Math and Set Theory Quiz

Currency Exchange

• If US1.00isequivalenttoEC1.00 is equivalent to EC1.00isequivalenttoEC2.68, then one would get US37.31forEC37.31 for EC37.31forEC100.

Set Theory

• If U = {1, 2, 3,... 10} and S = {4, 5, 6, 7, 8}, then S' = {1, 2, 3, 9, 10}.
• In a Venn diagram, the shaded portion can represent different sets, such as:
  • P ∪ Q: the union of sets P and Q
  • P ∩ Q': the intersection of set P and the complement of set Q
  • P' ∩ Q: the intersection of the complement of set P and set Q
  • P ∩ Q: the intersection of sets P and Q
• In a Venn diagram, the shaded area can also represent:
  • (P∪Q)': the complement of the union of sets P and Q
  • (Q ∪ R)': the complement of the union of sets Q and R
  • (P∩Q) ∪ R: the union of the intersection of sets P and Q, and set R
  • (P ∪ R)' ∩ Q: the intersection of the complement of the union of sets P and R, and set Q

Math Problems

• 32747 written to 4 significant figures is 32740
• Decimal equivalent of 7/8 is 0.875
• 2 2/5 + 3 1/10 = 5 3/15
• In a school of 910 pupils, 37/50 are boys, and 2/5 of the boys wear glasses, so 156 boys wear glasses
• 0.045 × 10^3 in scientific notation is 4.5 × 10^4

Ratio and Division

• If xisdividedamongthreeboysintheratio2:3:7,andAndrewgetsx is divided among three boys in the ratio 2:3:7, and Andrew gets xisdividedamongthreeboysintheratio2:3:7,andAndrewgets15 more than Keith, then x = $45
• If x = 3^2 × 2^3, then x^4 = 3^2 × 2^6 × 3^4

Sets and Numbers

• {multiples of 20} has an infinite number of members
• 31 is a prime number
• The number of members in {factors of 20} is finite

Time and Intervals

• Three lights flash at intervals of 4, 6, and 10 seconds respectively; they will next flash together again after 120 seconds

Discounts and Prices

• After a 10% discount, an article is sold for 360,sothepricebeforethediscountwas360, so the price before the discount was 360,sothepricebeforethediscountwas400
• A store charges 6% VAT on all sales, so the total cost of a shirt marked at 30is30 is 30is31.80
• A shopkeeper buys 48 radios for a wholesale price of 7200,andhesellseachradioat7200, and he sells each radio at 7200,andhesellseachradioat172.50 to make a profit of 15% on his cost

Interest and Investments

• The difference in annual interest on a deposit of 2000is2000 is 2000is120 when the interest rate decreases from 8.5% to 6%
• The interest on a loan of 120fortwoyearsatanannualrateof5.5120 for two years at an annual rate of 5.5% is 120fortwoyearsatanannualrateof5.526.40

Currencies and Exchange

• If US1.00isequivalenttoEC1.00 is equivalent to EC1.00isequivalenttoEC2.68, then one gets US37.31forEC37.31 for EC37.31forEC100
• If the marked price of a stove was 520,andaworkerboughtitonhire−purchasebymakingadownpaymentof520, and a worker bought it on hire-purchase by making a down payment of 520,andaworkerboughtitonhire−purchasebymakingadownpaymentof100, and twelve monthly payments of 40each,thenshecouldhavesaved40 each, then she could have saved 40each,thenshecouldhavesaved60

Venn Diagrams and Sets

• In the Venn diagram, the shaded portion represents P Q'
• In the Venn diagram, the shaded area represents (P Q ∪ )'
• In the Venn diagram, the shaded portion represents (XY Z ∪ ) ∩

Measurement and Units

• 2 kilograms is equivalent to 2000 grams
• A rectangular tank 100 cm long, 30 cm wide, and 12 cm deep holds a volume of 36 litres
• The area of the trapezium ABCD is 16 cm²

Geometry

• A quadrilateral with all its sides equal is a rhombus

Significant Figures

• When written to 4 significant figures, the number 32747 becomes 32740.

Decimal Equivalents

• The decimal equivalent of 7/8 is 0.875.

Fractions

• 2/2 × 5/3 + 3/1 × 10/1 = 5/1 × 15/1
• This equation simplifies to 5/1 × 15/1 = 5/1 × 15/1.

Ratio and Proportion

• In a school of 910 pupils, 3/7 are boys, and 2/5 of the boys wear glasses. Therefore, the number of boys who wear glasses is 390.

Scientific Notation

• 0.045 × 10^3 in scientific notation is 4.5 × 10^(-5).

Ratio and Proportion

• When x is divided among three boys in the ratio 2 : 3 : 7, and Andrew gets $15 more than Keith, the value of x is $45.

Sets

• The set with an infinite number of members is the multiples of 20.

Prime Numbers

• 31 is a prime number.

Indices

• If x = 3^2 × 2^3, then x^4 = 3^2 × 2^6 × 3^3.

Periodicity

• Three lights flash at intervals of 4, 6, and 10 seconds respectively. They will next flash together again after 120 seconds.

Algebraic Expression

• The given expression is: 3 × 2 + 5 + 3 × 1 - 10
• Simplifying the expression, we get: 6 + 5 + 3 - 10

Pupils in a School

• Total number of pupils in the school: 910
• Fraction of pupils who are boys: 3/7
• Fraction of boys who wear glasses: 2/5
• To find the number of boys who wear glasses, we need to multiply the total number of pupils by the fractions of boys and boys who wear glasses