FTCE 01, 02, 04 math practice

Multiple Select

Which of the following statements demonstrate the property of transitivity?

• If a > b and b > c, then a > c.

• If a = b and b = c, then a = c.

• If a < b and b < c, then a < c.

• If a + b = c and b + c = d, then a + b + c = d.

Multiple Choice

Explain the concept of transitivity and give an example from everyday life where this property is used.

• Transitivity is the property where if A is related to B and B is related to C, then A is related to C. An example is social relationships: if Alice is friends with Bob, and Bob is friends with Charlie, then Alice is connected to Charlie.
• Transitivity is the idea that if A is true, then B must be false. An example is social relationships: if Alice is friends with Bob, and Bob is friends with Charlie, then Alice is connected to Charlie.

• An example of transitivity is a recipe where A and B are ingredients. An example is social relationships: if Alice is friends with Bob, and Bob is friends with Charlie, then Alice is connected to Charlie.

• Transitivity means A is always equal to B.

  An example is social relationships: if Alice is friends with Bob, and Bob is friends with Charlie, then Alice is connected to Charlie.

Multiple Choice

A matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

• 5
• 4

• 3

• 2

Multiple Choice

B matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

• 2
• 3

• 6

• 7

Multiple Choice

C matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

• 7
• 8

• 9

• 6

Multiple Choice

D matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

• 6
• 7

• 8

• 9

Multiple Choice

H matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

• 9
• 8

• 7

• 6

Multiple Choice

If a tower is 20 m, a tree is 15 m, and a pole is 10 m, then the tallest object is ___.

• tower
• tree

• pole

Multiple Choice

Which of the following best describes tiling in geometry?

• Covering a plane with shapes without gaps or overlaps

• Arranging shapes randomly on a plane

• Stacking shapes on top of each other

• Filling a plane with only circles

Multiple Choice

If a student is having problems conceptualizing how to find the area of a shape, why would a teacher assign a titling question for finding the area?

• A teacher assigns a titling question to help students conceptualize the process of finding the area by focusing their thinking.
• A teacher assigns a titling question to distract students from the main topic of area.
• A titling question is used to test students' memorization of formulas for area.
• A teacher assigns a titling question to confuse students about area calculations.

Multiple Choice

If numbers are equal to the same number, then they are equal to each other. If a=b and b=c, then a=c is?

• Reflexive Property of Equality

• Transitive Property of Equality

• Symmetric Property of Equality

• Addition property of Equality

Multiple Choice

Given the following tile pattern, how many tiles would be in the 5th shape?

• b = 8
• b = 11
• b = 7
• b = 9

Multiple Choice

Is the pattern below a growing pattern or a repeating pattern?

• Repeating because it is an A B C pattern.

• Repeating because it uses the same shapes over and over.

• Growing because there is a change and it does not repeat.

• Shrinking because it gets smaller.

Multiple Choice

Are these patterns the same?

• Yes, they are both repeating. The core of the pattern is AB.

• Yes, both patterns are decreasing. The rule is subtracting by 1.

• The patterns are different. Top one is Repeating Core is AB. The bottom one is adding by 1.

• The patterns are different because one is shapes and the other is fruit.

Multiple Choice

What is the area of the following figure? (just type the number

• 23
• 23 square units
• 23 su

Multiple Choice

What does the term 'iteration' mean in the context of algorithms?

• Repeating a process or operation

• Sorting a list

• Adding numbers

• Drawing shapes

Multiple Choice

Find the rule for the table.

• Add 4
• Multiply by 2
• Multiply by 4
• Divide by 6

Multiple Choice

Hilda is making a repeating pattern with shapes shown in the image. The rule is "Heart, Square, Triangle." If Hilda continues the pattern, what will be the 11th shape?

• square

• heart

• triangle

Multiple Choice

The house numbers on a street follow the rule "Subtract 5". What are the next three house numbers if the first house is 25? Choose the correct house numbers and an accurate feature of the pattern.

• 20, 15, 10- they're all multiples of 5

• 21, 18, 15- they're all multiples of 3

• 30, 35, 40- they're all multiples of 5

• 20, 15, 10- they're all multiples of 10

Multiple Choice

Football players come out of the tunnel and their jerseys have the number pattern shown above:

What rule does the pattern follow

• Add 3

• Add 4

• Add 5

• Add 6

Multiple Choice

In the sequence 3, 7, 11, 15, ___, the next term is _______.

• 19
• 20

• 23

• 27

Multiple Choice

Explain how iteration can be used to generate a sequence in an algorithm. Give an example.

• Creating a sequence by multiplying the previous number by 2.
• Generating a sequence by randomly selecting numbers from a list.
• An example of using iteration to generate a sequence is creating the Fibonacci sequence: start with 0 and 1, then repeatedly add the last two numbers to generate the next number.
• Using recursion to generate a sequence of prime numbers.

Multiple Choice

In the sequence 20, 17, 14, 11, ___, the next term is _______.

• 8
• 9

• 7

Multiple Choice

What is the rule used in the sequence 2, 6, 18, 54, ...?

• Add 4

• Multiply by 3

• Subtract 2

• Divide by 2

Multiple Choice

Which type of assessment is used to identify students' strengths and weaknesses before instruction begins?

• Summative Assessment

• Formative Assessment

• Diagnostic Assessment

• Performance-Based Assessment

Multiple Choice

What does 'subitizing' refer to?

• Counting objects one by one

• Instantly recognizing the number of objects in a small group without counting

• Estimating large quantities

• Adding numbers quickly

Multiple Choice

Max is 183 cm tall. Ruby is 169 cm tall. How much taller is Max than Ruby?

• 12 cm
• 16cm
• 14 cm
• 18cm

Multiple Choice

The bakery has 381 chocolate cupcakes and 346 vanilla cupcakes. How many total cupcakes does the bakery have?

• 727 cupcakes
• 725 cupcakes
• 720 cupcakes
• 729 cupcakes

Multiple Choice

The bakery has 381 chocolate cupcakes and 346 vanilla cupcakes. How many more chocolate cupcakes are at the bakery?

• 25 cupcakes
• 45 cupcakes
• 35 cupcakes
• 36 cupcakes

Multiple Choice

Name the type of assessment utilized by an exit ticket.

• Formative
• Summative
• Traditional 
• Authentic

Multiple Choice

What type of assessment is a 3D model?

• formative
• summative
• traditional
• authentic

Multiple Choice

Name the type of assessment utilized by a unit test.

• Formative
• Summative

Multiple Choice

Which of the following best describes iteration in mathematics?

• Repeating a process or operation

• Covering a plane with shapes

• Instantly recognizing the number of objects

• Evaluating at the end of a unit

Multiple Choice

Name the type of assessment utilized by a performance rehearsal.

• Formative
• Summative

Multiple Choice

Name the type of assessment utilized by a final project

• formative
• summative

Multiple Select

Which of the following are included in the operations focused on in Competency 01?

• Fractions

• Decimals

• Integers

• Percentages

Multiple Choice

Which of the following is NOT a rational number?

• 3/4

• 0.25

• π

• 2

Multiple Choice

Numbers such as 1, 2, and 3 are called ___ numbers.

• natural
• rational

• integers

• non-Integers

Multiple Choice

what would we call these numbers, -2, -1, 0, 1, 2

• Rational numbers
• Natural numbers
• Whole numbers
• Integers

Multiple Choice

What would we call these group of numbers, 0.5, 1/2, Pi?

• integers

• Non-Integers

• Natural Numbers

• Rational numbers

Multiple Choice

What would we call these group of positive whole numbers- 1, 2, 3, 4...

• Non-Integers

• Rational numbers
• Natural numbers
• Integers

Multiple Choice

Which model represents fractions as parts of a divided area, such as 3/4 as 3 of 4 equal rectangle parts?

• Linear Model

• Set Model

• Area Model

• Decimal Model

Multiple Choice

Explain how you could use compensation to solve a subtraction problem more easily. Give an example.

• 23
• 10
• 30
• 15

Multiple Choice

Which problem does the model represent?

• $$\frac{1}{5}\times\frac{2}{6}$$

• $$\frac{1}{3}\times\frac{2}{5}$$

• $$\frac{2}{5}\times\frac{1}{5}$$

• $$\frac{2}{5}\times\frac{2}{5}$$

Multiple Choice

Linear Model: What is the value of the shaded region?

• $$5$$

• $$\frac{5}{2}$$

• $$5\ \frac{1}{2}$$

• $$11$$

• 6

Multiple Choice

What is the fraction of cups shaded in?

• 1/3

• 2/6

• 4/5

• 3/6

Multiple Choice

Fraction of Stickers
In a pack of 4 stickers, 3/4 are glittery. How many stickers are glittery?

• 3
• 2
• 4
• 1

Multiple Choice

Fraction of Cookies
A plate has 8 cookies, and 1/2 are chocolate chip. How many cookies are chocolate chip?

• 6
• 4
• 8
• 2

Multiple Choice

Linear Model: Use the model to answer the division problem:

$$3\ \frac{3}{4}\div\frac{3}{4}=?$$

• $$5$$

• $$3$$

• $$\frac{3}{4}$$

• $$4$$

Multiple Choice

Linear Model: Choose the equation that matches this tape model.

• $$\frac{2}{3}\div5=$$

• $$5\div\frac{2}{3}=$$

• $$5\ \frac{1}{4}\div\frac{2}{3}=$$

• $$8\div\frac{2}{3}=$$

Multiple Choice

Area Model: What decimal is represented by the shaded part model?

• 0.07
• 0.7
• 7.5
• 0.75

Multiple Choice

Nahom has $0.07. What fraction of a dollar is this?

• 7/100

• 7/10

• 70/100

• 100/7

Multiple Choice

Which fraction is the same as 0.05

• 1/5

• 1/50

• 5/100

• 5/10

Multiple Choice

Area Model: How much of the grid is shaded

• 0.40

• 0.38

• 3.8

• 4.0

Multiple Choice

Which model represents the answer $$\frac{6}{15}$$  ?

Multiple Choice

Set Model: What multiplication problem is represented by the model above?

• 5 x 5

• 1/5 x 5

• 4/5 x 1/5

Operations with fractions

Multiple Choice

Which model correctly shows the problem $$\frac{2}{6}\times\frac{1}{5}$$  ?

Multiple Choice

Which problem does the model represent?

• $$\frac{4}{5}\times\frac{3}{6}$$

• $$\frac{3}{6}\times\frac{4}{5}$$

• $$\frac{4}{5}\times\frac{5}{6}$$

• $$\frac{3}{4}\times\frac{4}{6}$$

Multiple Choice

Which model represents the answer $$\frac{1}{2}$$  ?

Multiple Select

Select TWO models that represent the problem $$\frac{3}{5}\times\frac{1}{4}$$  

Multiple Choice

Select a model that represents the answer $$\frac{4}{12}$$  

Multiple Choice

Which problem does this model represent?

• $$\frac{1}{2}\times\frac{1}{3}$$

• $$\frac{6}{8}\times\frac{1}{2}$$

• $$\frac{6}{8}\times\frac{1}{3}$$

• $$\frac{4}{8}\times\frac{1}{2}$$

Multiple Choice

Which problem does the model represent?

• $$\frac{3}{5}\times\frac{1}{3}$$

• $$\frac{3}{5}\times\frac{1}{5}$$

• $$\frac{1}{5}\times\frac{1}{2}$$

• $$\frac{1}{3}\times\frac{1}{5}$$

Multiple Choice

What multiplication problem is represented by the model above?

• 2 x 3

• 1/3 x 2

• 1/2 x 3

Multiple Choice

What multiplication problem is represented by the model above?

• 4/3 x 3

• 2/4 x 3

• 1/3 x 4

Multiple Choice

What multiplication problem is represented by the model above?

• 2/5 x 3

• 3/5 x 2

• 3 x 1/5

Multiple Choice

What multiplication problem is represented by the model above?

• 1/9 x 6

• 2/6 x 9

• 2/9 x 6

Multiple Choice

What multiplication problem is represented by the model above?

• 1/3 x 2

• 2/3 x 3

• 2/3 x 1

Multiple Choice

What multiplication problem is represented by the model above?

• 3/10 x 4

• 1/10 x 3

• 12/10 x 4

Multiple Choice

What multiplication problem is represented by the model above?

• 4/7 x 7

• 3/7 x 3

• 4/7 x 6

Multiple Choice

What multiplication problem is represented by the model above?

• 1/6 x 6

• 5/6 x 2

• 5/6 x 5

Multiple Choice

What multiplication problem is represented by the model above?

• 7/12 x 3

• 5/12 x 7

• 3/12 x 5

Multiple Choice

The sum of 7/8 and 1/4 is approximately what in fraction and decimal?

• 5/8 and 0.625
• 1 and 1.0
• 9/8 and 1.125
• 3/4 and 0.75

Multiple Choice

Which mental math strategy can be used to solve 48 ÷ 6?

• Use related multiplication

• Estimate using benchmarks

• Round to the nearest ten

• Use a number line

Multiple Choice

What mental math strategies could i used to solve a word problem involving both fractions and decimals?

• Use only multiplication for all calculations
• Convert fractions to decimals or vice versa, use estimation, and apply basic operations.
• Ignore the fractions and decimals entirely
• Rely solely on a calculator without any mental math

Multiple Choice

A bank account has -25 dollars. After a $40 deposit and $15 withdrawal, what is the balance?

• $0

• $30

• -$10

• $15

Multiple Choice

Lynn is simplifying the expression  

$$5\cdot8+9\div3^2$$   . Which steps below best represent how she should simplify this expression? 

Multiple Choice

$$\left(-10\right)\ -\left(-18\right)\ \div3$$  Solve.

• -4
• -3

• -5

• -4

Multiple Choice

$$6-8\div2+3\cdot7$$  

When simplifying the following, using order of operations, which operation should be performed first?

• $$6-4$$  

• $$8\div2$$  

• $$2+3$$  

• $$3\cdot7$$  

Multiple Choice

-8 + (15 - 3) ÷ 4 is equivalent to:

• -5

• 1

• -11

• 11

Multiple Choice

What are the steps to solve the following expression?

50 − 16 ÷ 2 (12 + 4)

• parentheses

  multiplication

  subtraction

  division

• parentheses

  multiplication

  division

  subtraction

• parentheses

  division

  multiplication

  subtraction

• parentheses

  subtraction

  multiplication

  division

Multiple Choice

$$6^2+\left(-14\right)÷\ 2\ –\ (-8)$$  

• 7

• 19

• 13

• 37

Multiple Choice

$$\frac{7\left(5+3\right)}{4\left(9-2\right)}$$  

• 0.5

• 98

• 32

• 2

Multiple Select

Which of the following are equivalent values?

• -3/2 and -1.5

• 5/4 and 1.25

• 2/3 and 0.75

• 3/4 and 0.5

Multiple Choice

What is the fraction at point A on the number line?

• 3/3
• 2/3
• 3/4
• 4/3

Multiple Choice

What is the fraction at point C on the number line?

• 2/6
• 2/5
• 2/4
• 6/2

Multiple Choice

What is the fraction at point B on the number line?

• 4/6
• 4/10
• 4/9
• 3/10

Multiple Choice

Write an Equation.
Joella makes $12.75 per hour. This is $2.50 more than her younger sister makes per hour. How much does Joella's sister make per hour?

• x + 2.50 = 12.75
• 2.50x = 12.75
• x - 2.50 = 12.75
• x/2.50 = 12.75

Multiple Choice

Write an Equation.
Gold costs $1,654 per ounce. How many ounces are needed to be worth $16,540?

• 1,654x = 16,540
• x/1,654 = 16,540
• x - 1,654 = 16,540
• x + 1,654 = 16,540

Multiple Choice

Jacob collects hats. He has 6 hats already and collects 2 more hats each week. How many week would it take Jacob to collect 32 hats?

• 13 weeks

• 12 weeks

• 14 weeks

• 11 week

Open Ended

Reflecting on the content overview, which competency do you feel most confident about, and which one would you like to learn more about?

Multiple Choice

Which of the following topics is NOT covered in the FTCE Mathematics Subtest according to the content overview?

• Operations with fractions, decimals, and integers

• Solving linear equations and identifying patterns

• Properties of 2D/3D shapes and coordinate geometry

• Advanced calculus and trigonometry