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Math Grade 8

Detailed Explanation
  • Integers: Whole numbers and their opposites. Operate using rules for positive and negative numbers.
  • Order of Operations: Follow BEDMAS (Brackets, Exponents, Division/Multiplication, Addition/Subtraction) in that order.
  • Square & Cube Numbers: Square = number × number (e.g., 5² = 25); Cube = number × number × number (e.g., 3³ = 27).
  • Square Roots: Reverse of squaring. Example: √36 = 6.
  • Rational Numbers: Any number expressible as a fraction. Includes terminating and repeating decimals.
  • Operations with Fractions: Find common denominators to add/subtract. Multiply numerators and denominators. Divide by flipping the second fraction and multiplying.
  • Decimals: Operate by aligning the decimal point. Multiply normally and place the decimal after.
  • Conversions: Convert between fractions, decimals, and percentages. Example: 0.75 = 3/4 = 75%.
  • Powers & Exponents: Exponent shows how many times the base is used as a factor. Example: 2⁴ = 16.
  • Scientific Notation: Compact way to write very large or small numbers. Format: a × 10ⁿ (e.g., 4.2 × 10³).
📝 Practice Questions (30)
  1. 5 + (-3)
  2. -4 - (-7)
  3. 6 × (-2)
  4. -15 ÷ 3
  5. (3 + 2) × 4
  6. 5²
  7. ∛27
  8. √81
  9. Compare: 3/4 and 0.7
  10. Convert 0.25 to a fraction
  11. Convert 3/5 to percent
  12. Subtract: 5 1/2 - 2 3/4
  13. Multiply: 2/3 × 3/4
  14. Divide: 3/5 ÷ 2/3
  15. Round 7.689 to the nearest tenth
  16. Add: -4.6 + 3.2
  17. Place value of 6 in 83.647
  18. Simplify: (8 - 3)²
  19. Evaluate: 2³ + 4²
  20. Convert 150% to a decimal
  21. Write 0.00042 in scientific notation
  22. Write 4.3 × 10⁵ in standard form
  23. √144 = ?
  24. Compare: -5 and -7
  25. Multiply: -3 × -2 × 4
  26. Convert 7/8 to a decimal
  27. Convert 0.6 to a fraction in lowest terms
  28. Evaluate: 10 - (2 + 3 × 2)
  29. What is the cube of 5?
  30. Simplify: 3² + 4²
Answers
  1. 2
  2. 3
  3. -12
  4. -5
  5. 20
  6. 25
  7. 3
  8. 9
  9. 3/4 > 0.7
  10. 1/4
  11. 60%
  12. 2 3/4
  13. 1/2
  14. 9/10
  15. 7.7
  16. -1.4
  17. 6 is in hundredths place
  18. 25
  19. 8 + 16 = 24
  20. 1.5
  21. 4.2 × 10⁻⁴
  22. 430,000
  23. 12
  24. -5 > -7
  25. 24
  26. 0.875
  27. 3/5
  28. 10 - (2 + 6) = 2
  29. 125
  30. 9 + 16 = 25

Detailed Explanation
  • Ratios: A comparison between two quantities (e.g., 3:4 or 3/4). Equivalent ratios represent the same relationship.
  • Rates: A ratio comparing two quantities with different units (e.g., 60 km per hour).
  • Unit Rates: A rate per 1 unit (e.g., $2.50 per item).
  • Proportions: An equation showing two ratios are equal. Can solve by cross-multiplication.
  • Percent Applications: Use percent formulas to find tax, tip, discount, and profit/loss. Example: 10% of $50 = 0.10 × 50 = $5.
  • Percent Increase & Decrease: Find the change, divide by original, then multiply by 100.
  • Real-world Proportional Problems: Involve ratios, scaling recipes, resizing images, or comparing distances.
  • Scale Diagrams & Maps: Use ratios to relate real-world measurements to diagram measurements (e.g., 1 cm : 100 m).
  • Direct Variation: As one quantity increases, so does the other (y = kx).
  • Inverse Variation: One quantity increases as the other decreases (xy = k).
📝 Practice Questions (30)
  1. Simplify the ratio 10:20
  2. Are 2:3 and 4:6 equivalent?
  3. Find the unit rate: $24 for 8 pens
  4. Rate: 300 km in 5 hours = ? km/h
  5. Solve: 3/4 = x/8
  6. Solve: 5/x = 15/9
  7. 20 is what percent of 80?
  8. Find 25% of $120
  9. If original price is $200 and discount is 15%, what is the new price?
  10. Increase $80 by 20%
  11. Decrease $50 by 10%
  12. If you pay $90 after 10% tax, what was the original price?
  13. You tip 18% on a $40 meal. How much is the tip?
  14. Profit: Buy for $50, sell for $70. What is the profit %?
  15. Loss: Buy for $100, sell for $80. What is the loss %?
  16. If a 1 cm line = 50 m in real life, how many meters is 6 cm?
  17. On a scale map, 3 cm = 1 km. What does 9 cm represent?
  18. If 5 books cost $45, how much do 8 books cost?
  19. Find the missing value: 7/10 = x/20
  20. What is the percent change from 50 to 65?
  21. What is the percent change from 100 to 85?
  22. If y varies directly with x and y = 10 when x = 2, find y when x = 6
  23. If y varies inversely with x and y = 12 when x = 3, find y when x = 6
  24. True or false: 5:8 and 10:16 are equivalent
  25. How many liters in 3 containers if each holds 2.5 L?
  26. Find the better buy: 3 kg for $12 or 4 kg for $15
  27. A recipe calls for 2 eggs for 5 servings. How many eggs for 15 servings?
  28. Solve: x/6 = 8/12
  29. A toy costs $60 before tax. How much after 13% tax?
  30. What is 0.75 as a percent?
Answers
  1. 1:2
  2. Yes
  3. $3 per pen
  4. 60 km/h
  5. x = 6
  6. x = 3
  7. 25%
  8. $30
  9. $170
  10. $96
  11. $45
  12. $81.82
  13. $7.20
  14. 40%
  15. 20%
  16. 300 meters
  17. 3 km
  18. $72
  19. x = 14
  20. 30%
  21. 15%
  22. y = 30
  23. y = 6
  24. True
  25. 7.5 L
  26. 4 kg for $15 is better ($3.75/kg vs $4/kg)
  27. 6 eggs
  28. x = 4
  29. $67.80
  30. 75%

Detailed Explanation
  • Evaluating Expressions: Replace variables with numbers and follow order of operations. Example: if x = 2, then 3x + 1 = 7.
  • Simplifying Expressions: Use exponent laws (like aⁿ × aᵐ = aⁿ⁺ᵐ) and combine like terms.
  • Expanding Binomials: Distribute using the distributive property: a(b + c) = ab + ac.
  • Factoring Binomials (Intro): Write expressions like 2x + 6 as 2(x + 3).
  • Combining Like Terms: Add/subtract terms with the same variables. Example: 3x + 2x = 5x.
  • Solving Equations: Solve one-step (x + 3 = 5), two-step (2x + 3 = 7), and variable-on-both-sides equations (3x = 2x + 5).
  • Solving Inequalities: Similar to equations but with <, >, ≤, ≥. Remember: flip the sign when multiplying/dividing by a negative.
  • Substitution: Plug values into expressions or formulas and solve. Example: A = lw, if l = 5 and w = 2, then A = 10.
  • Pattern Rules: Find algebraic rules from number patterns. Example: 2, 4, 6, 8 → rule: 2n.
  • Algebra Word Problems: Translate word problems into equations and solve. Example: "Sam has 3 more than twice what Emma has."
📝 Practice Questions (30)
  1. Evaluate: 3x + 2 when x = 4
  2. Evaluate: 2a² when a = 3
  3. Simplify: x + 3x + 2
  4. Simplify: 2x² × x³
  5. Simplify: (3x)(2x)
  6. Expand: 3(x + 5)
  7. Expand: 2(x - 4)
  8. Factor: 6x + 12
  9. Factor: 10x - 5
  10. Simplify: 2x + 3x - x
  11. Solve: x + 5 = 12
  12. Solve: 2x = 16
  13. Solve: 3x - 2 = 10
  14. Solve: 4x + 1 = 2x + 7
  15. Solve: x/3 = 5
  16. Solve: 2x/5 = 6
  17. Solve and graph: x > 3
  18. Solve and graph: 2x < 10
  19. What is the area if A = lw, l = 6, w = 3?
  20. Substitute into E = mc²: m = 2, c = 3
  21. What is the rule for 5, 10, 15, 20?
  22. What is the nth term of 3, 6, 9, 12?
  23. Translate: "Five more than twice a number" → Expression
  24. Translate and solve: "Three less than x is 12"
  25. If y = 2x + 1, find y when x = 5
  26. If x = 4, y = 3x² - x. Find y.
  27. Is 2x + 3 = 3x + 2 a linear equation?
  28. Solve: 3(x + 1) = 12
  29. Factor: 8x - 4
  30. Expand: -2(x - 5)
Answers
  1. 14
  2. 18
  3. 4x + 2
  4. 2x⁵
  5. 6x²
  6. 3x + 15
  7. 2x - 8
  8. 6(x + 2)
  9. 5(2x - 1)
  10. 4x
  11. x = 7
  12. x = 8
  13. x = 4
  14. x = 3
  15. x = 15
  16. x = 15
  17. x > 3
  18. x < 5
  19. 18
  20. 18
  21. Rule: 5n
  22. Rule: 3n
  23. 2x + 5
  24. x = 15
  25. y = 11
  26. y = 44
  27. Yes
  28. x = 3
  29. 4(2x - 1)
  30. -2x + 10

🧠 Detailed Explanation
  • Identifying Linear Relationships: A relation is linear if the rate of change between variables is constant and can be represented by a straight line.
  • Tables of Values: Organize pairs of x and y values showing how y changes as x changes.
  • Graphs of Linear Relationships: Plot points from tables and connect them with a straight line.
  • Writing Equations: Use patterns or graphs to write equations in forms like y = mx + b.
  • Slope (Rate of Change): Slope (m) = change in y ÷ change in x, measures steepness.
  • Y-Intercept and X-Intercept: Y-intercept (b) is where the line crosses y-axis; X-intercept is where it crosses x-axis.
  • Real-life Linear Models: Use linear equations to model situations like distance-time, cost calculations, or temperature changes.
📝 Practice Questions (30)
  1. Is the relation y = 2x + 3 linear?
  2. Fill the table: x = 0,1,2,3; y = 4x + 1
  3. Find y when x = 5 for y = 3x - 2
  4. Plot points (1,4), (2,7), (3,10). Are they linear?
  5. Calculate slope between points (2,3) and (5,9)
  6. Write the equation for a line with slope 2 and y-intercept 3
  7. Find x-intercept of y = 2x + 6
  8. Find y-intercept of y = -3x + 7
  9. If slope is 0, what kind of line is it?
  10. Find slope for points (4,5) and (4,9)
  11. Determine if points (1,2), (3,6), (5,10) are linear
  12. Write equation of line passing through (0, -2) with slope 4
  13. Find y when x = -1 for y = -2x + 5
  14. Graph the equation y = x - 3
  15. Identify slope and intercept of y = -0.5x + 4
  16. Explain why y = x² + 3 is not linear
  17. Write an equation for a line with slope -3 passing through (2,5)
  18. Find x if y = 7 for y = 2x + 1
  19. Describe what slope means in real life (e.g., speed)
  20. Find slope and intercept of y = 0
  21. Plot points (0,0), (1,2), (2,4) and write the equation
  22. Calculate slope between (6, 10) and (2, 2)
  23. Determine if relation x = 5 is linear
  24. Find y-intercept for y = 5x
  25. Write an equation for line crossing y-axis at -4 with slope 1
  26. Explain how to find slope from a graph
  27. Use equation y = 3x + 2 to find y when x = 0
  28. Explain what x-intercept represents
  29. Identify whether y = 5 is linear and find slope
  30. Real-life example of linear relation
  31. Write equation of line through points (1,2) and (3,6)

Types of Angles

Explanation: Angles are classified based on their degree measurements:
Acute (< 90°), Right (= 90°), Obtuse (> 90°), Straight (= 180°), Reflex (> 180°)

Angle Relationships

Explanation: Complementary angles add up to 90°, supplementary to 180°, opposite angles are equal, corresponding and alternate interior appear in parallel lines and are equal.

Properties of Triangles

Explanation: Triangle types: Isosceles (2 equal sides), Scalene (no equal sides), Equilateral (all equal sides), Right triangle (one 90° angle).

Triangle Angle Sum Theorem

Explanation: The sum of all interior angles in a triangle is always 180°.

Interior and Exterior Angles of Polygons

Explanation: The sum of interior angles = (n - 2) × 180°. Each exterior angle in regular polygon = 360° / n.

Constructing and Classifying Polygons

Explanation: Polygons are closed shapes with straight sides; they can be classified by sides and symmetry (triangle, quadrilateral, etc.).

Congruent and Similar Figures

Explanation: Congruent = identical in shape and size. Similar = same shape, different size, proportional sides and equal angles.

Pythagorean Theorem

Explanation: In right triangles, a² + b² = c², where c is the hypotenuse (longest side).

Nets and Surface Area of 3D Figures

Explanation: Nets are 2D patterns that fold into 3D shapes. Surface area = sum of areas of all faces.

Volume of Cylinders, Cones, and Spheres

Explanation: Volume formulas:
Cylinder: πr²h
Cone: (1/3)πr²h
Sphere: (4/3)πr³

30 Practice Examples:

  1. Classify an angle of 45°
  2. Are 30° and 60° complementary?
  3. Identify angle type: 120°
  4. Find the missing angle: triangle with 70°, 60°, ?
  5. Classify triangle with sides 3cm, 3cm, 3cm
  6. Sum of interior angles of hexagon?
  7. Find one interior angle of a regular octagon
  8. Identify opposite angles in intersecting lines
  9. Draw and name a scalene triangle
  10. Use Pythagorean Theorem: legs = 3, 4
  11. Volume of cylinder: r=2, h=5
  12. Volume of cone: r=3, h=6
  13. Volume of sphere: r=3
  14. Surface area of cube with edge 4
  15. Classify polygon with 5 sides
  16. What is the reflex of 220°?
  17. Do 100° and 80° form a supplementary pair?
  18. Triangle with angles 40°, 50°, ?
  19. Surface area of rectangular prism: 2×3×4
  20. Draw a net for a cube
  21. Are two rectangles with different size but same ratio similar?
  22. Isosceles triangle: angles 70°, 70°, ?
  23. Find x if a² + b² = c²: a=5, b=12
  24. Classify angle: 180°
  25. Draw corresponding angles in parallel lines
  26. Find area of circle: r = 7
  27. Volume of cone: r=2, h=9
  28. Identify alternate interior angles
  29. Draw similar figures and label proportions
  30. Find x: 2x + 60 = 180 (triangle)
Answers:
  1. Acute
  2. Yes
  3. Obtuse
  4. 50°
  5. Equilateral
  6. 720°
  7. 135°
  8. Equal
  9. Example: 3 unequal sides
  10. 5 (3² + 4² = 25)
  11. 20π ≈ 62.83
  12. 18π ≈ 56.55
  13. 36π ≈ 113.1
  14. 96
  15. Pentagon
  16. 140°
  17. No
  18. 90°
  19. 52
  20. Draw square net
  21. Yes
  22. 40°
  23. 13
  24. Straight
  25. Equal to one another
  26. 49π ≈ 153.9
  27. 12π ≈ 37.7
  28. Equal angles between lines
  29. Keep ratio, e.g., 2:1 sides
  30. 60

Converting Units of Measurement (metric system)

Explanation: Use powers of 10 to convert between mm, cm, m, and km. Multiply to go smaller, divide to go larger.

Perimeter, Area, and Surface Area (2D and 3D shapes)

Explanation: Perimeter is the total distance around a shape. Area is the amount of surface a shape covers. Surface area is the total area of all the faces of a 3D object.

Volume of Prisms and Cylinders

Explanation: Volume is the amount of space a 3D object occupies. Prism volume: base area × height. Cylinder volume: π × r² × height.

Estimating and Measuring with Precision

Explanation: Use the correct measuring tool and appropriate units. Round only when required and always state the degree of accuracy.

Use of Formulas for Area (triangles, circles, trapezoids)

Explanation: Triangle: 1/2 × base × height. Circle: π × radius². Trapezoid: 1/2 × (base1 + base2) × height.

30 Practice Examples:

  1. Convert 5 km to m
  2. Convert 3200 mm to m
  3. Find perimeter of rectangle 6cm × 4cm
  4. Area of a triangle with base=10, height=4
  5. Volume of rectangular prism: 2×3×4
  6. Volume of cylinder: r=2, h=10
  7. Convert 7500 mL to L
  8. Estimate area of circle: r = 5
  9. Surface area of cube (side = 3)
  10. Area of trapezoid: b1=4, b2=6, h=5
  11. Convert 2.5 km to cm
  12. Volume of triangular prism with b=6, h=3, length=5
  13. Estimate volume of cone: r=3, h=5
  14. Surface area of rectangular box: 3×2×1
  15. Convert 123 cm to m
  16. Area of square: side = 12
  17. Perimeter of equilateral triangle with side = 8
  18. Volume of cube: side = 4
  19. Convert 4.2 L to mL
  20. Convert 9000 cm to km
  21. Area of circle: d = 14
  22. Find perimeter of trapezoid with all sides 4
  23. Convert 0.003 km to mm
  24. Estimate surface area of sphere: r=6
  25. Convert 1000000 mm to km
  26. Volume of cylinder: r=3.5, h=8
  27. Area of parallelogram: b=9, h=3
  28. Convert 12.75 m to cm
  29. Estimate: area of 3 rectangles each 4×6
  30. Volume of triangular prism with b=5, h=4, l=10
Answers:
  1. 5000 m
  2. 3.2 m
  3. 20 cm
  4. 20 cm²
  5. 24 cm³
  6. 125.66 cm³
  7. 7.5 L
  8. 78.5 cm²
  9. 54 cm²
  10. 25 cm²
  11. 250000 cm
  12. 45 cm³
  13. 47.1 cm³
  14. 22 cm²
  15. 1.23 m
  16. 144 cm²
  17. 24 cm
  18. 64 cm³
  19. 4200 mL
  20. 0.09 km
  21. 153.9 cm²
  22. 16 cm
  23. 3000 mm
  24. 452.4 cm²
  25. 1 km
  26. 307.9 cm³
  27. 27 cm²
  28. 1275 cm
  29. 72 cm²
  30. 100 cm³

Collecting and Organizing Data

Explanation: Use surveys or experiments to collect data. Organize using tables or spreadsheets for clarity.

Reading and Interpreting Graphs (bar, line, circle/pie, histogram)

Explanation: Learn how to read key features and trends in various graph types and compare data visually.

Mean, Median, Mode, and Range

Explanation: Mean is the average. Median is the middle number. Mode is the number that occurs most often. Range is the difference between highest and lowest values.

Outliers and Their Effect on Data

Explanation: Outliers are data points that are far outside the normal range and can skew averages and graphs.

Choosing Appropriate Graphs for Data Sets

Explanation: Choose bar graphs for categories, line graphs for trends, and pie charts for percentages of a whole.

Misleading Graphs and Bias in Data Collection

Explanation: Be cautious of incorrect axes, improper scales, and survey wording that may mislead or introduce bias.

Making Inferences from Data

Explanation: Use trends and patterns in the data to draw logical conclusions or predictions.

Designing a Survey or Experiment

Explanation: Use clear, unbiased questions and an appropriate sample size. Identify what data you need and how to collect it fairly.

30 Practice Examples:

  1. Create a bar graph from sample data
  2. Find mean of 3, 6, 9
  3. Identify mode of 4, 4, 7, 8
  4. Find range: 2 to 11
  5. Design a 3-question survey
  6. Describe what outlier would affect: 3, 4, 5, 100
  7. Best graph type for pizza topping preference?
  8. Make inferences from line graph about sales
  9. Interpret pie chart on student device use
  10. Create frequency table for dice rolls
  11. Find median of 1, 4, 7
  12. Choose appropriate graph for time-series data
  13. Detect misleading scale on a bar graph
  14. Organize data: test scores of 10 students
  15. Find mode of 9, 10, 11, 11
  16. Describe histogram of shoe sizes
  17. Explain how bias can occur in survey
  18. Graph number of pets per household
  19. Estimate mean from grouped data
  20. Use chart to find highest value
  21. What makes a survey question biased?
  22. Sketch bar graph for daily hours online
  23. Analyze pie chart with 3 categories
  24. Summarize range in line graph
  25. Design experiment to test favorite apps
  26. Identify inappropriate graph used
  27. Compute mean with an outlier
  28. Create a survey question for shopping habits
  29. Describe data trend over a week
  30. Explain what graph shows misleading info
Answers:
  1. Draw 3 bars with equal spacing
  2. 6
  3. 4
  4. 9
  5. Open-ended answers
  6. Mean increases significantly
  7. Bar graph
  8. Look at trend line increase/decrease
  9. Each slice shows % usage
  10. List 6 face outcomes
  11. 4
  12. Line graph
  13. Axis scale uneven
  14. Organized in ascending order
  15. 11
  16. Shows concentration in ranges
  17. Leading question or small sample
  18. Bar with categories
  19. Estimate midpoint and multiply
  20. Max value from column
  21. Suggests answer with phrasing
  22. Bar height per day
  23. Percentages add to 100
  24. Look for steepness
  25. Controlled test
  26. Bar chart for continuous data
  27. Mean higher than expected
  28. Neutral phrasing and variety
  29. Upward or downward slope
  30. Exaggerated Y-axis scale

Detailed Explanation
  • Probability of Simple Events: Measures how likely an event is to occur. Probability = (Number of favorable outcomes) ÷ (Total number of outcomes).
  • Experimental vs Theoretical Probability: Theoretical is based on expected outcomes (e.g., 1/6 for rolling a 3 on a die). Experimental is based on actual results from trials.
  • Tree Diagrams and Organized Lists: Visual tools to list all possible outcomes systematically, helpful for calculating probabilities.
  • Independent and Dependent Events: Independent events’ outcomes don’t affect each other (e.g., flipping coins). Dependent events do affect each other (e.g., drawing cards without replacement).
  • Representing Probability: Express as fractions, decimals, and percentages.
  • Probability Word Problems: Apply concepts to solve real-world questions.
  • Simulations and Estimations: Use experiments or computer simulations to estimate probabilities when exact calculation is complex.
📝 Practice Questions (30)
  1. What is the probability of rolling a 4 on a fair six-sided die?
  2. What is the probability of flipping heads on a fair coin?
  3. If you roll two dice, what is the total number of possible outcomes?
  4. Use a tree diagram to list outcomes when flipping two coins.
  5. What is the probability of drawing a red card from a standard deck (26 red cards)?
  6. Define experimental probability.
  7. Define theoretical probability.
  8. A spinner has 4 equal sections: red, blue, green, yellow. What is the probability of landing on green?
  9. Are rolling a die and flipping a coin independent events?
  10. What is the probability of drawing an ace from a deck, then drawing a king without replacement?
  11. Convert probability 1/4 to decimal and percent.
  12. If the probability of rain is 0.3, what is the probability it won’t rain?
  13. What is the probability of NOT rolling a 5 on a die?
  14. List all possible outcomes when tossing three coins.
  15. If you draw a card and then replace it before drawing again, are these events dependent or independent?
  16. Calculate probability of drawing a heart or a spade from a deck.
  17. Estimate the probability of picking a red marble from a bag containing 5 red and 15 blue marbles.
  18. How would you use a simulation to estimate probability?
  19. What is the probability of rolling an even number on a six-sided die?
  20. Explain dependent events with an example.
  21. What is the probability of getting exactly two heads when flipping three coins?
  22. Find the probability of drawing a queen from a deck.
  23. Write the probability of an impossible event.
  24. Write the probability of a certain event.
  25. If P(A) = 0.4, what is P(not A)?
  26. Use a tree diagram to find the probability of getting a head then a tail in two coin flips.
  27. What is the probability of drawing a black card or a king?
  28. If you roll a die twice, what is the probability of getting two sixes?
  29. What does a probability of 0.75 mean?
  30. Estimate the probability of a rare event.

Detailed Explanation
  • Budgeting & Managing Money: Planning income and expenses to balance spending and saving.
  • Interest - Simple vs Compound: Simple interest = principal × rate × time. Compound interest adds interest on accumulated interest.
  • Saving, Spending & Investing: Different ways to manage money for short-term needs and long-term growth.
  • Understanding Credit & Debt: How borrowing money works, interest charges, and repayment.
  • Financial Planning & Goal Setting: Setting money goals and creating steps to achieve them.
  • Tax, Discounts & Markups: Calculating price changes with taxes, sales discounts, and markups.
  • Interpreting Financial Documents: Reading invoices, receipts, bank statements, and understanding their components.
📝 Practice Questions (30)
  1. Define budgeting.
  2. Calculate simple interest on $1000 at 5% for 3 years.
  3. What is compound interest?
  4. If you save $200 monthly, how much in 1 year?
  5. Explain difference between saving and investing.
  6. What is credit?
  7. List two advantages of using credit responsibly.
  8. What is debt?
  9. Define financial goal.
  10. Calculate price after 15% tax on $50.
  11. Calculate sale price after 20% discount on $80.
  12. What is a markup?
  13. Read this invoice: subtotal $100, tax 8%, total?
  14. What is the principal amount in a loan?
  15. What is APR?
  16. Calculate compound interest on $1000 at 5% for 2 years (annually).
  17. What’s the difference between debit and credit cards?
  18. Explain why budgeting is important.
  19. How do taxes affect buying goods?
  20. What does a receipt show?
  21. Calculate total cost if markup is 25% on $60.
  22. Explain why investing is riskier than saving.
  23. What is the difference between gross and net income?
  24. Calculate total payment for a $500 loan with 6% simple interest for 1 year.
  25. What is an interest rate?
  26. How can you avoid credit card debt?
  27. Define emergency fund.
  28. What is financial planning?
  29. List three common taxes.
  30. What is the purpose of a bank statement?

Detailed Explanation
  • Translations: Sliding a figure up, down, left, or right without rotating or flipping.
  • Reflections: Flipping a figure over a line (mirror image).
  • Rotations: Turning a figure around a fixed point by a certain angle.
  • Describing Transformations: Use coordinates to specify movements (e.g., translate right 3 units).
  • Congruency & Symmetry: Congruent shapes are identical in size and shape; symmetry means one half is a mirror of the other.
  • Dilations & Scale Factor: Enlarging or reducing shapes proportionally. Scale factor >1 enlarges; <1 reduces.
  • Compositions of Transformations: Applying multiple transformations one after another.
📝 Practice Questions (30)
  1. Define translation in geometry.
  2. Describe a reflection across the y-axis.
  3. What is a rotation of 90° clockwise around the origin?
  4. Find coordinates of point (3,4) translated 2 units left and 3 units down.
  5. Describe symmetry in a square.
  6. What is congruency?
  7. Find the scale factor if a shape enlarges from length 4 to 12.
  8. What does a dilation with scale factor 0.5 do?
  9. Describe composition of a reflection and a translation.
  10. Rotate point (1,2) 180° about the origin.
  11. Translate point (-3,5) up 4 units.
  12. Is a circle symmetric? Explain.
  13. How many lines of symmetry does a rectangle have?
  14. What are coordinates of (5,-2) after reflection over the x-axis?
  15. Describe a rotation of 270° counterclockwise.
  16. Find new coordinates of (0,0) after dilation with scale factor 3.
  17. Explain composition of two rotations.
  18. Is a triangle always congruent after a reflection?
  19. Describe translation of (2,3) 5 units right.
  20. What happens to area during dilation?
  21. Find coordinates after reflecting (4,6) over the y-axis.
  22. Rotate (2,-1) 90° counterclockwise.
  23. Explain how to describe a transformation using coordinates.
  24. What is a scale factor?
  25. What is the result of composing a translation and a rotation?
  26. How does reflection affect orientation?
  27. Calculate scale factor if original length is 10 and new length is 7.
  28. Find image of point (3,3) after dilation by factor 2.
  29. Describe symmetry in an equilateral triangle.
  30. Explain why rotations preserve shape and size.
  31. How do transformations help in real life?