TExES Mathematics 4-8 (115)

Which of the following best describes the relationship between the set of integers and the set of rational numbers?

• AEvery integer is a rational number, but not every rational number is an integer
• BEvery rational number is an integer, but not every integer is rational
• CThe two sets are identical
• DNo integer is a rational number

A student claims that 0.999... (repeating) is less than 1. Which argument correctly shows the two values are equal?

• ALet x = 0.999...; then 10x = 9.999..., so 10x - x = 9, giving 9x = 9 and x = 1
• B0.999... rounds up to 1, so they are equal
• C0.999... has infinitely many digits, so it cannot equal a whole number
• DSince 0.999... never reaches 1, the values are only approximately equal

What is the greatest common factor (GCF) of 48 and 60?

• A6
• B12
• C24
• D240

A recipe requires 3/4 cup of flour per batch. How many cups are needed for 2 1/3 batches?

• A1 1/2 cups
• B1 3/4 cups
• C2 cups
• D2 1/4 cups

Which statement correctly explains why dividing by a fraction is equivalent to multiplying by its reciprocal?

• ADividing asks how many groups of the divisor fit into the dividend, and scaling both by t…
• BReciprocals always equal the original fraction, so the operations are interchangeable
• CDivision and multiplication are the same operation for fractions only
• DThe reciprocal cancels the numerator, leaving the denominator unchanged

Using the standard algorithm for multiplication, what role does the partial product structure illustrate about place value?

• AEach digit is multiplied according to its place value, and partial products are shifted t…
• BPlace value is irrelevant once digits are aligned to the right
• CPartial products must always be added before any multiplication occurs
• DCarrying replaces the need to track place value

How many distinct prime numbers are factors of 360?

• A2
• B3
• C4
• D5

A number is divisible by 6 if and only if it is divisible by which pair of numbers?

• A1 and 6
• B2 and 3
• C3 and 4
• D2 and 4

Which expression is equivalent to writing 0.0000425 in scientific notation?

• A4.25 x 10^-5
• B4.25 x 10^5
• C42.5 x 10^-6
• D4.25 x 10^-4

A store offers a 20% discount, then applies an additional 10% off the discounted price. What single percent discount is equivalent to these two successive discounts?

• A28%
• B30%
• C25%
• D32%

Which of the following is an irrational number?

• Asqrt(2)
• B0.375
• C22/7
• D-4

A teacher wants students to model 3/4 + 1/6 using an area model. What is the most important first step for finding the sum?

• APartition both regions into twelfths so the parts are equal-sized before combining
• BAdd the numerators and denominators directly
• CConvert each fraction to a decimal before adding
• DMultiply the two fractions to combine them

What is the value of (-3)^2 - (-3^2)?

• A18
• B0
• C-18
• D6

Which property is illustrated by the equation 7 x (4 + 9) = 7 x 4 + 7 x 9?

• ADistributive property of multiplication over addition
• BAssociative property of multiplication
• CCommutative property of addition
• DIdentity property of multiplication

A whole number leaves a remainder of 3 when divided by 5 and a remainder of 2 when divided by 4. What is the smallest positive value of this number?

• A18
• B13
• C23
• D8

A sequence begins 2, 5, 10, 17, 26, .... Which expression gives the nth term?

• An^2 + 1
• B3n - 1
• C2n + 1
• Dn^2 + n

What is the slope of the line passing through the points (-2, 3) and (4, -9)?

• A-2
• B2
• C-1/2
• D-6

Which equation represents a line parallel to y = 3x - 4 and passing through the point (0, 2)?

• Ay = 3x + 2
• By = -3x + 2
• Cy = -1/3 x + 2
• Dy = 3x - 4

Solve the equation 3(x - 4) = 2x + 5 for x.

• A17
• B7
• C-7
• D1

The cost C to rent equipment is C = 25 + 8h, where h is the number of hours. What do the numbers 25 and 8 represent in this context?

• A25 is a fixed base fee and 8 is the hourly rate
• B25 is the hourly rate and 8 is the base fee
• C25 is the total cost and 8 is the number of hours
• DBoth represent fixed one-time charges

What are the solutions to the equation x^2 - 5x + 6 = 0?

• Ax = 2 and x = 3
• Bx = -2 and x = -3
• Cx = 1 and x = 6
• Dx = -1 and x = -6

Which feature of the graph of y = (x - 3)^2 + 1 is directly identified by the form of the equation?

• AThe vertex is at (3, 1)
• BThe vertex is at (-3, 1)
• CThe y-intercept is at (3, 1)
• DThe vertex is at (3, -1)

A population doubles every 3 years. If it starts at 500, which expression models the population after t years?

• A500 x 2^(t/3)
• B500 x 2^(3t)
• C500 + 2t/3
• D500 x 3^(t/2)

If f(x) = 2x^2 - 3x + 1, what is the value of f(-2)?

• A15
• B3
• C-1
• D11

Which system of equations has no solution?

• Ay = 2x + 1 and y = 2x - 3
• By = 2x + 1 and y = -2x - 3
• Cy = 2x + 1 and y = 3x - 3
• Dy = 2x + 1 and y = x + 1

The instantaneous rate of change of a function at a point is most closely associated with which concept from calculus foundations?

• AThe slope of the tangent line at that point
• BThe area under the curve up to that point
• CThe y-intercept of the function
• DThe average of all function values

A table shows that y is always 4 times x. Which type of relationship does this represent?

• ADirect proportional (linear through the origin)
• BInverse proportional
• CExponential
• DQuadratic

Simplify the expression 3x + 2(x - 5) - 4.

• A5x - 14
• B5x - 6
• Cx - 14
• D5x + 6

A ball is thrown and its height is modeled by h(t) = -16t^2 + 32t. At what time does the ball reach its maximum height?

• At = 1 second
• Bt = 2 seconds
• Ct = 0.5 second
• Dt = 16 seconds

Which representation best helps middle school students understand that a variable can represent a varying quantity rather than a single unknown?

• AA table of input-output values paired with a graph
• BA single equation solved for one value
• CA list of constants with no relationship
• DA definition stating a variable is always unknown

What is the area of a triangle with a base of 12 cm and a height of 7 cm?

• A42 square cm
• B84 square cm
• C19 square cm
• D21 square cm

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

• A10
• B14
• C48
• D7

What is the sum of the interior angles of a regular hexagon?

• A720 degrees
• B1080 degrees
• C540 degrees
• D360 degrees

A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use V = pi r^2 h.)

• A90 pi cubic cm
• B30 pi cubic cm
• C60 pi cubic cm
• D900 pi cubic cm

Two figures are similar with a scale factor of 3. How does the area of the larger figure compare to the smaller?

• AThe area is 9 times as large
• BThe area is 3 times as large
• CThe area is 6 times as large
• DThe area is 27 times as large