The **SAT Test **is taken by students and it assesses a student’s readiness for college. It has three sections: reading, mathematics and writing, and today we will be focusing on the math part, also known as the Quantitative Section. Within the math section of the SAT there are three sub-sections: one with 20 multiple choice questions (25 minutes), one with 8 multiple choice and 10 grid-in (write your answer in a provided box) questions (25 minutes) and finally, another section with 16 multiple choice questions (20 minutes).

Four-function, scientific and graphing calculators *are* allowed on the math section of the SAT, but not on the other two sections, and calculators with QWERTY keyboards are not permitted at all. The types of questions contained in the math section of the SAT are geometry, algebra, statistics, operations, probability and data analysis. The average score on the math section is 515.

## Practice Problems

Below are some SAT math practice problems, and they cover most of the types of questions a student may run into while taking the test, including multiple choice and grid-in questions. The answers are in the next section. Good luck!

**1.** Of the following, which is greater than ½ ?

A. 2/5

B. 4/7

C. 4/9

D. 5/11

E. 6/13

**2.** If an object travels at five feet per second, how many feet does it travel in one hour?

A. 30

B. 300

C. 720

D. 1800

E. 18000

**3.** What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

A. 90

B. 95

C. 100

D. 105

E. 110

**4.** A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

A. 48

B. 32

C. 24

D. 18

E. 12

**5.** In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6

B. 15

C. 24

D. 33

E. 54

**6.** If f(x) = │(x² – 50)│, what is the value of f(-5) ?

A. 75

B. 25

C. 0

D. -25

E. -75

**7.** ( √2 – √3 )² =

A. 5 – 2√6

B. 5 – √6

C. 1 – 2√6

D. 1 – √2

E. 1

**8.** 2^{30} + 2^{30} + 2^{30} + 2^{30} =

A. 8^{120}

B. 8^{30}

C. 2^{32}

D. 2^{30}

E. 2^{26}

**9.** Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not traveling any road twice on the same trip?

A. 10

B. 8

C. 6

D. 4

E. 2

**11.** A typist can type 45 words per minute. He increases his speed by 20 per cent. How many words can he now type per **hour** ?

**12.** If 2y – x = 8 , and 3x – y = 1, what is the value of x ?

**13.** The sum of four consecutive integers is 410. What is the value of the least of these integers?

**14.** On a map showing only four countries, A, B, C and D, A shares a border with B and C. Country D shares a border with B and C. But countries B and C and countries A and D do not share borders. If the map requires different colors for countries with common borders, what is the minimum number of colors required to complete the map?

**15.** A square has sides s and diagonal d. If 2s² + d² = 100, what is the value of s?

**16.** Different four-letter passwords can be constructed using the letters A, B, C and D only once. How many such passwords exist if either C or B must be in second position?

**17.** A book distributor sends out standardized packages weighing 1, 1.5 or 2 kilograms. If during one week 40 per cent of the packages weigh 1 kg, 50 per cent weigh 1.5 kg and 10 per cent weigh 2 kg, what is the average weight in kilograms of the parcels that week?

**18.** If two lines intersect at a point to form four angles, and one angle is twice as large as its adjacent (neighboring) angle, what is the degree measure of the smallest angle?

**19.** What is the area of the shaded region?

**20.** Two square flowerbeds are placed symmetrically in a rectangular garden as shown in the diagram. The distance between the beds is y and so is the width of the border around the beds on all sides. A seed blown into the garden by the wind is equally likely to land anywhere in the garden. What is the probability that it actually lands in a flowerbed?

**21.** 3x + y = 19 , and x + 3y = 1.

Find the value of 2x + 2y

A. 20

B. 18

C. 11

D. 10

E. 5

**22.** The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of

A. 45%

B. 40%

C. 35%

D. 32.5%

E. 30%

**23.** x and y are integers

x + y < 11 , and x > 6

What is the smallest possible value of x – y ?

A. 1

B. 2

C. 4

D. -2

E. -4

**24.** If x^{5}y^{4}z^{2} <0 , which of the following must be true?

I xy <0

II yz <0

III xz <0

A. I

B. II

C. III

D. I and II

E. None

**25.** In the figure above, BCD is a line segment and Angle BAC = ¼ Angle ACB ; Angle ACD = ?

A. 140

B. 100

C. 120

D. 60

E. it cannot be determined from the information given

**26.** Which of the following integers is in the solution set of │1 – 3x│ < 5 ?

I -1

II 1

III 2

A. I only

B. II only

C. III only

D. I and II only

E. I, II and III

**27.** In a certain village, m liters of water are required per household per month. At this rate, if there are n households in the village, how long (in months) will p liters of water last?

A. p /mn

B. mn / p

C. mp / n

D. np / m

E. npm

**28.** In the figure above, what is the slope of line l ?

A. – 3

B. – 1/3

C. 0

D. 1/3

E. 3

**29.** What digit appears in the units place in the number obtained when 2^{320} is multiplied out?

A. 0

B. 2

C. 4

D. 6

E. 8

**30.** Radius of circle center O is 3 times the radius of circle center C.

Angle ACB = Angle POQ

If the shaded area of circle C is 2 then what is the area of the shaded part of circle O ?

A. 6

B. 12

C. 18

D. 36

E. 3/2

**31.** A time lapse camera takes pictures once every 40 seconds. How many pictures does it take in a 24 hour period? (Assume that it takes its first picture 40 seconds after the start of the time period.)

**32.** Triangle ABC is equilateral. What is the degree measure of angle y ? (Ignore the degree sign when gridding your answer)

**33.** If a sack of dried dog food feeds 4 dogs or 5 puppies for one week, then 5 sacks of the food will feed 15 puppies and how many dogs ?

**34.** The sum of three numbers is 6. Each number is increased by 20 and the new numbers are multiplied by 10. What is the sum of the resulting numbers?

**35.** What is the largest odd-numbered factor of 4500 ?

**36.** Points A and B are on the top and bottom edges of a cylindrical roll of paper of height 8 and circumference 12. A and B are diagonally opposite each other. The paper is cut along line C and opened out. How far apart are A and B on the flat surface?

**37.** 2 cars travel from the same point along parallel lanes of a highway for a distance of 10 miles. When car M, travelling at 60 miles an hour reaches the end of the distance, how much further will car N have to travel if it is travelling at 48 miles an hour?

**38.** ♣ ♥ ¥ ♠ ¤

How many different **3-symbol** arrangements of the symbols above are possible if the symbol ¤ must be in the last position, and the symbol ♣ can be used in only one arrangement. The other symbols can be used more than once in an arrangement.

**39.** What one value for x can be correctly entered into the answer grid?

**40.** Family 1 comprising mother, father and son are to be seated at a table with family 2 comprising mother, father and daughter. The layout of the table is shown in the diagram. F represents one of the fathers and M represents one of the mothers. X represents any family member. If a male family member must sit opposite a female of the other family, how many different seating plans are possible?

**41. **Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

A. 1155

B. 1145

C. 1040

D. 950

E. 259

**42.** AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD ?

A. 100

B. 90

C. 80

D. 70

E. cannot be determined from the information

**43.** If x / y is an integer, which of the following statements must be true?

A. both x and y are integers

B. x is an integer

C. either x or y is negative

D. y / x is an integer

E. x = ny where n is an integer

**44.** What is the average of four tenths and five thousandths?

A. 25002

B. 2502

C. 0.225

D. 0.2025

E. 0.02025

**45.** What is the simplified result of following the steps below in order?

(1) add 5y to 2x

(2) multiply the sum by 3

(3) subtract x + y from the product

A. 5x + 14y

B. 5x + 16y

C. 5x + 5y

D. 6x + 4y

E. 3x + 12y

**46.** If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of line q which is a reflection of line p in the x-axis?

A. y = -3x + 2

B. y = -3x – 2

C. y = 3x – 2

D. y = -1/3x – 5

E. y = -1/3x + 5

**7.** If y ¤ x = y^{2x} for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 3^{8}

B. 3^{12}

C. 3^{16}

D. 3^{24}

E. 3^{32}

**48.** The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5

B. 3

C. 5

D. 25

E. 50

**49.** The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the large brick?

A. 32

B. 40

C. 60

D. 72

E. 80

**50.** (3x + 2) (2x – 5) = ax² + kx + n .

What is the value of a – n + k ?

A. 5

B. 8

C. 9

D. 10

E. 11

**51.** The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what percentage is the area too large?

**52.** Andy, Mark and Sean all have their birthdays today, but Andy is more than twice as old as Mark and Mark is more than four years older than Sean. If Andy is less than 16 years old, what is one possible value for Mark’s age in years ?

**53.** ABCD is a square. Also AP=PQ=QB=BR=RS=SC=CT=TU=UD=DV=VW=WA. The area of the octagon PQRSTUVW is what fraction of the square?

**54.** Triangle ABC is a right angled triangle. Also AC = 5, CB = 3 and angle ADB is a right angle.

What is the length of DB?

**55.** A football team has won 10 games and lost 5 games. If the team wins the remaining games of the season, it will have won 80 percent of its games. How many games in total will have been played?

**56.** Let the function f be defined by f(x) = x – 1

What is the value of y if y is a positive integer such that 1/3 f(y²) = 5?

**57.** The amount of time taken to paint a wall is inversely proportional to the number of painters working on the job. If it takes 3 painters 5 days to complete such a job, how many days longer will it take if there are only 2 painters working?

**58.** Line l and line m lie in the same plane but have no points in common. They are both tangent to a circle of area 9π. What is the shortest distance between any point on l and any point on m?

**59.** A box contains 5 chocolates with soft centers, 6 with nut centers, and 11 with hard caramel centers. Three students take turns to take a chocolate at random from the box and eat it. If the probability that all three students take soft centers is 1/x, what is the value of x?

**60.** At one point in a game the shooting team has a ratio of hits to misses of 5:1. After the team misses the next three shots, which are the last in the game, its ratio of hits to misses is 5:2. What is the total number of shots taken by the team in the game?

## Answers

1) B 2) E 3) C 4) A 5) C 6) B 7) A 8) C 9) B 10) D

11) 3240 12) 2 13) 101 14) 2 15) 5 16) 12 17) 1.35 18) 60 19) 7 20) 2/7

21) D 22) B 23) C 24) E 25) E 26) D 27) A 28) B 29) D 30) C

31) 2160 32) 80 33) 8 34) 660 35) 1125 36) 10 37) 2 38) 10 39) 3 40)16

41) B 42) C 43) E 44) D 45) A 46) B 47) E 48) B 49) B 50) A

51) 21 51) 6 52) 7/9 53) 2.4 54) 25 55) 4 56) 2.5 57) 6 58) 154 59) 21