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

Test your knowledge of math and set theory with these questions on currency exchange, set operations, and Venn diagrams.