Mathematics Knowledge Practice Test 12

Correct answer: B — 60°

The sum of all interior angles in any triangle is always 180°. To find the third angle, subtract the sum of the two known angles from $$180^\circ$$: $$180^\circ - (55^\circ + 65^\circ) = 180^\circ - 120^\circ = 60^\circ$$

Correct answer: A — 3

In the slope-intercept form of a linear equation, $$y = mx + b$$, the coefficient 'm' represents the slope of the line. For the equation $$y = 3x + \frac{5}{7}$$, the coefficient of x is 3, so the slope is 3.

Correct answer: C — 92 in²

The total surface area of a rectangular prism is calculated using the formula SA = 2(lw + lh + wh). Plugging in the values: SA = $$2(8 \times 2 + 8 \times 3 + 2 \times 3) = 2(16 + 24 + 6) = 2(46) = 92$$ in².

Correct answer: A — 37.68 cm²

Step 1: Find the radius of the larger circle ($$R = \frac{8}{2} = 4$$ cm) and calculate its area: $$A_1 = \pi(4)^2 = 16\pi \approx 50.24$$ cm².

Step 2: Find the radius of the smaller circle ($$r = \frac{4}{2} = 2$$ cm) and calculate its area: $$A_2 = \pi(2)^2 = 4\pi \approx 12.56$$ cm².

Step 3: Subtract the smaller area from the larger area: $$50.24 - 12.56 = 37.68$$ cm².

Correct answer: C — 60 mm

The volume of a rectangular prism is given by Volume = length × width × height ($$V = lwh$$). Given $$V = 3{,}600$$, $$l = 12$$, and $$w = 5$$: $$3600 = 12 \times 5 \times h \Rightarrow 3600 = 60h$$. Dividing both sides by 60 gives $$h = \frac{3600}{60} = 60$$ mm.

Correct answer: A — 343 cm³

The area of one face of a cube is given by $$s^2 = 49$$, which means the edge length $$s = 7$$ cm. The volume of a cube is calculated as $$V = s^3$$. Therefore, $$V = 7^3 = 7 \times 7 \times 7 = 343$$ cm³.

Correct answer: C — 792 cm²

The surface area of a rectangular prism is calculated using the formula SA = 2(lw + lh + wh). Here, length $$l = 12$$, height $$h = 15$$, and width $$w = 8$$. Plugging in the values: SA $$= 2(12 \times 8 + 12 \times 15 + 8 \times 15) = 2(96 + 180 + 120) = 2(396) = 792$$ cm².

Correct answer: B — 301.44 cm³

The volume of a cylinder is calculated using the formula $$V = \pi r^2h$$. Given radius $$r = 4$$ cm, height $$h = 6$$ cm, and $$\pi \approx 3.14$$: $$V = 3.14 \times (4)^2 \times 6 = 3.14 \times 16 \times 6 = 50.24 \times 6 = 301.44$$ cm³.

Correct answer: C — 244.92 cm²

The total surface area of a cylinder is given by SA = $$2\pi rh + 2\pi r^2$$. Given radius $$r = 3$$, height $$h = 10$$, and $$\pi \approx 3.14$$:

Lateral Area $$= 2 \times 3.14 \times 3 \times 10 = 188.4$$ cm².

Two Base Areas $$= 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52$$ cm².

Total Surface Area $$= 188.4 + 56.52 = 244.92$$ cm².

Correct answer: C — 16 square inches

The area of a trapezoid is calculated using the formula $$A = \frac{1}{2} (b_1 + b_2)h$$. Given height $$h = 4$$ inches, base $$b_1 = 5$$ inches, and base $$b_2 = 3$$ inches: $$A = \frac{1}{2} (5 + 3) \times 4 = \frac{1}{2} (8) \times 4 = 4 \times 4 = 16$$ square inches.