Mathematics Class: Operations and Geometry

How many books were lent out if there were originally 280 books and 147 are left?

What is the original price of the notebook if the original cost of the book is $18 and Maria received a total discount of $9.50?

If Sophie scores 90 points and loses 4 points for each fault, how many times did she fault if her final score is 74?

How many fouls did Mark commit if he originally scored 72 points and ended up with 56 points?

What is the final point total for Sophie after faults if she started with 90 points and lost 4 points per fault?

What is the correct expression for the area of a triangle with base 8 cm and height 13 cm?

Which of the following calculations correctly determines the circumference of a circle with a diameter of 14 cm?

What is the result of solving the equation $11x + 12 = -54$?

What is the total perimeter of a triangle with sides measuring 11 cm, 16 cm, and 18 cm?

How would you determine the remaining balance for Sophia after writing her checks?

What is the correct calculation for the sum of David's checks?

What is the area of a square with each side measuring 18 cm?

If the temperature dropped by 12 degrees from x degrees Celsius to reach -20 degrees Celsius, what was the original temperature?

Integer Operations

Adding negative integers: -12 + (-22) = -34
Subtracting negative integers: -34 - (-10) = -24

Perimeter of a Triangle

Formula: side1 + side2 + side3 = Perimeter
Example: 11cm + 16cm + 18cm = 45cm

Area of a Triangle

Formula: Area = (1/2) x base x height
Example: (1/2) x 8cm x 13cm = 52cm²

Area of a Square

Formula: Area = side x side
Example: 18cm x 18cm = 324 cm²

Circumference of a Circle

Formula (using diameter): Circumference = π x diameter
Example (diameter = 14cm): π x 14cm = 43.96 cm (approximated using π=3.14)
Formula (using radius): Circumference = 2 x π x radius
Example (radius = 5cm): 2 x π x 5cm = 31.4 cm (approximated using π=3.14)

Solving Equations (for x)

Example 9x - 20 = 16: x = 4
Example 11x + 12 = -54: x = -6

Solving Word Problems (using equations)

Example: 8 movie tickets for $104: Each ticket cost $13
Example: 12 concert tickets for $300: Each ticket cost $25

Evaluating Expressions

Example (for x = 12): 3x - 7 = 29

Temperature Change

Example (drop of 12°C to -20°C): Original temperature was 8°C
Example (drop of 8°C to -15°C): Original temperature was -7°C

Complementary Angles

The sum of complementary angles is 90°.
Example: If one angle is 32°, the other is 58°.

Checking Account Balances

Example (with multiple withdrawal): Final balance is 285.75
Example (with multiple withdrawal): Final balance is 221.75

Finding the difference

Example, books lent out: 280 - 147 = 133 books.

Discount Problems

Example (total discount and book price): Original price of notebook was $20.

Point Problems

Example (tennis faults): Sophie faulted 4 times.
Example (basketball fouls): Mark committed 8 fouls.

This quiz covers essential arithmetic operations, including adding and subtracting negative integers, as well as key geometric concepts such as perimeter and area of various shapes. You will also learn how to calculate the circumference of a circle and solve equations. Perfect for reinforcing your math skills!

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