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January 2018
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N.B. This is for SAT Subject Test Math Level 2 Problem:What is the sum of the infinite geometric series:
6 + 4 + 8/3 + 16/9 + ... ? (A) 18 (B) 36 (C) 45 (D) 60 (E) There is no sum.
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ProblemIn April of 2004, d dogs and c cats lived in an animal shelter. If 4 cats arrived at the shelter in May of 2004 and the ratio of dogs to cats remained unchanged, in terms of c and d, how many dogs arrived at the shelter in May of 2004?
(A) 4 (B) 4d/c (C) d/c (D) d^2  4d (E) (2cd + 4d)/c
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In the complex plane, the horizontal axis is called the real axis and the vertical axis is called the imaginary axis. The complex number a + bi graphed in the complex plane is comparable to the point (a, b) graphed in the standard (x, y) coordinate plane. The modulus of the complex number a + bi is given by:
\[\sqrt{a^2 + b^2}\]
Question:
Which of the complex numbers z1, z2, z3, z4 and z5 below has the greatest modulus?
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Two whole numbers have a greatest common factor of 8 and a least common multiple of 48. Which of the following pairs of whole numbers will satisfy the given conditions?
F. 4 and 9 G. 5 and 10 H. 10 and 16 J. 14 and 20 K. 16 and 24
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ProblemSamantha is making gluten free brownies for the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic?
N.B: Recipe is on the next page.
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Problem:
An interior designer is creating a custom coffee table for a client. The top of the table is a glass triangle that needs to balance on a single support. If the coordinates of the vertices of the triangle are at (3, 6), (5, 2), and (7, 10), at what point should the support be placed?
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A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve cooking problems, especially when the numbers are not friendly. But first, let's start with an easy problem.
Let's say you are cooking rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. However, you found out that there are 12 guests coming. How would the recipe change? If you’ve ever made rice, you know that this ratio — 1 part dry rice and 2 parts water — is important. Mess it up, and your rice will become soggy or something else. Because you are quadrupling your guest list (3 people * 4 = 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. This demonstrates how you can use ration to solve proportion problems in real life. What happens when the numbers are not so friendly? Let's say you are throwing a party for 25 people. How much water do you need?
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Question
What is the solution set for the above equation?
A) {5} B) {20} C) {−5, 20} D) {5, 20}
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QuestionA car is traveling at x feet per second. The driver sees a red light ahead, and after 1.5 seconds reaction time, the driver applies the brake. After the brake is applied, the car takes x/24 seconds to stop, during which time the average speed of the car is x/2 feet per second. If the car travels 165 feet from the time the driver saw the red light to the time it comes to a complete stop, which of the following equations can be used to find the value of x?
A) x^2 + 48x − 3,960 B) x^2 + 48x − 7,920 C) x^2 + 72x − 3,960 D) x^2 + 72x − 7,920
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QuestionMaizah bought a pair of pants and a briefcase at a department store. The sum of the prices before sales tax was $130.00. There was no sales tax on the pants and a 9% sales tax on the briefcase. The total Maizah paid, including the sales tax, was $136.75. What was the price, in dollars, of the pants?
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Question2y + 6x = 3
y + 3x = 2 How many solutions (x, y) are there to the system of equations above? A) Zero B) One C) Two D) More than two
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QuestionA voter registration drive was held in Town Y. The number of voters, V, registered T days after the drive began can be estimated by the equation V = 3,450 + 65T. What is the best interpretation of the number 65 in this equation?
A) The number of registered voters at the beginning of the registration drive B) The number of registered voters at the end of the registration drive C) The total number of voters registered during the drive D) The number of voters registered each day during the drive
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QuestionThe stratosphere is the layer of the Earth’s atmosphere that is more than 10 kilometers (km) and less than 50 km above the Earth’s surface. Which of the following inequalities describes all possible heights x, in km, above the Earth’s surface that are in the stratosphere?
A) x + 10 < 50 B) x − 10 < 50 C) x + 30 < 20 D) x − 30 < 20
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How to Find Slopes on the New SAT11/21/2016 Question:If f(x) = 2x + 2 is a linear function, which of the following is true for 4f(x)?
A) The slope is four times steeper than f(x). B) The slope is four times less steep than f(x). C) All values of x are four times greater than f(x) for the same values of y. D) The slope changes, but the yintercept remains the same as f(x).
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Question:
Given a polynomial p(x), the value of p(3) = 2.
Which of the following must be true for p(x)? (A) x  5 is a factor of p(x). (B) x  2 is a factor of p(x). (C) x + 2 is a factor of p(x). (D) The remainder when p(x) is divided by x  3 is 2.
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Rationalize and Simplify the Given Expressions:
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How to Tackle Ratio Problems on the ACT10/5/2016 Problem:Only tenth, eleventh, and twelfthgrade students attend Washington High School. The ratio of tenth graders to the school’s total student population is 86:255, and the ratio of eleventh graders to the school’s total student population is 18:51. If 1 student is chosen at random from the entire school, which grade is that student most likely to be in?
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Problem:
Which of the following is a rational number?
\[\sqrt2\]
\[\sqrt{\pi}\]
\[\sqrt7\]
\[\frac{\sqrt{5}}{\sqrt{25}}\]
\[\frac{\sqrt{64}}{\sqrt{49}}\]
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Problem:The first term is 1 in the geometric sequence 1, −3, 9, −27, .... What is the SEVENTH term of the geometric sequence?
A. −243 B. 0−30 C. 081 D. 189 E. 729
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Problem:Justine spends $122 to create a lemonade stand. If she sells p cups of lemonade at $2.50 per cup, which of the following expressions represents her profits after expenses?
A. p + 122 B. 2.5  p C. 2.5p  122 D. p  122
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How to Tackle Complex Numbers on the ACT8/24/2016
Problem: What is the value of
Note: i = sqrt(1)
A. i B. 1 C. i D. 1 E. sqrt(i)
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Even though she is only twentyseven years old, Cheryl is interested in beginning a retirement plan. The graph above shows the value of a market fund investment compared to a Certificate of Deposit (D). Which of the following cannot be concluded by Cheryl from the graph? (A) At one year, the market fund is worth more than the CD.
(B) The market fund shows exponential growth and the CD shows linear growth. (C) At 20 months, the two funds have the same value. (D) The intiial investment in each account was the same.
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The Tigers had five times as many losses as they had ties in a season. If the Tigers did not win any of their games, which could be the total number of games they played in the season?
(A) 16 (B) 5 (C) 10 (D) 12
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When Shondra makes an online purchase, a 15% discount is applied to the retail price and then a 6.25% tax is added to this discounted price. Which of the following represents the amount Shondra pays, in dollars, for an item with a retail price of x dollars?
A) x  0.15 + 0.0625x B) 1.0625x  0.15x C) 1.0625(0.85x) D) x  0.15(1.0625x) 