SAT Math Questions and EBRR Concepts that I struggle with

How should you chance the following sentence? "Having already made a few films in the vein of "thrill comedy," (the event inspired Lloyd) to create his most daring film yet, and he invited Strother to be involved".

"Lloyd was inspired by the event". This is right, because Lloyd (who the first dependent clause referred to) is immediately being referenced. The original sentence didn't make sense because the first and second clause weren't connected.

When altering a list, always...

...Maintain the stylistic patterns it has already established.

When enclosing an idea in commas, always...

...Make sure you have group the entire idea, and nothing else.

When asked, "Which choice provides the most relevant detail?", pick the choice that...

...Provides ADDITIONAL details, not the context for previous ones. ESPECIALLY not if that context is irrelevant.

When trying to place commas in a sentence...

...Say the sentence out loud with and without pauses. If it sounds unnatural, it is wrong.

When doing a "which is equivalent" problem...

...Sometimes just plug a easy to calculate number in.

If a word feels like it isn't supposed to be used in the context it is being used in, it is probably...

...The wrong fr*cking answer. Pay attention to how the sentence flows before you start spouting synonyms.

If you need to rewrite an equation in terms of certain variables...

...Those variables MUST be in the answer.

As soon as you finish reading the passage, try to decipher...

...the main idea.

Use elimination to solve the following system of equations; 8x - 4y = 7, 5y - 4x = 10.

1. 2(5y - 4x) = 2(10) is the same as 10y - 8x = 20. 2. Set up the following 8x - 4y = 7 + -8x + 10y = 20 6y = 27 ANSWER: y = 4.5

Transform (5x - 2)/(x + 3) into 5 - 17/(x + 3).

1. 5x - 2 = (5x+15) - 17 = 5(x + 3) - 17. 2. (5x+15) - 17 = 5(x + 3) - 17 3. (5(x + 3) - 17)/(x + 3) = 5(x + 3)/(x + 3) - 17/(x + 3). 4. 5(x + 3)/(x + 3) = 5. 5 - 17/(x + 3)

If 3x - y = 12, what is the value of 8^x/2^y?

1. 8 = 2^3, so 8^x/2^y = 2^3x/2^y. 2. 2^3x/2^y = 2^(3x - y). 3: 3x - y = 12, so 2^(3x - y) = 2^12. ANSWER: 8^x/2^y = 2^12.

The parabolic equation y = 3x^2 + bx + 5, where b is a constant, is always positive. State whether b = 9, 0, -6, or -15.

1. B is always positive. Therefore, the vertex of b must be positive. 2. The x-value of the vertex of a parabola is -b/2a. A = 3. 3. -9/6 is negative, -0/6 is 0, 6/6 is positive, 15/6 is positive. 4. The y value of the vertex must be positive as well. 4a. 3 - 6 + 5 is positive, so -6 can be a solution. 4b. 18.75 - 37.5 +5 is not, so -15 cannot. ANSWER: -6

At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

1. Make an equation where x is the number of calories that a hamburger has: 2(x) + 3(x-50) = 1700. 2. Solve the equation: 2x + 3x - 150 = 1700, 5x - 150 = 1700, 5x = 1850, x = 1850/5 = 370. ANSWER: A hamburger has 370 calories.

Rewrite R = F/(N + F) to find F in terms of R and N.

1. Multiply both sides by (N + F). R(N + F) = F. 2. F = R(N + F) = RN + RF. 3. Subtract RF from both sides. RN = F - RF 4. RN = F - RF = F(1 - R) ANSWER: Divide both sides by 1 - R. F = RN/(1 - R).

Rewrite (3 - 5i)/(8 + 2i) as 7/34 - 23i/34. NOTE: i = (-1)^(1/2)

1. Multiply the function by the conjugate of the denominator (8 + 2i). 1a. (8 + 2i)(8 - 2i) = 64 - 16i + 16i -4(-1) = 68. 1b. (3 - 5i)(8 - 2i) = 24 - 6i + -40i + 10(-1) = 14 - 46i. 2. Simplify: (14 - 46i)/68 = (7 - 23i)/34 = 7/34 - 23i/34.

Trisha and Stacy each work at their own constant rate, whether they work alone or work together. If working alone, Trisha can finish a job 15 minutes faster than Stacy can. The equation the fraction 1 over x, plus the fraction with numerator 1, and denominator x plus 15 equals the fraction 1 over 18 can be used to find the time x, in minutes, it takes Trisha to finish the job working alone. Which of the following is the best interpretation of the number 18 in the equation?

1. Since x is the number of minutes that it takes Trisha to finish the job 1/x is the fraction of the job Trisha can finish in one minute. 2. Since x + 15 is the number of minutes it takes Stacy to finish the job, 1/(x + 15) is the fraction of the job Stacy can finish in one minute. ANSWER: Since 1/18 is equal to 1/x + 1/(x + 15), the equation represents the fraction of the job that Trisha and Stacy working together can finish in one minute.

Imagine a hexagon with an area of 384(3^1/2). Attached to one of the sides is a square. Calculate the area of the square.

1. The hexagon can be split into 6 equilateral triangles with an area of 64(3^1/2). 2. These can be split into 30/60/90 triangles with an area of 32(3^1/2). 3. Take one of these triangles. Based on Sin (30) = 1/2, the value of opp(30) = x, and the hypotenuse = 2x. Based on the unit circle, adj(30) = (3^1/2)x. 4. To find the value of x, use the formula for the area of a triangle (bh/2); x*(3^1/2)x/2 = 32(x^1/2). 5. Multiply both sides by 2; x*(3^1/2)x = 64(3^1/2). 6. Divide both sides by 3^1/2; x^2 = 64. 7. Take the square root of both sides; x = 8. ANSWER: As 2x (16) = one side of the square, the square has an area of 256.

In triangle ABC, the measure of ∠B is 90∘, BC=16, and AC=20. Triangle DEF is similar to triangle ABC where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF the corresponding side of triangle ABC. What is the value of sin(F)?

1. The triangles are similar, so you can solve the problem by solving for angle C instead of F. Ignore Triangle #2. 2. B is the right angle, so AC is the hypotenuse. Therefore, 16^2 + AB^2 = 20^2 OR 256 + AB^2 = 400. After solving that, AB = 12. 3. Sin(C) = AB/AC = 12/20 = 3/5. ANSWER: Sin(F) = 3/5.

y = a(x − 2)(x + 4) In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). What is the value of d in terms of a?

1. The zeroes are 2 and -4. The midpoint of those should be the x-value of the vertex (c). Halfway between 2 an -4 is -1. 2. Plug in -1 for x. a(-1 - 2)(-1 + 4) = -9a. 3. ANSWER: d = -9a

Rewrite the equation y = x^2 - 2x - 15 in Vertex Form.

1. Vertex Form: y = a(x - h)^2 + k. (h, k) is the vertex of the parabola. 2. Find h (also known as x) and k (also known as y) from the original equation. 2a. Find the Zeros: y = (x - 5)(x + 3). y = 5, -3. 2b. Find the midpoint between the zeros. Halfway between 5 and -3 is 1. h = 1. 2c: Plug h into the original equation as x. y = 1^2 - 2(1) - 15 = -16. k = -16. 2d: Plug h and k into Vertex form. y = a(x - 1)^2 + 16. 3. Find the value of a at which x^2 - 2x - 15 = a(x - 1)^2 - 16. x^2 - 2x + 1 = a(x - 1)^2. x^2 - 2x +1 = (x - 1)^2. a = 1. ANSWER: y = (x - 1)^2 - 16.

For a polynomial p(x), the value of p(3) is -2. Prove that the remainder when p(x) is divided by (x - 3) is -2.

1. Write this problem in a mathematical form. p(x)/(x - 3) = q(x) + r/(x - 3). q(x) is a polynomial and r is the remainder. 2. Rewrite the mathematical form. p(x) = (x - 3)*q(x) + r. 3. Plug and chug. p(3) = (3 - 3)*q(3) + r = r. p(3) = r. 4. Since p(3) = -2, r = -2.

What do you need to do?

Actually read the f*cking question.

How do you make a EBRR answer more clear?

Be as concise as possible without losing clarity and avoid repeating information.

When starting a sentence with a phrase that implies a relationship with the previous sentence (IE, for example)...

Be careful! Double-check to see if that relationship actually exists.

What is a simple way to get ANY reading question right?

Eliminate the obviously wrong answers and see which of the remaining answers are directly supported by one or more specific pieces of text.

What can you assume about the connotation of words in EBRR answers?

If it is usually negative/positive, they wont give it to you in a situation that calls for a word of different connotation.

How do you know if a system of equations has infinite or no solutions?

Infinite: The lines are the same. No: The lines are parallel.

When do you use a semicolon?

Linking two independent causes.

Use ____ _____ as a hint when trying to place a sentence in a paragraph.

Verb tense.

What is the formula for the area of a triangle?

a=1/2bh