TCAP Mathematics — Grade 8

Which of the following numbers is irrational?

• A√16
• B3/8
• C√7
• D0.75

What is the repeating decimal 0.333... (the digit 3 repeats forever) written as a simplified fraction?

• A3/10
• B3/99
• C1/30
• D1/3

Between which two consecutive integers does √30 lie?

• A4 and 5
• B5 and 6
• C6 and 7
• D7 and 8

Simplify the expression 5^3 · 5^4 using the properties of integer exponents.

• A5^12
• B25^7
• C25^12
• D5^7

Simplify 8^9 / 8^3.

• A8^3
• B8^6
• C8^27
• D1^6

Express 0.00045 in scientific notation.

• A4.5 × 10^-3
• B4.5 × 10^-5
• C45 × 10^-5
• D4.5 × 10^-4

What is the value of √144?

• A11
• B12
• C14
• D72

Solve for x: x^3 = 64.

• A4
• B8
• C16
• D21.3

Car A's distance is described by the proportional equation d = 60t, where d is miles and t is hours. Car B's travel is shown by a graph through the origin that passes through the point (3, 195). Which statement correctly compares the two cars' speeds?

• ACar A is faster because its graph is steeper.
• BThe cars travel at the same speed because both graphs pass through the origin.
• CCar B is faster because its unit rate is 65 mph compared with Car A's 60 mph.
• DCar B is faster because 195 is greater than 60.

What is the slope of the line passing through the origin (0,0) and the point (4, 12)?

• A1/3
• B3
• C4
• D8

Solve for x: 2x + 5 = 17.

• A5
• B7
• C11
• D6

Solve for m: 4(m - 2) = 16.

• A4
• B6
• C8
• D10

Which value of x is the solution to 3x = 2x + 9?

• A3
• B6
• C9
• D12

What is the point of intersection for the system of equations y = 2x and y = x + 3?

• A(1, 2)
• B(2, 4)
• C(3, 6)
• D(4, 7)

Which set of ordered pairs represents a function?

• A{(1, 2), (1, 3), (2, 4)}
• B{(2, 5), (3, 5), (4, 5)}
• C{(3, 1), (3, 2), (3, 3)}
• D{(5, 8), (5, 9), (6, 10)}

What is the y-intercept of the linear function y = -4x + 7?

• A-4
• B4
• C7
• D-7

What is the rate of change (slope) of the linear function y = (2/5)x - 3?

• A-3
• B5/2
• C3
• D2/5

Which equation represents a non-linear function?

• Ay = 3x - 1
• By = x/4 + 2
• Cy = x^2 + 5
• Dy = -2x

A gym charges a $20 sign-up fee plus $15 per month. Which equation represents the total cost C for m months?

• AC = 20m + 15
• BC = 15m + 20
• CC = 35m
• DC = 15m - 20

Evaluate the function f(x) = 3x - 4 when x = 5.

• A15
• B19
• C7
• D11

On a distance-time graph, a horizontal straight line segment indicates that the object is:

• AMoving at a constant speed
• BAccelerating rapidly
• CAt rest (not moving)
• DReturning to the starting point

Point P(3, 4) is translated 2 units right and 5 units down. What are the coordinates of the image P'?

• A(1, 9)
• B(5, -1)
• C(5, 9)
• D(1, -1)

Point A(-2, 6) is reflected across the x-axis. What are the coordinates of A'?

• A(2, 6)
• B(-2, -6)
• C(2, -6)
• D(6, -2)

In a triangle, two of the interior angles measure 45° and 75°. What is the measure of the third interior angle?

• A50°
• B60°
• C70°
• D120°

What is the hypotenuse of a right triangle with legs of length 6 cm and 8 cm?

• A12 cm
• B14 cm
• C100 cm
• D10 cm

What is the volume of a cylinder with radius 3 cm and height 10 cm? (Use V = π r^2 h)

• A30π cm³
• B60π cm³
• C90π cm³
• D300π cm³

A cone has a radius of 3 inches and a height of 4 inches. What is its volume using V = (1/3)π r^2 h?

• A12π in.³
• B36π in.³
• C4π in.³
• D16π in.³

A scatter plot shows that as study hours increase, test scores increase. What type of association does this show?

• ANegative linear association
• BNo association
• CNon-linear negative association
• DPositive linear association

A line of best fit for height h (inches) vs shoe size s is s = 0.5h - 22. What shoe size does the model predict for a person 66 inches tall?

• A9
• B11
• C13
• D15

In a survey of 100 students, 60 like basketball and 40 do not. What is the relative frequency of students who like basketball?

• A0.40
• B0.60
• C0.67
• D1.50

Which list orders the numbers π, 3.8, 19/5, √15 from least to greatest?

• Aπ, 3.8 = 19/5, √15
• B√15, π, 3.8, 19/5
• C3.8, 19/5, π, √15
• Dπ, √15, 3.8, 19/5

Convert the repeating decimal 0.4545... (the block 45 repeats forever) to a fraction in simplest form.

• A45/100
• B5/11
• C9/20
• D45/90

Estimate √75 to the nearest tenth.

• A8.2
• B8.7
• C8.9
• D9.1

Convert 0.1666... (the digit 6 repeats forever) to a simplified fraction.

• A16/99
• B1/5
• C16/100
• D1/6

Which of the following describes the position of -√18 on a number line?

• ABetween -3 and -4
• BBetween -4 and -5
• CBetween -5 and -6
• DBetween -2 and -3

What is the exact value of √0.0064?

• A0.008
• B0.08
• C0.8
• D0.0008

Simplify (3 × 10^5) × (4 × 10^-2) and express the result in scientific notation.

• A1.2 × 10^3
• B12 × 10^3
• C1.2 × 10^7
• D1.2 × 10^4

How many times larger is 6 × 10^8 than 3 × 10^4?

• A200
• B2,000
• C20,000
• D200,000

Calculate (5.2 × 10^6) - (3.1 × 10^5) in scientific notation.

• A4.89 × 10^6
• B2.1 × 10^1
• C4.89 × 10^5
• D5.11 × 10^6

Simplify the expression (a^3 b^-2)^2 / (a^-1 b^4).

• Aa^5 b^-8
• Ba^7 b^0
• Ca^5 b^8
• Da^7 b^-8

Solve for x: √x + 9 = 15.

• A6
• B12
• C36
• D144

Solve for y: 5(y - 3) = 2(y + 6).

• A3
• B5
• C7
• D9

Solve for x: 0.4(x + 10) = 0.2x + 7.

• A10
• B15
• C20
• D25

Which equation has infinitely many solutions?

• A2(x + 3) = 2x + 5
• B2(x + 3) = 3x + 6
• C2x + 3 = 6
• D2(x + 3) = 2x + 6

How many solutions does the equation 4x - 7 = 4x + 9 have?

• AExactly one solution
• BNo solution
• CInfinitely many solutions
• DTwo solutions

Solve the system of equations by substitution: y = 3x - 5 and 2x + y = 10. What is the value of x?

• A2
• B3
• C4
• D5

Solve the system using elimination: 3x + 2y = 16 and 3x - 2y = 8. What is the solution (x, y)?

• A(4, 2)
• B(4, 3)
• C(2, 5)
• D(3, 4)