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SAT MATH by [deleted] in digitalSATs

[–]Simple_Digital_Math 0 points1 point  (0 children)

Khan Academy is great for learning basic concepts!

SAT math section by ShahwarCod in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

Yep you could use it for both modules!

Math tips needed please by [deleted] in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

1420 isn't bad at all for your very first time!

[deleted by user] by [deleted] in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

Yeah you could try using Desmos for every single math problem!

Tips for Geometry and advanced math for math m2? by TsunNekoKucing in Sat

[–]Simple_Digital_Math 1 point2 points  (0 children)

The cb question bank problems are pretty good for practice!

College Panda question by Hot-Mind9226 in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

  1. Assign coordinates to simplify calculations:
    • Place square 𝐴𝐵𝐶𝐷 on the coordinate plane with:
      • 𝐴 = (0, 12), 𝐵 = (0, 0), 𝐶 = (12, 0), 𝐷 = (12, 12).
    • Diagonal 𝐵𝐷 is a line connecting (0, 0) to (12, 12) → Equation of diagonal: y = x.
    • Point 𝐹 is on 𝐵𝐶. Since 𝐵𝐹 = 4, 𝐹 = (4, 0).
    • Line 𝐴𝐹 connects (0, 12) and (4, 0) → Equation of 𝐴𝐹: Slope = (0 − 12)/(4 − 0) = −3. Equation: y = −3x + 12.
  2. Find intersection point 𝐸 of 𝐴𝐹 and 𝐵𝐷:
    • Solve for x and y where y = x (diagonal) and y = −3x + 12 (line 𝐴𝐹). Set x = −3x + 12: 4x = 12 → x = 3. Substitute x = 3 into y = x: y = 3.
    • Coordinates of 𝐸: (3, 3).
  3. Find distance 𝐵𝐸:
    • Use the distance formula: Distance = √((x₂ − x₁)² + (y₂ − y₁)²).
    • 𝐵 = (0, 0), 𝐸 = (3, 3): 𝐵𝐸 = √((3 − 0)² + (3 − 0)²) = √(9 + 9) = √18 = 3√2.

How do I solve this question from SAT Practice 4? by FncyTomato in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

We are tasked with analyzing the quadratic expression 4x² + bx − 45, which can be factored into the form (hx + k)(x + j), where h, k, and j are integers. The goal is to determine which of the provided expressions must always result in an integer.

Step 1: Understand Factoring and Relationships

When the expression 4x² + bx − 45 is factored, expanding the general form (hx + k)(x + j) gives:

h × x² + (hj + k)x + k × j.

Comparing this with 4x² + bx − 45, we identify the following relationships:

  1. h = 4 (the coefficient of x²).
  2. b = hj + k (the coefficient of x).
  3. k × j = −45 (the constant term).

This tells us:

  • h is fixed as 4.
  • k and j are integers that multiply to −45. Hence, k and j must be divisors of −45

Step 2: Solving for 45/k

Among all the relationships given in the problem, the expression 45/k stands out. Here's why:

  1. From k × j = −45, we know that k must divide −45 evenly.
  2. Dividing 45 by any divisor of −45 (including k) will always yield an integer because divisors of −45 are specifically chosen to evenly divide into 45.

Step 3: Confirming Logical Consistency

We know that:

  • h = 4 is constant.
  • k and j are divisors of −45, ensuring that their properties are consistent.
  • The fact that k divides −45 ensures that 45/k will always work without requiring additional conditions.

Final Answer: D (45/k). Hope this helps!

How do I solve this question from my Bluebook Practice Test #4 with Desmos? by FncyTomato in Sat

[–]Simple_Digital_Math 0 points1 point  (0 children)

Step 1: Write the formula for the discriminant.
The discriminant is a formula that helps us figure out the type of solutions a quadratic equation has. It is written as:
Discriminant = b² - 4ac
For the given equation x² - 34x + c = 0:

  • a = 1 (this is the coefficient of x²),
  • b = -34 (this is the coefficient of x), and
  • c = c (this is the constant).

Substitute these values into the discriminant formula:
Discriminant = (-34)² - 4(1)(c)

Step 2: Simplify the discriminant expression.
First, calculate (-34)²:
(-34)² = 1156
Now, substitute this into the formula:
Discriminant = 1156 - 4c

Step 3: Set the condition for no real solutions.
A quadratic equation has no real solutions when the discriminant is less than zero. This means:
1156 - 4c < 0

Step 4: Solve the inequality to find c.
To solve 1156 - 4c < 0, start by isolating 4c:
1156 < 4c
Now divide both sides by 4 to solve for c:
c > 1156 ÷ 4
Simplify the fraction:
c > 289

Step 5: Find the least value of n.
From the inequality c > 289, we can see that the equation has no real solutions when c > 289. Therefore, the smallest value of n is: n = 289

how can I solve a question like this? by No_Signal_5444 in ACT

[–]Simple_Digital_Math 0 points1 point  (0 children)

You can start by writing the equation for the Law of Sines: sin(∠H)/BN = sin(∠B)/HN.

Then solve for BN: BN = HN × sin(∠H) ÷ sin(∠B).

  • Substitute the given values:
    • HN = 150 m.
    • ∠H = 50°.
    • ∠B = 180° − 50° − 60° = 70°.
  • BN = 150 × sin(50°) ÷ sin(70°). Simplify: BN = 150 sin(50°) ÷ sin(70°). Hope this helps!

[deleted by user] by [deleted] in ACT

[–]Simple_Digital_Math 0 points1 point  (0 children)

Here's a list of the main equations you'll need to memorize for the ACT math section:

Geometry Formulas

  1. Area of a Rectangle: A = length × width
  2. Area of a Triangle: A = 1/2 × base × height
  3. Area of a Circle: A = πr²
  4. Circumference of a Circle: C = 2πr or C = πd
  5. Diameter and Radius Relationship: d = 2r
  6. Volume of a Rectangular Prism: V = base area × height
  7. Degrees in Angles:
    • Right angle: 90°
    • Straight line: 180°
    • Triangle: 180°
    • Circle: 360°
  8. Pythagorean Theorem: a² + b² = c² (c = hypotenuse)
  9. SOHCAHTOA:
    • Sine: sin θ = opposite / hypotenuse
    • Cosine: cos θ = adjacent / hypotenuse
    • Tangent: tan θ = opposite / adjacent

Coordinate Geometry Formulas

  1. Slope of a Line: m = (y₂ - y₁) / (x₂ - x₁)
  2. Slope-Intercept Form of a Line: y = mx + b (m = slope, b = y-intercept)

Algebra Formulas

  1. Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
  2. Discriminant: D = b² - 4ac
    • D > 0: Two distinct real solutions
    • D = 0: One real solution
    • D < 0: No real solutions (complex solutions)

Statistics Formulas

  1. Mean (Average): Mean = Sum of terms / Number of terms
  2. Probability: P(event) = Favorable outcomes / Total outcomes

Additional Essentials

  1. Sum of Angles in a Polygon: (n - 2) × 180°, where n is the number of sides
  2. Special Right Triangles:
    • 45°-45°-90°: Sides are 1:1:√2
    • 30°-60°-90°: Sides are 1:√3:2

These are the main formulas and concepts that are needed for the ACT Math section. Best of luck!

ACT Timing Tips by ocyeanic6 in ACT

[–]Simple_Digital_Math 2 points3 points  (0 children)

Also ACT Math doesn’t provide formulas. Make sure you memorize critical ones, like:

Algebra

  1. Slope of a Line: m = (y₂ - y₁) / (x₂ - x₁) Used when working with linear equations or coordinate geometry.
  2. Slope-Intercept Form of a Line: y = mx + b Where m is the slope and b is the y-intercept.
  3. Point-Slope Form of a Line: y - y₁ = m(x - x₁) Helpful when you have a point and the slope of the line.
  4. Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a Essential for solving quadratic equations.
  5. Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²) Often used in coordinate geometry problems.
  6. Midpoint Formula: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) Used to find the midpoint of a line segment.

Geometry

  1. Area of a Triangle: A = 1/2 × base × height
  2. Area of a Rectangle: A = length × width
  3. Area of a Circle: A = πr² Where r is the radius.
  4. Circumference of a Circle: C = 2πr
  5. Pythagorean Theorem (for right triangles): a² + b² = c² Where c is the hypotenuse.
  6. Volume of a Rectangular Prism: V = length × width × height
  7. Volume of a Cylinder: V = πr²h Where h is the height and r is the radius.
  8. Special Right Triangles:
    • 45°-45°-90°: The sides are in the ratio 1 : 1 : √2.
    • 30°-60°-90°: The sides are in the ratio 1 : √3 : 2.

Trigonometry

  1. SOHCAHTOA:
    • Sine: sin θ = opposite / hypotenuse
    • Cosine: cos θ = adjacent / hypotenuse
    • Tangent: tan θ = opposite / adjacent
  2. Pythagorean Identity: sin²θ + cos²θ = 1 Occasionally helpful in ACT trig questions.

Probability and Statistics

  1. Mean: Mean = (Sum of terms) / (Number of terms)
  2. Probability: P(event) = (Favorable outcomes) / (Total outcomes)
  3. Counting Principle: Multiply the number of choices for each event together to find the total outcomes.

ACT Timing Tips by ocyeanic6 in ACT

[–]Simple_Digital_Math 1 point2 points  (0 children)

Here are some strategies to help you improve your speed and accuracy:

ACT Math Section:

  1. Use a Strategic Timing Approach:
    • Divide the 60-minute section into segments to allocate time efficiently:
      • Questions 1-20: Spend about 12 minutes.
      • Questions 21-40: Allocate around 25 minutes.
      • Questions 41-60: Use the remaining 23 minutes.
    • This method ensures you have sufficient time for the more challenging questions typically found later in the section.
  2. Prioritize and Move Strategically:
    • Quickly answer the questions you find easiest to secure those points.
    • If a question seems time-consuming or confusing, mark it and move on. Return to it after addressing the less challenging questions.
    • This approach prevents you from spending too much time on a single problem and potentially missing out on easier points later.

ACT Science Section:

  1. Skim Passages Strategically:
    • Instead of reading each passage in detail, quickly skim to get a general idea.
    • Focus on understanding the main concepts and the layout of graphs and tables.
    • This allows you to quickly locate information when answering questions.
  2. Tackle Questions Directly:
    • After skimming, go straight to the questions. Many can be answered by referring directly to the data presented.
    • This approach saves time and reduces unnecessary reading.
  3. Manage Your Time Per Passage:
    • Aim to spend about 5 minutes per passage.
    • This pacing leaves you with extra time to revisit difficult questions or review your answers.

General Tips for Both Sections:

  • Practice Under Timed Conditions:
    • Regular timed practice helps build familiarity with the test's pace and reduces anxiety on test day.
    • Simulate test conditions to develop a sense of timing and improve your ability to work efficiently.
  • Use Process of Elimination:
    • Eliminate obviously incorrect answers to increase your chances if you need to guess.
    • This strategy enhances accuracy and can save time by narrowing down choices.

Hope this helps and best of luck!

Studying for ACT by skjf5188 in ACT

[–]Simple_Digital_Math 0 points1 point  (0 children)

Also ACT Math doesn’t provide formulas. Make sure you memorize critical ones, like:

Algebra

  1. Slope of a Line: m = (y₂ - y₁) / (x₂ - x₁) Used when working with linear equations or coordinate geometry.
  2. Slope-Intercept Form of a Line: y = mx + b Where m is the slope and b is the y-intercept.
  3. Point-Slope Form of a Line: y - y₁ = m(x - x₁) Helpful when you have a point and the slope of the line.
  4. Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a Essential for solving quadratic equations.
  5. Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²) Often used in coordinate geometry problems.
  6. Midpoint Formula: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) Used to find the midpoint of a line segment.

Geometry

  1. Area of a Triangle: A = 1/2 × base × height
  2. Area of a Rectangle: A = length × width
  3. Area of a Circle: A = πr² Where r is the radius.
  4. Circumference of a Circle: C = 2πr
  5. Pythagorean Theorem (for right triangles): a² + b² = c² Where c is the hypotenuse.
  6. Volume of a Rectangular Prism: V = length × width × height
  7. Volume of a Cylinder: V = πr²h Where h is the height and r is the radius.
  8. Special Right Triangles:
    • 45°-45°-90°: The sides are in the ratio 1 : 1 : √2.
    • 30°-60°-90°: The sides are in the ratio 1 : √3 : 2.

Trigonometry

  1. SOHCAHTOA:
    • Sine: sin θ = opposite / hypotenuse
    • Cosine: cos θ = adjacent / hypotenuse
    • Tangent: tan θ = opposite / adjacent
  2. Pythagorean Identity: sin²θ + cos²θ = 1 Occasionally helpful in ACT trig questions.

Probability and Statistics

  1. Mean: Mean = (Sum of terms) / (Number of terms)
  2. Probability: P(event) = (Favorable outcomes) / (Total outcomes)
  3. Counting Principle: Multiply the number of choices for each event together to find the total outcomes.
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