# SAT Sample Paper-Mathematics

SAT(Scholastic Aptitude Test/ Scholastic Assessment Test) is organized for college admission in United States. It consists of 3 main sections-Mathematics,Critical reading & Writing. Each section score is judged on a scale of 200-800. This exam is offered 7 times a year in United States.The Mathematics section of SAT is the quantitative section or calculation section. It contains 3 scored sections-

- Two 25-minute Section
- One 20-minute section

One of the 25-minute section is totally MCQ type & 2nd 25-min section contains 8 MCQ type and 10 grid-in questions.One 20 min section is all multiple choice type.

Note- Use of graphing calculator is sometimes preferred generally for geometry problems & questions involving multiple calculations.

**SAT Sample Paper-Mathematics**

**NOTE:-**

• Answers must be written in English or the medium of instruction of the candidate in High school.

• Attempt all questions.

• Answer all the questions in the booklets provided for the purpose. No pages should be removed from the booklets.

• There is no negative marking.

• Answer all questions of section I at one place. Same applies to section II. The remaining questions can be answered in any order.

• Answers to sections I and II must be supported by mathematical reasoning.

• Use of calculators, slide rule, graph paper and logarithmic, trigonometric and statistical tables is not permitted.

**Time: Two Hours**

**Max.Marks: 60**

**Section A**

**This section has five questions. Each question is provided with five alternative answers. Only one of them is the correct answer. Indicate the correct answer by A,B,C,D,E. Order of the questions must be maintained.**

**1. n1, n2, ….., n1997 are integers, not necessarily distinct.**

A) (-1)X = 1, (-1)Y = 1

B) (-1)X = 1, (-1)Y = -1

C) (-1)X = -1, (-1)Y = 1

D) (-1)X = -1, (-1)Y = -1

E). None of these.

**2. The first hundred natural numbers are written down. Ni denotes the number of times the digit i appears. Then**

A) N0=12, N1=20, N2=20

B) N0=11, N1=20, N2=20

C) N0=11, N1=21, N2=20

D) N0=12, N1=20, N2=19

E) none of these

**3. If n is a natural number, then is a positive integer**

A) when n is even

B) when n is odd

C) only when n = 117 or n = 119

D) only when n = 1 or n = 3

E) none of these

**4. If a2+b2+c2 = D where a and b are consecutive positive integers and c = ab, then is**

(A) always an even integer

(B) sometimes an odd integer and sometimes not

(C) always an odd integer

(D) sometimes rational, sometimes not

(E) always irrational

**5.The number of equiangular octagons fixing 6 consecutive sides is [ ]**

A) Infinitely many

B) exactly 8

C) at most 8

D) 0

E) None of these

**SECTION – B**

**1. If a2+b2+c2 = D where a and b are consecutive positive integers and c = ab, then is**

(A) always an even integer

(B) sometimes an odd integer and sometimes not

(C) always an odd integer

(D) sometimes rational, sometimes not

(E) always irrational

**2. The smallest value of for all real values of x is**

(A) –16.25

(B) –16

(C) –15

(D) –8

(E) None of these

**3**. **If ABC is a triangle with AB = 7, BC = 9 and CA = n where n is a positive integer, then possible two values of n are ____________________.**

**4. The circle C1 has centre at (2,3) and radius 3. The circle C2 has centre at (-1,4) and radius 5. The number of common tangents they possess is ________________**

**5. The smallest value of for all real values of x is**

(A) –16.25

(B) –16

(C) –15

(D) –8

(E) None of these

**SECTION – C**

**1)**.**Solve in positive integers m,n the equation 23m+1 + 32n + 5m + 5n = 2003.**

**2). ABCD is a cyclic quadrilateral. bisects . AB = 10, AD = 12, DC = 11, Determine BC.**

**3).If X is a finite set, let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite sets A,B, n(P(A)) = n(P(B)) + 15, then n(B) = _____________, n(A) = ___________.**

**4). Numbers 1,2,3,…..,1998 are written in the natural order. Numbers in odd places are stricken off to obtain a new sequence. Numbers in odd places are stricken off from this sequence to obtain another sequence and so on, until only one term a is left. Then a=________**

**5. The circle C1 has centre at (2, 3) and radius 3. The circle C2 has centre at (-1, 4) and radius 5. The number of common tangents they possess is ________________**

**SECTION – D**

**1.A square is drawn in side a triangle with sides 3, 4 and 5 such that one corner of the square touches the side 3 of the triangle, another corner touches the side 4 of the triangle and the base of the square rests on the longest side of the triangle. What is the side of the square?**

**2. Let ABCD be a square. Let P, Q, R, S be respectively points on AB, BC, CD, DA such that PR and QS intersect at right angles. Show that PR=QS.**

**3. A right angled triangle has legs am,b, a>b. The right angle is bisected splitting the original triangle into two smaller triangles. Find the distance between the orthocenters of the smaller triangles using the co-ordinate geometry methods or otherwise.**

**4. A belt wraps around two pulleys which are mounted with their centers s apart. If the radius of one pulley is R and the radius of the other is (R+r) , show that the length of the belt is .**

**5. Let x be any real number. Let and** . Prove that .

SAT Sample Paper-Mathematics-II (objective questions)

**1. If f(z)=(z-1)/(z+1) , then f(f(z)) will be equal to**

a) 1/z

b)-1/z

c)-z

d) z

**2. How many 6-digit numbers have all their digits either all odd or all even?**

a) 15625

b) 30225

c) 28125

d) 18425

**3. A person has 4 children with at least two boys. Find the probability of having at least 3 boys among the children.**

a) 1/3

b) 3/4

c) 1/4

d) 1/2

**4. If w,v,x,y,z are non-negative integers less than 11 then the number of possible solution sets (w,v,x,y,z) such that 11^4 w+ 11^3 v+ 11^2 x +11 y +z= 151001 is?**

a) 2

b) 0

c) 3

d) 1

**5. The number of distinct triangles with integral valued sides and perimeter equal to 14 is?**

a) 3

b) 5

c) 2

d) 4

**6. 30 men working 5 hr. a day can do a work in 16 days. In how many days will 15 men working 8 hr. a day do the same work?**

a) 16 days

b) 21 days

c) 20 days

d) 15 days

**7. A certain sum of money trebles itself in 6 years. In how many years it wil be Seven times?**

a) 15 years

b) 18 years

c) 17 years

d) 20 years

**8. Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height?**

a) 1:2:3 ** **

b) 3:2:1

c) 1:3:4

d) 2:1:3

**9. Two numbers P and Q are 20% and 28% less than a third number R. Find by what percentage is the number Q less than P?**

a) 12

b) 8

c) 10

d) 9

**10. In what ratio should two quantities of coffee powder having the rates of Rs. 47 per kg and Rs. 32 per kg be mixed in order to get a mixture that would have a rate of Rs. 37 per kg?**

a) 2:1

b) 1:2

c) 3:1

d) 4:1

**11. A man bought 100 kg of rice for Rs. 1100 and sold it at a loss of as much money as he received for 20 kg rice. At what price did he sell the rice?**

a) Rs. 10.33 per kg

b) Rs. 9 per kg

c) Rs. 8.95 per kg

d) Rs. 9.166 per kg

**12. If x^2+ax+b leaves the same remainder 5 when divided by x-1 or x+1 then the values of a and b are respectively?**

a) 4 and 0

b) 0 and 3

c) 0 and 4

d) 3 and 4

**13. If log 2= 0.301, find the number of digits in (125)^25?**

a) 52

b) 53

c) 49

d) 64

**14. How many figures are required to number a book containing 150 pages?**

a) 324

b) 425

c) 360

d) 342

**15. A pair of fair dice are rolled together till a sum of either 4 or 7 is obtained. The probability that 4 comes before 7 is?**

a) 0.33

b) 0.4

c) 0.45

d) 0.67

**Solution for maths-II **

1- b 8- a

2- c 9- c

3- b 10- b

4- d 11- d

5- d 12- c

6- c 13- b

7- b 14- d

15- a

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A right triangle had sides a and b where a>b . if the right angle is bisected then find the distance between orthocenters of smaller triangles

SAT is a test used as one of the means to seek admission to higher education.Cracking this examination is like dream come true! The above set of sample question paper will be very helpful for those preparing for it.