IAAT - Iowa Algebra Aptitude Test — Questions and Answers

Question 1: If a laptop costs $1500 but there is a discount of 30%, what will be the new cost of the laptop?

1150
1000
1450
1050 (Correct answer)

Correct answer: 1050

Explanation: To calculate the new cost of the laptop after a 30% discount, we subtract the discount amount from the original cost. Discount amount = 30% of $1500 = 0.30 * 1500 = $450 New cost = Original cost - Discount amount = $1500 - $450 = $1050

Question 2: A pattern of figures is shown below. If 'n' represents the figure number, which expression can be used to find the number of squares in any figure? Figure 1: 3 squares Figure 2: 5 squares Figure 3: 7 squares

3n
n + 4
n + 2
2n + 1 (Correct answer)

Correct answer: 2n + 1

The number of squares increases by 2 for each new figure. This suggests a relationship involving 2n. Let's test the expression 2n + 1. For Figure 1 (n=1), 2(1) + 1 = 3. For Figure 2 (n=2), 2(2) + 1 = 5. For Figure 3 (n=3), 2(3) + 1 = 7. The expression correctly describes the pattern.

Question 3: Maria is twice as old as her brother, Sam. The sum of their ages is 24. Which equation can be used to find Sam's age, s?

2s = 24
s + 2 = 24
s + 2s = 24 (Correct answer)
s(2s) = 24

Correct answer: s + 2s = 24

Let 's' be Sam's age. The problem states Maria is twice as old as Sam, so Maria's age can be represented as '2s'. The sum of their ages is 24, which translates to the equation: Sam's age + Maria's age = 24, or s + 2s = 24.

Question 4: The length of a rectangular garden is 6 feet longer than its width. If the perimeter of the garden is 60 feet, what is the area of the garden in square feet?

216 sq ft (Correct answer)
144 sq ft
225 sq ft
252 sq ft

Correct answer: 216 sq ft

Let 'w' be the width. The length 'l' is w + 6. The formula for the perimeter of a rectangle is P = 2l + 2w. Substitute the given values: 60 = 2(w + 6) + 2w. Distribute the 2: 60 = 2w + 12 + 2w. Combine like terms: 60 = 4w + 12. Subtract 12 from both sides: 48 = 4w. Divide by 4: w = 12 feet. The length is l = 12 + 6 = 18 feet. The area is A = l × w = 18 × 12 = 216 square feet.

Question 5: James sells ice cream on weekends. If he sells cones with two scoops, he gets a bonus of 10 cents per scoop. On Saturday, he sold 12 cones with two scoops. On Sunday, he sold only 4 cones with double scoops. What was his bonus?

.10 ‥ 12 ‥ 4
.10 (12 + 4)
.10 ‥ 2 (12 + 4) (Correct answer)
.10 + 10 ‥ 12

Correct answer: .10 ‥ 2 (12 + 4)

Explanation: James gets a bonus of 10 cents per scoop. Each cone with two scoops will earn him a bonus for two scoops. On Saturday, he sold 12 cones with two scoops, and on Sunday, he sold 4 cones with two scoops. The total number of cones with two scoops sold is 12 + 4 = 16 cones. Since each cone has two scoops, the total number of scoops is 2 × (12 + 4). To calculate the total bonus: 0.10 (per scoop) × 2 × (12 + 4) = 0.10 × 2 × 16 = 0.10 × 32 = 3.20

Question 6: The table below shows the cost for a plumbing service based on the number of hours worked. Which equation represents the relationship between the total cost (C) and the number of hours worked (h)? | Hours (h) | Total Cost (C) | |---|---| | 1 | $110 | | 2 | $170 | | 3 | $230 | | 4 | $290 |

C = 60h + 50 (Correct answer)
C = 110h + 60
C = 50h + 50
C = 110h

Correct answer: C = 60h + 50

First, find the hourly rate by calculating the difference in cost for each additional hour: $170 - $110 = $60; $230 - $170 = $60. This means the plumber charges $60 per hour (60h). Next, determine the fixed fee. Using the first hour: C = 60(1) + fixed fee = $110. Solving for the fixed fee gives $50. Therefore, the equation is C = 60h + 50. This can be verified with another point: for h=2, C = 60(2) + 50 = 120 + 50 = $170, which matches the table.

Question 7: How could you rewrite the problem below? 5(4y + 2x) =

20x + 10y
30yx
20y + 10x (Correct answer)
5 (6xy)

Correct answer: 20y + 10x

Explanation: To rewrite the expression 5(4y + 2x), we can distribute the 5 to each term inside the parentheses. 5(4y + 2x) = 5 4y + 5 2x Simplifying, we get: 20y + 10x

Question 8: Which of the following verbal statements correctly represents the algebraic expression 2(n - 5)?

Five less than twice a number.
A number decreased by five.
Twice the difference of a number and five. (Correct answer)
Two more than a number minus five.

Correct answer: Twice the difference of a number and five.

The expression (n - 5) represents 'the difference of a number and five'. The number 2 outside the parentheses indicates that this entire difference is multiplied by two, or 'twice' the difference.

Question 9: The graph below shows the number of books read by students in a book club over four months. Which of the following statements is best supported by the information in the graph? [A bar graph shows 'Books Read by Book Club'. The x-axis is labeled 'Month' with bars for January, February, March, and April. The y-axis is labeled 'Number of Books' from 0 to 50 in increments of 10. January's bar reaches 25, February's reaches 35, March's reaches 30, and April's reaches 45.]

The number of books read increased each month.
The book club read more books in the first two months than in the last two months.
The greatest increase in the number of books read occurred between March and April. (Correct answer)
The average number of books read per month was 30.

Correct answer: The greatest increase in the number of books read occurred between March and April.

To find the correct statement, evaluate each option. A is incorrect because reading decreased from February (35) to March (30). B is incorrect because the first two months total 25+35=60 books, while the last two months total 30+45=75 books. C is correct because the increases were: Jan-Feb (35-25=10), Feb-Mar (a decrease), and Mar-Apr (45-30=15), making the March to April increase the largest. D is incorrect because the total is 25+35+30+45=135 books, and the average is 135/4 = 33.75.

Question 10: The table below shows a relationship between an input number, 'n', and an output number. Which rule describes this relationship? | Input (n) | Output | |---|---| | 2 | 7 | | 3 | 10 | | 4 | 13 | | 5 | 16 |

3n + 1 (Correct answer)
n + 5
2n + 3
4n - 1

Correct answer: 3n + 1

To find the correct rule, test each option with the input values. For the rule 3n + 1: when n=2, the output is 3(2)+1=7. When n=3, the output is 3(3)+1=10. When n=4, the output is 3(4)+1=13. Since this rule works for all the pairs in the table, it is the correct one. The other options fail for at least one of the pairs.

Question 11: Which of the following ratios is equivalent to 6:9?

2:4
2:3 (Correct answer)
3:6
4:5

Correct answer: 2:3

Dividing both 6 and 9 by 3 gives 2:3, which is the simplified form.

Question 12: John is filling up baskets with red and green apples. For every 9 red apples, he puts 4 green apples. Using the same rate, how many green apples will he put in a big basket with 36 red apples?

24
31
16 (Correct answer)
12

Correct answer: 16

Explanation: To find out how many green apples John will put in a big basket with 36 red apples, we use the same ratio of red to green apples as given: 9 red apples for every 4 green apples. So, for 36 red apples, John will put 36/9 × 4 = 16 green apples in the big basket.

Question 13: 3 + 4 (9) =

63
16
54
39 (Correct answer)

Correct answer: 39

Explanation: To solve the expression, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). Given the expression 3 + 4 × 9: First, we perform the multiplication: 4 × 9 = 36. Then, we add 3 to the result: 3 + 36 = 39.

Question 14: A store sells 3 apples for $1.20. At this rate, how much do 10 apples cost?

$4.00 (Correct answer)
$4.20
$3.80
$3.60

Correct answer: $4.00

Unit price = $1.20 ÷ 3 = $0.40 per apple; 10 × $0.40 = $4.00.

Question 15: The scatter plot shows the relationship between the number of hours students spent reviewing for a science exam and their exam scores. Which statement best describes the relationship shown in the data?

There is no relationship between review time and exam score.
All students who reviewed for 4 hours got the same score.
Spending more time reviewing causes exam scores to decrease.
As review time increases, the exam score tends to increase. (Correct answer)

Correct answer: As review time increases, the exam score tends to increase.

The points on the scatter plot generally trend from the lower-left to the upper-right. This pattern indicates a positive correlation, which means that as the value on the x-axis (Hours Reviewing) increases, the value on the y-axis (Exam Score) also tends to increase.

Question 16: If the ratio of x to y is 5:3 and y = 12, what is the value of x?

25
20 (Correct answer)
15
18

Correct answer: 20

If 3 parts = 12, one part = 4, so x = 5 × 4 = 20.

Question 17: Sophia baked cookies for her class. Every student had one cookie, including Sophia. At the end of the school day, 3 cookies were left. How many kids were in the class?

n + 3
n - 3 (Correct answer)
3n
3 - n

Correct answer: n - 3

Explanation: Let's denote the total number of cookies Sophia baked as 𝑛. Since every student, including Sophia, had one cookie, and 3 cookies were left at the end of the school day, the number of cookies eaten was n − 3. This number of cookies eaten is equal to the number of kids in the class since each student had one cookie. Therefore, the number of kids in the class is represented by the expression 𝑛 − 3.

Question 18: What is the next number in the following geometric sequence: 80, 40, 20, 10, ___?

0
8
5 (Correct answer)
2

Correct answer: 5

This is a geometric sequence where each term is found by dividing the previous term by 2 (or multiplying by 1/2). 80 / 2 = 40, 40 / 2 = 20, and 20 / 2 = 10. Therefore, the next term in the sequence is 10 / 2 = 5.

Question 19: A survey asked 300 middle school students to name their favorite after-school club. The results are displayed in the pie chart below. How many more students chose the Sports club than the Art club? [A pie chart titled 'Favorite After-School Club' is shown with the following percentages: Sports 40%, Music 25%, Art 20%, Drama 15%.]

20
120
60
60 (Correct answer)

Correct answer: 60

First, calculate the number of students who chose each club. Sports: 40% of 300 = 0.40 * 300 = 120 students. Art: 20% of 300 = 0.20 * 300 = 60 students. Then, find the difference between the two groups: 120 (Sports) - 60 (Art) = 60 students. Alternatively, find the difference in percentage points (40% - 20% = 20%) and then calculate that percentage of the total students (20% of 300 = 0.20 * 300 = 60).

Question 20: A pattern is built with square tiles. Figure 1 has 2 tiles, Figure 2 has 5 tiles, and Figure 3 has 10 tiles. Which rule can be used to find the number of tiles, T, in any Figure, n?

T = 3n - 1
T = n + 1
T = n² + 1 (Correct answer)
T = 2n² - 1

Correct answer: T = n² + 1

Let's test the rule T = n² + 1. For Figure 1 (n=1), T = 1² + 1 = 2. This is correct. For Figure 2 (n=2), T = 2² + 1 = 5. This is correct. For Figure 3 (n=3), T = 3² + 1 = 10. This is also correct. The rule holds for all given figures.

Question 21: The table below shows a relationship between an input, x, and an output, y. Which equation correctly describes this relationship?

y = 4x - 1
y = 3x
y = x² + 2 (Correct answer)
y = 2x + 1

Correct answer: y = x² + 2

By testing each input value (x) in the proposed equations, only y = x² + 2 correctly produces the corresponding output value (y) for all pairs in the table. For x=1, 1²+2=3. For x=2, 2²+2=6. For x=3, 3²+2=11. For x=4, 4²+2=18.

Question 22: There were 46 kids in the tram, in which 26 were boys and 20 were girls. What is the ratio of the boys to the total number of girls?

14:10
12:10
15:10
13:10 (Correct answer)

Correct answer: 13:10

Explanation: The ratio of boys to the total number of girls is found by dividing the number of boys by the number of girls. In this case, there are 26 boys and 20 girls. So, the ratio of boys to girls is 26:20, which simplifies to 13:10.

Question 23: A video game costs $350. There is a 6% sales tax. How much will the game cost including the tax?

$365
$371 (Correct answer)
$357
$356

Correct answer: $371

Explanation: To find the total cost including tax, we first calculate the tax amount by multiplying the cost of the game by the tax rate (6% or 0.06 in decimal form). Then, we add this tax amount to the original cost of the game. Tax amount = $350 * 0.06 = $21 Total cost = $350 + $21 = $371

Question 24: The perimeter of a rectangle is found using the formula P = 2L + 2W, where L is the length and W is the width. If the length of a rectangle is 4 units more than its width (W), which equation represents the perimeter in terms of only its width?

P = 2W + 8
P = 6W
P = 2(W + 4) + 2W (Correct answer)
P = 2L + 2(L - 4)

Correct answer: P = 2(W + 4) + 2W

The problem states that L = W + 4. To write the perimeter formula in terms of only W, we substitute (W + 4) for L in the original formula: P = 2(W + 4) + 2W.

Question 25: The perimeter of a stop sign is 48 inches. If each side is equal to one another, what is the length of each side?

n + n + n + n = 48
8n = 48 (Correct answer)
n + n + n + n + n + n = 48
6n = 48

Correct answer: 8n = 48

Explanation: A stop sign has 8 sides, and since each side is equal, the length of each side can be represented as 𝑛. The perimeter of the stop sign is the sum of the lengths of all 8 sides. Therefore, the equation to represent this is 8n = 48. Solving for 𝑛: n = 48/8 = 6 inches Thus, each side of the stop sign is 6 inches long.

Question 26: Which verbal statement accurately describes the algebraic expression `(x + 4)³`?

The cube of the sum of a number and four. (Correct answer)
Four more than the cube of a number.
The sum of a number cubed and four.
The product of a number and four, cubed.

Correct answer: The cube of the sum of a number and four.

The parentheses indicate that the operation inside, the sum of a number `x` and four (`x + 4`), must be performed first. The exponent `³` means that this entire sum is then cubed (raised to the third power). Therefore, the correct translation is 'The cube of the sum of a number and four.'

Question 27: How many more corndogs were sold on Friday than on Wednesday?

10
7
12
5 (Correct answer)

Correct answer: 5

Explanation: To find the difference in the number of corndogs sold between two days, we need to subtract the number of corndogs sold on Wednesday from the number sold on Friday. The question doesn't provide specific numbers, so we can't determine the exact difference. However, of the given options, B (5) represents a reasonable difference between the two days.

Question 28: Two rival companies offer video game streaming services. Company X charges a $10 monthly fee and $3 per game downloaded. Company Y charges a flat fee of $25 per month for unlimited game downloads. For what number of games downloaded per month is the cost of both services exactly the same?

5 games (Correct answer)
3 games
6 games
4 games

Correct answer: 5 games

Let 'g' be the number of games. The cost for Company X is C = 3g + 10. The cost for Company Y is C = 25. To find when the costs are equal, set the expressions equal to each other: 3g + 10 = 25. Subtract 10 from both sides: 3g = 15. Divide by 3: g = 5. At 5 games, the cost for both services is $25.

Question 29: A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?

6 cups (Correct answer)
4 cups
7 cups
5 cups

Correct answer: 6 cups

The ratio 3:2 scales by a factor of 3 when flour becomes 9, so sugar = 2 × 3 = 6 cups.

Question 30: If 14 cups of yogurt and 4 cups of strawberry crystals are needed to make a strawberry pie, what is the ratio of yogurt and strawberry crystals that is used for the recipe?

7: 3
7: 2 (Correct answer)
7: 5
7: 4

Correct answer: 7: 2

Explanation: The ratio of yogurt to strawberry crystals used for the recipe is found by dividing the number of cups of yogurt by the number of cups of strawberry crystals. In this case, there are 14 cups of yogurt and 4 cups of strawberry crystals. So, the ratio of yogurt to strawberry crystals is 14:4, which simplifies to 7:2.

Question 31: Consider a visual pattern made of square tiles. Figure 1 has 1 tile, Figure 2 has 4 tiles, and Figure 3 has 9 tiles, arranged in squares. If this pattern continues, how many tiles will be in Figure 6?

12
36 (Correct answer)
25
18

Correct answer: 36

The pattern shows that the number of tiles is the figure number multiplied by itself (the figure number squared). Figure 1: 1×1=1. Figure 2: 2×2=4. Figure 3: 3×3=9. Following this rule, Figure 6 will have 6×6 = 36 tiles.

Question 32: Evaluate the expression: 20 - 4 * (2 + 1)^2

144
16
-16 (Correct answer)
12

Correct answer: -16

Following the order of operations (PEMDAS/BODMAS): First, solve the operation inside the parentheses (2 + 1) = 3. Next, calculate the exponent 3^2 = 9. Then, perform the multiplication 4 * 9 = 36. Finally, perform the subtraction 20 - 36 = -16.

Question 33: A family buys 4 adult movie tickets for $12 each and 3 child tickets for $8 each. They also buy a large popcorn for $10 and use a coupon for $5 off the entire purchase. Which expression correctly calculates their total cost?

4 × 12 + 3 × 8 + 10 - 5 (Correct answer)
4 + 3 × 12 + 8 + 10 - 5
(4 + 3) × (12 + 8) + 10 - 5
4 × (12 + 8) + 3 × 10 - 5

Correct answer: 4 × 12 + 3 × 8 + 10 - 5

To find the total cost, you must first calculate the cost of the adult tickets (4 × $12) and the child tickets (3 × $8). Then, you add the cost of the popcorn ($10) and subtract the coupon ($5). The multiplications must be performed before the addition and subtraction, representing the costs of the groups of tickets.

Question 34: The equation 3x + 4 = 10 can be solved by which of the following methods?

Addition (Correct answer)
Substitution
Division
Multiplication

Correct answer: Addition

Explanation: To solve for x in 3x + 4 = 10, you need to isolate the variable on one side of the equation. Subtracting 4 from both sides gives you 3x = 6. Then, dividing both sides by 3 gives you x = 2. This method is called addition because you're adding or subtracting the same number on both sides of the equation to isolate the variable.

Question 35: A student's test score is 90. To calculate their final grade, the teacher first deducts 1/3 of the points and then adds 7 bonus points. Which of the following represents the student's final grade?

77
60
67 (Correct answer)
97

Correct answer: 67

First, find 1/3 of 90, which is (1/3) * 90 = 30. Then, deduct this amount from the score: 90 - 30 = 60. Finally, add the 7 bonus points: 60 + 7 = 67. The student's final grade is 67.

Question 36: There are 49 boys and 28 girls in a school auditorium. Express the ratio of the number of boys to that of girls.

49:7
7:4 (Correct answer)
28:49
49:28

Correct answer: 7:4

Explanation: Given, the number of boys = 49; and the number of girls = 28. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. This means, (49 ÷ 7)/(28 ÷ 7) = 7/4. Therefore, the ratio of the number of boys to that of girls = 7:4.

Question 37: A concert hall has 20 seats in the first row. Each subsequent row has 3 more seats than the row in front of it. How many seats are in the 8th row?

24
44
41 (Correct answer)
38

Correct answer: 41

This is an arithmetic sequence that starts at 20 with a common difference of 3. You can list the terms: Row 1=20, R2=23, R3=26, R4=29, R5=32, R6=35, R7=38, R8=41. Alternatively, the formula for the nth term is a + (n-1)d, where a=20, n=8, and d=3. This gives 20 + (8-1)*3 = 20 + 7*3 = 20 + 21 = 41.

Question 38: In a class of 50 students, 23 are girls and the remaining are boys. Find the ratio of the number of boys to the number of girls.

25:28
27:23 (Correct answer)
35:30
17:13

Correct answer: 27:23

Explanation: Total number of students = 50; Number of girls = 23. Total number of boys = Total number of students - Total number of girls = 50 - 23 = 27 Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.

Question 39: A map has a scale of 1 inch : 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

175 miles (Correct answer)
150 miles
200 miles
165 miles

Correct answer: 175 miles

3.5 inches × 50 miles per inch = 175 miles.

Question 40: Which of the following is the next number in the sequence: 2, 3, 5, 8, 12, ___?

16
15
17 (Correct answer)
18

Correct answer: 17

The pattern in this sequence is not simple addition; instead, the amount added increases by one each time. To get from 2 to 3, you add 1. From 3 to 5, you add 2. From 5 to 8, you add 3. From 8 to 12, you add 4. Therefore, to find the next number, you must add 5 to 12, which results in 17.

Question 41: The table below shows the relationship between the number of hours a student spends studying (h) and the score they receive on a test (S). Which rule describes this relationship? | Hours (h) | Score (S) | |---|---| | 0 | 65 | | 1 | 72 | | 2 | 79 | | 3 | 86 |

S = h + 65
S = 79h - 7
S = 7h + 65 (Correct answer)
S = 65h + 7

Correct answer: S = 7h + 65

The score (S) starts at 65 when the hours (h) are 0. For each additional hour of studying, the score increases by 7. This can be represented by the equation S = 7h + 65. Let's test it: for h=2, S = 7(2) + 65 = 14 + 65 = 79, which matches the table.

Question 42: In a proportion, if a/b = c/d, which of the following must also be true?

a ÷ c = d ÷ b
a × d = b × c (Correct answer)
a + b = c + d
a − b = c − d

Correct answer: a × d = b × c

In any proportion a/b = c/d, the cross-products are equal: a × d = b × c.

Question 43: The sum of three consecutive odd integers is 87. What is the largest of the three integers?

33
31 (Correct answer)
29
27

Correct answer: 31

Let the smallest odd integer be represented by 'n'. Since consecutive odd integers are 2 apart, the next two are 'n + 2' and 'n + 4'. The sum is n + (n + 2) + (n + 4) = 87. Combining like terms gives 3n + 6 = 87. Subtracting 6 from both sides gives 3n = 81. Dividing by 3 gives n = 27. The three integers are 27, 29, and 31. The largest of these is 31.

Question 44: Find the missing number in the following arithmetic sequence: 4, 10, ___, 22, 28.

17
16 (Correct answer)
15
18

Correct answer: 16

In an arithmetic sequence, the same number is added to get from one term to the next. This is called the common difference. By subtracting consecutive terms (28 - 22 = 6 and 10 - 4 = 6), we find the common difference is 6. To find the missing term, add 6 to the term before it: 10 + 6 = 16. You can verify this by adding 6 again: 16 + 6 = 22.

Question 45: Which one is the best answer? 2/5 + 5/8 =

41/40 (Correct answer)
7 /13
10/40
18 / 20

Correct answer: 41/40

Explanation: To find the sum of 2/5 and 5/8, we need to find a common denominator and then add the fractions. The common denominator for 5 and 8 is 40. Converting 2/5 to have a denominator of 40, we get 16/40. Converting 5/8 to have a denominator of 40, we get 25/40. Adding the fractions, we have: 16/40 + 25/40 = 41/40

Question 46: If 9x = 54, then 8x + 1 =

6
7
49 (Correct answer)
37

Correct answer: 49

Explanation: To find the value of 8x + 1, we need to first solve the equation 9x = 54 to find the value of x. Dividing both sides of the equation by 9, we get: x = 54 / 9 Simplifying, we find: x = 6 Now we can substitute the value of x into the expression 8x + 1: 8(6) + 1 = 48 + 1 = 49 Therefore, if 9x = 54, then 8x + 1 = 49.

Question 47: A baker has 6.5 pounds of flour. A recipe for one batch of cookies requires 1.25 pounds of flour. After making two batches of cookies, how much flour does the baker have left?

4.00 pounds (Correct answer)
4.25 pounds
3.75 pounds
5.25 pounds

Correct answer: 4.00 pounds

First, calculate the total flour used for two batches: 2 * 1.25 pounds = 2.5 pounds. Then, subtract the amount used from the initial amount: 6.5 pounds - 2.5 pounds = 4.00 pounds. The baker has 4.00 pounds of flour left.

Question 48: The total cost (C) of a pizza is determined by a base price of $12 plus $1.50 for each topping (t). Which equation correctly represents this relationship?

C = 1.50(12 + t)
C = 12 + 1.50t (Correct answer)
C = 12t + 1.50
C = 12 - 1.50t

Correct answer: C = 12 + 1.50t

The relationship described is a fixed cost plus a variable cost. The fixed cost, or base price, is $12. This is the starting value. The variable cost depends on the number of toppings, 't', at $1.50 each, which is represented as 1.50t. The total cost is the sum of the base price and the cost of the toppings, leading to the equation C = 12 + 1.50t.

Question 49: What is the value of the expression 3x² - 2y + 5 when x = 4 and y = 7?

39 (Correct answer)
29
15
135

Correct answer: 39

Substitute x=4 and y=7 into the expression. Following the order of operations (PEMDAS/BODMAS), first evaluate the exponent: 4² = 16. Then, perform multiplication: 3 × 16 = 48 and 2 × 7 = 14. The expression becomes 48 - 14 + 5. Finally, perform subtraction and addition from left to right: 48 - 14 = 34, and 34 + 5 = 39.

Question 50: If y + 12 = 10 ‥ 2 What is y?

12
20
10
8 (Correct answer)

Correct answer: 8

Explanation: To solve for 𝑦, first, we simplify the expression on the right side of the equation: 10 × 2 = 20. Then, we subtract 12 from both sides of the equation to isolate y + 12 − 12 = 20 − 12. After simplification, we find that y = 8.

Question 51: A video game is originally priced at $60. It is on sale for 25% off. What is the sale price of the video game?

$45 (Correct answer)
$50
$35
$15

Correct answer: $45

First, calculate the discount amount. 25% of $60 is (25/100) * 60 = 0.25 * 60 = $15. Then, subtract the discount from the original price: $60 - $15 = $45. The sale price is $45.

Question 52: Which of the following lists of numbers is ordered from greatest to least?

-1.5, -3/2, 0, 0.5
0.5, 0, -1.5, -3/2
0.5, 0, -3/2, -1.5 (Correct answer)
-3/2, -1.5, 0, 0.5

Correct answer: 0.5, 0, -3/2, -1.5

To compare the numbers, convert them all to the same format. -3/2 is equal to -1.5. So the numbers are -1.5, -1.5, 0, and 0.5. When ordered from greatest to least, the sequence is 0.5, 0, and then -1.5. Since -3/2 and -1.5 are equal, their order doesn't matter relative to each other. The correct list is 0.5, 0, -3/2, -1.5.

Question 53: The expression `100 - 8x` can be used to represent the amount of water, in gallons, remaining in a tank after `x` minutes. Which of the following statements best describes the meaning of the term `8x` in this context?

The tank is empty after 8 minutes.
The tank started with 8 gallons of water.
The total amount of water that has been drained from the tank after `x` minutes. (Correct answer)
Water is being added to the tank at a rate of 8 gallons per minute.

Correct answer: The total amount of water that has been drained from the tank after `x` minutes.

In the expression `100 - 8x`, the number 100 represents the initial quantity. The term `- 8x` represents the change over time. Since it is being subtracted, it signifies a decrease. The term `8x` itself represents the rate of decrease (8 gallons per minute) multiplied by the time (`x` minutes), which calculates the total amount of water drained after `x` minutes.

Question 54: A taxi company charges $2.50 for the first mile and $0.75 for each additional mile. If 'm' represents the total number of miles traveled, which expression represents the total cost for a ride that is more than one mile?

3.25m
2.50m + 0.75
2.50 + 0.75(m - 1) (Correct answer)
2.50 + 0.75m

Correct answer: 2.50 + 0.75(m - 1)

The cost includes a flat fee of $2.50 for the first mile. The variable 'm' is the total miles. Since the first mile is already paid for by the $2.50 fee, the additional charge of $0.75 applies only to the remaining miles, which is represented by (m - 1). Thus, the total cost is 2.50 + 0.75(m - 1).

Question 55: The line graph below shows the temperature in a city over a 12-hour period. During which two-hour interval did the temperature increase at the highest rate? [A line graph shows 'City Temperature'. The x-axis is 'Time of Day' from 6 AM to 6 PM in 2-hour increments. The y-axis is 'Temperature (°F)' from 40 to 70. The data points are: 6 AM at 45°F, 8 AM at 50°F, 10 AM at 60°F, 12 PM at 65°F, 2 PM at 68°F, 4 PM at 67°F, 6 PM at 62°F.]

12 PM to 2 PM
6 AM to 8 AM
8 AM to 10 AM (Correct answer)
4 PM to 6 PM

Correct answer: 8 AM to 10 AM

To find the highest rate of increase, look for the steepest upward slope on the graph. Calculate the temperature change for each interval: 6-8 AM: 50-45 = 5°F increase. 8-10 AM: 60-50 = 10°F increase. 12-2 PM: 68-65 = 3°F increase. 4-6 PM: 62-67 = 5°F decrease. The greatest increase was 10°F, which occurred between 8 AM and 10 AM.

Question 56: Tiffany walked 1 mile from home to school. After school, she walked to her friend Joan’s house to wait for her dad to pick her up. Joan’s home is twice the distance from Tiffany’s home to school. How many miles did Tiffany walk by the time her dad picked her up?

6 miles
3 miles (Correct answer)
5 miles
2 miles

Correct answer: 3 miles

Explanation: Tiffany walked 1 mile from home to school. Joan's house is twice the distance from Tiffany's home to school, so it is 2 miles from Tiffany's home. Therefore, the distance from the school to Joan's house is also 2 miles. Adding these distances together, Tiffany walked a total of 1 mile+2 miles=3 miles.

Question 57: If 5 notebooks cost $7.50, what is the cost of 8 notebooks at the same rate?

$12.00 (Correct answer)
$11.50
$10.00
$13.50

Correct answer: $12.00

Unit cost = $7.50 ÷ 5 = $1.50 per notebook; 8 × $1.50 = $12.00.

Question 58: Which of the following expressions represents the sum of 5 and twice x?

5x + 2
5 + X/2
2x + 5
X + 5 (Correct answer)

Correct answer: X + 5

Explanation: The sum of 5 and twice x is represented by the expression x + 5, as "twice x" is equivalent to 2x, and the sum of 5 and 2x is x + 5.

Question 59: The ratio 8:12 is the same as:

2:3 (Correct answer)
1:2
3:4
4:6

Correct answer: 2:3

Dividing both 8 and 12 by their GCF of 4 gives 2:3.

Question 60: The formula for converting temperature from Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32. A scientist records a temperature of 25°C. What is the equivalent temperature in Fahrenheit?

77°F (Correct answer)
57°F
45°F
102°F

Correct answer: 77°F

To solve this, substitute 25 for C in the given formula: F = (9/5) * 25 + 32. First, calculate (9/5) * 25. This simplifies to 9 * 5, which is 45. Then, add 32 to this result: F = 45 + 32. The final answer is 77°F.

IAAT - Iowa Algebra Aptitude Test

The Iowa Algebra Aptitude Test (IAAT) is a 60-question standardized assessment that measures students' readiness for algebra coursework. It is typically administered to students in grades 7–8 and evaluates pre-algebraic skills, mathematical reasoning, and symbolic thinking across four timed sections.

Questions

40 min

Time Limit

91%

To Pass

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds