1.
[latex]DFG[latex] is a straight line. What is the value of [latex]x[latex]?
A. 12
B. 14
C. 16
D. 18
E. 20
2. If the hypotenuse of an isosceles right triangle is [latex]7\sqrt { 2 }[latex] , what is the area of the triangle?
(A) [latex]14[latex]
(B) [latex]18[latex]
(C) [latex]24.5[latex]
(D) [latex]28[latex]
(E) [latex]49[latex]
3. If [latex]p[latex] is the perimeter of a triangle with one side of [latex]6[latex] and another side of [latex]9[latex], what is the range of possible values for [latex]p[latex]?
(A) [latex]3 < p < 15[latex]
(B) [latex]15 < p < 24[latex]
(C) [latex]18 < p < 30[latex]
(D) [latex]18 < p < 42[latex]
(E) [latex]21 < p < 42[latex]
4. A triangle has sides of [latex]8, m[latex], and [latex]n[latex].
| Quantity A | Quantity B |
| |[latex]m-n[latex]| | [latex]8[latex] |
5.
| Quantity A | Quantity B |
| The clockwise angle made by the hour hand and the minute hand at [latex]12:15[latex]pm | The counterclockwise angle made by the hour hand and the minute hand at [latex]12:45[latex]pm |
6. A [latex]10[latex] foot ladder leans against a vertical wall and forms a [latex]60[latex] degree angle with the floor. Assuming the ground below the ladder is perfectly horizontal, how far above the ground is the top of the ladder?
(A) [latex]5[latex] feet
(B) [latex]5\sqrt { 3 }[latex] feet
(C) [latex]7.5[latex] feet
(D) [latex]10[latex] feet
(E) [latex]10\sqrt { 3 }[latex] feet
7. In the figure, if line [latex]CE[latex] bisects ∠[latex]ACB[latex], then [latex]x[latex] =
(A) [latex]45[latex]
(B) [latex]50[latex]
(C) [latex]55[latex]
(D) [latex]65[latex]
(E) [latex]70[latex]
8. In the triangle, what is the value of [latex]x[latex] ?
(A) [latex]25[latex]
(B) [latex]55[latex]
(C) [latex]60[latex]
(D) [latex]77[latex]
(E) [latex]85[latex]
9. The following are the measures of the sides of five different triangles. Which one of them represents a right triangle?
(A) [latex]\sqrt { 3 },\sqrt { 4 },\sqrt { 5 }[latex]
(B) [latex]1, 5, 4[latex]
(C) [latex]7, 3, 4[latex]
(D) [latex]\sqrt { 3 },\sqrt { 7 },\sqrt { 4 }[latex]
(E) [latex]4, 8, 10[latex]
10. In the figure, [latex]ABC[latex] and [latex]ADC[latex] are right triangles. Which of the following could be the lengths of [latex]AD[latex] and [latex]DC[latex], respectively?
(I) [latex]3[latex] and [latex]4[latex]
(II) [latex]4[latex] and [latex]6[latex]
(III) [latex]1[latex] and [latex]24[latex]
(IV) [latex]1[latex] and [latex]26[latex]
(A) I and II only
(B) II and III only
(C) III and IV only
(D) IV and I only
(E) I, II and III only
11.
| Quantity A | Quantity B |
| [latex]X[latex] | [latex]Y[latex] |
12.
| Quantity A | Quantity B |
| [latex]\frac { x }{ y }[latex] | [latex]1[latex] |
13.
Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle [latex]ABC[latex] above?
Indicate all such statements.
(A) [latex]DBC[latex] is an equilateral triangle.
(B) [latex]ABD[latex] is an isosceles triangle.
(C) The length of [latex]BC[latex] is equal to the length of [latex]AD[latex].
(D) The length of [latex]BC[latex] is [latex]10[latex].
(E) The length of [latex]AD[latex] is [latex]10[latex].
14. In the figure below, [latex]AB=BC=CD[latex]. If the area of triangle [latex]CDE[latex] is [latex]42[latex], what is the area of triangle [latex]ADG[latex]?
15. What are the lengths of sides [latex]NO[latex] and [latex]OP[latex] in triangle [latex]NOP[latex] below?
Answers:
1 [latex]20[latex]
2 C
3 C
4 |[latex]m-n[latex]|<[latex]8[latex]
5 B
6 B
7 D
8 A
9 D
10 C
11 D
12 A
13 A and D
14 [latex]378[latex]
15 [latex]NO=30[latex] and [latex]OP=10\sqrt { 34 }[latex]
