Midterm Practice Exam

True or false: 5⁻³ is a negative number, since its exponent is negative.

True or false.

• True
• False

Which slope-intercept equation describes the line through (−2, 1) and (2, 13)?

Select one.

• y = (1⁄3)x + 5⁄3
• y = 3x + 7
• y = −3x − 5
• y = 3x + 1

Line P goes through (−2, 3) and (5, 3). Line Q goes through (1, −4) and (1, 2). What is true of these two lines?

Select one.

• Line P is x = 1 with slope 0, and line Q is y = 3 with an undefined slope
• Both lines have slope 0, because each pair of points shares a coordinate
• Both lines have an undefined slope, because each pair of points shares a coordinate
• Line P is y = 3 with slope 0, and line Q is x = 1 with an undefined slope

A function is defined by g(x) = 4x² + 3x − 7. Find g(−3) and enter it as a whole number.

Type a short answer.

Which interval is the domain of k(x) = √(x + 3)?

Select one.

• (−3, ∞)
• (−∞, −3]
• [3, ∞)
• [−3, ∞)

Find the difference (x² + 3x − 8) − (x² − 4x + 2) in simplest form.

Select one.

• 7x − 10
• −x − 10
• 2x² − x − 6
• 7x − 6

Following the standard order of operations, compute 5 + 2 · 3³.

Select one.

• 189
• 221
• 23
• 59

A rock's height in feet t seconds after it is thrown upward is h(t) = −16t² + 32t + 128. Setting −16t² + 32t + 128 = 0, dividing by −16, and factoring gives (t − 4)(t + 2) = 0. At what time does the rock hit the ground?

Select one.

• At t = 1 second
• At t = −2 seconds
• At t = 4 seconds
• At both t = 4 seconds and t = −2 seconds

To complete the square on x² + 8x + 7 = 0, move the 7 to the right side, halve 8, square that half, and add the result to both sides. What equation do you reach?

Select one.

• (x + 8)² = 57
• (x − 4)² = 9
• (x + 4)² = −7
• (x + 4)² = 9

Mark each pair of slopes that belongs to two perpendicular lines.

Select every option that applies.

• 4⁄5 and −4⁄5
• 4⁄5 and −5⁄4
• 4⁄5 and 5⁄4
• −4⁄5 and 5⁄4

Mark each value of y that satisfies |2y + 3| = 9.

Select every option that applies.

• −3
• 3
• 6
• −6
• 9

Subtracting 2x − y = 11 from 2x − y = 5 gives 0 = −6. What conclusion follows about this system?

Select one.

• Infinitely many solutions, since the system is dependent and its lines coincide
• No solution, since the system is inconsistent and its lines are parallel
• Exactly one solution, located at x = 0
• Exactly one solution, the pair (0, −6)

A smoothie uses three times as many cups of fruit y as cups of yogurt x, with 8 cups in all: y = 3x and x + y = 8. Use substitution to find (x, y).

Select one.

• (6, 2)
• (2, 6)
• (8, 24)
• (4, 4)

A runner totals three training runs as 6 + (8 + 12) kilometers and later as (6 + 8) + 12 kilometers, getting 26 both times. Which property of real numbers explains why regrouping the runs leaves the sum unchanged?

Select one.

• The commutative property
• The associative property
• The distributive property
• The identity property

Which inequality gives all values of m for which −4m ≥ 24?

Select one.

• m ≤ −6
• m ≥ −6
• m ≤ 6
• m ≥ 6

With the quotient rule, compute 3⁸ ⁄ 3⁵ and give the result as a whole number.

Type a short answer.

A ball's height in feet after t seconds is h(t) = −16t² + 32t + 48. At t = 0, 1, 2, 3 its heights are 48, 64, 48, 0, and it reaches the ground at t = 3. Over the domain [0, 3], which interval is the range of h?

Select one.

• [0, 3]
• [0, 64]
• [48, 64]
• [0, 1]

Mark each number that is a solution of x² = −5x.

Select every option that applies.

• 5
• 0
• 25
• −5

Expanding (x + 4)(x − 3) term by term with FOIL gives which polynomial?

Select one.

• x² − 12
• x² + 7x − 12
• x² + x + 12
• x² + x − 12

Using the square root property, which values of x satisfy (x + 2)² = 25?

Select one.

• x = 3 or x = −7
• x = 3 only
• x = −3 or x = 7
• x = 23 or x = −27

True or false: the graphs of y = −5x + 2 and y = −5x − 9 never meet, because the two lines are parallel.

True or false.

• True
• False

Let u(x) = 2x and v(x) = x − 3. Then (u ∘ v)(5) = 4 and (v ∘ u)(5) = 7, which shows that reversing the order of a composition can give a different output.

True or false.

• True
• False

A student plans to cancel y in the system 3x + 2y = 16 and x − y = 2 by multiplying each term of the second equation by 2 before adding. What does the second equation become?

Select one.

• 2x − 2y = 2
• 2x − y = 4
• 2x − 2y = 4
• x − 2y = 4

After distributing and combining like terms, which expression is equivalent to 6y − 4(2y − 3)?

Select one.

• −2y − 12
• −2y − 3
• 14y − 12
• −2y + 12

Multiplying every term of y ⁄ 4 + 1 ⁄ 6 = 7 ⁄ 12 by the least common denominator, 12, removes the fractions. What equation is left?

Select one.

• 3y + 2 = 7
• 3y + 2 = 7 ⁄ 12
• y + 2 = 7
• 3y + 1 = 7