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Discover Frequently Asked Math Questions and Their Answers

• How do you write the quadratic function #y=x^2+14x+11# in vertex form?
• How many points does #y=-2x^2+x-3# have in common with the vertex and where is the vertex in relation to the x axis?
• How do you solve #4x^4 - 16x^2 + 15 = 0#?
• How do you solve #2x^2+3x-2=0#?
• How do you solve #7(x-4)^2-2=54# using any method?
• How do you solve #x^2 + 5x + 6 = 0# algebraically?
• How do you use factoring to solve this equation #3x^2/4=27#?
• What is the vertex of # y = (1/8)(x – 5)^2 - 3#?
• How do you solve #| x^2+3x-2 | =2#?
• How do you solve #2x²+3x=5 # using the quadratic formula?
• How do you find the derivative of #y=tan(3x)# ?
• How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
• How do you differentiate #(3+sin(x))/(3x+cos(x))#?
• What is the derivative of this function #sin^-1(x/4)#?
• What is the derivative of this function #y=sin^-1(2x)#?
• What is the derivative of this function #arcsec(x^3)#?
• What is the derivative of #y=sin(tan2x)#?
• How do you differentiate #cos(pi*x^2)#?
• What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
• What is the derivative of #y=3sin(x) - sin(3x)#?
• A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
• How can we find the area of irregular shapes?
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
• An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
• A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?
• Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(0 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
• A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
• What is a quadrilateral that is not a parallelogram and not a trapezoid?
• Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#
• A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,9 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
• What is the GCF of the set #64, 16n^2, 32n#?
• How do you write the reciprocal number of 5?
• Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
• How do you find the GCF of #25k, 35j#?
• How do you write 132/100 in a mixed number?
• How do you evaluate the power #2^3#?
• How do you simplify #(4^6)^2 #?
• How do you convert 3.2 tons to pounds?
• How do you solve #\frac { 5} { 8} + \frac { 3} { 2} ( 4- \frac { 1} { 4} ) - \frac { 1} { 8}#?
• What are some acronyms for PEMDAS?
• How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
• How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you find the end behavior of #-x^3+3x^2+x-3#?
• How do you find the asymptotes for #(2x^2 - x - 38) / (x^2 - 4)#?
• How do you find the asymptotes for #f(x) = (x^2) / (x^2 + 1)#?
• How do you find the vertical, horizontal and slant asymptotes of: #(3x-2) / (x+1)#?
• How do you find the Vertical, Horizontal, and Oblique Asymptote given #s(t)=(8t)/sin(t)#?
• How do you find vertical, horizontal and oblique asymptotes for #(x^3+1)/(x^2+3x)#?
• How do you find vertical, horizontal and oblique asymptotes for #y = (4x^3 + x^2 + x + 5 )/( x^2 + 3x)#?
• What is a pooled variance?
• What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12?
• What is the z-score of sample X, if #n = 81, mu= 43, St. Dev. =90, and E[X] =57#?
• The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?
• How many permutations are there of the letter in the word baseball?
• How do you evaluate 6p4?
• What is the probability of #X= 6# successes, using the binomial formula?
• A lottery has a $100 000 first prize, a $25 000 second prize, and five $500 third prizes. A total of 50000 tickets are sold. What is the probability of winning a prize in this lottery?
• When a event is reported, the probability that is a negative event is 30%. What is the probability that 3 out of 5 reported events are negative?
• What is the median of 5, 19, 2, 28, 25?
• How do you solve this trigonometric equation?
• What is the frequency of #f(theta)= sin 3 t - cos2 t #?
• How do you evaluate #Sin(pi/2) + 6 cos(pi/3) #?
• How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=9, b=40, c=41?
• How do you express (5*pi)/4 into degree?
• Solve for θ on the interval [90°,180°]:2tanθ +19 = 0?
• Prove that #((cos(33^@))^2-(cos(57^@))^2)/((sin(10.5^@))^2-(sin(34.5^@))^2)= -sqrt2# ?
• A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#. If side B has a length of 26, what is the area of the triangle?
• How do you write the following in trigonometric form and perform the operation given #(sqrt3+i)(1+i)#?
• A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #32 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Mentoring preservice mathematics teachers for research

11 Aug 2024 | Errol Matthew C Garcia, PhD

The Didactics of Mathematics Research Group (DiMRG) of the Department of Mathematics recently hosted another installment of the Mathematics Research Seminar Series. The featured talk, entitled “Opportunities and Challenges in Mentoring Preservice Mathematics Teachers for Research,” was delivered by Dr. Leah Nillas of Illinois Wesleyan University given on 27 June 2024, both on-site and online. Dr. Nillas's research focuses on mentoring K-12 preservice teachers and exploring their experiences and practices worldwide. She began her presentation by sharing images from her observations of lesson study implementations in Taiwan and Japan, as well as professional development programs in Thailand, to illustrate her points.

Dr Nillas' talk particularly focused on self-study teacher research (Samsara, 2011), a reflective practice where teachers systematically investigate their own teaching methods to enhance educational practices and student outcomes. In her research, senior K-12 preservice teachers, deployed in local schools in Illinois, USA were asked to do self-study research during their preservice teaching. She highlighted the use of self-study research as opposed to lesson study in some schools, attributing the preference to cultural factors. For instance, in the context of Illinois, Dr Nillas noted a detachment between universities and K-12 schools, where lesson study is primarily seen as a short-term professional development tool rather than a sustained practice with long-term goals. Consequently, she identified an opportunity and a challenge: the need to adopt professional development methods superior to lesson study. Self-study, she argued, engages preservice teachers in reflective thinking, connects research to practice, and addresses problematic learning areas more effectively.

Furthermore, the implementation of self-study prompted a second opportunity, which is the rethinking of the traditional mathematics curriculum. This led Dr Nillas to enhance her curriculum and pedagogy courses, enabling preservice teachers to connect students to their culture and community. She emphasized the importance of making inequity, power, and activism explicit components of the teaching for social justice curriculum, thereby fostering a more inclusive and socially aware educational environment.

The third opportunity and challenge focused on making math relevant to students. Dr Nillas presented several examples to illustrate this point, showing how connecting math to students' communities can motivate them to learn important mathematical concepts. For instance, under the topic of linear algebra, students explored the issue of fair trade and labor by analyzing the cost of a pair of Kobe V shoes priced at $160 in relation to the meager wages of factory workers. In probability, they investigated where lottery dollars go. Other examples included discussions on religious tolerance and undocumented immigration in the US. These real-life situations prompted the critical question of how teachers can incorporate such relevant contexts into mathematics topics to enhance student engagement and understanding.

The fourth opportunity and challenge is connecting with students to improve learning, which promotes students’ self-esteem and motivation, and improves attitudes to dissolve boundaries based on differences in the classroom. Dr Nillas emphasized that fostering a positive and inclusive classroom environment is crucial for student success.

The fifth and final opportunity and challenge is improving practice through research. Dr Nillas emphasized that linking research and practice in mathematics education is essential for addressing critical issues (NCTM, 2012). By implementing formative assessments and reflecting on their impact, teachers can enhance both their instruction and students' learning. However, she highlighted that local issues can influence the choice of research topics. Dr Nillas stressed that social and cultural concerns can help shape relevant research topics.

Dr Nillas also shared some of the experiences of the preservice teachers who undertook the self-study research. One preservice teacher reflected on how engaging in self-study significantly enhanced their professional practice, stating that it pushed them to take risks in the classroom. They noted that without the self-study, they might not have tried various teaching methods and group activities. The process also required daily reflection, which led to continuous growth and frequent adjustments to their teaching style. Overall, the self-study helped in developing their teaching style and encouraged them to experiment in their classroom.

Dr Nillas concluded her talk by expressing pride in the global reach of their students’ self-study research projects, highlighting that they are being read by people around the world, as shown by the readership map available on their website.

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