MK Practice Test 6: Full Mathematics Knowledge Review

Answer: B

Correct answer: {1, 5, 9}. The range is every second coordinate that appears: 5, 9, 5 and 1. Listing each value once gives {1, 5, 9}.

• A: This keeps only the smallest and largest outputs and leaves out 5, which is also produced.
• B (correct): The range is the set of outputs produced: 5, 9, 5 and 1, which is {1, 5, 9} once the repeat is listed once.
• C: These are the inputs, so this is the domain, not the range.
• D: This mixes inputs and outputs together; the range uses only the outputs.

Answer: A

Correct answer: 12. Since

the principal square root is 12. The radical sign means the nonnegative root, so −12 is not the value.

• A (correct): 12 × 12 = 144, and the radical sign gives the nonnegative root.
• B: This divides 144 by 2 instead of finding a number that times itself gives 144.
• C: (−12)² is 144, but the radical sign means the principal, nonnegative root.
• D: 14 squared is 196, not 144.

Answer: C

Correct answer:

Divide both sides by −5. Because the divisor is negative, the sign reverses:

Check x = 0: 0 < 30 is true, and

• A: This treats −5 as +5, losing both the negative result and the required flip.
• B: This divides by −5 correctly but forgets to reverse the inequality sign.
• C (correct): Dividing both sides by −5 gives −6 and reverses the sign, so x > −6.
• D: The sign was reversed, but 30 divided by −5 is −6, not 6.

Answer: D

Correct answer: Quadrant II. The x-coordinate -4 means 4 units left and the y-coordinate 7 means 7 units up. Left and up is the upper-left region, Quadrant II, with signs (-, +).

• A: Quadrant I needs both coordinates positive, but x = -4 is negative.
• B: Quadrant IV has the pattern (+, -); this point has the opposite pattern.
• C: Quadrant III needs both coordinates negative, but y = 7 is positive.
• D (correct): x is negative and y is positive, the (-, +) sign pattern of Quadrant II.

Answer: C

Correct answer: 0. Substitute with parentheses: $2(-3{)}^2+5(-3)-3$.

Square first:

• A: This treats $(-3{)}^2$ as −9, but a squared negative number is positive.
• B: This multiplies 2 by −3 first and then squares, which ignores the order of operations.
• C (correct): Squaring first gives $2(9)+5(-3)-3=18-15-3=0$.
• D: This treats $5(-3)$ as +15 instead of −15.

Answer: B

Correct answer: 432 square inches. A square foot is 12 inches by 12 inches, or 144 square inches.

• A: This converts only one square foot and does not multiply by 3.
• B (correct): One square foot is 144 square inches, and 3 times 144 is 432.
• C: This multiplies by 1728, the cubic factor, which is for volume, not area.
• D: This multiplies by 12, the linear factor, instead of 12 squared.

Answer: B

Correct answer: 92°. Corresponding angles are equal when the lines are parallel:

Then 32 = 2x, so x = 16, and each angle is

°.

• A: This is the supplement of the correct angle, not the corresponding angle itself.
• B (correct): Setting 5x + 12 = 7x - 20 gives x = 16, and 5(16) + 12 = 92.
• C: This is the value of x; the question asks for the angle measure.
• D: This moves the -20 across without changing its sign, getting 2x = 8 and x = 4.

Answer: D

Correct answer: x = 9. Left side:

Right side: $2x+6$.

Then

Subtract 2x and add 12:

Check: both sides equal 24.

• A: This flips only the first sign after the minus, writing −x + 7 instead of −x − 7.
• B: This distributes the 2 on the right only to x, writing 2x + 3.
• C: This subtracts 12 from 6 instead of adding 12 to both sides.
• D (correct): Simplifying gives 4x − 12 = 2x + 6, so 2x = 18 and x = 9.

Answer: B

Correct answer: 2. Rewrite subtraction of a negative as addition: 5 + 8 + (−11). Then

• A: This drops all the signs and adds 5 + 8 + 11.
• B (correct): 5 + 8 = 13, and 13 + (−11) = 2.
• C: This swaps the signs of both terms, computing 5 − 8 + 11.
• D: This subtracts 8 instead of adding it, giving 5 − 8 − 11.

Answer: A

Correct answer: 188 square inches. Bottom: 10 times 6 is 60. Long sides: 2 times 10 times 4 is 80. Short sides: 2 times 6 times 4 is 48.

Total:

The open top is not counted.

• A (correct): Bottom 60 plus long sides 80 plus short sides 48 gives 188.
• B: This counts only the four sides and leaves out the bottom.
• C: This is the surface area of a closed box; the missing top of 60 was counted.
• D: This is the volume, 10 times 6 times 4, which measures capacity in cubic inches.

Answer: D

Correct answer: 24. Factor both:

Take the shared primes at their smaller powers:

• A: 12 divides both numbers, but it is not the greatest common factor; 24 is larger and also works.
• B: This uses only one 2 and one 3 instead of the lower power of each shared prime.
• C: This is the least common multiple, which uses the highest powers of every prime.
• D (correct): Shared primes at the lower powers give $2^3\times 3=24$, and 24 divides both numbers.

Answer: D

Correct answer: 115 degrees. The exterior angle equals the sum of the remote interior angles:

so 2x = 30 and x = 15. The exterior angle is 65 degrees, so the adjacent interior angle is

Check: the remote angles are 34 and 31, and

• A: This is the value of x, not an angle measure.
• B: This is the larger remote interior angle, 2x + 4, which does not touch the exterior angle.
• C: This is the exterior angle itself; the adjacent interior angle forms a straight line with it.
• D (correct): Solving 5x - 10 = 3x + 20 gives x = 15, so the exterior angle is 65 and the adjacent interior angle is 180 - 65 = 115.

Answer: B

Correct answer: 15 mph. Downstream speed is

Upstream speed is

Adding gives 2b = 30, so b = 15 mph and the current is 3 mph.

• A: This is the average speed for the round trip, 72 miles in 5 hours, not the still-water speed.
• B (correct): Downstream b + c = 18 and upstream b − c = 12; adding gives 2b = 30, so b = 15 mph.
• C: This is the downstream speed, which includes help from the current.
• D: This is the speed of the current, not the boat.

Answer: C

Correct answer: A rectangle that is not a square. Diagonals that bisect each other mean the figure is a parallelogram. A parallelogram with equal diagonals is a rectangle. Since the diagonals are not perpendicular, it cannot be a square, so it is a rectangle that is not a square.

• A: A rhombus's diagonals cross at right angles, and a non-square rhombus has unequal diagonals.
• B: A kite's diagonals are perpendicular, and generally only one of them is cut in half.
• C (correct): Bisecting diagonals make it a parallelogram, equal diagonals make it a rectangle, and non-perpendicular diagonals rule out a square.
• D: A square's diagonals are equal and bisect each other, but they are also perpendicular, which this figure lacks.

Answer: B

Correct answer: 64 - 16π square inches. The square has area

The quarter circle has area

Subtracting gives $64-16\pi$, about 13.7 square inches.

• A: This takes one eighth of the full circle's area, as if the slice were 45 degrees instead of 90.
• B (correct): The square is 64 and the quarter circle is one fourth of 64 pi, or 16 pi, so the outside part is 64 minus 16 pi.
• C: This subtracts the arc length, 4 pi, which is a length rather than the quarter circle's area.
• D: This is the area of the quarter circle itself, the part inside the arc rather than outside it.