[Math Center] 1. [latex]{ x }^{ 2 }y>0[latex] [latex]x{ y }^{ 2 }<0[latex] Quantity A Quantity B [latex]x[latex] [latex]y[latex] 2. On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers [latex]x, y[latex], and [latex]z[latex] must be true? Indicate all such statements. (A) [latex]xyz<0[latex] (B) […]
Category: Math Center
MC1: Geometry
MC2: Algebra
MC3: Number Properties
MC4: Decimals, Fraction, Percentage
MC5: Statistics and D.I.
MC6: Counting and Probability
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[Math Center] 1. Ashley and Beatrice received the same score on a physical fitness test. The scores for this test, [latex]t[latex], are determined by the formula [latex]t=3ps-25m[latex] where [latex]s[latex] and [latex]p[latex] are the numbers of sit-ups and push-ups the athlete can do in one minute and [latex]m[latex] is the number of minutes she takes to […]
ã2.3.bã āĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. [latex]y ={ 2x }^{ 2 } +7x-3[latex] Quantity A Quantity B [latex]x[latex] [latex]y[latex] 2. [latex]\frac{ 1-x }{ x-1 }=\frac{ 1 }{ x }[latex] Quantity A Quantity B [latex]x[latex] [latex]-\frac{ 1 }{ 2 }[latex] 3. [latex](x+3)(y-4)=0[latex] Quantity A Quantity B [latex]xy[latex] [latex]-12[latex] 4. If both expressions [latex]{ x }^{ 2 }-3x+2[latex] […]
ã2.2.bã āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻāĻŦāĻ āĻ¸ā§āĻāĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. If [latex]1+x+{ x }^{ 2 }+{ x }^{ 3 }=60[latex] then the average (arithmetic mean) of [latex]x,{ x }^{ 2 },{ x }^{ 3 },{ x }^{ 4 }[latex] is equal to which of the following? A [latex]12x[latex] B [latex]15x[latex] C [latex]20x[latex] D [latex]30x[latex] E [latex]60x[latex] 2. [latex]0 […]
ã2.1.bã āĻ¸āĻāĻā§āĻ¯āĻž āĻāĻ āĻ¨ āĻ āĻ āĻā§āĻāĻā§āĻ˛ā§āĻ° āĻ¸ā§āĻĨāĻžāĻ¨ āĻŦāĻŋāĻ¨āĻŋāĻŽā§ āĻāĻāĻ¨āĻž āĻŦāĻŋāĻˇā§āĻ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻž
[Math Center] 1. If [latex]2x=3y=4z=20[latex], then [latex]12xyz=[latex] A [latex]16,000[latex] B [latex]8,000[latex] C [latex]4,000[latex] D [latex]800[latex] E [latex]10[latex] 2. [latex]0<x<y<1[latex] Quantity A Quantity B [latex]1-y[latex] [latex]y-x[latex] 3. [latex]st=\sqrt { 10 }[latex] Quantity A Quantity B [latex]{ s }^{ 2 }[latex] [latex]{ t }^{ 2 }[latex] 4. [latex]x <1[latex] [latex]x[latex]â [latex]0[latex] Quantity […]
ã1.7.cã Practice Problems
[Math Center] 1. A closed rectangular tank contains a certain amount of water. When the tank is placed on its [latex]3[latex] ft by [latex]4[latex] ft side, the height of the water in the tank is [latex]5[latex] ft. When the tank is placed on another side of dimensions [latex]4[latex] ft by [latex]5[latex] ft, what is the […]
ã1.6.cã āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. In the [latex]xy[latex]-plane, the equation of line [latex]k[latex] is [latex]3x-2y=0[latex]. Quantity A Quantity B The [latex]x[latex]-intercept of line [latex]k[latex] The [latex]y[latex]-intercept of line [latex]k[latex] 2. In the [latex]xy[latex]-plane, line [latex]k[latex] is a line that does not pass through the origin. Which of the following statements individually provide(s) sufīŦcient additional information to determine […]
ã1.5.cã Mixed Geometric Shapes
[Math Center] 1. In the īŦgure above, the diameter of the circle is [latex]10[latex]. Quantity A Quantity B The area of quadrilateral [latex]ABCD[latex] [latex]40[latex] 2. For the rectangular solid below, īŦnd the following. (a) Surface area of the solid (b) Length of diagonal [latex]AB[latex] 3. A circle is inscribed in a square with […]
ã1.4.cã āĻŦāĻšā§āĻā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. Quantity A Quantity B The area of the shaded region [latex]36[latex] 2. In the rectangular solid above, and What is the area [latex]TU=3, UV=4, VR=2[latex]. of the shaded rectangular region? 3. [latex]A, B[latex], and [latex]C[latex] are three rectangles. The length and width of rectangle [latex]A[latex] are [latex]10[latex] percent greater and […]
ã1.3.cã āĻŦā§āĻ¤ā§āĻ¤ āĻāĻŦāĻ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. AB is a diameter of the circle. Quantity A Quantity B The length of [latex]AB[latex] The average (arithmetic mean) of the lengths of [latex]AC[latex] and [latex]AD[latex] 2. In the īŦgure above, [latex]O[latex] and [latex]P[latex] are the centers of the two circles. If each circle has radius [latex]r[latex], what is the area […]
ã1.2.cã āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻā§āĻ, āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. [latex]DFG[latex] is a straight line. What is the value of [latex]x[latex]? A. 12 B. 14 C. 16 D. 18 E. 20 2. If the hypotenuse of an isosceles right triangle is [latex]7\sqrt { 2 }[latex] , what is the area of the triangle? (A) [latex]14[latex] (B) [latex]18[latex] (C) [latex]24.5[latex] (D) [latex]28[latex] […]
ã1.1.cã āĻā§āĻ¨, āĻ°ā§āĻāĻž āĻāĻŦāĻ āĻĻā§āĻ°āĻ¤ā§āĻŦ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. In the figure, lines [latex]l[latex] and [latex]m[latex] are parallel. If [latex]y-z = 60[latex], then what is the value of [latex]x[latex] ? (A) [latex]60[latex] (B) [latex]75[latex] (C) [latex]90[latex] (D) [latex]120[latex] (E) [latex]135[latex] 2. In the figure, [latex]AD[latex] and [latex]BC[latex] are lines intersecting at [latex]O[latex]. What is the value of [latex]a[latex] […]
ã1.7.aãāĻ¤ā§āĻ°āĻŋāĻŽāĻžāĻ¤ā§āĻ°āĻŋāĻ āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻŦāĻ¸ā§āĻ¤ā§ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ āĻĒā§āĻ°āĻļā§āĻ¨
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã7ã 3D Objects āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.7.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.7.aãāĻ¤ā§āĻ°āĻŋāĻŽāĻžāĻ¤ā§āĻ°āĻŋāĻ āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻŦāĻ¸ā§āĻ¤ā§ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋ: Surface Area The surface area of a three-dimensional shape is the amount of space on the surface of that particular object. Surface area āĻŦāĻž āĻĒā§āĻˇā§āĻ āĻ¤āĻ˛ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻāĻ¤āĻā§āĻā§ āĻ¤āĻž āĻŽāĻ¨ā§ āĻ°āĻžāĻāĻžāĻ° āĻ¸āĻšāĻ āĻ¨āĻŋā§āĻŽ āĻšāĻ˛ā§ āĻāĻ āĻŦāĻ¸ā§āĻ¤ā§āĻāĻŋāĻā§ […]
ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã3ãPrimes and Signed Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ Primes āĻŦāĻž āĻŽā§āĻ˛āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž A prime number is any positive integer larger than [latex]1[latex] with exactly two factors: [latex]1[latex] and itself. In other words, a prime number has NO factors […]
ã5.3.aãāĻĄāĻžāĻŦāĻ˛-āĻ¸ā§āĻāĻŽā§āĻ¯āĻžāĻā§āĻ°āĻŋāĻā§āĻ¸ āĻāĻŦāĻ āĻā§āĻ¨ āĻĄāĻžā§āĻžāĻā§āĻ°āĻžāĻŽ
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (5) Statistics and D.I. āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã3ãOverlapping and Venn Diagrams āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã5.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã5.3.aãāĻĄāĻžāĻŦāĻ˛-āĻ¸ā§āĻāĻŽā§āĻ¯āĻžāĻā§āĻ°āĻŋāĻā§āĻ¸ āĻāĻŦāĻ āĻā§āĻ¨ āĻĄāĻžā§āĻžāĻā§āĻ°āĻžāĻŽ Overlapping Sets āĻ¸āĻžāĻ§āĻžāĻ°āĻŖāĻ¤āĻ āĻā§āĻ¨āĻāĻŋāĻ¤ā§āĻ° āĻŦāĻž āĻā§āĻ¨āĻĄāĻžā§āĻžāĻā§āĻ°āĻžāĻŽ āĻŦā§āĻ¯āĻŦāĻšāĻžāĻ° āĻāĻ°ā§ āĻ āĻ§āĻ°āĻŖā§āĻ° āĻ āĻā§āĻ āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻāĻ°āĻž āĻšā§āĨ¤ āĻ āĻāĻžā§āĻž āĻā§āĻ¨āĻĄāĻžā§āĻžāĻā§āĻ°āĻžāĻŽā§āĻ° āĻĒāĻ°āĻŋāĻŦāĻ°ā§āĻ¤ā§ āĻĄāĻžāĻŦāĻ˛-āĻ¸ā§āĻāĻŽā§āĻ¯āĻžāĻā§āĻ°āĻŋāĻā§āĻ¸ āĻ¨āĻŋā§ā§ āĻāĻŋāĻāĻžāĻŦā§ āĻāĻāĻžāĻ°āĻ˛ā§āĻ¯āĻžāĻĒāĻŋāĻ āĻ¸ā§āĻ āĻāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻāĻ°āĻ¤ā§ āĻšā§ āĻāĻŽāĻ°āĻž āĻāĻāĻžāĻ¨ā§ āĻ¸ā§ āĻŦāĻŋāĻˇā§āĻāĻž […]
ã5.4.aãāĻĒāĻ°āĻŋāĻ¸āĻāĻā§āĻ¯āĻžāĻ¨āĻ āĻā§ āĻ¨āĻŋāĻ°ā§āĻŖā§
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (5) Statistics and D.I. āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ãAverage āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã5.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã5.4.aãāĻĒāĻ°āĻŋāĻ¸āĻāĻā§āĻ¯āĻžāĻ¨āĻ āĻā§ āĻ¨āĻŋāĻ°ā§āĻŖā§ The average (or the arithmetic mean) of a set is given by the following formula: Average = sum/# of terms, which is abbreviated as [latex]A=S/n[latex] The sum, [latex]S[latex], refers to the sum of all the terms […]
ã5.2.aãPercentile Problems
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (5) Statistics and D.I. āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã2ãPercentile Problems āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã5.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] Percentile A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the [latex]20[latex]th percentile is the value (or score) below which […]
ã5.1.aãāĻĒāĻ°āĻŋāĻ¸āĻāĻā§āĻ¯āĻžāĻ¨-āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻāĻŦāĻ āĻŦāĻŋāĻā§āĻā§āĻ¤āĻŋ
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (5) Statistics and D.I. āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãGeneral Statistics āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã5.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã5.1.aãāĻĒāĻ°āĻŋāĻ¸āĻāĻā§āĻ¯āĻžāĻ¨-āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻāĻŦāĻ āĻŦāĻŋāĻā§āĻā§āĻ¤āĻŋ Median āĻŦāĻž āĻŽāĻžāĻāĻāĻžāĻ¨ā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻžāĻ The median is calculated in one of two ways, depending on the number of data points in the set. For sets containing an odd number of values, the median is the […]
ã6.2.aãāĻ¸āĻŽā§āĻāĻŦā§āĻ¯āĻ¤āĻž
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (6) Counting and Probability āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã2ãProbability āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã6.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã6.2.aãāĻ¸āĻŽā§āĻāĻŦā§āĻ¯āĻ¤āĻž Probability is a quantity that expresses the chance, or likelihood, of an event. In other words, it measures how often an event will occur in a long series of repeated trials. For events with countable outcomes, probability […]
ã6.3ãMiscellaneous Counting
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