End-Term Math Review
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Questions and Answers

Which of the following statements is true about integers?

  • Integers are only whole numbers above zero.
  • Integers are always greater than zero.
  • Integers can be fractions.
  • Integers include both positive and negative numbers. (correct)

What is the opposite of -95?

  • -5
  • -95
  • 0
  • 95 (correct)

When subtracting a negative integer, what is the correct method to use?

  • Change the first number to its opposite and subtract.
  • Subtract the absolute value of both numbers.
  • Add the two numbers together.
  • Change subtraction to addition and the second number to its opposite. (correct)

Which of the following pairs of integers would yield a positive product when multiplied?

<p>-4 and -6 (C)</p> Signup and view all the answers

What is the lowest common multiple (LCM) of 4 and 6?

<p>12 (B)</p> Signup and view all the answers

If the sum of -3 and -5 equals -8, what is true about adding two negative integers?

<p>The result is negative. (C)</p> Signup and view all the answers

When two integers have the same sign and are added together, what is the sign of the result?

<p>Positive (B), Negative (D)</p> Signup and view all the answers

What is the absolute value of -17?

<p>17 (A)</p> Signup and view all the answers

Which of the following numbers is NOT a prime number?

<p>15 (D)</p> Signup and view all the answers

What is the numerator in the fraction that represents 18 girls out of 30 students?

<p>18 (C)</p> Signup and view all the answers

Which step is necessary to simplify the fraction 18/30?

<p>Divide both the numerator and denominator by the HCF. (D)</p> Signup and view all the answers

When adding fractions with different denominators, which of the following must be done first?

<p>Find a common denominator. (D)</p> Signup and view all the answers

What are the first nine prime numbers?

<p>2, 3, 5, 7, 11, 13, 17, 19, 23 (C)</p> Signup and view all the answers

Which action is performed when multiplying fractions?

<p>Multiply the numerators together and multiply the denominators together. (D)</p> Signup and view all the answers

What should you do if the denominators of the fractions you are adding are different?

<p>Find a common denominator before adding. (D)</p> Signup and view all the answers

What do you call the numbers that exactly divide another number?

<p>Prime factors (B)</p> Signup and view all the answers

What fraction of students are girls if 70% of the students are boys?

<p>0.3 (B), 30/100 (C)</p> Signup and view all the answers

How do you express 3/7 as a decimal rounded to two decimal places?

<p>0.43 (C)</p> Signup and view all the answers

If the ratio of fish to hamsters is 25:95, what is the simplified ratio?

<p>5:19 (B)</p> Signup and view all the answers

What is the decimal representation of 0.23 as a percentage?

<p>23% (B)</p> Signup and view all the answers

How many candies does Mary have if John and Mary divide 500 candies in the ratio 3:2?

<p>200 candies (B)</p> Signup and view all the answers

What percentage change do you get when dividing by 100 and multiplying by a specified percentage?

<p>Multiply to find the percentage (B)</p> Signup and view all the answers

What is the total parts of the ratio 12:4:8 when simplified to the highest common factor?

<p>3 (D)</p> Signup and view all the answers

If 42% of students are boys, what fraction of them are girls?

<p>58% (B)</p> Signup and view all the answers

How many minutes are there in an hour and a half?

<p>90 minutes (B)</p> Signup and view all the answers

If a flight operates once every hour, how many passengers can travel in 3 hours with a capacity of 200 passengers per flight?

<p>600 passengers (D)</p> Signup and view all the answers

During bad weather, if a flight takes 50% longer than the usual time of 1.5 hours, what will be the total duration of the flight?

<p>2 hours 15 minutes (C)</p> Signup and view all the answers

What total revenue does the airline receive for a full flight, considering an average ticket price of $24 and full capacity of 200 passengers?

<p>$4,800 (B)</p> Signup and view all the answers

If flight #1 is at 90% capacity, flight #2 at 75%, and flight #3 at 60%, what total revenue does the airline receive from these flights?

<p>$10,800 (A)</p> Signup and view all the answers

What is the percentage change in average passenger capacity from weekdays (143) to weekends (188)?

<p>31.5% (D)</p> Signup and view all the answers

If a flight operates at 80% capacity, how many passengers will be on the flight if the capacity is 200?

<p>160 passengers (A)</p> Signup and view all the answers

If the average capacity on weekdays is 143 and on weekends is 188, how many more passengers can the airline accommodate on weekends?

<p>40 passengers (B)</p> Signup and view all the answers

What is the percentage change when the price of a toy decreases from $220 to $80?

<p>-63% (C)</p> Signup and view all the answers

If the price of a game increased from $120 to $150, what is the percentage change?

<p>25% (C)</p> Signup and view all the answers

To convert from centimeters to meters, you need to move the decimal point to:

<p>The left (A)</p> Signup and view all the answers

What does the symbol $\sqrt{}$ represent?

<p>A square root (B)</p> Signup and view all the answers

What is the value of $\sqrt{36}$?

<p>6 (A)</p> Signup and view all the answers

To find the cube root, the symbol $\sqrt[3]{}$ indicates that you are looking for a number that multiplied by itself how many times?

<p>Three times (A)</p> Signup and view all the answers

When converting 0.3 kg to grams, what is the correct conversion?

<p>300g (B)</p> Signup and view all the answers

What is the result of the calculation $6^3 + 7^3 + 8^3 + 9^3 + 10^3$?

<p>2800 (C)</p> Signup and view all the answers

What is the first step when dividing fractions?

<p>Multiply by the reciprocal of the second fraction (A)</p> Signup and view all the answers

What is the simplified form of $\frac{6}{9} \times \frac{8}{4}$?

<p>$\frac{4}{3}$ (B)</p> Signup and view all the answers

What is the correct method to convert 0.4 to a percentage?

<p>Multiply by 100 (D)</p> Signup and view all the answers

What percentage of a shop's 65 markers are not red if 5 are red?

<p>92% (A)</p> Signup and view all the answers

Which calculation gives you the simplest form of $\frac{2}{3} \div \frac{1}{5}$?

<p>$\frac{2 \times 5}{3 \times 1}$ (C)</p> Signup and view all the answers

What is 0.80 expressed as a fraction in simplest form?

<p>$\frac{4}{5}$ (C)</p> Signup and view all the answers

How would you convert 35% into decimal form?

<p>Divide by 100 (A)</p> Signup and view all the answers

What is the percentage of chocolate flavored donuts if out of 45 donuts, 10 are chocolate?

<p>77.78% (C)</p> Signup and view all the answers

Flashcards

Integers

Integers are whole numbers, including positive numbers, negative numbers, and zero.

Negative Numbers

Numbers below zero (left of zero) are called negative numbers.

Positive Numbers

Numbers above zero (right of zero) are called positive numbers.

Opposite of a Number

The opposite of a number is the same distance from zero on the number line, but in the opposite direction.

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Absolute Value

The absolute value of a number is its distance from zero, always expressed as a positive number.

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Integer Rules: Addition and Subtraction

When adding or subtracting integers with the same sign, the answer will have the same sign. When adding or subtracting integers with different signs, the answer will take the sign of the larger number. To subtract integers, change the subtraction to addition and change the second number to its opposite.

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Integer Rules: Multiplication and Division

When multiplying or dividing integers with the same signs, the answer is positive. When multiplying or dividing integers with different signs, the answer is negative.

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Lowest Common Multiple (LCM)

The LCM is the smallest common multiple shared by two or more numbers.

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Prime Numbers

A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

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List the first 9 prime numbers

The first 9 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23.

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Prime Factors

Prime factors are prime numbers that divide a number exactly, without leaving a remainder.

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Fraction

A fraction represents a part of a whole.

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Numerator

The numerator of a fraction is the number on top, representing the number of parts being considered.

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Denominator

The denominator of a fraction is the number on the bottom, representing the total number of parts.

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Simplifying Fractions

Simplifying a fraction means dividing the numerator and denominator by their highest common factor (HCF) to get the smallest equivalent fraction.

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Finding a Common Denominator

To add or subtract fractions with different denominators, you need to find a common denominator first.

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Dividing fractions

To divide fractions, we flip the second fraction (the divisor) and multiply.

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Converting fraction to decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

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Converting decimal to percentage

To convert a decimal to a percentage, multiply the decimal by 100, then add the percentage sign.

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Converting percentage to decimal

To convert a percentage to a decimal, divide the percentage by 100 and remove the percentage sign.

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Fraction in simplest form

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

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Calculating percentage

To calculate the percentage of a number, divide the part by the whole, then multiply by 100.

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Non-chocolate donuts

To find the percentage of donuts that are not chocolate flavored, first calculate the number of non-chocolate donuts, then divide by the total number of donuts and multiply by 100.

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Fraction to decimal

To convert a fraction to a decimal, divide the numerator by the denominator. Round to the specified decimal places.

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Decimal to percentage

To convert a decimal to a percentage, multiply the decimal by 100.

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What does a ratio compare?

A ratio compares the sizes of different parts or quantities to each other.

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How to simplify a ratio

To simplify a ratio, find the highest common factor (HCF) of all the numbers in the ratio and divide each number by the HCF.

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How to find the total parts?

To find the total parts of a ratio, add all the individual parts of the ratio together.

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How to divide a total in a ratio

To divide a total into a ratio, first add the parts of the ratio together. Then, divide the total by the sum of the parts. Finally, multiply each part of the ratio by the result.

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Percentage change

A percentage change is a way of expressing how much a quantity has changed relative to its original value.

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How to find a percentage

To find a percentage, divide the quantity you want to express as a percentage by the total quantity, then multiply by 100.

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Convert hours to minutes

To convert hours to minutes, multiply the number of hours by 60.

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Calculate passengers per flight

Multiply the number of flights by the number of passengers per flight to find the total number of passengers.

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Percentage to decimal

To convert a percentage to a decimal, divide the percentage by 100.

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Calculate flight time with delay

Multiply the original flight time by 1.5 to calculate the new flight time with a 50% delay.

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Calculate total revenue

Multiply the number of passengers by the average ticket price to find the total revenue.

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Calculate revenue for varying capacity

Multiply the total revenue for a full flight by the capacity percentage for each flight to find individual flight revenues.

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Average capacity

To find average capacity, add the weekday capacity and weekend capacity and divide by 2.

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Percentage Change Formula

Calculates the percentage increase or decrease between two values. It's the difference between the new value and the original value, divided by the original value, then multiplied by 100.

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Metric Units

A system of measurement based on multiples of 10, making conversions easier. Common units include meters (m), liters (L), and grams (g).

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Converting Metric Units

Moving the decimal point to the left or right to change the units.

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Powers (Index Notation)

A short way to write repeated multiplication of a number by itself. The base number is the number being multiplied, and the exponent indicates how many times it's multiplied.

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Square and Cube

Specific powers: a square is a number multiplied by itself twice (x²), and a cube is a number multiplied by itself three times (x³).

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Roots

The opposite of powers, finding what number multiplied by itself equals the original number. A square root (√) finds a number multiplied by itself twice, and a cube root (∛) finds a number multiplied by itself three times.

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Prime Factor Tree

A diagram that breaks a number down into its prime factors, showing the prime numbers that multiply to give that number.

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Study Notes

End-Term Math Review

  • Topics covered include integers, factors, multiples, prime numbers, fractions, decimals, percentages, ratios, percentage change, units of conversions, powers, and roots.

Integers

  • Integers are whole numbers including positive numbers, negative numbers, and zero.
  • Numbers below zero are called negatives.
  • Numbers above zero are called positives.
  • Examples of integers: -35, 17, -95

Integer Rules: + and -

  • If signs are the same, the answer has the same sign.
  • If signs are different, the answer takes the sign of the larger number.
  • To subtract, change subtraction to addition and change the second number to its opposite.

Integer Rules: x and ÷

  • If signs are the same, the answer is positive
  • If signs are different, the answer is negative.

Integer Rules - Examples

  • -56 - (-9) = -47
  • -8 - (-36) = 28
  • -3 + (-5)= -8
  • 29 + (-7) = 22
  • -9 x (-8) = 72

Multiples, Factors, and Prime Numbers

  • Multiples are the products of a number and any whole number
  • Factors are numbers that divide exactly into another number
  • Prime numbers have only two factors: 1 and themselves.

Lowest Common Multiples (LCM)

  • LCM is the smallest multiple shared by two or more numbers.
  • Find the multiples of each number.
  • Identify the smallest multiple shared by all numbers

Highest Common Factors (HCF)

  • HCF is the largest factor shared by two or more numbers.
  • Find the factors of each number.
  • Identify the largest factor shared by all numbers

Prime Numbers

  • Prime numbers are greater than 1 and have only two factors: 1 and themselves.
  • List examples: 2, 3, 5, 7, 11, 13, 17, 19, 23
  • Prime factors are prime numbers that divide another number.

Fractions

  • Fractions represent a part of a whole.
  • The number on top is the numerator, and the number on the bottom is the denominator.

Fraction Rules: + and -

  • To add or subtract fractions, find a common denominator first.
  • Add or subtract the numerators and keep the denominator the same.

Fraction Rules: x and ÷

  • To multiply fractions, multiply the numerators together and the denominators together.
  • To divide fractions, reciprocal the second fraction and change the divide to multiply.

Fraction Examples

  • 8/6 + 7/5 = 61/15
  • 2/6 + 3/4= 13/12
  • 6/9 x 7/8= 42/72= 7/12
  • 2/3 ÷ 3/4= 8/9

Converting Fractions, Decimals, and Percentages

  • To convert a fraction to a decimal, divide the numerator by the denominator.
  • To convert a decimal to a percentage, multiply by 100.
  • To convert a percentage to a decimal, divide by 100.

Units and Conversions

  • Metric units are multiples of 10.
  • To convert, move the decimal point to the left or right based on the unit conversion.

Powers and Roots

  • Powers represent repeated multiplication. The small number is the exponent.
  • Roots represent the inverse of powers.

Powers and Roots - Examples

  • 92 = 81
  • 53 = 125
  • 24 = 16
  • √64 = 8
  • ∛64 = 4

Extra Questions

  • These are additional problems designed to further test understanding

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Math End-Term 1 - Lesson with Answers 2024 PDF

Description

This quiz covers essential math concepts including integers, factors, multiples, prime numbers, and operations involving decimals and percentages. Prepare for your end-term exams by testing your knowledge on these foundational topics. Make sure you're comfortable with integer rules, conversion units, and the basics of powers and roots.

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