items in the store.
Item 
Price 
Discount 
Book 
7.55 
25% 
CD 
15.29 
10% 
Calendar 
11.99 
25% 
Greeting card 
2.75 
33% 
A table with three columns and five rows.
The left most column is labeled "Item," the middle column is labeled “Price,” and the right most column is labeled "Discount."
Reading down the rows and across the columns from left to right:
Book, seven dollars and fifty five cents, twenty five percent
CD, fifteen dollars and twenty nine cents, ten percent
Calendar, eleven dollars and ninety nine cents, twenty five percent
Greeting card, two dollars and seventy five cents, thirty three percent
A customer wants to purchase a book, 2 CDs, a calendar, and 3 greeting cards. Which of the following expressions is the best estimate of the total cost of the purchase?
 (8) + (2)(16) + (12) + (3)(3)
 (7) + (2)(15) + (12) + (3)(2)
 (8) + (2)(15) + (12) + (3)(3)
 (7) + (2)(15) + (12) + (3)(2)
 the quantity one fourth times eight plus the quantity one tenth times two times sixteen plus the quantity one fourth times twelve plus the quantity one third times three times three
 the quantity one fourth times seven plus the quantity one tenth times two times fifteen plus the quantity one fourth times twelve plus the quantity one third times three times two
 the quantity threefourths times eight plus the quantity ninetenths times two times fifteen plus the quantity three fourths times twelve plus the quantity two thirds times three times three
 the quantity threefourths times seven plus the quantity ninetenths times two times fifteen plus the quantity three fourths times twelve plus the quantity two thirds times three times two
2. (√36)(^{3}√27)(√10,000)
Which of the following expressions is equivalent to the expression above?
 (6)(3)(10^{2})
 (18)(9)(100^{2})
 (6)(9)(5)(100)
 (18)(9)(5)(1000)
 Answer
 Correct Response: A. (Objective 0010) This question requires the examinee to translate among equivalent representations of numbers. In this case, √36 represents the square root of 36, which is 6; ^{3}√27 represents the cube root of 27, which is 3 (3 × 3 × 3 = 27); and represents the square root of 10,000, which is 100, or 10^{2} (10 × 10 = 100).
Correct Response: A. (Objective 0010) This question requires the examinee to translate among equivalent representations of numbers. In this case, √36 represents the square root of 36, which is 6; ^{3}√27 represents the cube root of 27, which is 3 (3 times 3 times 3 equals 27); and represents the square root of 10,000, which is 100, or 10 squared (10 times 10 equals 100).
3. Which of the following expressions represents the difference between 8 × 10^{2} + 3 × 10^{1} + 5 × 10^{0} and 7 × 10^{2} + 6 × 10^{1} + 7 × 10^{0}?
 0 × 10^{2} + 6 × 10^{1} + 8 × 10^{0}
 1 × 10^{2} + 3 × 10^{1} + 2 × 10^{0}
 2 × 10^{2} + 0 × 10^{1} + 2 × 10^{0}
 3 × 10^{2} + 1 × 10^{1} + 8 × 10^{0}
 Answer
 Correct Response: A. (Objective 0010) This question requires the examinee to demonstrate knowledge of place value. The expression 8 × 10^{2} + 3 × 10^{1} + 5 × 10^{0} evaluates to 800 + 30 + 5 = 835 and 7 × 10^{2} + 6 × 10^{1} + 7 × 10^{0} =700 + 60 + 7 =767. The difference between 835 and 767 is 68, which can be written in expanded notation as 60 + 8 = 0 × 10^{2} + 6 × 10^{1} + 8 × 10^{0}.
Correct Response: A. (Objective 0010) This question requires the examinee to demonstrate knowledge of place value. The expression 8 times 10 exponent 2 plus 3 times 10 exponent one plus 5 times 10 exponent zero evaluates to 800 plus 30 plus 5 equals 835 and 7 times 10 exponent 2 plus 6 times 10 exponent one plus 7 times 10 exponent zero equals 700 plus 60 plus 7 equals 767. The difference between 835 and 767 is 68, which can be written in expanded notation as 60 plus 8 equals 0 times 10 exponent 2 plus 6 times 10 exponent one plus 8 times 10 exponent zero .
4.
The graphic shows the first seven positions of a pattern of adjacent dots.
Position one: one row containing two dots
Position two: two rows, each containing two dots
Position three: two rows, each containing three dots
Position four: three rows, each containing three dots
Position five: three rows, each containing four dots
Position six: four rows, each containing four dots
Position seven: four rows, each containing five dots
A set of ellipses
Position 11: a blank containing a question mark
If the pattern above continues, how many dots will be in the figure at position 11?
 30
 36
 42
 48
5.
5. graph showing a straight decreasing continuous line. Starting in the second quadrant and decreasing passing the x axis at open parenthesis negative four comma zero close parenthesis into the third quadrant crossing the y axis at open parenthesis zero comma negative two close parenthesis continuing to decrease into the fourth quadrant
What is the slope of the line in the graph above?
 4
 2
 Answer
 Correct Response: C. (Objective 0011) This question requires the examinee to use graphs to solve realworld and mathematical problems. To find the slope, choose two points on the line, such as (–4, 0) and (0, –2). The slope is m = , where Δy represents the change between the y coordinates of the two points, and Δx represents the change between the x coordinates of the two points. Thus, m = .
Correct Response: C. (Objective 0011) This question requires the examinee to use graphs to solve realworld and mathematical problems. To find the slope, choose two points on the line, such as (negative 4, 0) and (0, negative 2). The slope is m = delta y over delta x , where delta y represents the change between the y coordinates of the two points, and delta x represents the change between the x coordinates of the two points. Thus, m = start fraction numerator zero minus open parenthesis negative two close parenthesis denominator negative four minus zero end fraction equals two over negative four equals negative one half.
6. Which of the following values of t solves the equation
t equals one over eighteen
t equals seven over thirty six
t equals one over three
t equals seven over six
 Answer
 Correct Response: C. (Objective 0011) This question requires the examinee to solve an equation involving variables and rational numbers. Multiply all the terms on both sides of the equation by the least common multiple of the denominators 3, 4, 6, and 12 and solve the resulting equation. Thus,
.
Correct Response: C. (Objective 0011) This question requires the examinee to solve an equation involving variables and rational numbers. Multiply all the terms on both sides of the equation by the least common multiple of the denominators 3, 4, 6, and 12 and solve the resulting equation. Thus, twelve open parenthesis five twelfths plus seven sixths t close parenthesis equals twelve open parenthesis five sixths t plus three fourths minus two thirds t close parenthesis leads to five plus fourteen t equals ten t plus nine minus eight t leads to twelve t equals fours leads to t equals one third.
7.
Polygon A B C D E is shown. The polygon is composed of 5 line segments that are oriented as follows: AB is vertical on the right side, BC is horizontal on the bottom, CD is vertical on the left side. The top of the polygon, line segment DE slopes down to the right and line segment EA slopes up to the right forming a vshaped notch. Line m, a fortyfive degree line, touches the polygon at Point B.
Which of the following is a reflection over line m of the figure above?

The polygon is oriented with the line segments as follows: DC is horizontal at the bottom, CB is vertical on the left side, and BA is horizontal on the top

The polygon is oriented with the line segments as follows: AB is horizontal at the bottom, BC is vertical on the left side, and CD is horizontal on the top

The polygon is oriented with the line segments as follows: DC is vertical on the right side, CB is horizontal on the bottom, and BA is vertical on the left side.

The polygon is oriented with the line segments as follows: DC is vertical on the left side, CB is horizontal on the top, and BA is vertical on the right side.
8. A family took a road trip and intended to record the miles driven and the number of gallons of gas used every day in the table below.
Day 
1 
2 
3 
4 
Miles driven 
264 
420 
? 
273 
Gallons of gas used 
11 
15 
12 
9 
If the mean of the gas usage for the entire trip was 27 miles per gallon, how many miles were driven on day 3?
 298
 312
 324
 346
 Answer
 Correct Response: B. (Objective 0013) This question requires the examinee to apply knowledge of statistical measures. Since the mean is known to be 27 miles per gallon, then the sum of the miles driven must be the product of 27 and (11 + 15 + 12 + 9) = 47 total gallons of gas used or 27 × 47 = 1269 miles. The miles driven on day 3 are the total miles driven 1269 minus the miles driven on days 1, 2, and 4: 1269 – (264 + 420 + 273) = 1269 – 957 = 312 miles.
Correct Response: B. (Objective 0013) This question requires the examinee to apply knowledge of statistical measures. Since the mean is known to be 27 miles per gallon, then the sum of the miles driven must be the product of 27 and (11 plus 15 plus 12 plus 9) equals 47 total gallons of gas used or 27 times 47 equals 1269 miles. The miles driven on day 3 are the total miles driven 1269 minus the miles driven on days 1, 2, and 4: 1269 minus (264 plus 420 plus 273) equals 1269 minus 957 equals 312 miles.
9. In the sequence below, the nth term, s_{n} , can be represented by which of the following expressions?
In the sequence below, the nth term, s subscript n, can be represented by which of the following expressions?
2, 7, 22, 67, …ellipses
 3s_{n – 1} + 1
 4s_{n – 1} – 1
 (s_{n – 1})^{2} + 3(n – 1)
 (s_{n – 1})^{3} – s_{n}
 three times s subscript n minus one the quantity plus one
 four times s subscript n minus one the quantity minus one
 open parenthesis s subscript n minus one close parenthesis the quantity squared plus three times open parenthesis n minus one close parenthesis
 open parenthesis s subscript n minus one close parenthesis the quantity cubed minus s subscript n
10. Twelve people apply for 4 different jobs. If all of the 12 applicants are equally qualified to fill any of the 4 jobs, which of the following expressions can be used to represent the number of different ways the jobs can be filled?
twleve dot 4
start fraction numerator twelve dot eleven dot ten dot nine denominator eight dot seven dot six dot five end fraction
twelve dot eleven dot ten dot nine
start fraction numerator twelve dot eleven dot ten dot nine denominator four dot three dot two dot one end fraction
 Answer
 Correct Response: C. (Objective 0014) This question requires the examinee to apply knowledge of permutations and combinations and their realworld applications. This problem is an example of a permutation since placing persons A and B in positions 1 and 2 is not the same as placing persons B and A in those positions. Thus, there are 12 possibilities to fill the first job, 11 to fill the second, and so on. Since there are 4 different jobs, the number of different ways can be found by .
Correct Response: C. (Objective 0014) This question requires the examinee to apply knowledge of permutations and combinations and their realworld applications. This problem is an example of a permutation since placing persons A and B in positions 1 and 2 is not the same as placing persons B and A in those positions. Thus, there are 12 possibilities to fill the first job, 11 to fill the second, and so on. Since there are 4 different jobs, the number of different ways can be found by twelve dot eleven dot ten dot nine dot.
11. A function rule is that for some input n: double the input, subtract 4, and then add n. Which of the following ordered pairs could result from the application of this function rule?
 (1, 2)
 (2, 10)
 (3, 5)
 (4, 8)
 Answer
 Correct Response: C. (Objective 0015) This question requires the examinee to translate between different representations of mathematical concepts. By the function rule, the input, n, must be doubled, hence f(n) = 2n. Then "subtract 4" means f(n) = 2n – 4. Finally, "add n" means f(n) = 2n – 4 + n = 3n – 4. Consider that f(3) = 3(3) – 4 = 5. The only ordered pair that satisfies the function rule is (3, 5).
Correct Response: C. (Objective 0015) This question requires the examinee to translate between different representations of mathematical concepts. By the function rule, the input, n, must be doubled, hence f(n) = 2n. Then "subtract 4" means f(n) = 2n – 4. Finally, "add n" means f(n) = 2n – 4 + n = 3n – 4. Consider that f(3) = 3(3) – 4 = 5. The only ordered pair that satisfies the function rule is (3, 5).
12. An individual can best increase the amount of fiber in his or her diet by:
 preparing white rice for dinner instead of pasta.
 replacing frozen vegetables with fresh vegetables for cooking.
 eating greater quantities of fish and less red meat.
 substituting a piece of fruit for a glass of fruit juice at breakfast.
13. Children's diets should include adequate amounts of vitamin D and calcium because of the essential role these nutrients play in:
 activating the immune system to produce antibodies.
 reducing cholesterol levels in the blood.
 helping cells use oxygen to release energy from food.
 building and maintaining strong bones.
 Answer
 Correct Response: D. (Objective 0016) This question requires the examinee to demonstrate knowledge of personal and community health promotion, disease prevention and safety, and proper nutritional choices. An adequate intake of vitamin D and calcium is essential for children's bone health and growth. Vitamin D, a fatsoluble vitamin, and calcium, a mineral, work together to enable mineral deposition into bones, thereby increasing bone density and strength.
Correct Response: D. (Objective 0016) This question requires the examinee to demonstrate knowledge of personal and community health promotion, disease prevention and safety, and proper nutritional choices. An adequate intake of vitamin D and calcium is essential for children's bone health and growth. Vitamin D, a fatsoluble vitamin, and calcium, a mineral, work together to enable mineral deposition into bones, thereby increasing bone density and strength.
14. Folk dancing best illustrates the function of dance in many cultures as an expression of:
 community identity.
 concerns about social issues.
 individual creativity.
 universal aesthetic values.
 Answer
 Correct Response: A. (Objective 0017) This question requires the examinee to recognize the role of visual and performing arts in culture. Folk dancing is a broad term for many types of traditional dancing that serve to express cultural and community identity.
Correct Response: A. (Objective 0017) This question requires the examinee to recognize the role of visual and performing arts in culture. Folk dancing is a broad term for many types of traditional dancing that serve to express cultural and community identity.
Answer Key