MK Practice Test 3: Functions, Angles and Triangles

Answer: D

Correct answer: Isosceles. Classify by sides by counting equal lengths. Exactly two sides are 9 inches, so at least two sides match and the triangle is isosceles.

• A: This is an angle classification, and the sides fail the test anyway: 81 + 81 = 162 is not 196.
• B: Equilateral requires all three sides to be equal; the 14-inch side is different.
• C: A scalene triangle has no equal sides, but this one has two equal 9-inch sides.
• D (correct): Two of the sides are equal (9 and 9), which is exactly the definition of isosceles.

Answer: C

Correct answer: [-1, ∞). The solution starts at −1, which is included because of ≥, so use a bracket. It continues forever to the right, and infinity always gets a parenthesis: $[-1,\infty )$.

• A: A parenthesis at −1 would leave out the boundary, but ≥ includes it.
• B: Infinity is not a number that can be reached, so it never gets a bracket.
• C (correct): A bracket includes −1, and infinity always takes a parenthesis.
• D: This describes values at most −1, the side opposite the solution.

Answer: A

Correct answer: 48. A multiple of 12 is 12 times a whole number. Since

the number 48 is a multiple of 12. The numbers 4 and 6 are factors of 12, and 66 is not divisible by 12.

• A (correct): 12 × 4 = 48, so 48 is a multiple of 12.
• B: 6 divides 12, so it is a factor of 12, not a multiple of it.
• C: 4 divides 12, so it is a factor of 12, not a multiple of it.
• D: 66 = 6 × 11 is a multiple of 6, but 66 ÷ 12 leaves a remainder of 6.

Answer: A

Correct answer: {(1, 3), (2, 5), (1, 7)}. A relation fails to be a function only when one input has two different outputs. In {(1, 3), (2, 5), (1, 7)}, the input 1 goes to both 3 and 7.

• A (correct): The input 1 is paired with two different outputs, 3 and 7, so this relation breaks the one-output rule.
• B: Every input appears once with a single output, so this is a function.
• C: The pair (5, 1) is just listed twice; input 5 still has only one output, so this is a function.
• D: Several inputs sharing the output 4 is allowed; each input still has only one output.

Answer: A

Correct answer: 660 square feet. Lateral area is base perimeter times length: (5 + 12 + 13) times 20 = 600. Each triangular end is half of 5 times 12, or 30.

• A (correct): The side faces give perimeter 30 times 20, or 600, and the two triangle ends add 30 each, for 660.
• B: This is the lateral area only; the two triangular ends must be added.
• C: This adds only one triangular end; a prism has two matching bases.
• D: This treats each end as 5 times 12, forgetting the one half for a triangle.

Answer: C

Correct answer: HL. For right triangles, a matching hypotenuse and a matching leg are enough to prove congruence; this is the HL (hypotenuse-leg) shortcut.

• A: SSA is not a valid shortcut in general; only the right-triangle case, HL, works.
• B: AAA is not a congruence test; matching angles fix the shape but not the size.
• C (correct): HL applies to right triangles with an equal hypotenuse and an equal leg, exactly the facts given.
• D: ASA needs two angles and the side between them; here only one angle (the right angle) is known to match.

Answer: C

Correct answer: 15 hours. Set the rule equal to the output:

Subtract 840:

Divide by −35: h = 15 hours. Check:

• A: This divides 315 by 35, treating the amount remaining as the amount drained.
• B: This divides 840 by 35, which is the time to empty the tank completely.
• C (correct): Solving 840 − 35h = 315 gives 35h = 525, so h = 15.
• D: This adds 315 to 840 instead of subtracting, giving 1,155 ÷ 35.

Answer: C

Correct answer: 44 feet. Let L and S be the lengths:

Adding gives 2L = 88, so L = 44 feet (and S = 28 feet; check

).

• A: This is the shorter piece, (72 − 16)/2, not the longer one.
• B: This subtracts 16 from 72 without splitting the remainder between the two pieces.
• C (correct): Adding L + S = 72 and L − S = 16 gives 2L = 88, so the longer piece is 44 feet.
• D: This cuts the cable in half, ignoring that one piece is 16 feet longer.

Answer: D

Correct answer: 76°. Adjacent angles along a straight line total 180°:

so 3x = 114 and x = 38. The angle asked for is 2x = 76°.

• A: 38 is x; the question asks for the angle labeled 2x.
• B: This uses 360° instead of 180° (3x = 294), but angles along a line total 180°.
• C: This uses 90° as the total (3x = 24), but the angles fill a straight line, which is 180°.
• D (correct): 3x = 180 - 66 = 114, so x = 38 and 2x = 76°.

Answer: D

Correct answer: 36. The rises between points are 1, 3 and 5, so the rate of change is not constant and no single slope fits. Use the equation directly: y = 6 squared = 36.

• A: This extends a straight line using the last step's rise of 5 per unit, but the rate keeps changing on a curve.
• B: This draws a straight line from (0, 0) to (3, 9) with slope 3 and extends it, which a curve does not follow.
• C: This doubles x instead of squaring it.
• D (correct): The rule y = x squared gives 6 times 6, or 36.

Answer: B

Correct answer: 20 liters. Volume: 40 times 25 times 30 is 30,000 cubic centimeters. Since 1 liter is 1000 cubic centimeters, that is 30 liters. Two thirds of 30 is 20 liters.

• A: This is the full capacity; the cooler is filled only two thirds of the way.
• B (correct): The cooler holds 30,000 cubic centimeters, or 30 liters, and two thirds of that is 20 liters.
• C: This divides 20,000 cubic centimeters by 100 instead of 1000.
• D: This divides 20,000 cubic centimeters by 10,000; one liter is 1000 cubic centimeters.

Answer: C

Correct answer: 102°. The whole angle is

A linear pair totals 180°:

so 5x = 160 and x = 32. The partner is

°; check:

• A: This is angle JOL itself, not its partner in the linear pair.
• B: This is one half of angle JOL, 32 + 7.
• C (correct): The whole angle is 2x + 14, and (2x + 14) + (3x + 6) = 180 gives x = 32, so the partner is 3(32) + 6 = 102.
• D: This is the value of x, not an angle measure.

Answer: A

Correct answer: 1.6 × 10⁶. Divide the capacity by the size of one photo. Divide the fronts:

Subtract the exponents:

The drive holds $1.6\times 10^6$ photos.

• A (correct): 4 ÷ 2.5 = 1.6 and 12 − 6 = 6.
• B: This multiplies capacity by photo size instead of dividing.
• C: This divides 2.5 by 4, flipping the front numbers, which gives 0.625 instead of 1.6.
• D: This divides the exponents, 12 ÷ 6, instead of subtracting them.

Answer: B

Correct answer: (4, 11). A point is on the circle when its distance from the center equals the radius. For (4, 11), the changes are

The other points give sums of squares of 52, 68, and 200, none equal to 100.

• A: The changes are 10 and 10, so the distance is $\sqrt{200}\approx 14.1$ and the point is outside.
• B (correct): The changes from the center are 6 and 8, and $\sqrt{36+64}=10$, which equals the radius.
• C: The changes 8 and 2 add to 10, but the distance is $\sqrt{68}\approx 8.2$, so the point is inside.
• D: The changes 6 and 4 add to 10, but the distance is $\sqrt{52}\approx 7.2$, so the point is inside.

Answer: C

Correct answer: 16 + 2π feet. Count only the outside edges: two sides of 6 feet and the bottom of 4 feet give 16 feet. The semicircle has radius 2, so its curve is

The total trim is $16+2\pi$ feet.

• A: This uses a full circle's circumference with diameter 4 for the top instead of half of it.
• B: This also counts the rectangle's top edge, which is hidden inside the window where it meets the semicircle.
• C (correct): The outside edge is two 6-foot sides, the 4-foot bottom and a curved top of half of 4 pi, which totals 16 + 2 pi feet.
• D: This leaves out the 4-foot bottom edge, which is part of the outside of the window.