FREE MATHEMATICS QUESTION

• Given that​​ E={1,2,3, . . . . 20}​​ P={x:x is a prime number}​​ Q={x:x is an odd number}​​ elements of​​ P'∩Q'​​ is _________ A.​​ {2,3,5,7,11,13,17,19}​​ B.​​ {1,3,5,7,9,11,13,15,17}​​ C.​​ {2,4,6,8,10,12,14,16,18}​​ D.​​ {4,6,8,10,12,14,16,18,20}

• If​​ x​​ varies directly as the sum of​​ u​​ and​​ v​​ and inversely as the product of​​ ​​ u​​ and​​ v. Find the constant of proportionality when​​ x=24,​​ u=4​​ and​​ v=2. A. 64 B. 32 C. 16 D. 12

• The solution to the inequality​​ x2-x-12≤0​​ is A.​​ x≤-3, x≤4​​ B.​​ -3≤ x≤4​​ C.​​ -4≤ x≤3​​ D.​​ x≤-3, x≥4

• If​​ A∈B, then​​ Ac∪Bc​​ is A.​​ A​​ B.​​ B​​ C.​​ Ac​​ D.​​ Bc

• If​​ p​​ varies directly as​​ r2​​ and​​ r​​ varies inversely as​​ q3. The relationship between​​ p​​ and​​ q can be expressed as A.​​ p∝q6​​ B.​​ p∝1q2​​ C.​​ p∝q32​​ D.​​ p∝1q32

• The inequality represented in the above number line is ________ A.​​ -1   2≤ x<2​​ B.​​ -1   2< x≤2​​ C.​​ x≤-1   2, x>2​​ D.​​ x<12, x≥2

•  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

The set notation of the​​ shaded region in the above Venn diagram is A.​​ P∪Q∪R'​​ B.​​ P'∩Q'∩R​​ C.​​ (P∩Q)∪R'​​ D.​​ P∩Q∩R'

• The square of period, T of a pendulum varies directly and its length​​ l. When​​ T=1.2s l=80cm. Find the value of​​ l​​ when​​ T=1.5s​​ A. 125cm B. 105cm C. 100cm D. 90cm

• Solve​​ 2x+5<-3​​ A.​​ x<-4​​ B.​​ x<-1​​ C.​​ -4< x<-1​​ D.​​ -4> x>-1

• Given that​​ A=1,2,x,y,z,4,5,7​​ and​​ B=2,z,4,6,7,8,9,w​​ Find​​ A-B​​ A.​​ 1,x,y,5​​ B.​​ 6,8,9,w​​ C.​​ 1,x,y,5,6,8,9,w​​ D.​​ 1,2,x,y,z,4,5,6,7,9,w

• x​​ varies directly as​​ y2. When​​ x​​ is reduced by 19%, by how much will​​ y​​ change? A. reduced by 19% B. increase by 19% C. reduced by 10% D. increase by 10%

•  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

The inequality that satisfy the above shaded region above is _________ A.​​ 5y-3x≤15​​ B.​​ 5y-3x≥15​​ C.​​ 3y-5x<15​​ D.​​ 3y-5x>15

•  ​​ ​​​​ 

From the above Venn diagram, elements of​​ X∩Y'​​ is _________​​ A. {2,7} B. {4,8,10,13,15} C. {1,6,11,12,14} D. {3,5,9}

• l​​ varies directly as cube of​​ m​​ and inversely as the square root of​​ n.​​ l=144​​ when​​ m=2​​ and ​​ n=9. Find ​​ l​​ when ​​ m=3​​ and​​ n=36​​ A. 225 B. 243 C. 216 D. 284

• If​​ a>b, which of the following is not always true? A.​​ a+2>b+2​​ B.​​ -b>-a​​ C.​​ a2>b2​​ D.​​ a-1>b-1

• In a class of 65 students, those who like Rice and Beans are exactly half those who like neither rice or Beans. Those who like none, while those who like Rice is twice those who like Beans. How many like Rice only? A. 15 B. 25 C. 35 D. 45

• If it takes 24 men 15 days working at a rate of​​ 6 hours day to clear a bush. How many men will clear the same bush in 36 days working at a rate of 5 hours per day? A. 12 men B. 15 men C. 18 men D. 24 men

• x+23-x-24≤56​​ , the possible value of​​ x​​ that satisfy the inequality is _______ A. 3 B.​​ -3​​ C. 5 D.​​ -5

• In a class of 45 students, 20 offer​​ Physics, 22 offer Economics, 18 offer Government, 8 offer Physics and Economics and nobody offer Physics and Government. If 4 offer none of the three subjects. How many offer Economics and Government? A. 7 B. 8 C. 11 D. 12

• If​​ 1u+1v=1f​​ , make​​ v​​ the subject of the formula​​  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ A.​​ v=ufu-f​​ B.​​ v=uff-u​​ C.​​ v=u+fu-f​​ D.​​ v=u+fuf