📐 Geometry Mini Mock 25
Recommended: 75–90 minutes. No calculator.
Problems
1.
Tags: Basic Angles · Easy · source: Original (AMC-style)
What is the measure of a right angle?
A) $45°$ B) $60°$ C) $90°$ D) $120°$ E) $180°$
Answer & Solution
Answer: C
A right angle measures $90°$.
2.
Tags: Triangle Angles · Easy · source: Original (AMC-style)
What is the sum of angles in a triangle?
A) $90°$ B) $120°$ C) $150°$ D) $180°$ E) $360°$
Answer & Solution
Answer: D
The sum of angles in any triangle is $180°$.
3.
Tags: Circle Area · Easy · source: Original (AMC-style)
What is the area of a circle with radius 3?
A) $3\pi$ B) $6\pi$ C) $9\pi$ D) $12\pi$ E) $18\pi$
Answer & Solution
Answer: C
Area = $\pi r^2 = \pi \times 3^2 = 9\pi$.
4.
Tags: Rectangle Area · Easy · source: Original (AMC-style)
What is the area of a rectangle with length 5 and width 4?
A) $9$ B) $18$ C) $20$ D) $25$ E) $40$
Answer & Solution
Answer: C
Area = length × width = $5 \times 4 = 20$.
5.
Tags: Pythagorean Theorem · Easy · source: Original (AMC-style)
In a right triangle with legs 3 and 4, what is the hypotenuse?
A) $5$ B) $6$ C) $7$ D) $8$ E) $9$
Answer & Solution
Answer: A
Using $a^2 + b^2 = c^2$: $3^2 + 4^2 = 9 + 16 = 25 = 5^2$, so $c = 5$.
6.
Tags: Square Area · Easy · source: Original (AMC-style)
What is the area of a square with side length 6?
A) $12$ B) $24$ C) $30$ D) $36$ E) $48$
Answer & Solution
Answer: D
Area = side² = $6^2 = 36$.
7.
Tags: Circle Circumference · Easy · source: Original (AMC-style)
What is the circumference of a circle with radius 2?
A) $2\pi$ B) $4\pi$ C) $6\pi$ D) $8\pi$ E) $12\pi$
Answer & Solution
Answer: B
Circumference = $2\pi r = 2\pi \times 2 = 4\pi$.
8.
Tags: Triangle Area · Easy · source: Original (AMC-style)
What is the area of a triangle with base 8 and height 6?
A) $14$ B) $24$ C) $28$ D) $32$ E) $48$
Answer & Solution
Answer: B
Area = $\frac{1}{2} \times$ base × height = $\frac{1}{2} \times 8 \times 6 = 24$.
9.
Tags: Parallelogram Area · Easy · source: Original (AMC-style)
What is the area of a parallelogram with base 7 and height 5?
A) $12$ B) $24$ C) $28$ D) $35$ E) $42$
Answer & Solution
Answer: D
Area = base × height = $7 \times 5 = 35$.
10.
Tags: Trapezoid Area · Easy · source: Original (AMC-style)
What is the area of a trapezoid with bases 4 and 6 and height 3?
A) $12$ B) $15$ C) $18$ D) $21$ E) $24$
Answer & Solution
Answer: B
Area = $\frac{1}{2} \times$ (base1 + base2) × height = $\frac{1}{2} \times (4+6) \times 3 = 15$.
11.
Tags: Similar Triangles · Medium · source: Original (AMC-style)
If two triangles are similar with ratio 2:3, and the smaller triangle has area 4, what is the area of the larger triangle?
A) $6$ B) $8$ C) $9$ D) $12$ E) $16$
Answer & Solution
Answer: C
Area ratio = (side ratio)² = $(2/3)^2 = 4/9$. So larger area = $4 \times (9/4) = 9$.
12.
Tags: Coordinate Distance · Medium · source: Original (AMC-style)
What is the distance between points (0,0) and (3,4)?
A) $3$ B) $4$ C) $5$ D) $6$ E) $7$
Answer & Solution
Answer: C
Distance = $\sqrt{(3-0)^2 + (4-0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.
13.
Tags: Slope · Medium · source: Original (AMC-style)
What is the slope of the line through points (1,2) and (4,8)?
A) $1$ B) $2$ C) $3$ D) $4$ E) $6$
Answer & Solution
Answer: B
Slope = $\frac{8-2}{4-1} = \frac{6}{3} = 2$.
14.
Tags: Volume · Medium · source: Original (AMC-style)
What is the volume of a cube with side length 3?
A) $9$ B) $18$ C) $27$ D) $36$ E) $54$
Answer & Solution
Answer: C
Volume = side³ = $3^3 = 27$.
15.
Tags: Regular Polygon · Medium · source: Original (AMC-style)
What is the sum of interior angles in a hexagon?
A) $540°$ B) $720°$ C) $900°$ D) $1080°$ E) $1260°$
Answer & Solution
Answer: B
Sum = $(n-2) \times 180° = (6-2) \times 180° = 4 \times 180° = 720°$.
16.
Tags: Circle Sector · Medium · source: Original (AMC-style)
What is the area of a sector with central angle 60° in a circle of radius 6?
A) $\pi$ B) $2\pi$ C) $3\pi$ D) $6\pi$ E) $12\pi$
Answer & Solution
Answer: D
Area = $\frac{60°}{360°} \times \pi r^2 = \frac{1}{6} \times \pi \times 36 = 6\pi$.
17.
Tags: Triangle Inequality · Medium · source: Original (AMC-style)
Can a triangle have sides of length 3, 4, and 8?
A) Yes B) No C) Sometimes D) Cannot be determined E) Depends on angle
Answer & Solution
Answer: B
No, because $3 + 4 = 7 < 8$, violating the triangle inequality.
18.
Tags: Pythagorean Triples · Medium · source: Original (AMC-style)
What is the hypotenuse of a right triangle with legs 5 and 12?
A) $13$ B) $15$ C) $17$ D) $19$ E) $21$
Answer & Solution
Answer: A
Using $a^2 + b^2 = c^2$: $5^2 + 12^2 = 25 + 144 = 169 = 13^2$, so $c = 13$.
19.
Tags: Angle Bisector · Medium · source: Original (AMC-style)
In triangle ABC, if angle A is 60° and angle B is 40°, what is angle C?
A) $60°$ B) $70°$ C) $80°$ D) $90°$ E) $100°$
Answer & Solution
Answer: C
Since angles in a triangle sum to 180°: $60° + 40° + \angle C = 180°$, so $\angle C = 80°$.
20.
Tags: Area of Regular Polygon · Medium · source: Original (AMC-style)
What is the area of a regular hexagon with side length 2?
A) $3\sqrt{3}$ B) $6\sqrt{3}$ C) $9\sqrt{3}$ D) $12\sqrt{3}$ E) $18\sqrt{3}$
Answer & Solution
Answer: B
Area = $\frac{1}{2} \times$ perimeter × apothem = $\frac{1}{2} \times 12 \times \sqrt{3} = 6\sqrt{3}$.
21.
Tags: Complex Geometry · Hard · source: Original (AMC-style)
In a circle with radius 5, what is the area of a sector with arc length $\pi$?
A) $\frac{\pi}{2}$ B) $\pi$ C) $\frac{3\pi}{2}$ D) $2\pi$ E) $\frac{5\pi}{2}$
Answer & Solution
Answer: E
Arc length = $r\theta$, so $\pi = 5\theta$ and $\theta = \frac{\pi}{5}$. Area = $\frac{1}{2}r^2\theta = \frac{1}{2} \times 25 \times \frac{\pi}{5} = \frac{5\pi}{2}$.
22.
Tags: Advanced Triangles · Hard · source: Original (AMC-style)
In triangle ABC, if AB = 5, BC = 7, and AC = 8, what is the area?
A) $10\sqrt{3}$ B) $12\sqrt{3}$ C) $14\sqrt{3}$ D) $16\sqrt{3}$ E) $18\sqrt{3}$
Answer & Solution
Answer: A
Using Heron's formula: $s = \frac{5+7+8}{2} = 10$, so area = $\sqrt{10(10-5)(10-7)(10-8)} = \sqrt{10 \times 5 \times 3 \times 2} = \sqrt{300} = 10\sqrt{3}$.
23.
Tags: Coordinate Geometry · Hard · source: Original (AMC-style)
What is the area of the triangle with vertices (0,0), (4,0), and (2,3)?
A) $3$ B) $6$ C) $9$ D) $12$ E) $15$
Answer & Solution
Answer: B
Using the formula: area = $\frac{1}{2}|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)| = \frac{1}{2}|0(0-3) + 4(3-0) + 2(0-0)| = \frac{1}{2} \times 12 = 6$.
24.
Tags: Circle Properties · Hard · source: Original (AMC-style)
Two circles with radii 3 and 5 are externally tangent. What is the distance between their centers?
A) $2$ B) $3$ C) $5$ D) $8$ E) $15$
Answer & Solution
Answer: D
When circles are externally tangent, the distance between centers equals the sum of radii: $3 + 5 = 8$.
25.
Tags: Advanced Area · Hard · source: Original (AMC-style)
What is the area of the region bounded by the lines $y = x$, $y = -x$, $x = 1$, and $x = -1$?
A) $1$ B) $2$ C) $3$ D) $4$ E) $5$
Answer & Solution
Answer: B
This forms a square with vertices at (1,1), (1,-1), (-1,-1), and (-1,1). The side length is $\sqrt{2}$, so area = $(\sqrt{2})^2 = 2$.
Answer Key
| # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ans | C | D | C | C | A | D | B | B | D | B | C | C | B | C | B | D | B | A | C | B | E | A | B | D | B |