Math 2025 - Middle Grades Exam Review

MATH 2025 – Middle Grades – Assessment Overview

Question 1: Sum of Consecutive Integers

• Problem: What is the greatest number of consecutive integers that has a sum of 60?
• Options:
    a. 16
    b. 32
    c. 90
    d. 120
• Correct Answer: d. 120

Question 2: Camera Timers

• Problem: Two cameras take pictures at different intervals. Camera 1: every 15 minutes, Camera 2: every 18 minutes. At what time will both capture the same picture for the second time?
• Options:
    a. 11 a.m.
    b. 11:15 a.m.
    c. 11:30 a.m.
    d. 11:45 a.m.
• Correct Answer: c. 11:30 a.m.

Question 3: Rational Numbers

• Problem: Which would NOT be considered a rational number?
• Options:
    a. 1.142857
    b. 3.141592653…
    c. √144
    d. 272/3
• Correct Answer: b. 3.141592653…
    - Explanation: This is an irrational number since it cannot be expressed as a quotient of integers.

Question 4: Theater Seating

• Problem: In a theater, each row has 2 more seats than the previous one. First row has 50 seats. How many in the 30th row?
• Options:
    a. 108
    b. 110
    c. 112
    d. 106
• Correct Answer: a. 108

Question 5: Pattern Recognition

• Problem: Given the first four illustrations of a pattern, how many triangles will the 14th drawing have?
• Options:
    a. 144
    b. 169
    c. 196
    d. 225
• Correct Answer: c. 196

Question 6: Arithmetic Sequence

• Problem: A sequence starts at -14 with a common difference of 8. What is the sum of the first 10 terms?
• Options:
    a. 206
    b. 226
    c. 200
    d. 220
• Correct Answer: d. 220

Question 7: Student Enrollment Calculation

• Problem: Enrollment at Governor’s Cup Middle School is 440, which is 20 more than twice what it was ten years ago. Find past enrollment.
• Options:
    a. 198
    b. 205
    c. 210
    d. 220
• Correct Answer: c. 210

Question 8: Greatest Common Factor

• Problem: For positive integers x and y, if the greatest common factor for x³y² and x²y is 63, what could y equal?
• Options:
    a. 3
    b. 7
    c. 9
    d. 21
• Correct Answer: b. 7

Question 9: Pool Filling Time

• Problem: If a hose takes 12 hours to fill a pool, and a second hose takes half that time, how long will both take together?
• Options:
    a. 9 hours
    b. 4 hours
    c. 6 hours
    d. 5.5 hours
• Correct Answer: b. 4 hours

Question 10: Discount Price Calculation

• Problem: Kendra buys a book for $16.80, which is a 30% discount. What was the original price?
• Options:
    a. $24.50
    b. $27.00
    c. $22.50
    d. $24.00
• Correct Answer: d. $24.00

Question 11: Building Proportionality

• Problem: If windows are proportional to building height (4 feet tall, 3 feet wide), find width for a building 76 feet tall.
• Options:
    a. 63 feet
    b. 101 feet
    c. 83 feet
    d. 57 feet
• Correct Answer: d. 57 feet

Question 12: Distance Calculation between Cities

• Problem: Given City A (4, 5) and City B (-3, -6), calculate the distance in kilometers (1 unit = 50km).
• Options:
    a. 130
    b. 652
    c. 340
    d. 200
• Correct Answer: b. 652 kilometers

Question 13: Triangle Angle Measures

• Problem: Angles are in the ratio of 2:3:5. What is the smallest angle?
• Options:
    a. 18°
    b. 36°
    c. 54°
    d. 24°
• Correct Answer: b. 36°

Question 14: Speed Conversion

• Problem: Convert 35 miles per hour to kilometers per minute.
• Options:
    a. 9.40
    b. 0.94
    c. 56.40
    d. 5.64
• Correct Answer: b. 0.94 km/min

Question 15: Baseball Field Distance

• Problem: If each base measures 90 feet apart, how many meters does a batter run for a home run?
• Options:
    a. 90
    b. 100
    c. 120
    d. 110
• Correct Answer: d. 110 meters

Question 16: Water Consumption

• Problem: Average woman needs 11.5 cups of water daily. How much for 30 days in liters?
• Options:
    a. 79
    b. 186
    c. 82
    d. 345
• Correct Answer: c. 82 liters

Question 17: Rectangular Prism Diagonal

• Problem: Given dimensions of a prism, find length of the diagonal.
• Options:
    a. 13.04
    b. 22.9
    c. 13.96
    d. 12.08
• Correct Answer: c. 13.96

Question 18: Tangent Line and Circle

• Problem: A line is tangent to a circle, with arc measures. Find angle measure at point AEC.
• Options:
    a. 50°
    b. 90°
    c. 40°
    d. 70°
• Correct Answer: c. 40°

Question 19: Trapezoid Median

• Problem: In trapezoid ABCD, find the length of the median given various sides.
• Options:
    a. 22
    b. 28
    c. 25
    d. 26.5
• Correct Answer: c. 25

Question 20: Sphere Surface Area

• Problem: A sphere has a surface area of $864 ext{π}$ square inches. Calculate the radius.
• Options:
    a. 11.9
    b. 14.7
    c. 8.2
    d. 6.0
• Correct Answer: b. 14.7 inches

Question 21: Garden Maximization Problem

• Problem: Albert has 800 feet of fencing to create gardens. Maximize area—what dimensions should each section be?
• Options:
    a. 28.3 x 28.3
    b. 50 x 100
    c. 100 x 66.67
    d. 100 x 200
• Correct Answer: c. 100 x 66.67

Question 22: Rhombus Perimeter

• Problem: If a rhombus has diagonals measuring 10cm and 24cm, find the perimeter.
• Options:
    a. 44
    b. 52
    c. 34
    d. 6
• Correct Answer: b. 52 cm

Question 23: Cylinder Volume Calculation

• Problem: Given the circumference and height of a cylinder, calculate its volume.
• Options:
    a. 3233
    b. 1029
    c. 3993
    d. 1452
• Correct Answer: a. 3233 cubic units

Question 24: Cone Radius Calculation

• Problem: The volume of a cone is $1764 ext{π}$ cubic inches, height is 27 inches. Find the radius.
• Options:
    a. 12
    b. 12.5
    c. 14
    d. 14.5
• Correct Answer: a. 12 inches

Question 25: Cone and Cylinder Volume Relationship

• Problem: A cone fits within a cylinder. Compare their volume relationship.
• Options:
    a. 1/2
    b. 1/9
    c. 2/3
    d. 1/3
• Correct Answer: d. 1/3

Question 26: Bus Route Distance

• Problem: Return distance calculation for a journey traveling 88 miles east and 33 miles south.
• Options:
    a. 121 miles
    b. 94 miles
    c. 98 miles
    d. 102 miles
• Correct Answer: b. 94 miles

Question 27: Radio Tower Cable Length Calculation

• Problem: Calculate the length of a cable from the top of a 2080 ft tower to a point 1000 ft away on the ground.
• Options:
    a. 2150 feet
    b. 2200 feet
    c. 2308 feet
    d. 2419 feet
• Correct Answer: c. 2308 feet

Question 28: Triangle Similarity Proof

• Problem: Given parallel lines AD and BC, determine the similarity method for triangles AED and CEB.
• Options:
    a. AA similarity
    b. SAS similarity
    c. SSS similarity
    d. ASS similarity
• Correct Answer: a. AA similarity

Question 29: Tire Longevity Statistics

• Problem: Calculate the probability of tires lasting 75,000 miles or more given standard deviation.
• Options:
    a. 2.5%
    b. 13.5%
    c. 98%
    d. 7.5%
• Correct Answer: a. 2.5%

Question 30: Percentile Rank Calculation

• Problem: Calculate Andrea's percentile for votes received versus competitors.
• Options:
    a. 80%
    b. 85%
    c. 90%
    d. 78%
• Correct Answer: a. 80%

Question 31: Statistical Values Matching

• Problem: Match statistical values with their choices provided.
• Options:
    a. w-3, x-1, z-2
    b. w-2, x-3, z-1
    c. w-3, x-2, z-1
    d. w-1, x-2, z-3
• Correct Answer: b. w-2, x-3, z-1

Question 32: License Plate Calculation

• Problem: Calculate the number of possible vanity license plates consisting of letters and digits.
• Options:
    a. 6,760,000
    b. 6,250,000
    c. 3,628,800
    d. 7,257,600
• Correct Answer: a. 6,760,000

Question 33: Probability with Dice Rolls

• Problem: Determine the probability that a rolled pair of dice sums to either 5 or 7.
• Options:
    a. 2/9
    b. 5/18
    c. 1/6
    d. 11/36
• Correct Answer: b. 5/18

Question 34: Inequality Graph Interpretation

• Problem: Identify the graphed inequality from given options.
• Options:
    a. 2/3 x + 6 ≥ y
    b. x - 6 ≥ y
    c. y ≥ x + 6
    d. y ≤ x - 5
• Correct Answer: c. y ≥ x + 6

Question 35: Inequality Solutions

• Problem: Determine which inequality has Z ≥ 16/3 as a solution.
• Options:
    a. -4 ≥ -3/4 z
    b. -4 < -3/4 z
    c. -4 ≤ -3/4 z
    d. 4 ≥ 3/4 z
• Correct Answer: a. -4 ≥ -3/4 z

Question 36: Solve for x in Equation

• Problem: Solve rac{x+3}{2} = rac{4x}{9} for x.
• Options:
    a. -12
    b. 9
    c. -27
    d. 10
• Correct Answer: c. -27

Question 37: Circle Center from Equation

• Problem: Find the center of a circle given its equation: $x^2 + y^2 - 8x - 4y + 4 = 0$.
• Options:
    a. (8, 4)
    b. (4, 8)
    c. (4, 2)
    d. (2, 4)
• Correct Answer: c. (4, 2)

Question 38: Expression Simplification Exclusion

• Problem: When simplifying $rac{x^2 + 4x + 3}{x^2 - 2x - 3}$, which value should be excluded?
• Options:
    a. -3, -1
    b. 3, -1
    c. -3
    d. 1
• Correct Answer: b. 3, -1

Question 39: Function Evaluation

• Problem: For the function $f(x) = ext{√}(x^5)$, calculate $f(125)$. The options:
• Options:
    a. 5
    b. √5
    c. 5√5
    d. 1/5
• Correct Answer: a. 5

Question 40: Direct Variation Problem

• Problem: Y varies directly as √x. At x = 49, y = 14. Determine y when x = 20.
• Options:
    a. 2√5
    b. 54.8
    c. 7
    d. 4√5
• Correct Answer: d. 4√5

Question 41: Linear Points Truth Condition

• Problem: Consider the points (2, -3), (4, -2), (6, y), and (x, 0). Determine valid x and y values.
• Options:
    a. y = 8; x = -1
    b. y = -1; x=8
    c. y = -2, x = 8
    d. y = 2, x = 4
• Correct Answer: b. y = -1; x = 8

Question 42: X-Intercept Calculation

• Problem: Find the x-intercept of the line $2x + 3.5y = 7$.
• Options:
    a. (0, 2)
    b. (3.5, 0)
    c. (3.5, 2)
    d. (2, 0)
• Correct Answer: b. (3.5, 0)

Question 43: Slope Calculation

• Problem: Calculate the slope between points (-4, 3) and (2, 5).
• Options:
    a. 3
    b. -3
    c. 1/3
    d. -1/3
• Correct Answer: c. 1/3

Question 44: Equation Value of x

• Problem: Determine the value of x in the equation: $32 = 4^x$.
• Options:
    a. 5/3
    b. 5/2
    c. 8
    d. 8/3
• Correct Answer: b. 5/2

Question 45: Expression: y/z Calculation

• Problem: Given $rac{xy}{z} = 73$ and $X = 49$, find y/z value making the statement true.
• Options:
    a. 2/3
    b. 3/2
    c. 3/4
    d. 5/4
• Correct Answer: b. 3/2

Question 46: Polynomial Expansion Coefficient

• Problem: Expand $(x + 4)^7$ and find the coefficient of the fourth term.
• Options:
    a. 1200
    b. 1344
    c. 2240
    d. 8960
• Correct Answer: c. 2240

Question 47: Quadratic X-Intercepts

• Problem: Determine x-intercepts for the quadratic function $f(x) = -(x + 2)^2 - 1$.
• Options:
    a. (5, 0) and (-1, 0)
    b. No x-intercepts
    c. (2, 0) and (-1, 0)
    d. (-1, 0)
• Correct Answer: b. No x-intercepts

Question 48: Quadratic Factor Analysis

• Problem: If one factor is $(x - 1)$, what could be the other factor for a perfect square trinomial?
• Options:
    a. x - 1
    b. x
    c. $x^2 - 2x + 1$
    d. $x^2 - 1$
• Correct Answer: c. $x^2 - 2x + 1$

Question 49: Equation Representation

• Problem: Identify the correct equation representation.
• Options:
    a. $f(x) = |x - 3|$
    b. $f(x) = x^2 + 6x + 9$
    c. $f(x) = (x - 3)^2$
    d. $f(x) = (x + 3)^2$
• Correct Answer: c. $f(x) = (x - 3)^2$

Question 50: Simplification Result

• Problem: Simplify $ext{√}200 ext{√}32$. What is the denominator?
• Options:
    a. 2
    b. 1
    c. 3
    d. 4
• Correct Answer: b. 1

TIEBREAKERS

Question 51: Sphere Volume Calculation

• Problem: If the volume of a sphere is 682 rac{2}{3} ext{π}, what is its radius?
• Options:
    a. 8
    b. 6
    c. 7.8
    d. 8.2
• Correct Answer: a. 8

Question 52: Probability Rain and Umbrella

• Problem: The probability of rain is 68%, Susan forgetting her umbrella is 40%. Find the probability she gets wet.
• Options:
    a. 19.2%
    b. 1.08%
    c. 27.2%
    d. 54%
• Correct Answer: c. 27.2%

Question 53: Problems Range Representation

• Problem: Amar averages 60 problems daily; variation is ±10 problems. Which inequality represents this?
• Options:
    a. $|q - 60| ≤ 10$
    b. $|q| - 60 ≤ 10$
    c. $|q - 60| ≥ 10$
    d. $|q| - 60 ≥ 10$
• Correct Answer: a. $|q - 60| ≤ 10$

Question 54: Volume Capacity Calculation

• Problem: Calculate sand volume in a prism after inserting a pipe.
• Options:
    a. 2609
    b. 2992
    c. 2708
    d. 2845
• Correct Answer: b. 2992 cubic inches

Question 55: Polynomial Division Remainder

• Problem: Find the remainder of $rac{x^5 - 7x^3 - x^2 - 18x + 9}{(x + 3)}$.
• Options:
    a. 0
    b. 1
    c. 2
    d. ½
• Correct Answer: a. 0

Question 56: Triangle Perimeter Calculation

• Problem: Determine the perimeter of a triangle defined by the vertices (-3, 6), (-4, 2), and (6, -4).
• Options:
    a. 25.73 units
    b. 33.33 units
    c. 23.06 units
    d. 29.24 units
• Correct Answer: a. 25.73 units

Question 57: Inverse Variation Function

• Problem: Identify the function for inverse variation where x = 3 and y = 19.
• Options:
    a. f(x) = rac{57}{x}
    b. $f(x) = 57x$
    c. $f(x) = x + 57$
    d. $f(x) = |57 - x|$
• Correct Answer: a. f(x) = rac{57}{x}

Question 58: Butterfly Population Growth

• Problem: Given the formula $P(t) = P_0 (2^{t/3})$ for butterfly population growth, determine years needed for population to reach 1600 from 100.
• Options:
    a. 9
    b. 12
    c. 15
    d. 18
• Correct Answer: b. 12

Question 59: Quadratic Roots Derivation

• Problem: A quadratic equation with roots’ sum = -6 and product = -55; find the two roots.
• Options:
    a. 5, -11
    b. -5, 11
    c. rac{55}{6}, -rac{55}{6}
    d. -55, 1
• Correct Answer: a. 5, -11

Question 60: Functional Composition Evaluation

• Problem: Find $(f ∘ g)(36)$ where $f(x) = x^2 - 5x$ and $g(x) = ext{√}x$.
• Options:
    a. 6
    b. 33.4
    c. 5
    d. 36
• Correct Answer: a. 6