This document provides 10 strategies for solving math problems on standardized tests like the PSAT and SAT. Some of the key strategies include recognizing when figures are not drawn to scale, testing the extremes of ranges, finding patterns by trying different numbers, avoiding generic answers, and directly doing the math to solve problems.
What is the SAT? What is it good for? What does it tell us? Why do we have a test like this in the first place? In better understanding both the context and content of the SAT, students (and parents) can cultivate a more relaxed and informed approach to taking the test.
What is the SAT? What is it good for? What does it tell us? Why do we have a test like this in the first place? In better understanding both the context and content of the SAT, students (and parents) can cultivate a more relaxed and informed approach to taking the test.
College Algebra MATH 107 Spring, 2015, V4.8 Page 1 of .docxmonicafrancis71118
College Algebra MATH 107 Spring, 2015, V4.8
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [0, 4]; Range [–1, 3]
B. Domain [–1, 3]; Range [0, 4]
C. Domain [–1, 0]; Range [1, 4]
D. Domain [–1, 1]; Range [1, 4]
2. Solve: 19 3 3x x− = − 2. ______
A. No solution
B. 8
C. −2, 5
D. −2
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2015, V4.8
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3. Determine the interval(s) on which the function is increasing. 3. ______
A. ( ), 0.5−∞ − and (3, 6.5)
B. [– 2, 2]
C. (1, 5)
D. ( ), 1−∞ and ( )5, ∞
4. Determine whether the graph of 2xy += is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. symmetric with respect to the x-axis only
B. symmetric with respect to the y-axis only
C. symmetric with respect to the origin only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
5. Solve, and express the answer in interval notation: | 7 – 3x | ≤ 11. 5. ______
A. [–4/3, 6]
B. (–∞, –4/3]
C. (–∞, –4/3] ∪ [6, ∞)
D. (–∞, 6] ∪ [–4/3, ∞)
College Algebra MATH 107 Spring, 2015, V4.8
Page 3 of 11
6. Which of the following represents the graph of 9x − 4y = 36 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2015, V4.8
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x – 3y = 8 which passes through
the point (– 12, 7). 7. ______
A.
1
11
3
y x= +
B.
1
3
3
y x= − +
C. 3 29y x= − −
D.
1
7
3
y x= +
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function but not one-to-one.
C. It is not the graph of a function.
D. It is the graph of a parabolic relation.
College Algebra MATH 107 Spring, 2015, V4.8
Page 5 of 11
9. Express as an equivalent expression: log (x + 2) + log 1 – 3 log y 9. ______
A.
3
log( 2)
log
x
y
+
B. ( )log 3 3x y+ −
C.
3
2
log
x
y
+
D.
3
log
3
x
y
+
10. Which of the functions corresponds to the .
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The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
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Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2. LEARN SPECIAL MATH STRATEGIES
Strategy #6: Recognize “Figure not drawn to scale” –
assume the picture is misleading, closest answer to visual is
incorrect, you should redraw the figure
In the figure below, AB = BC. If x = 30 , what is
the degree value of m?
B
x
A. 75
B. 105
C. 130 m
D. 135 A C
E. 150 Note: Figure not drawn to scale
3. LEARN SPECIAL MATH STRATEGIES
Strategy #7: Test the extremes – given a range of values
(4 < x < 9), tests the extremes (4 and 9) and not the
numbers in between; the answer should be obvious
If y = 4x – 3 and 0 < x < 3, then y is between
A. -3 and 9
B. -2 and 10
C. 0 and 12
D. 1 and 5
E. 1 and 9
4. LEARN SPECIAL MATH STRATEGIES
Strategy #8: Find a pattern – try a few numbers to see
a pattern that will help you answer the question
If n is a positive integer, which of the following
cannot be the units digit of .
A. 1
B. 3
C. 5
D. 7
E. 9
5. LEARN SPECIAL MATH STRATEGIES
Strategy #9: Don’t by misled by generic answers – if you
find you’re guessing, ignore choices like “None of the above” or
“It cannot be determined from the information given”
If x, y, and z are positive numbers and
2x = 3y = 4z, then the value of x + y + z is how
many times the value of x?
A.
B.
C.
D.
E. It cannot be determined from the information given
6. LEARN SPECIAL MATH STRATEGIES
Strategy #10: Do the math – don’t go searching for wild
gimmicks and tricks; it is a math test so sometimes you
just need to do the math and solve the problem
What is the area of the shaded region in the figure
below?
(3, 10)
A. 30
B. 21 (0, 4)
C. 18
D. 12
(3, 0)
E. 9
Editor's Notes
Since AB=BC, triangle ABC is an isosceles triangle so angles A and C must be equal.Since the angles in a triangle sum to 180, the other two angles (which must be equal) are 75 (180 – 30=150; 150/2 = 75).We are trying to find the exterior angle of angle A which is 75, so 180-75 = 105.
(A). y= 4(0)-3 = 0-3 = -3; y= 4(3)-3 = 12-3 = 9
(C).7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5 = 16807, 7^6 = 117649, 7^7 = 823543, 7^8 = 5764801As you can see from the pattern above, the units digits are 7, 9, 3, 1 and then the units digits begin to repeat. The only number they do not reach is 5.
(A).Since 2, 3, and 4 are all factors of 12 (in fact this is the least common multiple of the three numbers), we can find x, y, and z such that each product (2x, 3y, and 4z) is equal to 12. Therefore, x=6, y=4, and z=3. So x+y+z=13.If x=6 and x+y+z=13, then this sum is 13/6 times the value of x which is 6.To check, (13/6)*6=13, the sum of the three variables.
(B). The shape in the shaded region forms a trapezoid, so we can use this area formula if we know it, but it is not one of the formulas listed at the beginning of the math section. We can cut the figure into a rectangle and triangle and use the given area formulas to find these two areas and finally the sum of the areas.The dimensions of the rectangle is 3 x 4 so the area of the rectangular part is 12.The base of the triangle is 10-4 = 6, and the height is 3 (same as the rectangle). So the area of the triangle is (1/2)*6*3 = 9Therefore the total area of the shaded region is 12+9 = 21.
