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SAT Math - Numbers and Operations Practice Test

Test your SAT Math - Numbers & Operations skills with 30 random practice test questions. Great for students preparing for the SAT Math - Numbers & Operations section!

1 / 30

1. What is 8/11 × 22/32?

A) 1/8

B) 1/2

C) 1/3... 8×22/(11×32)=176/352=1/2.

D) 1/4

2 / 30

2. The Euler characteristic of a connected planar graph satisfies V-E+F=

A) 1

B) 0

C) F

D) 2

3 / 30

3. What is the square root of 0.25?

A) 0.5

B) 0.025

C) 5

D) 0.05

4 / 30

4. The sum of reciprocals of all divisors of 12 is:

A) 7/8

B) 7/3

C) 7/4

D) 7/6... sum=1+1/2+1/3+1/4+1/6+1/12=12/12+6/12+4/12+3/12+2/12+1/12=28/12=7/3

5 / 30

5. How many positive divisors does 2^5 × 3^3 have?

A) 18

B) 30

C) 20

D) 24

6 / 30

6. What is the 8th Fibonacci number?

A) 55... F:1,1,2,3,5,8,13,21. F₈=21.

B) 21

C) 13

D) 34

7 / 30

7. What is the number of solutions to x+y+z=10 in non-negative integers?

A) 55

B) 78

C) 91... C(10+2,2)=C(12,2)=66

D) 66

8 / 30

8. For the sequence defined by xₙ₊₁=xₙ(2-axₙ) (Newton iteration for 1/a), starting at x₀≈1/a, it converges to:

A) a

B) 0

C) 1/a

D) √a

9 / 30

9. The Ramanujan sum S_k(n) for k=1: S₁(n)=μ(n/gcd(n,1))φ(n)/φ(n/1)... For simple case: sum of primitive n-th roots of unity=μ(n). For n=6, S₁(6)=μ(6)=

A) 0

B) 1

C) 2

D) −1

10 / 30

10. For the generating function G(x) = ∑aₙxⁿ where aₙ=n², G(1/2) =

A) 14... ∑n²(1/2)^n=2/(1-1/2)³×... =(1/2)(3/2)/(1/2)³=(3/4)/(1/8)=6

B) 8

C) 6

D) 12

11 / 30

11. What is 2/3 + 5/9?

A) 1/9... LCD=9. 6/9+5/9=11/9.

B) 7/3

C) 11/9

D) 7/9

12 / 30

12. Simplify: √(36)×√(4)

A) 24

B) 48

C) 144

D) 12

13 / 30

13. The units digit of 13^99 is:

A) 9

B) 7

C) 3

D) 1... 13≡3(mod10). 3^99: cycle 3,9,7,1. 99 mod4=3. Units=7.

14 / 30

14. What is 4/9 + 2/3?

A) 6/12

B) 10/9

C) 4/3

D) 2/9

15 / 30

15. For large prime p, Fermat's little theorem: a^p≡

A) 1(mod p)

B) p(mod a)

C) a(mod p)

D) 0(mod p)

16 / 30

16. A bag of 12 apples costs $3.60. Cost per apple:

A) $0.35

B) $0.28

C) $0.30

D) $0.25

17 / 30

17. What is the value of 7! ÷ 5!?

A) 14

B) 21

C) 35

D) 42

18 / 30

18. For positive reals: if AM=6 and GM=4, what is HM?

A) 3

B) 9/8

C) 8/3

D) 4/3

19 / 30

19. The number of positive integer solutions to x+y+z=12 is:

A) 77

B) 55

C) 66

D) 88... C(12-1,3-1)=C(11,2)=55

20 / 30

20. The number of solutions to φ(n)=24 is:

A) 20... φ(n)=24 for n=25,35,39,45,50,52,56,70,72,78 and their multiples... counting: n=25,35,39,45,50,52,56,70,72,78 gives 10

B) 5

C) 15

D) 10

21 / 30

21. What is the generating function for the number of ways to make change for n cents using 1,5,10 cent coins?

A) x/(1-x^10)

B) (1+x)(1+x⁵)(1+x^10)

C) 1/(1+x+x⁵)

D) 1/((1-x)(1-x⁵)(1-x^10))

22 / 30

22. What is the number of zeros at the end of 30!?

A) 6

B) 5

C) 8... floor(30/5)+floor(30/25)=6+1=7.

D) 7

23 / 30

23. How many 2-digit numbers are perfect squares?

A) 5

B) 7

C) 6

D) 4

24 / 30

24. What is the value of 12P2?

A) 110

B) 120

C) 132

D) 66

25 / 30

25. The largest known Fermat prime (2^(2^n)+1 prime) corresponds to n=

A) 6

B) 7... F₀-F₄ are prime. F₄=65537 is the largest known Fermat prime.

C) 4

D) 5

26 / 30

26. For positive a,b,c with abc=1, minimum of a+b+c is:

A) e

B) 3

C) 3(abc)^(1/3)=3

D) 1

27 / 30

27. What is (3/5)³?

A) 27/125

B) 9/25

C) 9/125

D) 27/15

28 / 30

28. The number 407 = 7×58+1. What is 407 mod 7?

A) 1

B) 3

C) 2

D) 0

29 / 30

29. How many solutions does x² ≡ 1 (mod 8) have in {0,1,2,...,7}?

A) 2

B) 4

C) 3

D) 5

30 / 30

30. The value of ∑(k=0 to n) (-1)^k·C(n,k) is:

A) 1

B) 2^n

C) n

D) 0 for n>0

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