SAT Quick Challenge - Week 14
Saturday, October 17, 2020
Providence Baptist Church is concerned about you, your family, your friends, and the community. We are following the recommendations to limit the number of people in our in-person gatherings. For this reason, all SAT Preparation classes at the church are cancelled until further notice.
Although the current COVID-19 pandemic abruptly ended the Spring 2020 SAT classes, technology offers an opportunity for students to refresh, retain, and/or acquire SAT knowledge and skills essential for answering various kinds of questions often found on the SAT. Therefore, the Providence Baptist Church SAT Preparation Program has provided this “SAT Quick Challenge” website. Each Saturday morning, this site will be updated with a set of activities that will help students acquire and maintain mastery of important skills that help lead to high SAT scores. Check out this week's lessons below!
Please note that no new lessons were developed for the week of October 10, 2020.
SAT Verbal - This Week's Questions (October 17, 2020)
SAT QUICK CHALLENGE O
Saturday, October 17, 2020
What Is Parallelism? When you list two or more things that have the same level of importance in a sentence, maintain parallelism by using the same format for each item you have listed. That is, if you use a noun to name one of the items, use a noun to name each of the others. If you use a phrase to identify an item, use phrases to list them all. Parallelism helps the reader see connections between ideas and makes it easier for the reader to grasp and understand the point(s) being made. For example, read Sample Sentences 1A and 1B and their explanations in the chart below.
|PARALLELISM SAMPLE SENTENCES AND EXPLANATIONS, Part I|
|Sentence 1A -- Because there was no direct flight from Washington, DC to New York City, driving to New York actually took less time than to fly there.
||This sentence compares two different ways of getting from Washington, DC to New York, but it does not use the same format to list the two ways. It lists one as a gerund -- "driving" -- and the other one as an infinitive -- "to fly." Since the sentence does not use the same format for both travel methods, it is not parallel. Therefore, it is incorrect.
|Sentence 1B: Because there was no direct flight from Washington, DC to New York City, driving to New York actually took less time than flying there.||In this sentence, the two actions compared are both in the same format -- gerunds. Therefore, this sentence is parallel, it is more effective, and it is correct. Now, note the parallelism in the explanation you just read: three independent clauses -- all of which can also be identified as three sentences.|
The FANBOYS Conjunction. When a FANBOYS conjunction connects the underlined part of a question with the part that is not underlined, that conjunction is a reminder that the format for the two parts of the question must match. That is, if the part of the question before the conjunction is a single word, the part after the conjunction must also be a single word. If a clause is on one side, a clause must also be on the other side. Whatever the format, however, you must always remember to read the entire sentence. Sometimes the clue you need in order to find the answer is in the part of the sentence that is not underlined.
|PARALLELISM SAMPLE SENTENCES AND EXPLANATIONS, Part II|
|Sentence 2A: Many students complain about math, but some high school students say that high school math can be more challenging than middle school math. They support that claim by saying that high school math is really hard, and that the assignments take a really long time to read.||This sentence is not parallel because after saying that high school math is more challenging than middle school math, it describes only high school math. The sentence needs to talk about both. Therefore, the sentence is not written correctly. Also, to maintain parallelism, remember to use the same format for describing the two items.
|Sentence 2B -- Many students complain about math, but some high school students say that high school math can be more challenging than middle school math because high school math is harder and requires more study time than middle school math did.||This sentence is parallel because after saying that high school math is more challenging than middle school math, it supports its position by describing the same two characteristics of both kinds of math, using the same format. Therefore, the sentence is written correctly.|
Repeated Key Words in a Series -- Optional. Sometimes a parallelism question involves a series of phrases which all have a key word in common such as a preposition (for), a helping verb (were), or an infinitive (to + a verb). The repeated word clearly applies to each phrase in the series. In the answer choices, however, that word is sometimes included for only the first phrase in the series. Nevertheless, because it is clear that the key word applies to each phsase, parallelism is maintained. Note Sentences 3A and 3B below. Both are parallel, and both are correct.
Sentence 3A: We haven't decided whether to travel by plane, by train, or by car when we visit Granny.
Sentence 3B: We haven't decided whether to travel by plane, train, or car when we visit Granny.
SAT QUICK CHALLENGE EXERCISE O
Directions. If a sentence is written correctly, place the letter "A" (NO CHANGE) on the blank line which follows the question. Otherwise, place the letter of the answer choice which corrects the sentence on that blank line.
1. Terri looked in the car, the yard, and in the house, but still could not find her phone. _____
2. Schools are facing tremendous problems because of two major issues: teacher shortages and many schools do not have enough money to purchase what they need. _____
3. Many people are concerned about getting COVID-19, so people not eating out as much in restaurants. _____
4. Believing that careless mistakes had cost the team the championship, the players felt embarrassed, the coaches becoming humiliated, and the fans getting furious. _____
SAT Verbal - Answers to This Week's Questions (October 17, 2020)
SAT QUICK CHALLENGE Exercise O
Saturday, October 17, 2020
|1. C||2. C||3. B||4. D|
SAT Math - Answers to Questions from October 3, 2020
- What does the graph of a parabola look like?
The graph of a parabola looks like the letter U: U or an upside down U: Ո
- What is the standard form of a parabola equation?
y = ax2 + bx + c
- What is the significance of a, the coefficient of the x2 term?
The sign of a tells whether the parabola opens upward (like the letter U) or downward (like an upside down U: Ո ).
If a is positive, the parabola opens upward and there is a minimum value of y.
If a is negative, the parabola opens downward and there is a maximum value of y.
- There is also a vertex form of the parabola equation. What is it?
y = a(x – h)2 + k
- What does the term vertex mean?
The vertex is the point on the graph where the parabola is at its minimum value (if the parabola opens upward) or its maximum value ( if the parabola opens downward).
- From the vertex form of the equation, what is the point that indicates the vertex?
The vertex is the point (h,k).
- How do you convert from the standard form of a parabola equation to the vertex form?
You convert by completing the square.
These are the steps for completing the square:
- Step 1: Begin with the equation in standard form: ax2 + bx + c = 0 (set y = 0)
- Step 2: Divide every term in the equation by the coefficient of the x2 term.
- Step 3: Move the constant term (the term without a variable) to the opposite side of the equation (by adding or subtracting)
- Step 4: Take half of the coefficient of the x term, square it, and add the squared term to both sides of the equation.
- Step 5: Factor the side of the equation that is a perfect square trinomial (we just created it) into the square of a binomial, in the form of (x – h)2 or (x + h)2.
- Convert the equation y = x2 - 4x - 12 to the vertex form.
- Step 1: x2 - 4x – 12 = 0
- Step 2: x2 - 4x – 12 = 0
Note: Remember that in Step 2, we divide each term in the equation by the coeffcient of the x2 term. Since the coefficient of the x2 term is 1, the equations in Step 1 and Step 2 are identical.
- Step 3: x2 - 4x = 12
- Step 4: x2 - 4x + 4 = 12 + 4
x2 - 4x + 4 = 16
- Step 5: (x - 2)2 = 16
- Step 6: (x - 2)2 – 16 = y
What is the vertex?
Remember, the vertex is the point (h,k) from the vertex form of the equation y = a(x – h)2 + k.
In this case, h = 2 and k = -16.
Thus, the vertex is (2, -16).
SAT Math - This Week's Questions (October 17, 2020 )
Answer the following questions. The solutions will be provided next week.
In the Princeton Review, read chapter 15, Functions and Graphs.
The SAT will also ask questions about the equation of a circle in the xy-plane.
- What is the equation of a circle in standard form?
- What two values related to a circle does the equation of the circle provide?
- The SAT may give you an equation for a circle that is not in the standard form. How would one convert it to standard form?
- x2 + y2 – 6x + 8y = 144
The equation of a circle in the xy-plane is shown above. What is the diameter of the circle?
SAT Math Formulas
Formulas Given in the Test Booklet
At the beginning of each math section these formulas are given in the test booklet. If you haven’t memorized them, you should be familiar with what they mean.
- Area of a circle: A = πr2
- Circumference of a circle: c = 2πr
- Area of a rectangle: A = lw
- Area of a triangle: A = ½ bh
- Pythagorean theorem: c2 = a2 + b2
- 30° – 60° right triangle:
- the length of the hypotenuse = twice the length of the side opposite the 30° angle.
- the length of the side opposite the 60° angle = the length of the side opposite the 30° angle times √3
- the length of the side opposite the 30° angle = ½ the length of the hypotenuse
- 45° – 45° right triangle:
- the two legs are equal
- the length of the hypotenuse = the length of the either leg times √2
- The volume of a rectangular solid: V = lwh
- The volume of a cylinder: V = πr2h
- The volume of a sphere: V = (4/3) πr3
- The volume of a cone: V = (1/3)πr2h
- The volume of a pyramid: V = (1/3)lwh
- The number of degrees in a circle = 360
- The number of degrees in a triangle = 180
- The number of radians in a circle = 2π
You are given these 12 formulas and three geometry laws on the test itself. It can be helpful and save you time and effort to memorize the given formulas, but it is ultimately unnecessary, as they are given on every SAT math section.
Formulas NOT Given in the Test Booklet
The following formulas are not printed on the test booklet; you will have to memorize them.
- The area of a square: A = s2
- The perimeter of figure = the sum of all of the sides
- Area of a parallelogram: A = lw
- Area of a trapezoid: A = ½ h(b1 + b2)
- Given a radius and a degree measure of an arc from the center of a circle, find the area of the sector that is defined by the angle and the arc:
Area of a sector of a circle: A = (t/360) πr2 when t = the number of degrees in the central angle
- Given a radius and a degree measure of an arc from the center, find the length of the arc:
Length of an arc: L = (t/360) (2πr) when t = the number of degrees in the central angle
- When the angles of triangle A are equal to the angles of triangle B, the sides of triangle A are proportional to the sides of triangle B.
- x2 – y2 = (x + y)(x – y)
- (x + y)2 = x2 + 2xy + y2
- (x - y)2 = x2 - 2xy + y2
- A function in the form of f(x) = 3x + 12 is the same as y = 3x + 12.
- The equation of the line in the slope/intercept form:
y = mx + b, where the slope = m, and the y-intercept = b.
- The equation of the line in standard form:
Ax + By = C, where the slope = -A/B and the y-intercept = C/B.
- Slope – four ways to determine the slope:
- Slope = rise (vertical change)/run (horizontal change)
- Given two points on a line, (x1, y1) and (x2, y2), the slope = (y2 – y1)/(x2 – x1).
- If the equation of the line is in the slope/intercept form, y = mx + b, the slope = m.
- If the equation of the line is in standard form, Ax + By = C, the slope = -A/B
- The standard form of a parabola equation: y = ax2 + bx + c
- Vertex form of the parabola equation:
y = a(x – h)2 + k, where the vertex is the point (h,k).
- Equation of a circle? (x – h)2 + (y – k)2 = r2 where the center of the circle is the point (h,k)
and the radius of the circle is r.
- The quadratic formula:
For ax2 + bx + c = 0, the value of x is given by:
x = (−b ± √ b2 − 4ac ) / 2a
- The key to solving average problems is to find the total of the items before doing anything else.
There are two ways to find the total:
- Total= sum of the items
- Total = the average times the number of items. This method is usually required on SAT problems.
- Average speed = total distance / total time; Distance = (speed) x (time)
- SOHCAHTOA (applies to a right triangle)
- sine of an angle = side opposite the angle over the hypotenuse (SOH)
- cosine of an angle = side adjacent to the angle over the hypotenuse (CAH)
- tangent of an angle = side opposite the angle over the side adjacent to the angle (TOA)
- 180 degrees = π radians
- Imaginary numbers
- i = √-1
- i2 = -1
- i3 = -i
- i4 = 1
- i5 = i
- i6 = -1
- i7 = -i
- i8 = 1
- A present amount P increases at an annual rate r for t years. The future amount F in t years is:
F = P(1 + r)t
- A present amount P decreases at an annual rate r for t years. The future amount F in t years is:
F = P(1 - r)t
- Item sold at discount: discount amount = original price x discount percent
- Item sold at discount: reduced price = original price x (1-discount percent)
- Given two points, A(x1,y1), B(x2,y2), find the midpoint of the line that connects them:
Midpoint = the average of the x coordinates and the y coordinates:
(x1 + x2) / 2, (y1+y2) / 2
- Given two points, A(x1,y1), B(x2,y2), find the distance between them:
Distance = √[ (x2 - x1)2 + (y2 - y1)2 ]
Actually, this is one formula you do not need to memorize, since you can simply graph your
points and then create a right triangle from them. The distance will be the hypotenuse, which
you can find by using the Pythagorean Theorem.
- Probability of x = (number of outcomes that are x)/(total number of possible outcomes)
SAT Math Operations
Operations You Need to be Able to Perform
- Substitute values for a variable and simplify.
- Add fractions with different denominators, where the denominators are numbers.
- Add fractions with different denominators, where the denominators are variables.
- Know how to simplify complex fractions.
- In a fraction, the denominator cannot equal zero. If an equation is solved and the value of the variable makes the denominator = zero, then that value cannot be a solution to the problem.
When picking numbers, consider positive numbers, negative numbers, zero, decimals, and extreme numbers.
Understand the definitions of the terms digit, integer, number, prime number, factor, multiple, divisible, reciprocal of a number, absolute value of a number.
Know the absolute value sign.
Know the common fraction-decimal-percent equivalents.
Know how to change a fraction to a decimal or to a percent.
Know how to change a decimal to a percent.
Know how to change a percent to a decimal.
Understand the factorial concept.
Know how to compute permutations and combinations: n items taken x at a time.
Know when to use Venn diagrams.
When angles are formed when a line crosses parallel lines, several equal angles are created.
When a diagram is given in a geometry problem, consider adding one or more lines to create another figure.
Geometric figures are not necessarily drawn to scale; lines that look equal may not be equal; angles that look equal may not be equal.
In a triangle, the length of sides opposite equal angles are equal.
In a triangle, the length of a side opposite a larger angle is greater than the side opposite a smaller angle.
Know the third side rule for triangles: the length of any one side of a triangle must be less than the sum of the other two sides, and greater than the difference between the other two sides.
Two triangles are congruent if the sides of one triangle are equal to the corresponding sides of the other triangle and the angles of one triangle are equal to the corresponding angles of the other triangle.
Two triangles are similar if the angles of one triangle are equal to the corresponding angles of the other triangle and the sides of one triangle are not equal to the corresponding sides of the other triangle.
If two triangles are similar, their corresponding sides are proportional.
The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc.
The length of an arc is a fraction of the circumference of a circle.
A line tangent to a circle produces a right angle at the point of tangency between the line and another line that connects the point of tangency to the center of the circle.
Know the exponent rules.
Know how to express a number with alternative bases using appropriate exponents; the most common problems involve changing a number to a base of 2 or a base of 3.
Know how to determine the three averages: mean, median, and mode.
Know how the normal curve, mean, and standard deviation interact.
- Read ratio problems carefully,
- A ratio can express a part to part relationship.
For example, a ratio of 1 to 2 = 1:2 = ½.
- A ratio can express a part to whole relationship.
For example, a ratio of 1 to 2 has two parts and a whole (1 + 2 = 3). One part is ⅓, the other part is ⅔.
- Solve linear equations when the answer is a number (one equation and one unknown.)
- Solve linear equations when one variable is in terms of other variables (one equation with all variables.)
- Solve simultaneous equations (two equations in 2 unknowns.)
- Solve quadratic equations by factoring, by using the quadratic equation, and by completing the square.
- Find the radius of a circle from the formula of a circle.
- Know how to write the formula of a circle in standard form.
- Factor an expression.
- Type 1: 3xy + 7x = x(3y + 7)
- Type 2: 2x2 + 13x + 15 = (2x + 3)(x + 5)
- Type 3: 213 – 211 = 211(22 – 1) = 211(4-1) = 211(3)
- Solve inequalities.
- Find the price of an item after a sales tax is added.
- Find the price of an item after a percent increase.
- Find the price of an item after a percent decrease.
- Find the percent of a number.
- When one number is greater than another, find the percent greater.
- When an amount changes, find the percent change.
- Know the three averages: mean, median, and mode.
- In an average problem, the first thing to do is to find the total; there are two ways to find the total.
- Find the average of a set of numbers.
- Find the missing number in a set of numbers when the mean is known.
- From the equation of a line, determine the y intercept, x intercept, and slope.
- Understand positive slopes, negative slopes, and slope = zero.
- Equation of a parabola.
- Coordinate geometry: locate points in the xy plane.
- Know the I, II, III, and IV quadrants.
- Evaluate information in a chart.
- Word problems: write down each detail; proceed in a step by step fashion.
- Trigonometry: find the sine of an angle; find the cosine of an angle; find the tangent of an angle (remember SOH-CAH-TOA.)
The sine of an angle = the side opposite the angle divided by the hypotenuse (SOH)
The cosine of an angle = the side adjacent to the angle divided by the hypotenuse (CAH)
The tangent of an angle = the side opposite the angle divided by the side adjacent to the angle (TOA)
- In right triangle ABC, if angle B is the right angle, then the sine of angle A = the cosine of angle C.