🦋 Yann's Tutoring Services

Grade 1 Practice Test

Name: _________________ Date: _________________

Addition Problems

• 2 + 3 = _____
• 5 + 1 = _____
• 4 + 4 = _____
• 7 + 2 = _____
• 6 + 3 = _____

Subtraction Problems

• 8 - 2 = _____
• 5 - 3 = _____
• 9 - 4 = _____
• 7 - 1 = _____
• 10 - 5 = _____

Counting and Number Recognition

• Write the number that comes after 6: _____
• Write the number that comes before 10: _____
• Count the apples: 🍎🍎🍎🍎🍎🍎🍎 = _____

Word Problems

• Sarah has 3 apples. Her mom gives her 2 more apples. How many apples does Sarah have now? _____
• There are 8 birds on a tree. 3 birds fly away. How many birds are left? _____
• Tom has 5 toy cars. He buys 4 more toy cars. How many toy cars does Tom have in total? _____

Shape Recognition

• How many sides does a triangle have? _____
• How many corners does a square have? _____

Bonus Challenge

• 4 + 5 + 1 = _____

Great job! Remember to check your answers!

Grade 2 Practice Test

Name: ___________________ Date: ___________________

Section 1: Addition

• 5 + 3 = ___
• 12 + 7 = ___
• 8 + 8 = ___
• 15 + 4 = ___
• 9 + 6 = ___

Section 2: Subtraction

• 10 - 4 = ___
• 18 - 9 = ___
• 14 - 6 = ___
• 20 - 5 = ___
• 13 - 7 = ___

Section 3: Word Problems

• Emma has 7 apples. Her friend gives her 5 more apples. How many apples does Emma have now?
• There are 16 birds sitting on a fence. 8 birds fly away. How many birds are left on the fence?
• Alex has 12 toy cars. He buys 6 more toy cars at the store. How many toy cars does Alex have altogether?

Section 4: Counting and Numbers

• Write the number that comes after 29: ___
• Write the number that comes before 45: ___
• Count by 5s: 5, 10, 15, ___, ___, ___
• What number is 10 more than 32? ___

Section 5: Shapes and Measurement

• How many sides does a triangle have? ___
• How many corners does a rectangle have? ___
• Which is longer: a pencil or a crayon? (Circle your answer)

Bonus Question! 🌟

• If you have 2 groups of 5 cookies, how many cookies do you have in total?

Great job! 🎉

Grade 3 Practice Test

Name: ________________ Date: ________________

Section 1: Addition and Subtraction

• 45 + 37 = ____
• 82 - 29 = ____
• 156 + 248 = ____
• 500 - 167 = ____

Section 2: Multiplication and Division

• 6 × 7 = ____
• 9 × 4 = ____
• 56 ÷ 8 = ____
• 45 ÷ 5 = ____

Section 3: Word Problems

• Sarah has 24 stickers. She gives 8 stickers to her friend. How many stickers does Sarah have left?
• There are 5 boxes of crayons. Each box has 8 crayons. How many crayons are there in total?
• A baker made 72 cookies. He wants to put them equally into 9 boxes. How many cookies will be in each box?

Section 4: Fractions

• Color 1/2 of this shape: ⬜⬜⬜⬜
• Which is larger: 1/3 or 1/4? ____
• What fraction of the shape is shaded if 3 out of 6 parts are colored? ____

Section 5: Measurement and Time

• How many inches are in 1 foot? ____
• If the time is 3:15, what time will it be in 30 minutes? ____
• A pencil is 7 inches long. How long are 3 pencils placed end to end? ____

Section 6: Geometry

• How many sides does a triangle have? ____
• How many corners does a rectangle have? ____
• Name this shape: A shape with 4 equal sides. ____

Bonus Challenge

• Emma has 3 bags with 12 marbles in each bag. She gives 9 marbles to her brother. How many marbles does Emma have now?

Grade 4 Practice Test

Name: ________________ Date: ________________

Section 1: Addition and Subtraction

• 457 + 289 = _______
• 1,024 - 568 = _______
• 3,456 + 2,789 = _______
• 5,000 - 2,347 = _______

Section 2: Multiplication and Division

• 8 × 7 = _______
• 56 ÷ 8 = _______
• 12 × 9 = _______
• 144 ÷ 12 = _______
• 25 × 4 = _______

Section 3: Fractions

• What is 1/2 + 1/4? _______
• What is 3/4 - 1/4? _______
• Circle the larger fraction: 2/3 or 1/2
• Write an equivalent fraction for 1/2: _______

Section 4: Word Problems

• Sarah has 24 cookies. She wants to share them equally among 6 friends. How many cookies will each friend get? _______
• A book costs $8. If you buy 3 books, how much will you spend in total? _______
• There are 345 students in a school. If 128 students are in the gym, how many students are not in the gym? _______
• A farmer has 48 apples. He puts them into baskets with 8 apples in each basket. How many baskets does he need? _______

Section 5: Geometry

• How many sides does a hexagon have? _______
• What is the perimeter of a rectangle with length 10 cm and width 5 cm? _______
• A square has sides of 6 inches. What is its area? _______

Section 6: Measurement and Data

• Convert 3 meters to centimeters: _______
• If a movie starts at 2:45 PM and lasts 1 hour and 30 minutes, what time does it end? _______
• Look at the following data: 12, 15, 18, 12, 20. What is the mode? _______

Good luck! Show your work on a separate sheet of paper.

Grade 5 Practice Test

Name: ___________________ Date: ___________________

Section 1: Basic Operations

• 345 + 678 = ___________
• 1,205 - 847 = ___________
• 4,562 + 3,789 = ___________
• 5,000 - 2,436 = ___________

Section 2: Multiplication and Division

• 7 × 8 = ___________
• 54 ÷ 6 = ___________
• 12 × 15 = ___________
• 144 ÷ 12 = ___________
• 9 × 7 = ___________
• 81 ÷ 9 = ___________

Section 3: Fractions

• What is 1/2 + 1/4? ___________
• What is 3/4 - 1/4? ___________
• Which is larger: 2/3 or 1/2? ___________
• Simplify: 4/8 = ___________

Section 4: Word Problems

• Sarah has 24 apples. She wants to share them equally among 6 friends. How many apples will each friend get? ___________
• A book costs $12 and a pencil costs $3. How much do 2 books and 4 pencils cost in total? ___________
• Tom ran 3 miles on Monday, 5 miles on Wednesday, and 4 miles on Friday. How many miles did he run in total? ___________
• A rectangle has a length of 12 inches and a width of 5 inches. What is its perimeter? ___________

Section 5: Measurement and Geometry

• How many inches are in 2 feet? ___________
• What is the area of a square with sides of 6 cm? ___________
• How many sides does a hexagon have? ___________
• If a clock shows 3:15, what time will it be in 45 minutes? ___________

Bonus Questions

• What is 25 × 4? ___________
• If you have $50 and spend $17.50, how much money do you have left? ___________

Good luck! 🌟

Grade 6 Practice Test

Name: __________________ Date: __________________

Instructions: Show all your work. Each question is worth the points indicated.

Section 1: Number Operations (20 points)

1. Solve: 456 + 789 = ______ (2 points)

2. Subtract: 1,205 - 687 = ______ (2 points)

3. Multiply: 24 × 15 = ______ (3 points)

4. Divide: 144 ÷ 12 = ______ (2 points)

5. What is 3/4 + 1/2? Express your answer as a fraction in simplest form. (3 points)

6. Convert 0.65 to a fraction in simplest form. (3 points)

7. What is 20% of 80? (3 points)

8. Order these numbers from least to greatest: -5, 3, -2, 0, 7 (2 points)

Section 2: Algebra and Expressions (15 points)

9. Solve for x: x + 15 = 42 (3 points)

10. Evaluate the expression: 3(4 + 2) - 5 = ______ (3 points)

11. If y = 7, what is the value of 4y - 10? (3 points)

12. Write an expression for "six more than twice a number n." (3 points)

13. Simplify: 5x + 3x - 2x = ______ (3 points)

Section 3: Geometry (20 points)

14. What is the area of a rectangle with length 12 cm and width 7 cm? (3 points)

15. Find the perimeter of a square with sides of 9 inches. (3 points)

16. A triangle has angles measuring 45° and 55°. What is the measure of the third angle? (3 points)

17. What is the volume of a rectangular prism with length 5 cm, width 4 cm, and height 3 cm? (4 points)

18. Find the area of a circle with radius 6 cm. (Use π = 3.14) (4 points)

19. Name two types of quadrilaterals. (3 points)

Section 4: Ratios, Rates, and Proportions (15 points)

20. Write the ratio 12:18 in simplest form. (3 points)

21. If 3 apples cost $2.25, how much do 5 apples cost? (4 points)

22. A car travels 180 miles in 3 hours. What is the car's speed in miles per hour? (3 points)

23. Solve the proportion: 4/5 = x/20 (5 points)

Section 5: Data and Statistics (15 points)

24. Find the mean (average) of these numbers: 12, 15, 18, 20, 25 (3 points)

25. What is the median of this data set: 7, 3, 9, 5, 11? (3 points)

26. Find the mode of: 4, 7, 4, 9, 4, 6, 7 (3 points)

27. What is the range of the following data: 22, 15, 30, 18, 25? (3 points)

28. If you flip a coin, what is the probability of getting heads? Express as a fraction. (3 points)

Section 6: Word Problems (15 points)

29. Sarah has $45. She wants to buy books that cost $8 each. How many books can she buy, and how much money will she have left? (5 points)

30. A recipe calls for 2/3 cup of sugar. If you want to make half the recipe, how much sugar do you need? (5 points)

31. A rectangular garden is 15 feet long and 8 feet wide. If you want to put a fence around it, how many feet of fencing do you need? (5 points)

Total: 100 points

Good luck! 🎯

Grade 7 Practice Test

Name: ________________ Date: ________________

Part 1: Multiple Choice (2 points each)

1. What is the value of 3² + 4²?

a) 12

b) 25

c) 49

d) 7

2. Simplify: -5 + 8 - 3

a) 0

b) -16

c) 6

d) -6

3. What is 25% of 80?

a) 15

b) 20

c) 25

d) 30

4. Solve for x: 2x + 5 = 17

a) x = 5

b) x = 6

c) x = 7

d) x = 11

5. What is the area of a rectangle with length 9 cm and width 4 cm?

a) 13 cm²

b) 26 cm²

c) 36 cm²

d) 18 cm²

Part 2: Short Answer (3 points each)

6. Calculate: 3/4 + 2/3

Answer: __________

7. A shirt originally costs $45. It is on sale for 20% off. What is the sale price?

Answer: __________

8. Find the circumference of a circle with radius 7 cm. (Use π ≈ 3.14)

Answer: __________

9. Solve the equation: 3(x - 4) = 21

Answer: x = __________

10. What is the mean (average) of these numbers: 12, 15, 18, 21, 24?

Answer: __________

Part 3: Word Problems (5 points each)

11. A rectangular garden is 12 feet long and 8 feet wide. If you want to put a fence around the entire garden, how many feet of fencing do you need?

12. Sarah scored 85, 92, and 88 on her first three tests. What score does she need on her fourth test to have an average of 90?

13. A recipe calls for 2.5 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

Part 4: Show Your Work (6 points each)

14. A store is having a sale. A jacket is marked down from $80 to $60. What is the percent decrease?

15. The ratio of boys to girls in a class is 3:5. If there are 24 students in total, how many boys and how many girls are in the class?

Total Points: 60

Grade 8 Practice Test

Name: ________________________ Date: ________________________

Instructions: Show all your work. Each question is worth 5 points.

Section 1: Number Sense and Operations

1. Simplify: -3(4 - 7) + 2(-5)

2. Calculate: 2/3 ÷ 4/5

3. Evaluate: 3² + 4³ - √64

Section 2: Algebra

4. Solve for x: 3x - 7 = 2x + 11

5. Simplify: 4(2x - 3) - 2(x + 5)

6. If y = 2x - 5, what is the value of y when x = 7?

7. Solve the inequality: 5x + 3 ≤ 23

Section 3: Geometry

8. Find the volume of a rectangular prism with length = 8 cm, width = 5 cm, and height = 3 cm.

9. A circle has a radius of 6 inches. What is its circumference? (Use π ≈ 3.14)

10. What is the measure of the third angle in a triangle if the other two angles measure 45° and 68°?

Section 4: Functions and Graphs

11. What is the slope of the line passing through the points (2, 5) and (6, 13)?

12. Write the equation of a line with slope = -3 and y-intercept = 4.

Section 5: Statistics and Probability

13. Find the mean of the following data set: 12, 15, 18, 20, 25

14. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Section 6: Word Problems

15. Sarah bought 3 notebooks for $2.50 each and 2 pens for $1.75 each. How much did she spend in total?

16. A rectangular garden is 12 feet long and 8 feet wide. If you want to put a fence around the entire perimeter, how many feet of fencing do you need?

17. A train travels 240 miles in 4 hours. What is its average speed in miles per hour?

18. Mike has $150. He spends 40% of his money on a new video game. How much money does he have left?

Grade 9 (Algebra 1) Practice Test

Name: _____________________ Date: _____________________

Instructions: Answer all questions. Show your work where applicable.

Section A: Algebra (40 points)

1. Solve for x: 3x + 7 = 22 (5 points)

2. Simplify: 4(2x - 3) + 5x (5 points)

3. Solve the equation: 2(x - 4) = 3x + 1 (5 points)

4. If y = 2x + 3, find the value of y when x = 5 (5 points)

5. Factor completely: x² + 7x + 12 (5 points)

6. Solve for x: (x + 2)/3 = 4 (5 points)

7. Expand and simplify: (x + 3)(x - 5) (5 points)

8. Solve the system of equations: (5 points)

2x + y = 10

x - y = 2

Section B: Geometry (30 points)

9. Find the area of a triangle with base 12 cm and height 8 cm (5 points)

10. Calculate the circumference of a circle with radius 7 cm (use π ≈ 3.14) (5 points)

11. Find the volume of a rectangular prism with length 6 cm, width 4 cm, and height 5 cm (5 points)

12. Two angles are complementary. If one angle measures 35°, what is the measure of the other angle? (5 points)

13. Find the surface area of a cube with side length 3 cm (5 points)

14. A right triangle has legs of 6 cm and 8 cm. Find the length of the hypotenuse using the Pythagorean theorem (5 points)

Section C: Number Sense and Operations (20 points)

15. Evaluate: (-3)² + 4 × 2 - 5 (5 points)

16. Convert 0.75 to a fraction in simplest form (5 points)

17. Find 15% of 240 (5 points)

18. Arrange in order from least to greatest: -2, 0.5, -1/2, 1, -3 (5 points)

Section D: Word Problems (10 points)

19. A store is offering a 20% discount on all items. If a jacket originally costs $80, what is the sale price? (5 points)

20. Maria is 3 years older than twice her brother's age. If her brother is 8 years old, how old is Maria? (5 points)

Total: 100 points

Good luck! 📝

Grade 10 (Geometry) Practice Test

Time: 60 minutes | Total Points: 100

Part A: Algebra (30 points)

1. Solve for x: 3x - 7 = 2x + 11 (3 points)

2. Simplify the expression: (2x² + 5x - 3) - (x² - 2x + 4) (4 points)

3. Factor completely: x² - 9x + 14 (4 points)

4. Solve the system of equations: (6 points)

2x + y = 8

x - y = 1

5. If f(x) = 2x² - 3x + 1, find f(-2) (4 points)

6. Solve for x: x² - 5x - 24 = 0 (5 points)

7. Simplify: (3x³y²)² (4 points)

Part B: Geometry (25 points)

8. Find the area of a triangle with base 12 cm and height 8 cm. (3 points)

9. Calculate the circumference of a circle with radius 7 cm. (Use π ≈ 3.14) (4 points)

10. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, find the length of the hypotenuse. (5 points)

11. Find the volume of a rectangular prism with length 10 cm, width 4 cm, and height 5 cm. (4 points)

12. Two angles are supplementary. If one angle measures 65°, what is the measure of the other angle? (3 points)

13. Find the surface area of a cube with side length 6 cm. (6 points)

Part C: Functions and Relations (20 points)

14. Determine if the following relation is a function: \{(1, 2), (2, 3), (3, 4), (2, 5)\} (4 points)

15. Find the slope of the line passing through points (3, 5) and (7, 13). (5 points)

16. Write the equation of a line in slope-intercept form with slope m = -2 and y-intercept b = 4. (4 points)

17. Graph the inequality: y \< 2x + 1 (sketch and describe the solution region) (7 points)

Part D: Word Problems (25 points)

18. A store is having a 25% off sale. If a jacket originally costs $80, what is the sale price? (5 points)

19. John has $500 in a savings account that earns 3% simple interest per year. How much money will he have after 2 years? (6 points)

20. A car travels 240 miles in 4 hours. What is the average speed of the car in miles per hour? (4 points)

21. The length of a rectangle is 3 meters more than twice its width. If the perimeter is 48 meters, find the dimensions of the rectangle. (10 points)

Bonus Question (5 points): Solve for x: 2(x - 3) + 4 = 3(x + 1) - 5

Grade 11 (Algebra 2) Practice Test

📝 Directions: Show your work. Simplify answers. Round decimals to the nearest hundredth when needed.

Part A — Core Skills (short answer)

• Solve: 3(2x−5) − 4(x+1) = 2x + 7
• Solve the system:
• 2x + y = 11
• x − y = 1
• Factor completely: 6x² − x − 2
• Simplify (no negative exponents): (3x²y⁻¹)²/(9x³y)
• Simplify the radical: √(72x⁴)

Part B — Quadratics

• Solve by factoring: x² − 9x + 20 = 0
• Solve using the quadratic formula: 2x² + 5x − 3 = 0
• A quadratic has zeros at x = −2 and x = 5.
• Write the equation in factored form.
• Expand to standard form.

Part C — Polynomials & Rational Expressions

• Divide using synthetic division: (2x³ − 3x² + 4x − 5) ÷ (x − 2)
• Simplify: (x² − 16)/(x² − 8x + 16) (state restrictions)
• Solve: 3/(x − 1) + 2/(x + 1) = 2 (check for extraneous solutions)

Part D — Functions

• For f(x) = 2x² − 3x + 1:
• Find f(−2).
• Find the x-intercepts.
• If f(x) = x + 4 and g(x) = x² − 1:
• Find (f∘g)(x).
• Find (g∘f)(x).
• Find the inverse of f(x) = (x − 5)/2 and state its domain.

Part E — Exponentials & Logarithms

• Solve: 5ˣ = 125
• Solve: 2^x+1 = 20 (use logs, approximate)
• Expand completely: log(9x²/√y)
• Condense into a single log: 2log a − ½log b + log c

Part F — Trigonometry (right triangle & unit circle basics)

• Convert degrees to radians: 135°
• Find exact values:
• sin 60°
• cos 45°
• tan 30°
• If sin θ = 3/5 and θ is in Quadrant II, find cos θ and tan θ.

Part G — Modeling & Word Problems

• A ball is thrown upward from a platform. Its height (in feet) is given by h(t) = −16t² + 48t + 20.
• What is the maximum height?
• How long until it hits the ground? (nearest hundredth)
• A phone costs $900 and loses 18% of its value each year.
• Write an exponential model for its value after t years.
• Find its value after 3 years.

Bonus Challenge

• Solve: |2x − 7| = 3x + 1 (state all solutions)

✅ Self-check reminders:

- For rational equations, check restrictions.

- For quadratics, you can verify solutions by substitution.

- For logs, make sure arguments stay positive.

Grade 12 (Pre-Calculus) Practice Test

🧪 Grade 12 Math Practice Test (Pre-Calculus)

Directions: Show all work. Use a calculator only when needed. Write exact answers (fractions, radicals, and (pi)) unless the problem asks for a decimal.

Part A — Functions & Graphs

• Determine whether the function is even, odd, or neither: f(x) = x⁴ − 3x² + 2.
• Find the domain of: f(x) = √(2x − 1)/(x − 4).
• Given f(x) = √(x + 3), find the inverse function f⁻¹(x) and state its domain.
• Write an equation for a transformation of y = x² that results in y = −2(x − 3)² + 5. Describe the transformations.

Part B — Polynomial & Rational Functions

• Solve: x³ − 4x² − x + 4 = 0 (factor by grouping).
• Divide using synthetic division: (x⁴ − 3x³ + 0x² + 7x − 5) ÷ (x − 2).
• Find all real zeros of: f(x) = 2x³ − x² − 8x + 4.
• Simplify and state restrictions: (x² − 9)/(x² − x − 6).

Part C — Exponential & Logarithmic Functions

• Solve: 3^2x−1 = 27.
• Solve for x (approximate to the nearest hundredth): 5·2ˣ = 37.
• Solve: log(x − 1) + log(x + 3) = 1 (base 10).
• Expand completely: ln(√(x³)/(5y²)).
• Condense into a single log: ½ln a + 3ln b − ln c.

Part D — Trigonometry

• Convert to radians: 225°.
• Evaluate exactly:
• sin(π/6)
• cos(3π/4)
• tan(π/3)
• Solve for x on [0, 2π): 2sin x − 1 = 0.
• If cos θ = −4/5 and θ is in Quadrant III, find sin θ and tan θ.
• Verify the identity: (1 − cos(2x))/sin(2x) = tan x.

Part E — Sequences, Series, & Modeling

• Find the 12th term of the arithmetic sequence with a₁ = 7 and d = −3.
• A geometric sequence has a₁ = 5 and common ratio r = 2/3. Find a₈.
• Find the sum: ∑ from k = 1 to 6 of (2k − 1).
• A population starts at 18,000 and grows by 6% per year.
• Write an exponential model P(t).
• Find the population after 5 years.

Part F — Conics (Pre-Calc)

• Write the standard form and identify the center and radius: x² + y² − 6x + 8y − 11 = 0.
• Put in standard form and identify the vertex and focus direction: y² + 4y − 8x = 0.

Bonus Challenge

• Solve exactly: 2cos x = √2 on [0, 2π).

✅ Self-check reminders:

- Watch domain restrictions for logs and radicals.

- For trig equations, list all solutions in the interval.

- For sequences, confirm whether it’s arithmetic or geometric.

Math Tips & Tricks (K–5)

Note: These practice tests are customizable based on student needs and current curriculum requirements. Contact me for personalized versions. Test will be administered the first session before tutoring can begin. This is just to assess the student's strengths.

Kindergarten Tips and Tricks

• Counting with fingers: Use your fingers to count objects. Each finger represents one item.
• Number songs: Sing counting songs to help remember numbers in order (1, 2, 3, 4, 5...).
• Recognize shapes: Practice identifying circles, squares, triangles, and rectangles in everyday objects.
• Use manipulatives: Count with blocks, beads, or toys to make math hands-on and fun.
• Pattern practice: Create simple patterns with colors or shapes (red, blue, red, blue).

Grade 1 Tips and Tricks

• Number line for addition: Draw a number line and hop forward to add numbers together.
• Doubles facts: Memorize doubles (1+1=2, 2+2=4, 3+3=6) - they're easy and helpful!
• Ten frames: Use ten frames to visualize numbers and understand counting to 10.
• Subtract by counting back: To subtract, start at the bigger number and count backwards.
• Skip counting by 2s, 5s, and 10s: Practice counting: 2, 4, 6, 8... or 5, 10, 15, 20...

Grade 2 Tips and Tricks

• Making 10: Break numbers into parts that make 10 (8+5 = 8+2+3 = 10+3 = 13).
• Place value: Remember that in 45, the 4 means 40 (4 tens) and 5 means 5 ones.
• Fact families: Learn related facts together (3+4=7, 4+3=7, 7-3=4, 7-4=3).
• Even and odd: Even numbers end in 0, 2, 4, 6, 8. Odd numbers end in 1, 3, 5, 7, 9.
• Money counting: Practice counting pennies, nickels, dimes, and quarters.

Grade 3 Tips and Tricks

• Multiplication as repeated addition: 4×3 means 4+4+4 or 3+3+3+3.
• Times table tricks: For 9s, use your fingers: hold down the finger for the number you're multiplying (9×3 = hold down 3rd finger, count fingers before and after = 27).
• Arrays for multiplication: Draw rows and columns to visualize multiplication problems.
• Division as equal groups: 12÷3 means "split 12 into 3 equal groups."
• Rounding rules: If the ones digit is 5 or more, round up. If it's 4 or less, round down.

Grade 4 Tips and Tricks

• Break apart multiplication: For 23×4, think (20×4)+(3×4) = 80+12 = 92.
• Equivalent fractions: Multiply or divide the top and bottom by the same number (1/2 = 2/4 = 3/6).
• Fraction comparison: Use common denominators or cross-multiply to compare fractions.
• Long division steps: Remember D-M-S-B (Divide, Multiply, Subtract, Bring down).
• Factor pairs: Find all factor pairs for a number to help with multiplication and division.

Grade 5 Tips and Tricks

• Decimal place value: In 3.45, the 4 is in the tenths place, the 5 is in the hundredths place.
• Multiply decimals: Multiply as if they're whole numbers, then count total decimal places to place the decimal point.
• Convert fractions to decimals: Divide the numerator by the denominator (3/4 = 3÷4 = 0.75).
• Order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
• Finding percentages: To find 10% of a number, move the decimal point one place left (10% of 50 = 5.0).
• Area and perimeter: Perimeter is adding all sides. Area is length × width for rectangles.

General Study Tips for All Grades

• Practice regularly: Do a little bit of math every day rather than cramming.
• Use visual aids: Draw pictures, use counters, or create diagrams to understand problems.
• Check your work: Always go back and verify your answers.
• Ask questions: If you don't understand something, ask your teacher or tutor for help.
• Make it fun: Use math games, apps, and real-life situations to practice skills.

Practice Tests

Kindergarten Practice Test

• Count the objects: 🍎🍎🍎 How many apples are there?
• What shape is this? ⭕ (Circle, Square, or Triangle?)
• What comes next in the pattern? Red, Blue, Red, Blue, ___
• Use your fingers to show the number 5.
• Which number is bigger: 3 or 7?

Grade 2 Practice Test

• What is 8 + 5? (Try making 10 first!)
• In the number 67, what does the 6 represent?
• Complete the fact family: 5 + 3 = 8, 3 + 5 = 8, 8 - 5 = ____, 8 - 3 = ____
• Is 17 even or odd?
• How much money is 2 dimes and 3 pennies?
• 45 + 32 = ?
• What is 50 - 27?

Grade 3 Practice Test

• What is 6 × 4?
• Use the finger trick: What is 9 × 7?
• Draw an array to show 3 × 5.
• What is 15 ÷ 3?
• Round 47 to the nearest ten.
• What is 8 × 9?
• If you have 24 cookies and divide them equally among 6 friends, how many cookies does each friend get?

Grade 4 Practice Test

• Use breaking apart: What is 34 × 3?
• Are 2/4 and 3/6 equivalent fractions? Explain.
• Which is larger: 3/5 or 2/3?
• Solve using long division: 156 ÷ 12 = ?
• List all factor pairs of 24.
• What is 7/8 + 1/8?
• Multiply: 25 × 16 = ?

Grade 5 Practice Test

• In the number 12.67, what digit is in the tenths place?
• Multiply: 3.4 × 2.5 = ?
• Convert 3/5 to a decimal.
• Solve using PEMDAS: 6 + 3 × (8 - 5) = ?
• What is 10% of 80?
• Find the area of a rectangle with length 9 cm and width 5 cm.
• Find the perimeter of a square with sides of 7 inches.
• Convert 0.6 to a fraction in simplest form.

Math Tips & Tricks (Grades 6–8)

🎯 Goal: quick, practical strategies that help you earn more points on daily work, quizzes, and tests in grades 6–8.

1) The “Read → Plan → Solve → Check” routine (every problem)

• Read: Circle what the problem is asking.
• Plan: Write what you will do in one short sentence (example: “I will set up a proportion.”).
• Solve: Show steps neatly.
• Check: Ask: “Does my answer make sense?” and “Did I answer the question?”

2) Word-problem translation tips

• Underline units (miles, dollars, minutes, tiles, grams). Units guide the math.
• Make a quick sketch (even a simple box model or number line).
• Turn words into operations:
• total, sum, in all → add
• difference, how many more/less → subtract
• of, per, each → multiply (often)
• split equally, average, per → divide
• Write an equation before you calculate.

3) Fractions: fastest accuracy moves

• Simplify early (reduce before multiplying).
• Multiply fractions: multiply tops and bottoms, then simplify.
• Divide fractions: “Keep, Change, Flip.”
• Keep first fraction
• Change ÷ to ×
• Flip the second fraction
• Add/Subtract fractions: same denominator first.
• If different, find a common denominator.
• Mixed numbers: convert to improper fractions when multiplying/dividing.

4) Decimals: placement + estimation

• Line up decimals when adding/subtracting.
• Multiply decimals:
• Multiply like whole numbers.
• Count total decimal places and place the decimal.
• Divide decimals:
• Move decimals to make the divisor a whole number.
• Move the decimal the same amount in the dividend.
• Estimation check: round first to see if your final answer is reasonable.

5) Percents: one “super method”

Use Percent = Part ÷ Whole.

• Convert percent to decimal: move the decimal 2 places left.
• 35% = 0.35
• Find the part: Part = (Percent as a decimal) × Whole
• 20% of 50 = 0.20 × 50 = 10
• Find the percent: Percent = Part ÷ Whole
• 12 out of 48 = 12 ÷ 48 = 0.25 = 25%

6) Ratios & proportions (cross-multiply with confidence)

• Set up equal ratios with matching labels:
• a/b = c/d
• Cross-multiply: a · d = b · c
• Keep units matched (students often flip one ratio by accident).

7) Integers: rules you can remember

• Same signs (++ or −−) → add and keep that sign.
• Different signs → subtract and keep the sign of the bigger absolute value.
• Multiplication/Division:
• Same signs → positive
• Different signs → negative
• Use a number line if unsure.

8) Expressions & equations: “undo” steps

When solving x:

• Combine like terms.
• Get x terms on one side.
• Use inverse operations (undo addition/subtraction, then multiplication/division).
• Check by substitution (plug your answer back in).

9) Geometry: easy point-savers

• Label your diagram with given numbers.
• Common formulas:
• Rectangle: A = lw
• Triangle: A = ½bh
• Parallelogram: A = bh
• Circle: C = 2πr, A = πr²
• Perimeter is around the outside. Area is inside.
• If you forget a formula, write what you do know (units help):
• Area ends in square units (like cm²).

10) Graphs & coordinate plane

• (x, y) means go x first, then y.
• Slope (when you learn it): “rise over run.”
• Always label axes and use consistent scale.

11) Test-taking strategies that raise grades

• Do the easy problems first to lock in points.
• Box final answers (and include units).
• Show work even if you can do it mentally. Work earns partial credit.
• If stuck, write:
• what is given
• what is asked
• a formula or equation you might use

12) Neat work = fewer mistakes

• One problem per space.
• Align equals signs.
• Keep fractions stacked (not slanted).
• Write “therefore” statements:
• “So the probability is 3/8.”

Quick checklist (use before turning it in)

• [ ] Did I answer the question asked?
• [ ] Did I include units?
• [ ] Did I simplify?
• [ ] Does my answer make sense (estimate)?
• [ ] Did I check my equation/steps?

🧠 Practice tip: Do 10 minutes a day.

- 3 problems you already know (confidence)

- 2 problems that are challenging (growth)

Math Tips & Tricks (Grades 9–12)

🎯 Goal: strategies that carry you through Algebra 1, Geometry, Algebra 2, and Pre-Calculus — and onto the SAT/ACT.

1) Master the algebra moves that never go away

• Isolate x with inverse operations: whatever you do to one side, do to the other.
• Distribute first when parentheses block you: 3(x − 4) = 15 → 3x − 12 = 15 → 3x = 27 → x = 9.
• Clear fractions early: multiply every term by the common denominator.
• Keep = signs aligned down the page so sign errors can't hide.

2) Factoring: your #1 power tool

• Always look for a GCF first: 6x² + 12x = 6x(x + 2).
• Trinomials: find two numbers that multiply to c and add to b: x² + 7x + 12 = (x + 3)(x + 4).
• Difference of squares: x² − 25 = (x + 5)(x − 5).
• Zero product property: if (x − 2)(x + 6) = 0, then x = 2 or x = −6.
• When factoring fails, the quadratic formula always works: x = (−b ± √(b² − 4ac)) / 2a.

3) Functions: think input → output machines

• f(3) means "plug 3 in for x": if f(x) = 2x² − 1, then f(3) = 2(9) − 1 = 17.
• Domain = allowed inputs; range = possible outputs.
• Vertical line test: if a vertical line hits the graph twice, it's not a function.
• Learn the parent graphs: line, parabola, absolute value, square root, exponential.

4) Graphing lines without plotting 20 points

• Slope-intercept form y = mx + b: m is the slope (rise/run), b is where the line crosses the y-axis.
• Example: y = −2x + 5 → start at (0, 5), go down 2, right 1, repeat.
• Parallel lines share slopes; perpendicular lines have slopes that multiply to −1 (like 2 and −1/2).

5) Quadratics: three forms, three superpowers

• Standard form y = ax² + bx + c — use it for the quadratic formula and the y-intercept.
• Vertex form y = a(x − h)² + k — the vertex is (h, k). For y = (x − 3)² + 2, the vertex is (3, 2).
• Factored form y = a(x − r1)(x − r2) — the x-intercepts are r1 and r2.
• The discriminant b² − 4ac tells you: positive → two real solutions, zero → one, negative → none (two complex).

6) Exponent rules (write these on a card until they're automatic)

• xᵃ · xᵇ = xᵃ⁺ᵇ; xᵃ / xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ.
• x⁰ = 1 (any nonzero base); x⁻ᵃ = 1/xᵃ.
• Example: (2x³)² = 4x⁶.

7) Radicals and rational exponents

• √x = x^(1/2); ∛x = x^(1/3).
• Simplify by pulling out perfect squares: √50 = √(25×2) = 5√2.
• Rationalize denominators: never leave a radical on the bottom: 1/√2 = √2/2.

8) Geometry: prove it like a lawyer

• Two-column proofs: left side = statements, right side = reasons. Every claim needs a reason.
• Mark the diagram first: right angles, equal tick marks, parallel arrows.
• Know your triangle shortcuts: SSS, SAS, ASA, AAS (and HL for right triangles).
• CPCTC: once triangles are congruent, their matching parts are congruent too.

9) Trigonometry in one picture

• SOH CAH TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
• In a 3-4-5 right triangle, the sine of the angle across from the 3 is 3/5.
• Pythagorean identity: sin²θ + cos²θ = 1.
• For non-right triangles: Law of Sines and Law of Cosines.

10) Exponentials and logarithms are inverses

• Growth: y = a(1 + r)^t; decay: y = a(1 − r)^t.
• log₂(8) = 3 because 2³ = 8 — "log asks: to what power?"
• Log rules: log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n·log a.
• e ≈ 2.718; ln means log base e.

11) Word problems: translate, don't panic

• Name your variable in words first: "Let t = hours driven."
• Common setups: distance = rate × time; total cost = fixed + per-unit × quantity.
• Systems: two unknowns need two equations — look for two relationships in the story.

12) Test-day strategies that save points

• Write the formula before you plug in — partial credit lives there.
• Estimate first on multiple choice, then eliminate wild answers.
• If a problem eats 3+ minutes, circle it and move on; come back with fresh eyes.
• Check by plugging back in — especially for equations and systems.

Quick checklist (use before turning it in)

• [ ] Did I copy the problem correctly?
• [ ] Did I answer what was asked (x? the vertex? the probability)?
• [ ] Did I simplify completely (fractions reduced, radicals simplified)?
• [ ] Are units and labels included?
• [ ] Did I check my answer by substituting back?

🧠 Practice tip: Do 15 minutes a day.

- 2 problems from today's lesson (fresh)

- 2 mixed review problems (keeps old skills sharp)

Math Tips & Tricks (College Prep)

🎯 Goal: walk into college placement tests and your first college math class confident and ready.

1) Know what placement tests actually check

• They test high-school foundations: fractions, exponents, factoring, functions, basic trig.
• Most are adaptive — early questions decide your level, so go slow at the start.
• You can usually retake after brushing up; ask the testing center about the rules.

2) Rebuild your algebra foundation first

• Fractions without a calculator: 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12.
• Factor fluently: x² − 5x + 6 = (x − 2)(x − 3).
• Solve linear equations in your sleep: 4x − 7 = 2x + 9 → 2x = 16 → x = 8.
• If these feel shaky, that's exactly where to start — everything in college math stacks on them.

3) Functions are the language of college math

• Read function notation cold: f(x), g(x), f(g(x)).
• Composition: if f(x) = x + 1 and g(x) = 2x, then f(g(3)) = f(6) = 7.
• Inverse functions "undo" each other: f(x) = 2x has inverse f⁻¹(x) = x/2.

4) Get fluent with your calculator — before test day

• Learn: fractions, exponents, parentheses, and the ANS/replay keys.
• Know when NOT to use it: mental math for 15% of 200 (= 30) is faster.
• Graphing calculators: practice window settings and finding intersections now, not during the exam.

5) Trigonometry quick-refresh

• Unit circle landmarks: 0°, 30°, 45°, 60°, 90° — know sin and cos at each.
• sin 30° = 1/2, cos 60° = 1/2, sin 45° = √2/2.
• Radians: 180° = π radians, so 90° = π/2.

6) Study like a college student

• Do homework the day it's assigned — college moves twice as fast as high school.
• The 3-pass method: read examples, do guided problems, then close the book and redo from memory.
• Keep an error log: every missed problem, rewritten correctly with the reason you missed it.

7) Use the free help around you

• Professor office hours are the highest-value hour on campus — go with specific questions.
• Tutoring centers are free and judgment-free; that's literally what they're for.
• Study groups: explaining a problem to someone else is the fastest way to learn it.

8) Word problems and applications

• Translate to math first: define variables in a sentence before writing equations.
• Finance flavors: simple interest I = Prt; compound A = P(1 + r/n)^(nt).
• Example: $500 at 4% simple interest for 3 years → I = 500 × 0.04 × 3 = $60.

9) Manage test anxiety like a skill

• Box breathing: in 4 counts, hold 4, out 4 — resets a racing mind.
• Brain dump: the second the test starts, write every formula you memorized on scratch paper.
• If you freeze, do the easiest problem on the page first — momentum beats perfection.

10) Know your course path

• College Algebra → Pre-Calculus → Calculus 1 is the classic STEM track; Statistics serves most other majors.
• Your major decides your math — check the degree plan before choosing.
• Placement ≠ intelligence: it just tells you the right starting line.

11) The week before the test

• Sleep beats cramming: 8 hours the night before beats 3 extra hours of study.
• Do one full timed practice run under real conditions.
• Lay out ID, calculator, and pencils the night before.

12) After the test, keep the momentum

• Review every mistake within 24 hours while it's fresh.
• Preview the first chapter of your actual course — day one will feel familiar instead of scary.

Quick checklist (use before turning it in)

• [ ] Can I do fractions, factoring, and linear equations without a calculator?
• [ ] Do I know my calculator's key functions?
• [ ] Have I done a timed practice test?
• [ ] Do I know the test center's rules (retakes, calculator policy)?
• [ ] Did I sleep and eat before test day?

🧠 Practice tip: Do 20 minutes a day for the month before your test.

- 5 foundation problems (fractions, exponents, factoring)

- 2 mixed word problems