51.

A.

B.

C.

D.

E.

52. If of is , what is of ?

F.

G.

H.

J.

K.

53. If and , what is the value of ?

A.

B.

C.

D.

E.

54.

F.

G.

H.

J.

K.

55.

How many units is it from midpoint of to the midpoint of ?

A.

B.

C.

D.

E.

56. Jack scored a mean of points per game in his first 3 basketball games. In his th game, he scored points. What was Jack’s mean score for the games?

F.

G.

H.

J.

K.

57. If , what is the value of ?

A.

B.

C.

D.

E.

58. Judy is years older than Carmen and twice as old as Frances. If Frances is , how old is Carmen?

F.

G.

H.

J.

K.

59. sind ricks

sind dalts

Using the conversions above, how many dalts are equivalent to rick?

A. dalts

B. dalts

C. dalts

D. dalts

E. dalts

60.

How many more people in Center City walk to work than ride their bicycles to work?

F.

G.

H.

J.

K.

61.

The figure above is drawn to scale. Which point best shows the location of ?

A. R

B. S

C. T

D. V

E. W

62. On a scale drawing, a distance of foot is represented by a segment inch in length. How long must a segment on the scale drawing be to represent a -inch distance?

F. in.

G. in.

H. in.

J. in.

K. in.

63. What is the greatest common factor of and ?

A.

B.

C.

D.

E.

64. The set consists of all prime numbers greater than and less than . What is the median of the numbers in ?

F.

G.

H.

J.

K.

65. Ms. Grant’s car gets between and miles per gallon, inclusive. The gasoline she uses costs between and per gallon, inclusive. What is the **greatest** amount Ms. Grant will spend on gasoline to drive her car miles?

A.

B.

C.

D.

E.

66. A group of mountain climbers started the day at an elevation of feet below sea level. At the end of the day, they camped at feet above sea level. What was the climbers’ elevation gain for the day?

F. ft

G. ft

H. ft

J. ft

K. ft

67. What is the solution to ?

A.

B.

C.

D.

E.

68. There are eighth graders and seventh graders in a school club. The president of this club wants of the club’s members to be seventh graders. How many **more** seventh graders must join the club in order to meet the president’s wishes? (Assume that the number of eighth graders remains the same.)

F.

G.

H.

J.

K.

69.

Point is to be placed on the number line one-third of the way from point to point . What number will be at the midpoint of segment ?

A.

B.

C.

D.

E.

70. How many different two-digit numbers can be formed from the digits if the numbers must be even and no digit can be repeated?

F.

G.

H.

J.

K.

71. How many integers are between and ?

A.

B.

C.

D.

E.

72.

In the figure above, , , and are straight line segments. What is the value of ?

F.

G.

H.

J.

K.

73. A roofing contractor uses shingles at a rate of bundles for each square feet of roof covered. At this rate, how many bundles will he need to cover a roof that is square feet?

A.

B.

C.

D.

E.

74.

Figure above is composed of congruent rectangular panels. The area of figure is square centimeters. What is the perimeter of figure in centimeters?

F. cm

G. cm

H. cm

J. cm

K. cm

75. Three gallons of gasoline are needed to drive miles. At this rate, how many gallons are needed to drive miles?

A. gal.

B. gal.

C. gal.

D. gal.

E. gal.

76. 8:54 a.m.

9:12 a.m.

9:24 a.m.

10:24 a.m.

11:18 a.m.

Light A flashes every minutes, and light B flashes every minutes. The two lights flash at the same time at 8:00 a.m. At how many of the times listed above will they again both flash at the same time?

F.

G.

H.

J.

K.

77.

Nikolai bought a packet of pens. His receipt is shown above. Assume that sales tax is rounded to the nearest cent. If the sales tax had been computed on the sale price

instead of on the regular price, how much lower would the tax have been?

A.

B.

C.

D.

E.

78.

A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the vehicles that passed the checkpoint yesterday morning. How many of the vehicles contained **at least** people?

F.

G.

H.

J.

K.

79. Jack and Roberto were assigned to guard a tower. Each was to watch for hours, then rest hours while the other watched. If Roberto began his first watch at 6:00 p.m., at what time will he begin his third watch?

A. 11:00 p.m.

B. 14:00 a.m.

C. 19:00 a.m.

D. 17:00 p.m.

E. 12:00 p.m

80. If Crystal multiplies her age by and then adds , she will get a number equal to her mother’s age. If is her mother’s age, what is Crystal’s age in terms of ?

F.

G.

H.

J.

K.

81.

Points P and Q are points on the number line above, which is divided into equal sections. What is the value of PQ?

A.

B.

C.

D.

E.

82.

The table above shows two rows of integers, Row A and Row B, and the relationship between them. Assume each row continues in the pattern shown. When the number appears in Row A, what is the corresponding number that will appear in Row B?

F.

G.

H.

J.

K.

83. A certain insect has a mass of milligrams. What is the insect’s mass in grams?

A. g.

B. g.

C. g.

D. g.

E. g.

84.

On the number line above, A is located at –, B is located at , and C is located at . D (not shown) is the midpoint of , and E (not shown) is the midpoint of . What is the midpoint of ?

F.

G.

H.

J.

K.

85. A video game originally priced at was on sale for off. Julian received a employee discount applied to the sale price. How much did Julian pay for the video game?

(Assume that there is no tax.)

A.

B.

C.

D.

E.

86. A box contains marbles— red and green. Five of these marbles are removed at random. If the probability of drawing a green marble is now , how many red marbles were removed from the box?

F.

G.

H.

J.

K.

87. Ryan must read pages for school tomorrow. It took him minutes to read the first of the assigned pages. At this rate, how much **additional** time will it take him to finish the reading?

A. hrs

B. hrs

C. hrs

D. hrs

E. hrs

88. In how many different ways can you make exactly using only nickels, dimes, and quarters, if you must have at least one of each coin?

F.

G.

H.

J.

K.

89. A cylindrical oil drum can hold 4,320 liters when it is completely full. Currently, the drum is full of oil. How many **kiloliters** (kL) of oil need to be added to fill the drum completely?

A. kL

B. kL

C. kL

D. kL

E. kL

90.

The end of a tent has a trapezoidal cross-section as shown above. What is the depth () of the tent if its volume is cubic feet?

F. ft

G. ft

H. ft

J. ft

K. ft

91. Ang has x dollars in his savings account, and Julia has y dollars in her savings account. Ang gives Julia of the money in his savings account, which Julia deposits into her savings account. Julia then spends of the total in her savings account.

Express the amount of money Julia spent in terms of and .

A.

B.

C.

D.

E.

92. Set R contains all integers from to , inclusive, and Set T contains all integers from to , inclusive. How many integers are included in R, but **not** in T?

F.

G.

H.

J.

K.

93. If can be any integer, what is the greatest possible value of the expression ?

A.

B.

C.

D.

E.

94. A recent survey asked students what pets they have. Based on the results, the following statements are all true:

students have dogs.

students have cats.

students have both dogs and cats.

students have no cats or dogs.

How many students were surveyed?

F.

G.

H.

J.

K.

95.

The table above shows prices for newspaper advertising. A store purchased quarter pages, half pages, and full pages of space in equal numbers for a total of . What is the total amount of page space the store purchased?

A. pages

B. pages

C. pages

D. pages

E. pages

96. A -gram mixture contains three items, X, Y, and Z. The ratio of the weights of X and Y is , and the ratio of the weights of Y and Z is . If all of item Z were removed, what would be the new weight of the mixture?

F. g

G. g

H. g

J. g

K. g

97.

A.

B.

C.

D.

E.

98. A car travels at 4,400 feet per minute. If the radius of each tire on the car is one foot, how many revolutions does one of these tires make in a single minute? (Use the approximation for .)

F.

G.

H.

J.

K.

99. Which number line below shows the solution to the inequality ?

A.

B.

C.

D.

E.

100. Nam worked on a job for days. On each of the last days, he worked hours more than the mean number of hours he worked per day during the first days. If he worked hours in all, how many hours did he work during the last days together?

F.

G.

H.

J.

K.

===========================

51.

A.

B.

C.

D.

E.

52. Carlos is picking colored pencils from a large bin that contains only red pencils, green pencils, and blue pencils. Without looking, Carlos pulls out pencils. If the pencils were distributed randomly in the bin, how many pencils of each color is it most likely that he picked?

F. red, green, blue

G. red, green, blue

H. red, green, blue

J. red, green, blue

K. red, green, blue

53. What time will it be hours after 9:30 p.m. on Friday?

A. 7:30 p.m. Saturday

B. 7:30 a.m. Sunday

C. 6:30 p.m. Sunday

D. 7:30 p.m. Sunday

E. 9:30 p.m. Sunday

54. Each child in a certain class is required to have school supplies of notebook and pencils. One notebook costs and one pencil costs . With , what is the maximum number of children that can be provided with the required supplies?

(Assume no tax.)

F.

G.

H.

J.

K.

55. How many positive integers satisfy the inequality ?

A.

B.

C.

D.

E.

56.

In the figure above, the base of is a side of rectangle , and point is the midpoint of . If the area of the shaded region is square centimeters, what is the area of the region that is **not** shaded?

F. sq cm

G. sq cm

H. sq cm

J. sq cm

K. sq cm

57. If and are positive integers such that , what is the **least** possible value for ?

A.

B.

C.

D.

E.

58.

F.

G.

H.

J.

K.

59.

The table above shows the number of songs played during a specific hour by different radio stations. What is the mean number of songs played during that hour by these stations?

A.

B.

C.

D.

E.

60.

In the equation above, what is the value of ?

F.

G.

H.

J.

K.

61. dollar lorgs

dollar dalts

Kwamme has lorgs and dalts. If he exchanges the lorgs and dalts for dollars according to the rates above, how many dollars will he receive? (Assume there are no exchange fees.)

A.

B.

C.

D.

E.

62.

The table above shows the distribution of eye color and hair color for children. How many of these children have blond hair or brown eyes, but **not both**?

F.

G.

H.

J.

K.

63.

One state has a sales tax on clothing items priced at or higher, and no sales tax on clothing items priced under . What is the total tax on the items in the table above?

A.

B.

C.

D.

E.

64. ,

,

,

,

.

.

.

,

,

______

If the missing terms in the problem above were filled in according to the pattern, what would be the sum of all the terms?

F.

G.

H.

J.

K.

65. A pitcher contained 32 ounces of orange juice and 12 ounces of grapefruit juice. More grapefruit juice was added to the pitcher until grapefruit juice represented of the pitcher’s contents. How many ounces of grapefruit juice were added?

A. oz

B. oz

C. oz

D. oz

E. oz

66.

According to the figure above, what was the median score for the test?

F.

G.

H.

J.

K.

67. The fuel mix for a small engine contains only ingredients: gasoline and oil. If the mix requires ounces of gasoline for every ounces of oil, how many ounces of gasoline are needed to make ounces of fuel mix?

A.

B.

C.

D.

E.

68. Which of the following shows the fractions , , and in order from least to greatest?

F. , ,

G. , ,

H. , ,

J. , ,

K. , ,

69. A prom dress originally priced at is on sale for off the original price. In addition, Alia has a coupon for off the discounted price. If there is a sales tax on the final price of the dress, what would Alia’s total cost be?

A.

B.

C.

D.

E.

70. ft, ft, ft, ft, ft

Jordan has trees with the heights shown above. He plans to plant the trees in a row with the tallest tree in the middle, the next shorter trees on either side, and the shortest trees on either end of the row. How many different ways of ordering the trees follow Jordan’s plan?

F.

G.

H.

J.

K.

71. In the set of consecutive integers from to , inclusive, there are integers that are multiples of both and . How many integers in the set are multiples of neither nor ?

A.

B.

C.

D.

E.

72. What is the prime factorization of ?

F.

G.

H.

J.

K.

73. If R, S, and T are integers and R + S and T – S are both odd numbers, which of the following must be an **even** number?

A. R + T

B. S + T

C. R

D. S

E. T

74.

On the number line above, point E (not shown) is the midpoint of and point F (not shown) is the midpoint of . What is the length of ?

F. unit

G. units

H. units

J. units

K. units

75. The regular price of a -ounce bag of candy is . Lily has a coupon for off one of these bags. What is the price per ounce (to the nearest cent) that Lily will pay if she uses the coupon?

A.

B.

C.

D.

E.

76. For what value of is ?

F.

G.

H.

J.

K.

77. On a particular vehicle, the front tire makes three revolutions for every one revolution the back tire makes. How many times larger is the radius of the back tire than the radius of the front tire?

A.

B.

C.

D.

E.

78. If and for or , what is the **least** possible value of ?

F.

G.

H.

J.

K.

79.

A.

B.

C.

D.

E.

80. To paint a room, Suzanne uses blue and white paint in the ratio of blue: white . What was the **total** number of gallons of paint used if she used gallons of blue paint?

F. gal.

G. gal.

H. gal.

J. gal.

K. gal.

81. Which sum below can be expressed as a non-repeating decimal?

A.

B.

C.

D.

E.

82. There are cubic centimeters in liter and cubic millimeters in milliliter. How many cubic millimeters are there in cubic centimeters?

F.

G.

H.

J.

K.

83. A radio station plays Samantha’s favorite song times each day at random times between 8:00 a.m. and 5:00 p.m. The song is minutes long. If Samantha turns on the radio at a random time between 8:00 a.m. and 5:00 p.m., what is the probability that her favorite song will be playing at that time?

A.

B.

C.

D.

E.

84. On the first leg of its trip, a plane flew the miles from New York City to Atlanta in hours. On the second leg, it flew the miles from Atlanta to Albuquerque in hours. How much greater was the plane’s mean speed, in miles per hour, on the second leg than on the first?

F. mph

G. mph

H. mph

J. mph

K. mph

85. A water tank is full; then, gallons of water are added to the tank, making it full.

How many gallons of water could the tank hold if it were completely full?

A. gal.

B. gal.

C. gal.

D. gal.

E. gal.

86. Today, Tom is of Jordan’s age. In 2 years, Tom will be of Jordan’s age. How old is Jordan today?

F.

G.

H.

J.

K.

87. Let . What is the value of ?

A.

B.

C.

D.

E.

88. Joe began to increase the speed of his car at 2:00 p.m. Since that time, the speed of Joe’s car has been steadily increasing by miles per hour for each half minute that has passed. If the car is now traveling miles per hour, for how many minutes has the car been exceeding the speed limit of miles per hour?

F. min

G. min

H. min

J. min

K. min

89. How many positive two-digit numbers are evenly divisible by ?

A.

B.

C.

D.

E.

90. If and are numbers such that , what is the value of ?

F.

G.

H.

J.

K.

91. A steel container is shaped like a cube feet on each side. This container is being filled with water at a rate of cubic feet per minute. At the same time, water is leaking from the bottom of the container at a rate of cubic feet per minute. If the container is exactly half-filled at 9:00 a.m., at what time will the container begin to overflow?

A. 9:55 a.m.

B. 10:00 a.m.

C. 10:11 a.m.

D. 10:40 a.m.

E. 12:20 p.m.

92.

The figure above shows three intersecting straight lines. What is the value of ?

F.

G.

H.

J.

K.

93. Each week, Arnold has fixed expenses of at his furniture shop. It costs Arnold to make a chair in his shop, and he sells each chair for . What is Arnold’s profit if he makes and sells chairs in week?

A.

B.

C.

D.

E.

94.

The drawing above represents a rectangular lot containing a building, indicated by the shaded region. The dashed lines divide the lot into twelve equal-sized squares. If the unshaded portion of the lot is to be paved, about how many square feet will be paved?

F. sq ft

G. sq ft

H. sq ft

J. sq ft

K. sq ft

95. In a restaurant, the mean annual salary of the chefs is , and the mean annual salary of the waiters is . What is the mean annual salary of all employees?

A.

B.

C.

D.

E.

96. One week the price of gasoline dropped by per gallon. Madison’s car travels miles each way to work, and her car travels miles on each gallon of gasoline. What were her total savings, to the nearest cent, over the -day work week?

F.

G.

H.

J.

K.

97. Marta and Kim are sisters. Five years ago, Kim’s age was twice as great as Marta’s age. If Marta is now years old, which expression represents Kim’s age now?

A.

B.

C.

D.

E.

98. {}

Company X wants to assign each employee a 3-digit ID number formed from digits in the set shown above. No digit may appear more than once in an ID number, and no two employees may be assigned the same ID number. What is the greatest total number of possible different ID numbers?

F.

G.

H.

J.

K.

99. A rectangular floor is feet wide and feet long. It must be covered with square tiles that are inches on each side. Assume there is no space between adjacent tiles. If the tiles cost each, how much will it cost to buy the tiles needed to cover the floor?

A.

B.

C.

D.

E.

100. What is the greatest prime factor of ?

F.

G.

H.

J.

K.

==========================

Grade 9 Math

There are students in a class. The frequency table above shows the number of these students that own or pets. What is the mean number of pets owned per student in this class?

A.

B.

C.

D.

E.

2.

On the number line above, which letter could represent the location of ?

F. R

G. S

H. T

J. U

K. V

3.

A.

B.

C.

D.

E.

4. If , what is the value of ?

F.

G.

H.

J.

K.

5.

In the figure above, all lines are straight. and intersect at point . What is the value of ?

A.

B.

C.

D.

E.

6. Raul has two containers. One is a cylinder with an inner radius of inches and an inner height of inches. The other is a cube with inner height, width, and length each equal to inches. The cylinder is filled with water and the cube is empty. If Raul pours the contents of the cylinder into the cube, how deep will the water be in the cube?

F. in.

G. in.

H. in.

J. in.

K. in.

7. The translation of point to is equivalent to rotating point by which of the following clockwise rotations about the origin?

A.

B.

C.

D.

E.

8. If , what is the value of ?

F.

G.

H.

J.

K.

9.

A swimming pool is being filled with water at a constant rate. The figure above is a portion of a graph that shows how the number of gallons of water in the pool changes over time. Starting with an empty pool, at the end of hour there are gallons in the pool. If the pool continues to fill at this rate, how much water will be in the pool at the end of hour ? (Assume that the pool holds a total of gallons.)

A. gal.

B. gal.

C. gal.

D. gal.

E. gal.

10. Let . Using that rule, if , what is ?

F.

G.

H.

J.

K.

11.

In the figure above, what is the value of ?

A. cm

B. cm

C. cm

D. cm

E. cm

12. Straight line passes through the point with an -intercept of . What is the equation of line ?

F.

G.

H.

J.

K.

13.

The line defined by the equation intercepts the -axis at point P as shown above. What are the coordinates of point P?

A.

B.

C.

D.

E.

14. Seven consecutive integers are arranged in increasing order. Their sum is . What is the value of the second integer in terms of ?

F.

G.

H.

J.

K.

15. , , , ,

If , which one of the expressions above does **not** represent a rational number?

A.

B.

C.

D.

E.

16. A tiny robot sits on the point of the coordinate plane. At each flash of a blue light, it moves units to the right and units down. At each flash of a red light, it moves unit to the left and units up. If, at the end of red flashes and n blue flashes, the robot is sitting on the line , what is ?

F.

G.

H.

J.

K.

17. ,

,

How many integer values of satisfy both inequalities shown above?

A.

B.

C.

D.

E.

## Additional SHSAT Resources

SHSAT Prep

SHSAT: Everything You Need to Know About the Test

9th Grade SHSAT

SHSAT 2016-2017

SHSAT 2018-2019