Sep 2026 – May 2027 · Tue/Wed/Thu schedule · Florida MAFS standards
Equivalent Fractions: Same value, different look. 1/2 = 2/4 = 4/8. Create by multiplying or dividing numerator and denominator by the same number. To simplify: find GCF, divide both by it. Example: 12/18 → GCF=6 → 2/3.
Mixed Numbers: 3 3/4 to improper: (3×4+3)/4 = 15/4. Back: 15 ÷ 4 = 3 R 3 → 3 3/4.
1. Equivalent to 2/3?
2. Simplify 12/18.
3. Convert 2 3/4 to improper fraction.
4. Greater: 3/5 or 5/8?
5. Simplify 15/20.
Click a fraction, then click its matching decimal. Match all 5 pairs!
LCD Method: For 1/4 + 1/6: LCD=12. Convert: 3/12 + 2/12 = 5/12. Always simplify final answer.
Mixed Numbers: Add whole and fraction parts separately. To subtract, borrow from whole if needed.
1. LCD of 1/4 and 1/6?
2. 1/3 + 1/4 = ?
3. 5/6 - 1/4 = ?
4. 2 1/2 + 1 3/4 = ?
5. Maria walked 3/5 then 1/3 mile. Total?
Pick two fractions and watch the full addition process unfold.
+Multiplying: Numerator × numerator, denominator × denominator. No LCD needed! Example: 2/3 × 3/5 = 6/15 = 2/5. Cross-cancel to simplify early.
Keep-Change-Flip (KCF): Dividing by a fraction = multiplying by its reciprocal. 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2.
1. 3/4 × 2/5 = ?
2. Reciprocal of 4/7?
3. 5/6 ÷ 1/3 = ?
4. Garden 2.5m wide, strips 5/8m each. How many fit?
5. 1 1/3 × 2 1/4 = ?
Click the correct answer before the timer runs out!
Conversions: Fraction to decimal: divide numerator by denominator (3/4=0.75). Decimal to fraction: write over place value, simplify (0.35=35/100=7/20). Percent to decimal: move decimal left 2 places.
Operations: Add/subtract: align decimal points. Multiply: count decimal places. Divide: make divisor a whole number, shift both.
1. 3/8 as decimal?
2. 0.45 as simplest fraction?
3. Round 3.4872 to nearest hundredth.
4. 4.5 × 0.3 = ?
5. 3 books at $12.75. Total?
8 questions, 15 sec each. Fraction ↔ Decimal ↔ Percent!
25-30 question comprehensive test covering all September topics: fractions, decimals, and percents. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Ratios compare two quantities. The ratio 3:5 can be written as 3/5 or '3 to 5'. Always simplify by dividing both numbers by their GCF.
Ratio Tables show equivalent ratios. Multiply or divide both values by the same number to stay proportional.
1. What is the ratio of 4 apples to 6 oranges in simplest form?
2. How do you write the ratio 5 to 8 as a fraction?
3. Simplify: 12:18
4. A class has 10 boys and 15 girls. Ratio of boys to total?
5. Which is an equivalent ratio to 3:4?
Click pairs of equivalent ratios to match them!
Unit Rate = rate with denominator 1. To find: divide the first quantity by the second. Example: 150 miles / 3 hours = 50 miles per hour.
Best Buy: Divide price by quantity for each option. The lower unit price is the better deal.
1. A car travels 300 miles on 10 gallons. Unit rate?
2. Best deal: 5 lb for $4 or 8 lb for $6?
3. 120 words in 4 minutes. Words per minute?
4. A runner runs 2.5 km in 10 min. Rate per minute?
5. $3.60 for 12 oz. Unit price per oz?
For each pair, click the better deal!
Proportion: two equal ratios. a/b = c/d. Cross-multiply: a*d = b*c. Then solve for the variable.
Example: 3/4 = x/12 → 4x = 36 → x = 9.
1. Solve: 2/5 = x/20
2. Is 3/4 = 9/12 a true proportion?
3. Solve: 6/x = 3/8
4. A recipe uses 2 eggs per 12 cookies. How many eggs for 36 cookies?
5. Solve: x/7 = 4/14
Enter 3 of the 4 values and solve for the missing one!
Scale: 1 cm = 5 m means every cm on the drawing represents 5 real meters. Multiply drawing measurement by scale factor to find real size.
1. Scale 1 cm = 10 m. Drawing is 4 cm. Real size?
2. Map scale: 1 in = 50 mi. Cities 3 in apart. Real distance?
3. Real length 60 m, scale 1 cm = 15 m. Drawing length?
4. A pool is 25 m. At 1 cm = 5 m, drawing length?
5. Scale 1:20. Drawing door is 0.1 m. Real height?
Enter scale (1 cm = ? m) and convert measurements in both directions.
25-30 question comprehensive test covering all October topics: ratios, unit rates, proportions, and scale drawings. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Variable: a letter representing an unknown number. '5 more than n' = n + 5. 'Twice a number' = 2n.
Evaluate: replace the variable with a number and calculate. Example: 3x + 2 when x=4 → 3(4)+2 = 14.
1. Which expression means '6 less than n'?
2. Evaluate 4x + 3 when x = 2
3. Which means 'the product of 5 and y'?
4. Evaluate 2a - b when a=5, b=3
5. Write: 'half of a number plus 9'
Click word clues to build the algebraic expression!
Substitution: plug in the given value(s) and evaluate following PEMDAS.
Example: 2m + 3n when m=4, n=2 → 2(4) + 3(2) = 8 + 6 = 14.
1. Evaluate 5x - 2 when x = 4
2. Evaluate a + 2b when a=3, b=5
3. Evaluate 3(x + 2) when x = 4
4. Evaluate n^2 - n when n = 5
5. Evaluate (a + b)/2 when a=10, b=6
Enter a value for x and see four expressions evaluated!
Like Terms have the same variable and exponent. 3x and 5x are like (combine to 8x). 3x and 5y are NOT like.
Steps: identify like terms, group them, add/subtract coefficients.
1. Simplify: 4x + 3x
2. Simplify: 8y - 3y + y
3. Simplify: 5a + 2b + 3a
4. Simplify: 3x + 4 + 2x - 1
5. Simplify: 2(x + 3) + 4x
Click terms to sort them into the correct bucket!
Distributive Property: a(b + c) = ab + ac. Multiply the outside factor by each term inside the parentheses.
Example: 3(x + 4) = 3x + 12. Then combine like terms: 3(x + 4) + 2x = 5x + 12.
1. Expand: 4(x + 3)
2. Expand: 5(2a - 1)
3. Expand: -2(y + 6)
4. Simplify: 3(x + 2) + 5x
5. Factor: 6x + 9
Enter factor a and expression (b + c) to see expansion steps!
25-30 question comprehensive test covering all November topics: variables, algebraic expressions, equations, and inequalities. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Integers include positives, negatives, and zero. On a number line, negative numbers are to the left.
Absolute Value: distance from zero. |-7| = 7. |4| = 4. Always non-negative.
1. Which is greater: -5 or -2?
2. What is |-9|?
3. Order: -3, 5, -7, 2 from least to greatest
4. Submarine at -200 ft, airplane at 800 ft. Difference?
5. True or false: |-6| > |4|?
Click to place a random integer on the number line!
Same sign: add absolute values, keep sign. -3 + (-5) = -8.
Different signs: subtract smaller from larger, use sign of the bigger. -7 + 4 = -3.
Subtracting: Add the opposite. 5 - (-3) = 5 + 3 = 8.
1. Calculate: -6 + (-4)
2. Calculate: 8 + (-11)
3. Calculate: -4 - (-7)
4. Temp was -3F. Dropped 8 degrees. New temp?
5. Simplify: 6 + (-9) + 3
Move the submarine up and down using integer operations!
25-30 question comprehensive test covering all December topics: integers, absolute value, and integer operations. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Coordinate Plane: Two number lines cross at the origin (0,0). Horizontal = x-axis, vertical = y-axis. Quadrant I (+,+), II (-,+), III (-,-), IV (+,-). Always go right/left first, then up/down.
Ordered Pair: (x, y). To plot (3,-4): move right 3, then down 4. That lands in Quadrant IV.
1. What quadrant is the point (-3, 5)?
2. What are the coordinates of the origin?
3. Point A is at (4, -2). What quadrant?
4. The reflection of (3, 7) across the x-axis is:
5. Distance between (2, 5) and (2, -3)?
Enter any (x, y) point and find out which quadrant it lives in!
Input-Output Table: A rule like y = 2x + 1 produces a pattern. For each input (x), apply the rule to get the output (y). Graph the (x,y) pairs.
Proportional: passes through origin (0,0), constant ratio y/x. Non-proportional: y-intercept is not 0, or the ratio y/x changes.
1. Which table shows a proportional relationship?
2. Rule is y = 3x. What is y when x = 5?
3. Table: x: 0,1,2,3 y: 0,4,8,12. The rule is:
4. A proportional relationship always passes through:
5. Rule: y = x + 5. Is this proportional?
Enter a multiplier and starting value to build an input-output table!
Slope = Rise/Run = (y2 - y1)/(x2 - x1). Positive slope: line goes up left to right. Negative slope: goes down. Zero slope: horizontal. Undefined: vertical line.
Example: points (1,3) and (4,9) → slope = (9-3)/(4-1) = 6/3 = 2.
1. Slope between (0, 0) and (4, 8)?
2. A line goes DOWN from left to right. Its slope is:
3. Slope of a horizontal line?
4. Points (2, 5) and (6, 13). Slope?
5. A ramp rises 3 ft over 12 ft horizontal. Slope?
Enter two points to calculate the slope (rise/run) step by step.
y = mx + b: m = slope (rise/run), b = y-intercept (where line crosses y-axis). To graph: start at (0, b), then use slope to find next point.
Example: y = 2x + 1 → start at (0,1), go up 2 right 1 → (1,3), (2,5)...
1. In y = 3x - 5, the slope is:
2. In y = -2x + 7, the y-intercept is:
3. A line with m=1 and b=4 passes through:
4. What is y when x=3 in y = 2x - 1?
5. Line through (0,2) with slope 3. Equation?
Set slope (m) and y-intercept (b) to describe your line and find 3 points on it.
25-30 question comprehensive test covering all January topics: coordinate plane, linear relationships, slope, and y=mx+b. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Bar graph: comparing categories. Line graph: change over time. Circle/Pie: parts of a whole. Histogram: distribution of grouped data. Box plot: shows min, Q1, median, Q3, max.
Five-number summary for {2,5,7,8,10,12}: min=2, Q1=5, med=7.5, Q3=10, max=12.
1. Best graph for showing change in temperature over a week?
2. A box plot shows the ____ in the center box.
3. For {3, 7, 8, 9, 15} the median is:
4. Best graph to show what percent of students prefer each sport?
5. A histogram shows data grouped into:
Read each scenario. Click the best graph type for that data!
Mean: add all values, divide by count. Median: middle value when sorted. Mode: most frequent. Range: max - min. IQR: Q3 - Q1.
Outliers drag the mean, not the median. Use median when data is skewed or has outliers. Use mean when data is symmetric.
1. Data: 4, 7, 7, 9, 13. What is the mode?
2. Data: 3, 5, 7, 9, 11. What is the mean?
3. Data: 2, 4, 6, 8, 10. What is the median?
4. Adding an outlier of 100 to {5,6,7,8,9} most changes:
5. Data: 12, 15, 15, 18, 20. What is the range?
Enter up to 8 numbers (comma separated) to find mean, median, mode, and range!
Probability = favorable outcomes / total outcomes. Always between 0 (impossible) and 1 (certain).
Theoretical: what math says should happen. Experimental: what actually happened when you ran the trial. They get closer as you run more trials.
1. A bag has 3 red and 7 blue marbles. P(red)?
2. Rolling a 6-sided die: P(even)?
3. P(impossible event) = ?
4. Flipping a coin 10 times: 7 heads. Experimental P(heads)?
5. A deck has 52 cards. P(drawing a king)?
Flip a coin or roll a die many times. Watch experimental probability approach theoretical!
Independent events: outcome of one doesn't affect the other. P(A and B) = P(A) x P(B). Example: flipping two coins.
Dependent events: first event changes what's available. Example: drawing cards without replacing. Multiply using updated sample space.
Counting Principle: total outcomes = choices1 x choices2 x ...
1. P(heads) = 1/2 and P(rolling 3) = 1/6. P(both)?
2. Bag: 5 red, 3 blue. Draw 1, don't replace, draw again. P(red then red)?
3. 3 shirt colors and 4 pant options. Total outfits?
4. Spinner: 4 equal sections (A,B,C,D). Predict A in 100 spins?
5. Flipping two coins: P(both tails)?
Choose an event for each stage and see all possible outcomes listed!
25-30 question comprehensive test covering all February topics: data displays, measures of center and spread, basic probability, and compound probability. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Integers: positive, negative, zero. Order on the number line: more negative = further left. Absolute value = distance from zero. |-8| = 8.
Rational numbers include all fractions and decimals that terminate or repeat. Operations: same-sign add, different-sign subtract (use the sign of the larger absolute value).
1. Which is furthest left on a number line?
2. Calculate: -4 + (-7)
3. Calculate: -3 - (-9)
4. Is 0.333... a rational number?
5. Temp drops from 8°F to -12°F. Change?
10 rapid-fire integer problems. Click your answer!
Read-Draw-Write strategy: (1) Read carefully. (2) Draw/label a diagram. (3) Write an equation. (4) Solve. (5) Check - does the answer make sense?
Multi-step tip: break into sub-problems. Find intermediate answers first. Watch for hidden conversions (percents to decimals, mixed to improper).
1. A shirt costs $24. It's on sale for 25% off, then 10% tax. Final price?
2. Maria earned $45. She saved 2/3. How much saved?
3. A tank has 80 gallons. 3/4 used on Monday, then 5 gallons added. Left?
4. In a class of 30, 40% have pets and 50% of THOSE have dogs. Dog owners?
5. 2.5 hrs at $12/hr + 4 hrs at $15/hr. Total earned?
Use this template to organize any word problem!
Exponent rules: a^m x a^n = a^(m+n) a^m / a^n = a^(m-n) (a^m)^n = a^(mn) a^0 = 1
Scientific notation: a x 10^n where 1 ≤ a < 10. Large: 93,000,000 = 9.3 x 10^7. Small: 0.00045 = 4.5 x 10^-4. Move decimal left to make smaller = multiply by positive power of 10.
1. Simplify: 3^4 x 3^2
2. Simplify: (2^3)^2
3. Write 450,000 in scientific notation.
4. Write 3.2 x 10^-3 as a standard number.
5. Anything raised to the power of 0 equals:
Convert between standard form and scientific notation!
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... √49 = 7. Non-perfect: estimate by finding closest perfect squares. √50 ≈ 7.07 (between √49=7 and √64=8).
Pythagorean Theorem: in a right triangle, a² + b² = c² where c is the hypotenuse. Used to find any missing side.
1. √144 = ?
2. √50 is between which two integers?
3. Right triangle: legs 3 and 4. Hypotenuse?
4. Hypotenuse = 13, one leg = 5. Other leg?
5. A 10 ft ladder leans against a wall. Base is 6 ft from wall. Height?
Enter any two sides of a right triangle to find the third!
25-30 question comprehensive test covering all March topics: integers, rational numbers, multi-step word problems, exponents, scientific notation, square roots, and the Pythagorean Theorem. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Translation: slide a figure. Rule: (x, y) → (x+a, y+b). Point (3,4) shifted right 2, up 5 = (5,9). Every point moves the same way.
Reflection: flip over a line. Over x-axis: (x,y) → (x,-y). Over y-axis: (x,y) → (-x,y). The line of reflection is the mirror.
1. Translate (3, 5) by (right 2, down 4). New point?
2. Reflect (4, -2) over the x-axis.
3. Reflect (-3, 7) over the y-axis.
4. Which transformation preserves size and shape?
5. A figure shifts left 5 and up 2. Rule?
Enter a point and choose a transformation to see the result!
Rotation rules (about origin): 90° CCW: (x,y)→(-y,x). 180°: (x,y)→(-x,-y). 270° CCW (=90° CW): (x,y)→(y,-x).
Dilation: multiply all coordinates by scale factor k. Center (0,0): (x,y)→(kx,ky). k>1 = enlarge. 0<k<1 = shrink. Dilation preserves shape but NOT size.
1. Rotate (4, 2) 90° CCW about origin.
2. Rotate (3, -1) 180° about origin.
3. Dilate (5, 10) by scale factor 1/2.
4. A dilation with k=3 will:
5. Which transformation creates a SIMILAR (not congruent) figure?
Enter a point and try different transformations!
Congruent figures (≅): exact same size AND shape. Produced by rigid motions (translation, rotation, reflection). Corresponding parts are equal.
Similar figures (~): same shape, proportional sides. Produced by dilation (+ rigid motions). Set up ratios of corresponding sides to find unknowns.
1. Two figures are congruent. They must have:
2. Triangles: sides 3,4,5 and 6,8,10. Are they similar?
3. Similar rectangles: 4x6 and 6x?. Find ?
4. Which transformation produces a CONGRUENT figure?
5. All congruent figures are also similar. True or false?
Two similar figures have corresponding sides. Find the missing side!
Mural Project: Start with a simple polygon. Apply all four transformations (translation, reflection, rotation, dilation) and plot each result on a coordinate grid. Label each transformation with its rule and name.
Make it artistic - color each transformation's image differently, then write a "transformation story" paragraph explaining the journey of your shape.
1. Which transformation does NOT preserve size?
2. Which transformations produce CONGRUENT figures? (choose best answer)
3. A figure is rotated 90° CCW, then reflected over the y-axis. This is called a:
4. Translate (2,3) by (+1, -2) then rotate 180°. Final point?
5. Which is a rigid transformation?
Describe what happened to a figure and identify the transformation!
25-30 question comprehensive test covering all April topics: translations, reflections, rotations, dilations, similarity, and congruence. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Unit 1: Fractions/Decimals/Percents — equivalent fractions, operations, conversions.
Unit 2: Ratios/Proportions — ratios, unit rates, proportions, scale.
Unit 3: Algebra — variables, expressions, equations, inequalities.
Unit 4: Integers — absolute value, integer operations.
1. Simplify 18/24.
2. Solve: 4/5 = x/25
3. Evaluate 3x - 7 when x = 5.
4. Calculate: -6 + 4 - (-3)
5. 40% of 75 = ?
8 rapid-fire mixed review questions from Units 1-4!
Unit 5: Coordinate Plane — quadrants, slope, y=mx+b.
Unit 6: Data & Probability — mean/median/mode, graphs, probability fractions.
Unit 7: Number Systems — exponents, scientific notation, Pythagorean Theorem.
Unit 8: Transformations — all four types, congruence vs. similarity.
1. Slope between (1, 3) and (4, 9)?
2. Data: 5,7,9,9,10. Mode = ?
3. Reflect (5,-2) over x-axis.
4. 8.4 x 10^3 in standard form?
5. Legs 5 and 12 in a right triangle. Hypotenuse?
10 mixed questions from across the whole year!
Year Reflection: Look back at your September Week 1 quiz vs. today. How much did you grow? Write 3 things you learned this year that surprised you, and 1 math topic you'd love to learn next.
Portfolio Share-out: Choose your favorite piece of work from this year and explain to a partner why you're proud of it.
Comprehensive cumulative exam covering all 9 units from the full year. 30-40 questions: multiple choice, short answer, show-your-work, and word problems. Printable PDF with complete teacher answer key.
📥 Lower Level Final Exam (PDF) 📥 Upper Level Final Exam (PDF)Fill in your personal year in review!
Great work this year! You showed up, you worked hard, and you grew. That matters.
Real Number System: Natural (1,2,3) ⊂ Whole (0,1,2) ⊂ Integer (-2,-1,0,1) ⊂ Rational (p/q) ⊂ Real. Irrational: √2, π, e — non-repeating, non-terminating decimals.
Expressions: Evaluate by substituting; apply PEMDAS. Distributive: a(b+c)=ab+ac. "Seven less than three times n" = 3n-7.
1. Which is irrational?
2. Evaluate 3x² - 2x + 5 when x = -2.
3. Property: 5(x+3)=5x+15?
4. "Seven less than three times n."
5. Simplify: 4(2x-3)+5x
Click a number to select it, then click a category box to sort it there. Check when done!
Multi-Step: Distribute → combine like terms → move variables to one side → isolate. Example: 3(x-2)+4=2x+7 → 3x-2=2x+7 → x=9.
Special cases: 0=0 → infinite solutions. 3=5 → no solution. Literal equations: isolate one variable (A=lw → w=A/l).
1. Solve: 2(3x-4)+6=22
2. Solve: 5x-7=3x+11
3. Solve: 3(x+2)=3x+10. Solution?
4. Solve A=(1/2)bh for b.
5. $30/month + $0.10/text = $43 bill. Texts sent?
Enter the value of x that keeps the equation balanced.
Key rule: Multiply/divide both sides by NEGATIVE → flip the inequality sign. Example: -3x < 12 → x > -4.
Compound: AND = intersection (-2 < x ≤ 4). OR = union (x<-1 OR x>3). Interval notation: ( ) = exclusive, [ ] = inclusive.
1. Solve: -4x+3>11
2. Graph of x ≤ 3?
3. -1 ≤ 2x+3 < 9 in interval notation?
4. x<-1 OR x≥4?
5. Need avg ≥ 85 on 4 tests. Scores: 78,92,81. Min test 4?
Solve each inequality, select the correct symbol and enter the value.
Abs Value Equations: |x-3|=7 → x-3=7 OR x-3=-7 → x=10 or x=-4. If c<0: no solution. Always check both cases.
Abs Value Inequalities: |x|<a means -a<x<a (AND). |x|>a means x<-a OR x>a. Tolerance example: |L-5.00|≤0.02 → 4.98≤L≤5.02.
1. Solve: |x-3|=7
2. Solve: |2x+1|=9
3. |x| < 4 means:
4. Solve: |3x-6| > 12
5. Gear 8.00cm ± 0.05cm. Write inequality for acceptable length L.
Click highlighted words to reveal what they represent, then solve for m.
25-30 question comprehensive test covering all September topics: variables, expressions, equations, and inequalities. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Slope (m) = (y2 - y1) / (x2 - x1). Positive slope rises left-to-right. Negative slope falls. Zero slope = horizontal. Undefined = vertical.
Memorize: rise over run.
1. Slope between (1,2) and (3,6)?
2. Slope between (0,5) and (4,5)?
3. Slope between (2,3) and (2,7)?
4. Which slope is steepest?
5. Point (1,3) on line y = 2x + 1?
Enter two coordinate pairs to calculate slope.
In y = mx + b: m is slope, b is y-intercept (where line crosses y-axis).
To graph: plot b on y-axis, use slope to find next point (rise/run), connect.
1. In y = 4x - 3, what is the y-intercept?
2. What is the slope of y = -2x + 7?
3. Which equation has slope 3 and y-int -1?
4. Line through (0,5) with slope 2: equation?
5. Parallel lines have _____ slopes.
Adjust slope and y-intercept with sliders to see how the equation changes.
Intercept Method: Set y=0 for x-intercept, x=0 for y-intercept. Plot both, draw line.
Horizontal lines: y = constant (slope=0). Vertical lines: x = constant (undefined slope).
1. X-intercept of y = 3x - 6?
2. Graph of y = -2 is?
3. Which two lines are parallel?
4. Y-intercept of 3x + 2y = 12?
5. Does (-1, 5) lie on y = -2x + 3?
Enter slope and y-intercept to find x- and y-intercepts.
From graph: Identify y-intercept (b). Count rise/run for slope (m). Write y = mx + b.
From table: Slope = change in y / change in x. Y-int = y when x = 0.
1. Table: x=0,1,2,3 y=3,5,7,9. Equation?
2. Graph crosses y-axis at 4, slope is -1. Equation?
3. Is x=0,1,2,3 y=1,4,9,16 linear?
4. Table: x=2,4,6 y=7,11,15. Slope?
5. Two points (0,3) and (2,7). Equation?
Fill in y-values for x=0,1,2,3 and find the linear equation!
| x | y |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 |
25-30 question comprehensive test covering all October topics: linear equations, slope, and graphing. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
System: two equations with same variables. Solution = intersection point.
Types: One solution (lines cross), No solution (parallel), Infinite (same line).
1. System: y=x+2 and y=-x+4. Solution?
2. Two parallel lines have ___ solutions.
3. If two equations are identical, they have ___ solutions.
4. Is (2,5) a solution to y=2x+1 and y=3x-1?
5. System: y=3 and x=4. Solution?
Enter a point and two equations to check if it's a solution to the system.
Steps: 1) Solve one equation for a variable. 2) Substitute into the other. 3) Solve. 4) Back-substitute. 5) Check both equations.
1. Solve: y=3x, x+y=8
2. Solve: y=x+2, 2x+y=8
3. Best to use substitution when?
4. Solve: x=4-y, x+2y=6
5. Two numbers sum 30; one is twice the other. Numbers?
Eq.1: y = ax + b. Eq.2: cx + dy = e. See the substitution steps.
Elimination: Add or subtract equations to cancel one variable. Multiply one (or both) equations first if needed to make coefficients cancel.
1. Add to eliminate: x+y=7, x-y=3. Solution?
2. Eliminate y: 2x+y=9, x-y=3
3. When should you multiply before adding?
4. Solve: 3x+2y=12, 3x-y=3
5. Solve: 2x+3y=13, 4x-3y=11
Enter two standard-form equations (ax+by=c) to see the elimination process.
Strategy: 1) Define variables. 2) Write two equations from the problem. 3) Solve the system. 4) Check answer in original context.
1. Sum of two numbers = 30; difference = 8. Larger number?
2. Adult tickets $6, child $4. 100 sold, $460 total. Adults?
3. Coins: 25 dimes and nickels = $1.75. Number of dimes?
4. Two cars, 300 mi apart, drive toward each other at 50 and 70 mph. Meet after?
5. One number is 3 more than twice another; sum is 24. Numbers?
Click the highlighted clues to reveal the setup!
25-30 question comprehensive test covering all November topics: systems of equations (graphing, substitution, elimination). Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Polynomial: sum of terms with non-negative exponents. Degree = highest exponent.
Add: combine like terms. Subtract: distribute the negative, then combine.
1. Degree of 4x^3 - 2x + 7?
2. Add: (3x+5)+(2x-3)
3. Subtract: (5x^2+3x)-(2x^2-x+1)
4. Leading coefficient of -7x^3+2x?
5. 3x^2-5x+2 is a?
Enter a polynomial expression to identify its type and degree.
FOIL: (x+3)(x+2) = x^2 + 2x + 3x + 6 = x^2 + 5x + 6. First, Outer, Inner, Last.
Special: (a+b)^2 = a^2 + 2ab + b^2. (a+b)(a-b) = a^2 - b^2.
1. Use FOIL: (x+4)(x+3)
2. Use FOIL: (x-2)(x+5)
3. Multiply: 3x(x^2+2x-1)
4. (x+5)(x-5) is?
5. Expand (x+3)^2
Enter values for a and b in (x+a)(x+b) to see FOIL work!
25-30 question comprehensive test covering all December topics: polynomials, operations, and FOIL method. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Quadratic function: y = ax² + bx + c. Graph is a U-shaped parabola. If a>0, opens up; if a<0, opens down.
Vertex: turning point of the parabola. x = -b/2a. Axis of symmetry: vertical line through the vertex. x-intercepts: where y=0 (solutions to quadratic equation).
1. y = x² + 4 opens:
2. Vertex of y = (x-3)² + 5?
3. For y = -2x² + 3x, direction of opening?
4. Axis of symmetry for y = x² - 6x + 5?
5. Where does y = x² - 4 cross the x-axis?
Enter a, b, c for y = ax² + bx + c to find the vertex and axis of symmetry.
Zero Product Property: if ab = 0, then a=0 or b=0. Factor first: x² + 5x + 6 = (x+2)(x+3) = 0 → x=-2 or x=-3.
Square Roots Method: Works when no x term. x² = 25 → x = ±5. Completing the square: rearrange to (x+h)² = k, then take square root.
1. Solve: x² - 9 = 0
2. Factor: x² + 7x + 12
3. Solve: (x-4)(x+2) = 0
4. Solve: x² = 49
5. Solve: x² + 5x + 6 = 0
Enter b and c for x² + bx + c. Find two numbers that multiply to c and add to b!
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a. Works for ANY quadratic.
Discriminant (b²-4ac): >0 = two real solutions; =0 = one real solution (double root); <0 = no real solutions (complex).
1. For 2x² + 3x - 5 = 0, what is a, b, c?
2. Discriminant of x² - 4x + 4 = 0?
3. Disc. < 0 means the quadratic has:
4. Solve x² - 5x + 6 = 0 using the quadratic formula. Solutions?
5. Best method for x² - 25 = 0?
Enter a, b, c for ax² + bx + c = 0 and get step-by-step solutions!
Projectile Motion: h(t) = -16t² + v₀t + h₀ (feet) or -4.9t²+v₀t+h₀ (meters). Find max height by finding vertex t = -b/2a, then substitute back.
Optimization: Maximize area of a rectangle given a fixed perimeter. Revenue = price × quantity. Set up the quadratic, find vertex = max.
1. h(t) = -16t² + 64t. When does the ball reach max height?
2. h(t) = -16t² + 64t. What IS the max height?
3. h(t) = -16t² + 80t + 6. Initial height (t=0)?
4. Rectangle perimeter = 20 ft. Area A = x(10-x). Max area?
5. Revenue R(x) = x(200-2x). Best price per unit x?
Enter launch speed (v₀) and initial height (h₀) in feet. Find max height and time in air!
25-30 question comprehensive test covering all January topics: graphing quadratics, solving by factoring/square roots, the quadratic formula, and real-world applications. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Conditional Statement: "If p, then q" (p → q). Converse: "If q, then p." Inverse: "If not p, then not q." Contrapositive: "If not q, then not p" (always same truth value as original).
Two-Column Proof: Left column = statements. Right column = reasons (given, definition, theorem, property). Every statement must have a reason.
1. Converse of "If it rains, the ground gets wet"?
2. In a two-column proof, the right column contains:
3. Which has the same truth value as a conditional?
4. Segment Addition Postulate: if B is between A and C, then:
5. Vertical angles are:
Enter a conditional "if P then Q" and see its related forms!
SSS: 3 sides equal. SAS: 2 sides + included angle. ASA: 2 angles + included side. AAS: 2 angles + non-included side. HL: right triangles only - hypotenuse + one leg.
CPCTC (Corresponding Parts of Congruent Triangles are Congruent): once you prove ΔABC ≅ ΔDEF, you can state any corresponding parts are equal.
1. Two sides and the INCLUDED angle are equal. Which postulate?
2. CPCTC can only be used AFTER:
3. HL applies only to:
4. Isosceles triangle theorem: if two sides are equal, then:
5. Know two angles and NON-included side. Use:
Pick what information you have. Find out which congruence theorem applies!
Similar triangles (∼): same shape, different size. Corresponding angles equal, corresponding sides proportional. Scale factor k = ratio of corresponding sides.
AA Similarity: if two angles of one Δ equal two of another, they're similar. Midsegment Theorem: midsegment = half the parallel side and parallel to it.
1. Two triangles share 2 equal angles. This proves:
2. ΔABC ~ ΔDEF. AB = 6, DE = 9. Scale factor?
3. Midsegment of a triangle is parallel to the base and equals:
4. ΔABC ~ ΔDEF. AC = 8, DF = 12. If AB = 10, then DE = ?
5. A tree casts 15 ft shadow; 5 ft stick casts 3 ft shadow. Tree height?
Use similar triangles to find an unknown height from shadow measurements!
SOH-CAH-TOA: Sin = Opposite/Hypotenuse Cos = Adjacent/Hypotenuse Tan = Opposite/Adjacent.
45-45-90: sides are x, x, x√2. 30-60-90: sides are x, x√3, 2x. Use these ratios to find missing sides without a calculator.
1. sin(angle) = ?
2. In a 45-45-90 right triangle, if a leg = 5, hypotenuse = ?
3. tan(angle) = Opposite/Adjacent. If opp=3, adj=4, tan = ?
4. 30-60-90: short leg = 7. Hypotenuse = ?
5. cos(30°) = ?
Enter the three sides of a right triangle. Get all three trig ratios for angle A (opposite = a, adjacent = b, hypotenuse = c)!
25-30 question comprehensive test covering all February topics: geometric logic/proofs, triangle congruence, similarity and proportionality, and intro to trigonometry. Includes multiple choice, matching, show-your-work problems, and word problems. Printable PDF with teacher answer key.
Measures of center: Mean = sum/n. Median = middle value. Mode = most frequent. Midrange = (max+min)/2. Outliers pull the mean but not median.
Spread: Range = max-min. IQR = Q3-Q1 (resistant to outliers). Standard deviation (informal) = average distance from the mean. A larger SD means more spread.
1. Dataset: 4, 7, 7, 9, 13. Median = ?
2. Adding a value of 100 to dataset 2,3,4,5 will MOST affect the:
3. Q1=10, Q3=22. IQR = ?
4. Two datasets have the same mean. Dataset A has SD=2, Dataset B has SD=8. Dataset B is:
5. Which measure is most resistant to extreme outliers?
Enter comma-separated numbers and get full descriptive stats!
Correlation strength: Strong = points cluster tightly on a line. Weak = loosely scattered. Positive: as x increases, y increases. Negative: as x increases, y decreases.
Line of best fit: minimizes total distance from all points. Use it to make predictions. Remember: correlation ≠ causation. Lurking variables can create false correlations.
1. Study hours and test scores increase together. This shows:
2. Line of best fit: y = 2x + 5. Predict y when x = 10.
3. "Ice cream sales and drowning rates are correlated." This likely means:
4. r ≈ -0.95 indicates:
5. A point far from the line of best fit is called:
Enter data point pairs and classify the correlation!
Permutation (order matters): nPr = n! / (n-r)! Example: Arranging 3 people from 5: 5P3 = 60.
Combination (order doesn't matter): nCr = n! / [r!(n-r)!] Example: Choosing 3 people from 5: 5C3 = 10. Key question: does order matter? If yes = permutation.
1. How many ways to arrange 4 books in a row (from 4)?
2. 5C2 = ?
3. Choosing a 3-person committee from 8 people uses:
4. P(A and B) where P(A)=0.3 and P(B)=0.5 (independent). Answer?
5. 4P2 = ?
Calculate nPr and nCr!
Normal distribution: bell-shaped, symmetric about the mean. Empirical rule: 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD.
Z-score: z = (x - μ) / σ. Tells you how many standard deviations a value is from the mean. z=0 is at the mean. z=+1 is one SD above.
1. In a normal distribution, what % of data falls within 2 SDs of the mean?
2. Mean = 70, SD = 5. Z-score for x=80?
3. Test scores: mean=75, SD=10. Score of 55 is how many SDs below the mean?
4. A normally distributed variable with mean=50, SD=4. About what percent of values are between 42 and 58?
5. The normal curve is symmetric about the:
Enter mean and standard deviation to see the 68-95-99.7 ranges!
25-30 question comprehensive test: descriptive statistics, scatter plots, correlation, counting methods, permutations, combinations, compound probability, and the normal distribution. Printable PDF with teacher answer key.
Simplifying: √72 = √(36·2) = 6√2. Find the largest perfect square factor. √a · √b = √(ab).
Solving: isolate the radical, then square both sides. ALWAYS check for extraneous solutions (squaring can introduce false answers). Example: √(x+3) = 5 → x+3=25 → x=22. Check: √25 = 5 ✓
1. Simplify √50.
2. Simplify 3√2 + 5√2.
3. Solve √x = 7.
4. √3 · √12 = ?
5. Why do we check for extraneous solutions after solving a radical equation?
Enter a number under the radical and see it simplified!
Rational expression: a fraction with polynomials in numerator & denominator. Simplify by factoring and canceling common factors.
Excluded values: set the denominator = 0 and solve. Those values are NOT in the domain. Example: (x+3)/(x-2) excludes x=2. Multiply: multiply tops & bottoms, then simplify. Divide: multiply by the reciprocal.
1. Excluded value(s) of (x+1)/(x-3)?
2. Simplify: (6x²)/(3x)
3. Excluded values of x/(x²-4)?
4. (3/x) × (x²/6) simplified = ?
5. To divide by a fraction, you:
Find what x values are excluded from a rational expression!
Arithmetic sequence: add d each time. a_n = a_1 + (n-1)d. Example: 3,7,11,15... d=4, a_n = 3+(n-1)4 = 4n-1.
Geometric sequence: multiply by r each time. a_n = a_1 · r^(n-1). Example: 2,6,18,54... r=3, a_n = 2·3^(n-1). Geometric sequences model exponential growth.
1. Sequence: 5, 11, 17, 23... What is the 10th term?
2. Geometric: 3, 6, 12, 24... What is the 6th term?
3. Sequence 2, -6, 18, -54 has common ratio:
4. Arithmetic sequence: a_1=10, d=-3. Find a_5.
5. Compound interest models which type of sequence?
Find the nth term of an arithmetic or geometric sequence!
Exponential function: y = a·b^x. a = starting value (y-intercept). b = base (growth/decay factor). b>1 = growth. 0<b<1 = decay. Domain: all reals. Range: y > 0.
Models: Population: P(t) = P_0 · (1+r)^t. Half-life: A(t) = A_0 · (1/2)^(t/h). Compound interest: A = P(1+r/n)^(nt).
1. y = 100 · (0.5)^x. As x increases, y:
2. y = 50 · 2^x. Find y when x=4.
3. A population of 1,000 grows 5% per year. After 3 years:
4. The y-intercept of y = 3·5^x is:
5. All exponential functions y = a·b^x (a>0) have range:
Model real-world exponential situations!
25-30 question comprehensive test: radical expressions, radical equations, rational expressions, excluded values, arithmetic sequences, geometric sequences, exponential functions (growth, decay, models). Printable PDF with teacher answer key.
Units 1-4 recap:
Unit 1: Equations & Inequalities (one/two-step, multi-step, absolute value)
Unit 2: Systems (substitution, elimination, graphing)
Unit 3: Linear Functions (slope-intercept, standard form)
Unit 4: Polynomials (operations, FOIL, factoring GCF, trinomials)
1. Solve: 3x - 7 = 14
2. System: x + y=10, x - y=2. Solve for x.
3. Slope of 3x - 4y = 12?
4. Factor: x² - 9
5. Multiply: (2x+3)(x-4)
10 rapid questions from the first half of the year!
Units 5-8 recap:
Unit 5: Quadratics (parabolas, factoring, quad formula, applications)
Unit 6: Geometry (logic, proofs, congruence, similarity, trig SOH-CAH-TOA)
Unit 7: Statistics & Probability (normal dist., permutations, combinations)
Unit 8: Algebra II Bridge (radicals, rational expressions, sequences, exponentials)
1. Vertex of y = x² - 4x + 3?
2. Right triangle: opposite=4, hypotenuse=5. sin(θ) = ?
3. 6C3 = ?
4. Geometric sequence: 5, 10, 20, 40... Find the 7th term.
5. Simplify: √48
10 questions spanning all second-semester topics!
Year Reflection: You covered 8 full units from systems of equations all the way through exponential functions and normal distributions. You've built the foundation for Algebra 2, Pre-Calculus, and beyond.
Write: 3 things you learned this year that surprised you. 1 concept you want to keep exploring. 1 example of something you found hard in September that now feels easy.
Comprehensive cumulative exam covering all 9 units. 35-45 questions: multiple choice, short answer, show-your-work, and mixed application problems. Printable PDF with complete teacher answer key.
📥 Lower Level Final Exam (PDF) 📥 Upper Level Final Exam (PDF)Wrap up the year with a quick self-assessment!
You made it. From systems of equations to the normal curve - that's a full year of real mathematics. Be proud of what you built.