Summer Math Pre and Post Tests for
Post Geometry (for students who have completed nonhonors Geometry this past year)
________________________________________ Name
Please read the directions (separate document) completely before starting your packet!
Print out the packet so you can record your work. This will be turned in to your teacher in August. REMEMBER – ALL ANSWERS (letter choice or student generated response) MUST BE INPUTTED ONLINE AT THE WEBSITE www.classmarker.com. If you lose or forget your username and password, email Mr. Toth at
[email protected] Even though you will be inputting your answers online we have included a blank “answer sheet” to help organize your answers. You can write your letter choice (or numeric value for student generated responses) in the blank next to each problem number as you work out your solutions. When you actually log in to input answers, this should make the process much smoother and less prone to error. Obviously, it is of utmost importance to make sure you are entering answers in the correct tests. *Please make notes and comments about the problems that caused difficulty so that you can recall the process you undertook when we go over the packets in the fall. *If you encounter any typos or errors, please email me with the problem and the issue at
[email protected]
Answer Sheet for Post nonhonors Geometry Pretest
Test 1 Section 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Test 1 Section 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Test 1 Section 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Answer Sheet for Post nonhonors Geometry Post Tests Test 2
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
Test 3 Section 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Test 3 Section 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Test 3 Section 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Diagnostic Model SAT Geometry and Measurement: Test 1, Section 1
1. For the intersecting lines above, which of the following must be true? I.
b
(a) I only
2c
II.
a
III.
a + 120 = b + c
(b) II only (c) I and II only (d) II and III only (e) I, II, and III
2. On the line segment, above, RT = 10 and RM = 8. What is the length of the line segment joining the midpoints of ̅̅̅̅ and ̅̅̅̅̅ (a) 1 (b) 3 (c) 5
(d) 7 (e) 9
3. If each edge of cube M with a unit length of 3 is increased by 50%, creating a second cube B, then what is the volume of cube B? (a) 20.5 (b) 36 (c) 64 (d) 91.125 (e) 216
4.
In the figure above, square ABCD is inscribed in a circle with area 18 . What is the area of the shaded region? (a) 9 (b) 9π (c) 18  9π (d) 18π  9 (e) 18π – 36
5.
In the figure above, if side RS = ST, and x = 115⁰, what is the measure of angle y? (a) 65 (b) 75 (c) 85 (d) 115 (e) 130
6. In circle O above, ⃐ ̂?
is the diameter and the circumference is 24π . If POR + 60⁰, what is the length of arc
(a) 4π (b) 6π (c) 8π (d) 12π (e) 16π
7.
The perimeter of rectangle MATH in the figure is 48. What is the area of each square? (a) 24 (b) 32 (c) 64 (d) 128 (e) 256
8. If the unequal sides of a triangle are 3, x, and 7, where 3 x (a) 3 (b) 4 (c) 5 (d) 6 (e) 10
, then what is the smallest integer value of x?
Note: Figure not drawn to scale. 9.
If AB = 12 and the circumference of circle A is 3 times the circumference of circle B, what is the length of ⃐ ? (a) 2 (b) 3 (c) 3
(d) 4 (e) 4
10. If the points (2,3) and (5,y) lie on a line whose slope is
a) 6.5
b) 0.5
11. In the figure, if 90 (a) 0 b + d 90
c) 0
, what does y equal?
d) 0.5
e) 6.5
a + c 180, which of the following describes all possible values of b +d? (b) 90 b + d 180 (c) 180 b + d 270 (d) 180 b + d 360 (e) 270
Questions 12 and 13 refer to the figure below.
DAB = 15 and ABC = 45 .
12. What is the length of ̅̅̅̅? (a) 10 (b) 10√
(c) 10√
(d) 20√  10 (e) 20√ – 10
13. What is the length of ̅̅̅̅? (a)
20 – 10 √
(b) 20 – 10 √
(c) 10 √  10 (d) 10 √  10 (e) 10 √
b+d
360
14.
What is the perimeter of the triangle formed by joining the vertices A, B, and C of the cube above, with an edge of 1? (a) 1.5 √
(b) 3 (c) 4 (d) 3√
(e) 6
15. In the figure above, find the value of x. (a) 2 (b) 4 (c) 8 (d) 12 (e) 16
16. If the wheels of a train make 16 revolutions when it rolls a distance of 60 feet, what is the radius of the wheel? (a)
(b)
(c)
(d)
(e)
17. Each of the four outside walls of the large wooden box shown above is to be covered with a waterproof plastic that comes in 3foofwiderolls. The plastic does not overlap. What is the total length, in feet, of plastic, needed to cover the four walls? (a) (b) 42 ft. (c) (d) (e)
18. If the diagonal of the square inscribed in the circle is 8, what is the sum of the shaded areas? (a)
(b)
(c)
(d)
(e)
19. In the figure above, if b = 54 and c = 75, what is the value of a? (a) (b) 119 (c) (d) (e)
20. The surface areas of the rectangular prism above are given. If the lengths of the edges are integers, what is the volume in cubic feet? (a) (b) 168 (c) (d) (e)
Test 1, Section 2 1. If the angles of a triangle are in the ratio of 2 : 3 : 5, what kind of triangle is it? (a) (b) Obtuse (c)Equilateral (d) (e) 2. If the diameter of circle A is twice as large as the diameter of circle B, what is the ratio of the area of the larger circle to the area of the smaller circle? (a) (b) 6:1 (c) (d) (e)
3. If x = 60 in the scalene triangle above, then which of the following must be true? (a) (b) (c) (d) (e) 4. Which of the following could be the graph of
?
5. If the diameter of the circle is 10, what is the ratio of the area of the small square to the area of the large square? (a) (b) 1: (c) (d) (e)
6. In the figure above, point M has the greatest ycoordinate on the semicircle. What is the xcoordinate of point P? (a) (b) 2 (c) (d) (e)
7. In the figure above, if the radius of the inscribed circle is 8, then the perimeter of the shaded region is… (a) (b) 2 (c) 4 (d) 4 (e) 16
8. In rectangle OEAD in the figure above is inscribed in the circle OBC, which of the following statements must be true? I. (a)
II.
III.
(b) I and II Only
(c)
(d)
(e)
Free Response:
9. In the figure above, S is parallel to T,
. What is the measure of
10. What is the average of the marked angles 1, 2, and 3 in the figure above? 11. If the area of triangle T, sides 5, 12, and 13, equals the area of rectangle R, width 8, then what is the perimeter of rectangle R?
12. In the figure above, what is the value of altitude x? 13. If Jack’s house is 7.1 miles due north of the Senior Citizen Center and Belinda’s house is 6.3 miles due west of it, then to the nearest tenth, what is the shortest distance between their houses?
14. In the figure above, what is the coordinate of point N? 15. To the nearest tenth, what is the circumference of a circle with an area of 16. If a line with a slope of
?
passes through the points (5, 0) and (x, 2), then what is the value of x?
17. In the figure above, the radius of the small circle A is onehalf the radius of the large circle B. What is the ratio of the area of the small circle to the area of the large circle?
18. On circle O above, what is the value of x?
Test 1 Section 3 1. Four equal squares are arranged to form one larger square. If the perimeter of each of the smaller squares is 36, what is the area of the larger square? (a) (b) 81 (c) (d) (e) 2. If triangle A and triangle B are each equilateral, which of the following much be true about these triangle? I.
II.
(a)
(b) II Only
III. (c)
(d)
(e)
3. In triangle ABC, AB = BC = CA = s. In terms of s, what is the height of the triangle? (a)
√
(b)
√
(c)
√
(d)
√
(e)
4. The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude? (a)
(b) 20
(c)
(d)
(e)
5. In the isosceles triangle ACB, if side AC is decreased by 4 and side BC is increased by 4, a new triangle ECD is formed. What is the difference in the areas of the two right triangles? (a)
(b) 2
(c)
6. If the area of the circle above is (a)
(b) 18
(d)
(e)
and AB = BC, then what is the area of (c)
(d)
(e)
?
7. In the two concentric circles with center O, the radius of the large circle is twice the radius of the small circle. What is the ratio of the area of the small circle to the area of the large circle? (a)
(b)
(c)
8. In the figure above, what is the perimeter of (a)
(b)
(b) 4 √
(e)
?
(c) √
9. A square is inscribed in a circle with a radius of (a)2 √
(d)
(c) 6 √
(d) √
(e)
√
. What is the perimeter of the square? (d) 8 √
(e) 10 √
10. Which of the following points (when plotted) will be three times as far from A (7, 10) as from B (3, 4)? (a)
(b) (2, 4)
(c)
(d)
(e)
11. In the figure above, if (a)
√
(b)
(c)
, the x = (d) √
(e)
12. In the figure above, the radius of circle B is 12 and the tangent segments AD and DC are each 16. What is the value of x? (a)
(b)
(c)
(d)
(e)
13. In the figure above, with line parallel to line m, which of the following statements must be true? I. (a)
II. (b) III Only
(c)
III. (d)
(e)
14. In the cube drawn above, which statement is NOT true? (a)
(b)
(c)
(d)
15. In the figure above, circle O has a radius of 4 and shaded region? (a)
(b)
(c)
(e)
is an isosceles right triangle. What is the area of the
(d)
(e)
1st Post Test Test 2 Studentproduced Response Questions 1. What is the diameter of a circle whose area is 2. A triangle has sides that measure 3, 8, and n. If possible?
? and n is an integer, how many different triangles are
3. If the area of triangle A, with sides of 6, 8, and 10, equals the area of rectangle B, with width of 4, what is the perimeter of the rectangle? 4. How many degrees are there in the angle formed by the hand of a close at 8:30? (do not grid in the degree symbol) 5. Claudia has a cylindrical telescope with a circular base of area space it occupies (the volume) is ?
. What is the length of the telescope if the
6. In the figure above, two 7 X 7 squares overlap to form a 7 X 11 rectangle. What is the area of the shaded region? 7. If the area of square S is the same as the area of triangle T, with base equal to 12 and altitude equal to 9, then, to the nearest tenth, what is the length of a side of the square?
8. If the area of the circle is
, what is the length of a side of the inscribed square, to the nearest hundredth?
9. In the figure above, the radius of the inner circle of the tire is twice the width of the tire itself. To the nearest integer, what percent of the entire area is the area of the tire? (Do not grid in the percent sign)
10. Given a rectangle ABCD with length 10 and width 4. If
and the area of ECDF is the area of rectangle
ABCD, what is the measure of FD?
11. In the figure above, the three concentric circles have radii lengths of 3, 7, and 12. What is the shortest line segment that can be drawn containing exactly one point on each of the three circles?
12. In the figure above, circle P is inscribed in half of the circle N, which is inscribed in half of circle M. What is the ratio of the area of circle P to the area of circle M?
13. In the figure above, hat is the value of x? 14. The three sides of a triangle are 4, 5, and 8. If the length of one side of a similar triangle is 16, what is the least possible perimeter of the larger triangle?
15. In the figure, H is the midpoint of side DE of rectangle DEFG. If GH is 12, to the nearest tenth, what is the area of triangle GDH? 16. What is the largest number of 3inch by 5inch cards that can be cut from a sheet of construction paper 17 inches by 22 inches?
17. In the circle above, the center is B, the diameter AC= 18, and region to the nearest integer?
is a right angle. Find the area of the shaded
18. In the figure above, if point A is (3, 2) and point B is (5, 5), then what is the length of AB, to the nearest tenth? 19. A rectangular planting field, 50 yards by 100 yards, is surrounded on all sides by a concrete pedestrian walk 6 feet wide. What is the number of square feet in the surface of the walk?
20. In the circle above, he diameter is 15 and the inscribed angle has a length of 12. What is the width of the rectangle? 21. What is the sum of the root of the quadratic equation
22. In the figure above, if
, then the measure of
?
in degrees is…
23. If the radius of circle O in the figure above is 12 and AB is tangent to the circle at point B, with AC = 8, what is the value of x? 24. If the length of a side of an equilateral triangle is 10 inches, what is the length of an altitude of the triangle to the nearest hundredth? 25. What is the smallest value in the range for the parabola
?
2nd Post Test Test 3 Section 1 1. If , and is the value of
?
(b)
(c)
(d)
(e)
2. If the endpoint of a line segment AB is (5, 2) and the midpoint is (2, 5), what is the other endpoint? (b) 3. If
(c)
(d)
(e)
(d)
(e)
, what is the value of x? (b)
(c) 21
4. If v, w, x, y, and z are consecutive odd integers, what is the value of (b)
(c) 3
(d)
?
(e)
5. If the length of one side of a regular polygon is 25% of its perimeter, then polygon has how many sides? (b) (c) 5 (d) (e) 6. If
, which of the following inequalities much be true? (b)
(c)
7. If x – y = 5 and x + y = 11, what is the value of (b) (c) 16
8. In the figure above, if (b) 9. If
, then (b)
(d)
(e) ?
(d)
(e)
is equilateral and AD = AB what is the value of x? (c) (d) (e) _____ (c)
(d)
(e)
10. If set S consists of all odd multiples of 3, that is, S = (…,9, 3, 3, 9,…). If the integers x and y are in S, which of the following must also be in S? (b) (c) (d) (e) 11. A square with a side of 2
(b)
is equal in area to a circle. What is the diameter of the circle? (c) √
(d) √
(e)√
12. In the figure above, 3PR = PS. What is the value of (b)
(c)
13. If the shaded area in the figure above is (b) (c)
(d)
? (e)
, what is the circumference of the circle? (d) (e)
14. If the average of an integer N and its reciprocal is , what is that integer? (b)
(c)
(d)
(e)
15. If x books cost d dollars, how much will m books cost at the same rate? (b)
(c)
(d)
(e)
16. If the surface area of a cube is , what is the volume of the cube? (b) (c) (d) (e)
17. In the figure above, three lines intersect. What is the sum of the degree measures of the marked angles? (b) (c) (d) (e) 18. If the sum of 3 unequal positive integers equals 20, what is the largest possible value of the smallest number? (b) (c) (d) (e)
19. If
, what is the value of x in terms of m? (b)
(c)
(d)
(e)
20. In the figure above, if AD is extended to the right to point B (not shown) so that D is the midpoint of ADB, and if the length of AB is 2y, what is the length of CD in terms of y? √
(b) √
(c) √
(d)
(e)
Test 3 Section 2 1. The vaue of
is (b)
(c)
(d)
(e)
2. What graph on the number line represent the solution to
3. If
, which one of the following is the solution for (b)
(c)
(d)
?
? (e)
4. In the figure above, if sin B = n(cos B), then n is (b)
√
(c)
√
(d)
√
(e) √
5. In the graph above, two linear functions are shown. Which of the following are true for these functions? I. II. III. (a) (b) (c) (d) (e) 6.
If
, then an expression for x in terms of a, n, and r is… (b) (c) (d) (e)
7. In the figure above, a wheel with center O rolls in a straight line (without slipping) along a level track. Two spots of red dye on the wheel leave measuring marks on the track as indicated by the dots on the rack above. What is the degree measure of x? (b) (c) (d) (e)
8. In the figure above, if the slope of the line m is , what is the area of the shaded region? (b)
(c)
(d)
(e)
Studentproduced Response Questions 9. If 2x + 1 = 10, then 4x + 1 = 10. If the average of and its reciprocal is N, what is the value of N?
11. In the figure above, if x + y =100, what is the average of a + b? 12. If the perimeter of a right triangle is 60 and the sides are x, 2x + 4, and 3x – 4, what is the area of the triangle? 13. If
, what is the value of x?
14. As square, as shown in the figure above, is inscribed in a circle. If the circumference of the circle is √ , what is the area of the square?
15. In the addition problem above, A, B, and C are different digitis from 1 to 5, inclusive. What digit does C represent? 16. If the operations * is defined as
, then what does
equal?
17. If a rectangular solid has two faces the same size and shape as Figure I and four faces the same size and shape as Figure II, what is the volume of the solid?
18. If √
, then what is the value of x?
Test 3 Section 3
1. If rectangle A and isosceles triangle B shown above have the same perimeter, what is the value of x? (b) (c) (d) (e) 2. For which of the following values of N is 3N – 1 not a prime number? (b) (c) (d) (e) 3. If the area of a lawn is 360 square meters, and Dave cuts the lawn at the rate of 12 square meters a minute, what fraction of an hour does it take to cut his lawn? (b) 4. If
(c)
(d)
(e)
is multiplied out completely, what is the units digit of the resulting number? (b) (c) (d) (e)
5. A circle is inscribed in a square as shown above. If a side of the square is , what is the ratio of the perimeter of the square to the circumference of the circle? (b)
(c)
6. If k >0 and (b)
(c)
(d)
(e)
, for all values of x, what is the value of k – b? (d) (e)
7. If AB = AC and
, what is the value of x? (b) (c)
(d)
(e) 8. A perfect square is the result of squaring an integer. If K is a perfect square, then which of the following must represent the next consecutive perfect square? (b) 9. What percent of (b)
√
(c)
√
(d)
√
(e)
√
? (c)
(d)
(e)
10. Leo rested a ladder against his house to repair a window. The ladder just reached the bottom of the window. The base of the ladder was 4.5 feet from the house. At a horizontal distance of 1.5 feet from the base of the ladder toward the house, the vertical rise was 5 feet. What is the distance from the bottom of Leo’s window to the ground? (b) (c) (d) (e)
11. If x = 2, what is the value of  (b)
 (c)

? (d)
(e)
12. All of the following equations are examples of a direct variation except for… (b)
(c)
(d)
(e)
13. In the figure above, if the real numbers, a, b, and c are related as shown on the number line, which of the following is false?      (b)     (c)   (d)   (e)  14. If
and (b)
, where x > 1 and y > 0, what is the product of x and y? (c)
(d)
(e)
15. In the figure above, BC is the tangent to circle O. If AO = x and OB = y, then (b) (c) (d) (e)
equals…