Mathematics Knowledge Practice Test 11

Correct answer: C — 16 feet

Let the two equal sides be s. The third side is $$s + 4$$. The perimeter is the sum of all three sides: $$s + s + (s + 4) = 40$$. Simplify: $$3s + 4 = 40$$. Subtract 4: $$3s = 36$$. Divide by 3: $$s = 12$$. The third side is $$s + 4 = 12 + 4 = 16$$ feet.

Correct answer: C — 35°, 35°, 70°, 220°

Let the two equal angles be x and x. The third angle is $$x + x = 2x$$. The sum of these three angles is $$x + x + 2x = 4x$$. The fourth angle is $$2(4x) - 60 = 8x - 60$$. The sum of all four interior angles in any quadrilateral is $$360^\circ$$: $$x + x + 2x + (8x - 60) = 360$$. Combine terms: $$12x - 60 = 360 \Rightarrow 12x = 420$$ (Let's verify: for 35°, 35°, 70°, 220° sum is 360, and $$2(35+35+70) - 60 = 2(140) - 60 = 220$$). Therefore, the angles are 35°, 35°, 70°, and 220°.

Correct answer: A — 140°

A full pie represents 360°, so half a pie represents 180°. After cutting out a 40° slice for your roommate, the remaining portion of your half-pie is $$180^\circ - 40^\circ = 140^\circ$$

Correct answer: D — 100°

The remaining half of the pizza is 180°. After cutting a 30° slice for Jeff, there is $$180^\circ - 30^\circ = 150^\circ$$ left for Sadie and Angie. Let Sadie's share be x, making Angie's share $$2x$$. Together they eat $$x + 2x = 3x = 150^\circ$$. Solving for x gives $$x = 50^\circ$$ (Sadie's share). Angie's piece is twice as much: $$2 \times 50^\circ = 100^\circ$$

Correct answer: A — 45°, 135°

Supplementary angles add up to 180°. Let the first angle be x, so the second angle is $$3x$$. Their sum is $$x + 3x = 4x = 180^\circ$$. Solving for x gives $$x = 45^\circ$$. The other angle is $$3 \times 45^\circ = 135^\circ$$. Thus, the angles are 45° and 135°.

Correct answer: A — $$(1, 2), (2, 4), (3, 6)$$

Collinear points lie on the exact same straight line. For the points (1, 2), (2, 4), and (3, 6), all points satisfy the linear equation $$y = 2x$$ (constant slope of 2), meaning they are collinear.

Correct answer: B — 30°, 60°

In a right triangle, the two acute angles must sum up to 90°. Given the ratio $$1:2$$, let the angles be x and $$2x$$. Therefore, $$x + 2x = 90^\circ \Rightarrow 3x = 90^\circ \Rightarrow x = 30^\circ$$. The angles are 30° and $$2x = 60^\circ$$

Correct answer: C — approximately 0.503 in²

Step 1: Find the area of the larger token using $$A = \pi(\frac{d}{2})^2$$. Radius = 0.5 in, so Area $$= \pi(0.5)^2 = 0.25\pi \approx 0.7854$$ in².

Step 2: Find the area of the small disk. Radius = 0.3 in, so Area $$= \pi(0.3)^2 = 0.09\pi \approx 0.2827$$ in².

Step 3: Subtract the disk's area from the token's area: $$0.7854 - 0.2827 = 0.5027$$ in², which rounds to approximately 0.503 in².

Correct answer: C — 35 cm²

The formula for the area of a trapezoid is $$A = \frac{1}{2} (b_1 + b_2)h$$, where b₁ and b₂ are the lengths of the bases and h is the height. Plugging in the given values: $$A = \frac{1}{2} (6 + 8) \times 5 = \frac{1}{2} (14) \times 5 = 7 \times 5 = 35$$ cm².

Correct answer: C — approximately 13.19 inches

The circumference of a circle is calculated using the formula $$C = \pi d$$. Given that the diameter (d) is 4.2 inches, multiply 4.2 by $$\pi$$ (approximately 3.14159): $$C = 4.2 \times 3.14159 \approx 13.19$$ inches.