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Grade 11 Trigonometry CCSS: HSG-SRT.D.9

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What is the missing reason in step 3?
  1. Sum of an exterior angle of a triangle and any interior angle is 180°
  2. Sum of the angles on a straight line is 180°
  3. Sum of the angles of the triangle is 180°
  4. Exterior Angle Theorem
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
How can one determine the coefficients of the Binomial Theorem expansion for (x+y)n, where n is an integer? There may be more than one correct answer.
  1. Pascal's Triangle
  2. Binomial Permutation
  3. (nk), k=0,...,n
  4. n!k!(n-k)!, k=0,...,n
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 1?
  1. Given
  2. All acute triangles have altitudes from each vertex that intersect the opposite side
  3. Perpendicular Bisector Theorem (for triangles)
  4. All acute triangles have an orthocenter that lies within the triangle
Grade 10 Circles

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What is the missing reason in step 3?
  1. Measure of central angle is 1/2 the measure of intercepted arc
  2. Intersecting Secant Theorem
  3. Sum of the angles in a triangle is half of the sum of the non-overlapping central angles in a circle
  4. Measure of inscribed angle is 1/2 the measure of intercepted arc
Grade 11 Quadratic Equations and Expressions CCSS: HSG-GPE.A.2

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Which of the following equations is correct, and why?
  1. d21+d22=x2, by the Pythagorean Theorem.
  2. d1+d2=0, because the distances will always be opposite.
  3. d1=d2, by definition of a parabola.
  4. kd1=hd2, because the ratio kh is always constant.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 12?
  1. Each of the three altitudes of an acute triangle intersects the side opposite the vertex through which the altitude passes
  2. The orthocenter of all acute triangles lies within the triangle
  3. Perpendicular Bisector Theorem (for triangles)
  4. All triangles have three altitudes
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

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Which of the following conclusions can be reached, using the information above and the triangle theorem which states that if a line is parallel to one side of a triangle, and intersects the other two sides, then the line divides these two sides proportionally. Reminder: points B4 and Q are coincident.
  1. A4B4QP=A4C4PR
  2. B4C4QR=A4C4PR
  3. A4PA4B4=C4RB4C4
  4. QA4QC4=A4C4PR
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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It can be shown that the value b from the previous question relates to the vertices of the minor-axis. Specifically, the vertices are (0,-b) and (0,b). Looking at the positive vertex, it forms an isosceles triangle with the two foci. What is the length of the two congruent sides? How is this related to the previous question?
  1. They each have a length of 2c. Using the distance formula and looking at the difference of distances between the lengths just found and the other vertices of the major axes, one finds that b=a2-c2.
  2. They each have a length of c. Then, the right triangle formed between the vertices and the origin, and applying the Pythagorean theorem, results in a2+b2=c2.
  3. They each have a length of a. Looking at the right triangle formed by the origin, F1, and the vertex (0,b), and applying the Pythagorean theorem results in a2=b2+c2.
  4. They each have a length of a2. Therefore, the sum of their lengths, a, can be used as a value equal to the sum of the lengths of b and c.
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Jeremy is working with the Fundamental Theorem of Algebra, and thinks he's found an exception. Looking at f(x)=4(x-1)2, this will result in only one root, x=1. Therefore, despite this being a second degree polynomial, there is only one root. Is this correct?
  1. Yes, this is a known exception.
  2. No, this is not a polynomial, it is a quadratic function.
  3. No, if the quadratic formula is used, the other root is found.
  4. No, this root has multiplicity of 2, which means it counts as two roots.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Grade 12 Statistics and Probability Concepts
Scores for a standardized test taken by all American public school 11th graders have a mean of 80% and a standard deviation of 4.5%. Forty-five 11th grade public school students who took the exam were randomly selected, and the average score of this sample was 70%.
Which of the following is true about the sampling distribution?
  1. The sampling distribution cannot be assumed to be approximately Normal since 45(1-0.80)=9 <10.
  2. The sampling distribution can be assumed to be approximately Normal since 45(0.80)=36 > 10. The mean is 0.80 and the standard deviation is 0.0596.
  3. The sampling distribution cannot be assumed to be approximately Normal since the population size is not given.
  4. The sampling distribution can be assumed to be approximately Normal since n>30, according to the Central Limit Theorem. The mean score is 80% and the standard deviation is 0.671%.
  5. The sampling distribution can be assumed to be approximately Normal since n>30, according to the Central Limit Theorem. The mean score is 80% and the standard deviation is 4.5%.
  6. The sampling distribution cannot be assumed to be approximately Normal since the scores are not normally distributed.
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Looking at the graph of a quadratic polynomial, roots or zeros correspond to where the graph crosses the x-axis. When the graph just touches the x-axis, this corresponds to a double root. The Fundamental Theorem of Algebra states that a quadratic polynomial will always have 2 roots. How is this reconciled with a quadratic polynomial whose graph does not intersect the x-axis?
  1. Quadratic polynomials always intersect the x-axis.
  2. If a quadratic polynomial doesn't cross the x-axis it is no longer a polynomial, and the Fundamental Theorem of Algebra no longer applies.
  3. When a quadratic polynomial doesn't cross the x-axis, this simply implies that its roots are complex with non-zero imaginary parts.
  4. Simply translate the quadratic polynomial till it does cross the x-axis.
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