Geometry

1)Points E, F and G all lie on line m, with E to the left of F. EF=10, FG=8 and EG>FG. what is EG?

2)In the parallelogram ABCD with bases AD and BC, the lengths AB, BD and CD are all 3√2 and the angles A and C are both 45°. What is the perimeter of ABCD?

3)What is the area of ABCD?

4)In a circumference with center A, AB and AC are two perpendicular radius. The area of the circle is 25π. What is the length of line segment BC?

5)Given that the length and the width of a rectangular piece of paper are, respectively, 6cm and 4 cm, the paper is rolled into the shape of a cylinder. If it is assumed that the 4- centimeter sides of the rectangle meet with no overlap, what is the area, in square centimetres, of the base of the cylinder?

a) 16πb) 9πc) 4πd) 9/πe) 4/π

6)Given the points P(1,1) and Q(k,7), the slope of line PQ is 3/2. What is the value of k?

a) 4b) 5c) 6d) 7e) 8

7)In the xy-plane, point R(2,3) and point S(5,6) are two vertices of triangle RST. If the sum of the slopes of the sides of the triangle is 1, which of the following angles could be a right angle?

I. R

II. S

III. T

a) noneb) I onlyc) III onlyd) I and II onlye) I, II and III

8)

Note: Figure not drawn to scale

The perimeter of the rectangle above is p inches and the area of the rectangle is 36 square inches. If the length l and the width w are integers, what is one possible value of p?

9)In the triangle ABC, D is the end of the height BD. The angles BAD, and DBA are x°, the angles DBC and DCB are , respectively y° and z°. If AD=1 and DC=√3, what is the value of z°?

a) 15b) 20c) 25d) 30e) 35

10)

Note: Figure not drawn to scale

In the figure above, rectangle ABCD is made up of seven nonoverlapping rectangles. The two smallest rectangles have the same area. Each of the other rectangles has twice the area of the next smaller rectangle. The area of the shaded rectangle is what fraction of the area of ABCD?

a) 1/128b) 1/64c) 1/32d) 1/16e) 1/7

11)In the xy-plane, the line with equation y=5x-10 crosses the x-axis at the point with coordinates (a,b). What is the value of a?

a) -10b) -2c) 0d) 2e) 5

12)Line l has a positive slope and passes through the point (0,0). If line k is perpendicular to l, which of the following must be true?

a) k passes through (0,0)b) k has a positive slopec) k has a negative slope

d) k has a positive x-intercepte) k has a negative y-intercept

13)In the figure, the arc of circle has a centre-angle of 30°. If the length of the arc is 6π, what is the area of the sector?

a) 108πb) 72πc) 54πd) 36πe) 9π

14)Tameka cut a circular pizza into wedge-shaped pieces like that of exercise 13. The tip of each piece is at the center of the pizza and the angle at the tip is always greater than 20°, but less than 30°. What is one possible value for the number of pieces in which the pizza is cut?

15)Note: Figure not drawn to scale

In the triangles above, the ratio between the bases and the heights is ¾. what is the value of their areas?

16)In the xy-plane, the distance between point B(10,18) and A(x,3) is 17. What is one possible value of x?