SAT Practice Test
1. The dots on the square grid are equally spaced by one unit horizontally and vertically. How many squares have all their vertices among the dots of the 6 x 6 grid and such that all their sides have either integer length or non-integer length?
a. / 104b. / 105
c. / 103
d. / 108
e. / 102
2. Points X=(0,0), Y=(6,8) and Z=(12,0 ) are given. How many units are in the length of the radius of the circle which passes through the points X,Y and Z ? Express your answer to the nearest tenth.
a. / 5.3b. / 4.3
c. / 9.3
d. / 3.3
e. / 6.3
3. Let ABC be right triangle in C . Suppose that points D, E are on the side AB such that AC = CD = DE = EB . Suppose also that AE = 14 sqrt(3) in. What is the number of inches in DE ?
b. / 14
c. / 16
d. / 11
e. / 17
4. Consider the triangle XYZ where X=(16,0) , Y=(0,8) , and Z=(24,0) . Let M be the mid-point of XY , N the mid-point of YZ and P the midpoint of XZ . How many square units are in the area of the triangle YMN ?
a. / 9b. / 10
c. / 5
d. / 11
e. / 8
5. The ratio of the height of a triangle ABC to the height of a triangle MNP is 5/12. If the two triangles are similar, what is the ratio of the area of the triangle ABC to the area of the triangle MNP? Give your answer as a common fraction.
a. / 5/12b. / 25/144
c. / 125/1728
d. / 12/5
e. / 1728/125
6. Let ABC be a triangle having an area of 45 cm2. Let M, N be the midpoints of is AB and AC respectively. Let P be the point of intersection of BN and CM . How many square centimeters are in the area of the triangle PBC ?
a. / 14b. / 13
c. / 18
d. / 15
e. / 12
7. A convex polygon has n sides and 12 n diagonals. Find the value of n .
a. / 25b. / 38
c. / 37
d. / 36
e. / 27
8. A circle of radius 7 cm is inscribed in an equilateral triangle and is tangent at three points. Three smaller circles are inscribed so that they are each tangent to two sides of the triangle and to the larger circle. The process is continued with circles of ever decreasing diameters. What is the number of centimeters in the sum of the circumferences of all such circles? The answer is x Pi . Find x .
a. / 30b. / 25
c. / 50
d. / 20
e. / 35
9. How many digits are in the number 572 * 274 ?
a. / 73b. / 74
c. / 75
d. / 70
e. / 76
10. Two integers are randomly selected from the set of integers greater than or equal -9 and less than or equal to 9 . The two numbers need not be different. What is the probability that the sum of the two integers is less than their product? Give your answer as a common fraction in lowest terms.
a. / 162/361b. / 128/361
c. / 98/361
d. / 288/361
e. / 72/361
11. What is the probability that a randomly selected factor of 70 11 is a multiple of 70 6 ? Express your answer as a common fraction.
a. / 125/1728b. / 1/8
c. / 216/1331
d. / 343/1331
e. / 343/1000
12. Two number cubes (number cube=dice), each with the digits 1-6 on the six faces, are rolled. What is the probability that the product of the numbers on the top faces will be greater than 6 ? Express your answer as a common fraction in lowest terms.
a. / 5/9b. / 11/18
c. / 17/36
d. / 13/36
e. / 5/18
13. A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter of the garden? Round your answer to the nearest whole number.
a. / 67b. / 66
c. / 71
d. / 65
e. / 68
14. There are 16 red, 16 blue and 16 yellow marbles in a jar. What is the fewest marbles you can remove from the jar so that the ratio of red to non-red marbles is 13 to 29 and the ratio of yellow to non-yellow marbles is 13 to 29?
a. / 6b. / 7
c. / 5
d. / 4
e. / 9
15. A triangle ABC has an area of 16 square centimeters. We extend the side AC to obtain a point M such that A is between M and C and AM=(1/2) AC . We extend the side AB to obtain a point N such that B is between N and A and BN=(1/2)AB . We extend the side BC to obtain a point P such that C is between P and B and CP=(1/2)BC . How many square centimeters are in the area of the triangle MNP ?
b. / 53
c. / 54
d. / 49
e. / 55
16. How many integers from 1 to 3528 inclusive have at least one prime divisor in common with 3528 ?
a. / 2521b. / 2520
c. / 2522
d. / 2517
e. / 2523
17. The dots on the rectangular grid are equally spaced horizontally and vertically. How many rectangles have all their vertices among the dots of the 5 x 4 grid and such that all their sides have integer length?
b. / 60
c. / 58
d. / 63
e. / 57
18. A square ABCD has side length of 8 inches. Let P be the center of a circle passing by C and D and tangent to AB . What is the area in square inches of the triangle PDC ?
a. / 13b. / 14
c. / 9
d. / 15
e. / 12
19. Let ABC be a right isosceles triangle with hypotenuse AC=24 units. A circle is drawn through B that is tangent to AC at P . How many square units are in the area of the region inside the circle but outside the triangle? The answer is x*(Pi-2). Find x.
a. / 18b. / 17
c. / 16
d. / 21
e. / 15
20. A caterer offers 5 different appetizers, 6 different drinks and 7 different sandwiches. How many combinations of 2 appetizers, 2 drinks and 2 sandwiches can someone choose for his party?
a. / 1575b. / 3150
c. / 1260
d. / 22050
e. / 210
21. If an angle measures 42 -n degrees and n is not equal to zero. What is the degree measure of the supplement of this angle?
a. / 138 -nb. / 48 + n
c. / 48 -n
d. / 138 + n
e. / 318 + n
22. A positive integer less than 100 is randomly chosen. What is the probability that at least one of its digits is 7 or that the number is divisible by 7. ? Express your answer as a common fraction in lowest terms.
a. / 1/3b. / 3/11
c. / 4/11
d. / 10/33
e. / 8/33
23. On a four-by-four grid (see below), the points are 1 unit apart horizontally and vertically. Two distinct points P and Q are randomly selected from this grid. What is the probability that the distance between P and Q is less than 2 ? Express your answer as a common fraction.
. . . .
a. / 3/10b. / 2/5
c. / 1/4
d. / 9/20
e. / 7/20
24. The side length of square ABCD is 8 centimeters. Points M, N, P and Q are the midpoints of sides AB, BC, CD and DA , respectively. How many centimeters are in the sum of the lengths of all diagonals of hexagon QMBNPD ? Express your answer as a decimal rounded to the nearest tenth.
a. / 73.4b. / 72.4
c. / 77.4
d. / 71.4
e. / 74.4
25. Trapezoid ABCD is such that AB=47 cm is parallel to CD=145 cm. The angle ADC is equal 45 degrees. If the area of the trapezoid is 7680 sq cm, what is the number of centimeters in the length of line segment BC ?
a. / 81b. / 80
c. / 82
d. / 85
e. / 79
26.
Compare the quantities in Column A and Column B.
Column A / Column B| 2 x2 - 5 x + 3 | for x=3 / | 2 x2 - 4 x - 3 | for x=1
a. / The quantity in Column A is greater.
b. / The quantity in Column B is greater.
c. / The two quantities are equal.
d. / The relationship cannot be determined from the information given.
27.
Let m and n be two positive integers with m > n.
Column A / Column B(1/m) (1 + 2 + 3 + ... + m) / (1/n)( 1 + 2 + 3 + ... + n)
a. / The quantity in Column A is greater.
b. / The quantity in Column B is greater.
c. / The two quantities are equal.
d. / The relationship cannot be determined from the information given.
28. Consider a real number y < 0 .
Column A / Column BThe quantity
y7 . / The quantity
y6 .
a. / The quantity in Column A is greater.
b. / The quantity in Column B is greater.
c. / The two quantities are equal.
d. / The relationship cannot be determined from the information given.
29.
The figure above is not drawn to scale.
AB=5 cm, AC=5 cm.
Angle ACB / Angle ABC
a. / The quantity in Column A is greater.
b. / The quantity in Column B is greater.
c. / The two quantities are equal.
d. / The relationship cannot be determined from the information given.
30.
Column A / Column BThe area of a rectangle having
a perimeter of 404 cm. / The area of a rectangle having
a perimeter of 12 cm.
a. / The quantity in Column A is greater.
b. / The quantity in Column B is greater.
c. / The two quantities are equal.
d. / The relationship cannot be determined from the information given.