Semester 3B · Original public practice · Internally reviewed; external trial pending
Complete worked solutions
Detailed explanations for the cumulative review and practice examination.
Complete worked solutions for all original Semester 3B review and exam questions. Keep this page separate while students attempt the exam.
Review answer key
3B-REVIEW-001 · 48
5 × 8 = 40. One additional group contains 8, giving 40 + 8 = 48.
Related competency: MATH-3B-C08-L01
3B-REVIEW-002 · 42
(5 × 6) + (2 × 6) = 30 + 12 = 42. Both parts represent all seven groups.
Related competency: MATH-3B-C08-L02
3B-REVIEW-003 · 54
6 × (10 − 1) = 60 − 6 = 54; or (5 × 9) + 9 = 45 + 9 = 54. Both partition the same groups.
Related competency: MATH-3B-C08-L03
3B-REVIEW-004 · 12
Because 7 × 12 = 84, each group contains 84 ÷ 7 = 12.
Related competency: MATH-3B-C08-L04
3B-REVIEW-005 · 56
4 × 7 = 28. Doubling the number of groups doubles the total: 28 + 28 = 56.
Related competency: MATH-3B-C08-L06
3B-REVIEW-006 · 72
10 × 8 = 80. Remove one group of 8: 80 − 8 = 72.
Related competency: MATH-3B-C08-L07
3B-REVIEW-007 · 72 books
Eight equal groups of nine give 8 × 9 = 72 books. An 8-by-9 array has the same 72 cells.
Related competency: MATH-3B-C08-L08
3B-REVIEW-008 · 9 full boxes; 3 pencils remain
8 × 9 = 72, and 75 − 72 = 3. The remainder 3 is less than 8.
Related competency: MATH-3B-C08-L09
3B-REVIEW-009 · 3/8
The whole has eight equal parts, so the denominator is 8; three are shaded, so the numerator is 3.
Related competency: MATH-3B-C09-L01
3B-REVIEW-010 · 3/5
Each step is 1/5 of the unit interval; three equal steps from zero reach 3/5.
Related competency: MATH-3B-C09-L02
3B-REVIEW-011 · 5/9 < 7/9
Both fractions refer to ninths of the same-sized whole, and five ninths is less than seven ninths.
Related competency: MATH-3B-C09-L03
3B-REVIEW-012 · 3/5
If the whole is the same size, fifths are larger pieces than eighths. Three larger fifth-pieces make more than three eighth-pieces.
Related competency: MATH-3B-C09-L04
3B-REVIEW-013 · 3 cells; 3/6
Half of six equal cells is three cells. Thus 1/2 and 3/6 describe the same portion of the same whole.
Related competency: MATH-3B-C10-L01
3B-REVIEW-014 · 9/12
Multiply the denominator by 3, so also multiply the numerator by 3: 3 × 3 = 9. Same amount, smaller named parts.
Related competency: MATH-3B-C10-L02
3B-REVIEW-015 · 2/3
Divide numerator and denominator by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. No common factor greater than 1 remains.
Related competency: MATH-3B-C10-L03
3B-REVIEW-016 · 3/4 > 5/8
3/4 = 6/8. Six eighths is greater than five eighths.
Related competency: MATH-3B-C10-L04
3B-REVIEW-017 · 5/6 > 7/9
5/6 = 15/18 and 7/9 = 14/18. Therefore 5/6 is larger by 1/18.
Related competency: MATH-3B-C10-L05
3B-REVIEW-018 · 4/5
3 tenths + 5 tenths = 8/10. Divide top and bottom by 2 to get 4/5.
Related competency: MATH-3B-C10-L07
3B-REVIEW-019 · 3/4
Rename 1/2 as 2/4, then 2/4 + 1/4 = 3/4. The whole is divided consistently into fourths.
Related competency: MATH-3B-C10-L08
3B-REVIEW-020 · 435 cm
Four meters is 4×100 = 400 cm. Add 35 cm to get 435 cm.
Related competency: MATH-3B-C11-L01
3B-REVIEW-021 · 4 m 37 cm
Exchange one meter for 100 cm: 5 m 12 cm = 4 m 112 cm. Subtract 75 cm to leave 4 m 37 cm.
Related competency: MATH-3B-C11-L02
3B-REVIEW-022 · 3,450 m
One kilometer is 1,000 m; 3,000 m + 450 m = 3,450 m.
Related competency: MATH-3B-C11-L03
3B-REVIEW-023 · 5 km 255 m
Regroup 6 km 40 m as 5 km 1,040 m. Then 1,040−785=255 m, giving 5 km 255 m.
Related competency: MATH-3B-C11-L04
3B-REVIEW-024 · 2,350 mL
2 liters = 2,000 mL; add 350 mL to obtain 2,350 mL.
Related competency: MATH-3B-C11-L05
3B-REVIEW-025 · 4,090 g
Four kilograms = 4,000 g, and 4,000 + 90 = 4,090 g.
Related competency: MATH-3B-C11-L06
3B-REVIEW-026 · 2 L 350 mL
3,200 mL − 850 mL = 2,350 mL = 2 L 350 mL. Convert to one unit before subtracting.
Related competency: MATH-3B-C11-L07
3B-REVIEW-027 · 10 cm
A diameter passes through the center between two boundary points, so it is twice the radius: 2×5=10 cm.
Related competency: MATH-3B-C12-L01
3B-REVIEW-028 · Smaller (acute)
A right angle is 90°, and 65° < 90°. Ray length does not affect angle size.
Related competency: MATH-3B-C12-L02
3B-REVIEW-029 · Acute; right; obtuse
35° is less than 90°, 90° is exactly a right angle, and 130° is between 90° and 180°.
Related competency: MATH-3B-C12-L03
3B-REVIEW-030 · Isosceles triangle
Exactly two lengths match (6 and 6), so the triangle is isosceles; the third side is different.
Related competency: MATH-3B-C12-L04
3B-REVIEW-031 · True under that inclusive definition
An equilateral triangle has three equal sides, so it certainly has at least two equal sides. Naming conventions may distinguish “exactly two” in some classrooms.
Related competency: MATH-3B-C12-L05
3B-REVIEW-032 · Yes
A rectangle has four right angles. A square has four right angles and four equal sides, so it satisfies the rectangle definition.
Related competency: MATH-3B-C12-L06
3B-REVIEW-033 · A circle centered at O, with a labeled 3 cm radius
Keep the compass point fixed at O and its opening at 3 cm. Every boundary point is 3 cm from O. Label one segment from O to the boundary as 3 cm.
Related competency: MATH-3B-C12-L07
3B-REVIEW-034 · 20 square units
Each of 5 rows contains 4 tiles; 5×4=20 equal square units cover the region without gaps.
Related competency: MATH-3B-C13-L01
3B-REVIEW-035 · 18 cm²
3×6=18 tiles, each measuring 1 square centimeter. Area is 18 cm², not 18 cm.
Related competency: MATH-3B-C13-L02
3B-REVIEW-036 · 36 cm²
Nine columns of four square centimeters, or 9×4, give 36 cm².
Related competency: MATH-3B-C13-L03
3B-REVIEW-037 · 42 square units
Outer area 8×6 = 48. Remove the missing area 3×2 = 6. Result 48−6=42 square units.
Related competency: MATH-3B-C13-L04
3B-REVIEW-038 · 16 cm
Perimeter adds the outside edges: 5+3+5+3 = 16 cm. It is a length.
Related competency: MATH-3B-C13-L06
3B-REVIEW-039 · 36 m
Perimeter = 2(11+7) = 2×18 = 36 m, adding all four sides.
Related competency: MATH-3B-C13-L07
3B-REVIEW-040 · Same area 24; perimeters 22 and 20
Areas: 3×8=24 and 4×6=24. Perimeters: 2(3+8)=22 and 2(4+6)=20. Equal area need not give equal perimeter.
Related competency: MATH-3B-C13-L08
3B-REVIEW-041 · 205 seconds
Three minutes is 3×60=180 seconds; add 25 to obtain 205 seconds.
Related competency: MATH-3B-C14-L01
3B-REVIEW-042 · 45 minutes
From 9:20 to 10:00 is 40 min; from 10:00 to 10:05 is 5 min; total 45 min.
Related competency: MATH-3B-C14-L02
3B-REVIEW-043 · 5:50 p.m.
Add one hour to 5:15 p.m., then 35 minutes to 5:50 p.m.
Related competency: MATH-3B-C14-L04
3B-REVIEW-044 · 40 minutes
11:50 a.m. to noon is 10 min, and noon to 12:30 p.m. is 30 min. Total 40 min.
Related competency: MATH-3B-C14-L05
3B-REVIEW-045 · 65 minutes (1 hour 5 minutes)
The complete schedule includes both reading periods and the rest: 25+10+30=65 minutes.
Related competency: MATH-3B-C14-L06
3B-REVIEW-046 · $4.07
There are 100 cents in a dollar. Seven cents is 07 in the two cent places, so $4.07 rather than $4.70.
Related competency: MATH-3B-C15-L01
3B-REVIEW-047 · $3.15
$6.85→$7.00 adds $0.15; $7.00→$10.00 adds $3.00, so total $3.15.
Related competency: MATH-3B-C15-L02
3B-REVIEW-048 · $16.23
48 cents + 75 cents = 123 cents = $1.23. Dollars 12+3+1=16; total $16.23.
Related competency: MATH-3B-C15-L03
3B-REVIEW-049 · $12.14
Rename $20.00 as $19 and 100 cents. 100−86=14 cents, 19−7=12 dollars, giving $12.14.
Related competency: MATH-3B-C15-L04
3B-REVIEW-050 · $23.80
Total spent $13.45+$2.75=$16.20. Subtract $40.00−$16.20=$23.80.
Related competency: MATH-3B-C15-L05
3B-REVIEW-051 · 50
The eight rows hold 8×7=56 seats in total. Six seats are empty, so 56−6=50 people are seated.
Related competency: MATH-3B-C08-L06, MATH-3B-C08-L08
3B-REVIEW-052 · 108
10×12=120; remove one twelve: 120−12=108.
Related competency: MATH-3B-C08-L07
3B-REVIEW-053 · 10 groups and 3 extra
83 = 8×10 + 3; the remainder is less than 8.
Related competency: MATH-3B-C08-L09
3B-REVIEW-054 · 6/10
Six of ten same-sized parts is six tenths; unequal pieces would not each be one tenth.
Related competency: MATH-3B-C09-L01
3B-REVIEW-055 · 4/7 > 4/9
Sevenths are larger pieces than ninths, and both amounts have four pieces.
Related competency: MATH-3B-C09-L04
3B-REVIEW-056 · Ninth tick; by 5/12
Positions are 4/12 and 9/12. Subtract 9/12−4/12=5/12 of the unit.
Related competency: MATH-3B-C09-L02, MATH-3B-C09-L03
3B-REVIEW-057 · 5/6
Five of six equal parts are shaded. Five and six share no factor >1.
Related competency: MATH-3B-C10-L07
3B-REVIEW-058 · 3/8
One whole is 8/8. The missing part is 8/8−5/8 = 3/8, because the two amounts must combine to a whole.
Related competency: MATH-3B-C10-L07
3B-REVIEW-059 · 5/6
The parts need a common size: 2/3 = 4/6. Then 4/6+1/6=5/6. Adding denominators is invalid.
Related competency: MATH-3B-C10-L08
3B-REVIEW-060 · 4 L 400 mL
First convert 5 L 150 mL to 5,150 mL. Subtract 750 mL to get 4,400 mL, which is 4 L 400 mL.
Related competency: MATH-3B-C11-L05, MATH-3B-C11-L07
3B-REVIEW-061 · 1 kg 225 g
Convert both to grams: 3 kg 25 g = 3,025 g and 1 kg 800 g = 1,800 g. Their difference is 1,225 g = 1 kg 225 g.
Related competency: MATH-3B-C11-L06
3B-REVIEW-062 · 3,430 m
First distance is 2,080 m. Add 2,080+1,350=3,430 m.
Related competency: MATH-3B-C11-L03, MATH-3B-C11-L07
3B-REVIEW-063 · Square
A square satisfies both the rectangle condition (four right angles) and rhombus condition (four equal sides).
Related competency: MATH-3B-C12-L06
3B-REVIEW-064 · Scalene
All three side lengths differ, so it is scalene. The lengths also satisfy the triangle inequality, since 5+7>9.
Related competency: MATH-3B-C12-L04
3B-REVIEW-065 · 8 cm
That segment is a diameter, twice the 4 cm radius: 8 cm.
Related competency: MATH-3B-C12-L01, MATH-3B-C12-L07
3B-REVIEW-066 · 40 m² and 26 m
Area=8×5=40 m². Perimeter=2(8+5)=26 m.
Related competency: MATH-3B-C13-L03, MATH-3B-C13-L07
3B-REVIEW-067 · 30 square units
Whole 9×4=36. Corner cutout 2×3=6. Remaining area=36−6=30.
Related competency: MATH-3B-C13-L04
3B-REVIEW-068 · Areas 25 and 27; perimeters 20 and 24
5×5=25; 3×9=27. Perimeters are 4×5=20 and 2(3+9)=24.
Related competency: MATH-3B-C13-L08
3B-REVIEW-069 · 12:15 p.m.
80 minutes is 1 h 20 min. 10:55 a.m. + 1 h =11:55 a.m.; +20 min reaches 12:15 p.m.
Related competency: MATH-3B-C14-L04, MATH-3B-C14-L05
3B-REVIEW-070 · 54 hours
Each day is 24 hours, so two days = 48 hours. Add another 6 hours: 48+6 = 54 hours.
Related competency: MATH-3B-C14-L01
3B-REVIEW-071 · 4:45 p.m.
35+10+20=65 minutes = 1 h 5 min. Start 3:40 p.m., finish 4:45 p.m.
Related competency: MATH-3B-C14-L06
3B-REVIEW-072 · $3.45
Total spent $6.55; subtract from $10.00 to obtain $3.45.
Related competency: MATH-3B-C15-L03, MATH-3B-C15-L05
3B-REVIEW-073 · 99 cents
The dollar amounts have the same whole-dollar part. Subtract $9.00 from $9.99 to get $0.99, which is 99 cents.
Related competency: MATH-3B-C15-L01, MATH-3B-C15-L04
3B-REVIEW-074 · $15.90
2×$6.75=$13.50; add $2.40 to get $15.90.
Related competency: MATH-3B-C15-L05
Examination answer key
3B-EXAM-001 · 42 chairs
Five groups of 7 give 35 chairs; another group adds 7, so 35 + 7 = 42.
Related competency: MATH-3B-C08-L01
3B-EXAM-002 · 56 plants
Four rows have 4 × 8 = 32 plants; three rows have 3 × 8 = 24. Together 32 + 24 = 56.
Related competency: MATH-3B-C08-L02
3B-EXAM-003 · No; 7 × 8 = 7 × 5 + 7 × 3 = 56
The groups must have the same factor 7 in both pieces: 7 × (5+3) = 35+21 = 56. The proposed second term, 8 × 3, changes the quantity.
Related competency: MATH-3B-C08-L03
3B-EXAM-004 · 13 stacks
91 ÷ 7 = 13; 13 × 7 = 91, with no books remaining.
Related competency: MATH-3B-C08-L04
3B-EXAM-005 · 72
2 × 9 = 18; doubling gives 4 × 9 = 36; doubling again gives 8 × 9 = 72.
Related competency: MATH-3B-C08-L06
3B-EXAM-006 · 63
Ten sevens is 70; remove one seven to make nine sevens: 70 − 7 = 63.
Related competency: MATH-3B-C08-L07
3B-EXAM-007 · 8 × 6 is larger by 3
Eight sixes is 48; nine fives is 45. Their difference is 48 − 45 = 3.
Related competency: MATH-3B-C08-L08
3B-EXAM-008 · 9 minibuses
74 ÷ 9 = 8 remainder 2. Eight full minibuses carry 72 children; two remain, requiring a ninth minibus.
Related competency: MATH-3B-C08-L09
3B-EXAM-009 · 4/6
Four of six equal pieces are colored. The unit fraction 1/6 is the amount in one of those six equal pieces.
Related competency: MATH-3B-C09-L01
3B-EXAM-010 · 6/8 (equivalent to 3/4)
Eight equal intervals span 0 to 1. Each tick adds 1/8, so the sixth tick is 6/8. Counting intervals—not just interior tick marks—sets the denominator.
Related competency: MATH-3B-C09-L02
3B-EXAM-011 · 9/11, by 5/11
With the same whole and denominator, compare numerators: 9 > 4. Difference = (9−4)/11 = 5/11.
Related competency: MATH-3B-C09-L03
3B-EXAM-012 · 2/7 < 2/5 < 2/3
All have numerator 2. Splitting the same whole into more equal parts makes each part smaller; sevenths are smallest and thirds largest.
Related competency: MATH-3B-C09-L04
3B-EXAM-013 · Each equals the same quantity
Dividing each of the three equal thirds into two equal parts creates six parts; four sixths covers the same interval as two thirds.
Related competency: MATH-3B-C10-L01
3B-EXAM-014 · 10/16 and 15/24
5/8 = (5×2)/(8×2) = 10/16, and (5×3)/(8×3) = 15/24. Multiplying by 1 in fractional form preserves the value.
Related competency: MATH-3B-C10-L02
3B-EXAM-015 · 2/3
Subtracting equal amounts does not preserve a fraction. Divide both by their common factor 5 instead: 10/15 = 2/3.
Related competency: MATH-3B-C10-L03
3B-EXAM-016 · 3/4
4/6 = 8/12; 3/4 = 9/12. Nine twelfths is greater than eight twelfths.
Related competency: MATH-3B-C10-L04
3B-EXAM-017 · No; 4/7 < 3/5
4/7 = 20/35; 3/5 = 21/35. Fractions are not ordered by denominator size alone.
Related competency: MATH-3B-C10-L05
3B-EXAM-018 · 1/3 L
9/12 − 5/12 = 4/12 = 1/3 L; subtract like-sized twelfths.
Related competency: MATH-3B-C10-L07
3B-EXAM-019 · 5/8 m
1/4 = 2/8; subtract 7/8 − 2/8 = 5/8 m. The fractions refer to the same-sized meter whole.
Related competency: MATH-3B-C10-L08
3B-EXAM-020 · 2 m 78 cm
Two complete groups of 100 cm are 2 meters, leaving 78 cm.
Related competency: MATH-3B-C11-L01
3B-EXAM-021 · 2 m 52 cm
3 m 8 cm = 2 m 108 cm. Then 108−56=52 cm, so 2 m 52 cm remains.
Related competency: MATH-3B-C11-L02
3B-EXAM-022 · 5 km 26 m
5 groups of 1,000 m make 5 km, with 26 m remaining.
Related competency: MATH-3B-C11-L03
3B-EXAM-023 · 3 km 440 m
4 km 90 m = 3 km 1,090 m; 1,090−650=440 m, so 3 km 440 m remains.
Related competency: MATH-3B-C11-L04
3B-EXAM-024 · 3 L 75 mL
Three thousands of milliliters are 3 L, with 75 mL remaining.
Related competency: MATH-3B-C11-L05
3B-EXAM-025 · 2 kg 640 g
Two complete 1,000 g units are 2 kg; 640 g remain.
Related competency: MATH-3B-C11-L06
3B-EXAM-026 · 3 m 63 cm
175 cm + 248 cm = 423 cm; 423−60=363 cm = 3 m 63 cm.
Related competency: MATH-3B-C11-L07
3B-EXAM-027 · Radii 4 cm and 7 cm; second circle is larger
Each radius is half the diameter. The second radius is larger, so its circle is larger.
Related competency: MATH-3B-C12-L01
3B-EXAM-028 · Yes, obtuse
Angle size is the amount of turn between rays. A 120° turn is greater than 90° and less than 180°, regardless of ray lengths.
Related competency: MATH-3B-C12-L02
3B-EXAM-029 · Right angle, 90°
A square corner provides a right-angle reference, which is precisely a quarter turn of 360° or 90°.
Related competency: MATH-3B-C12-L03
3B-EXAM-030 · Equilateral; three equal angles
All three sides are equal, so it is equilateral. In Euclidean geometry its three interior angles are equal (each 60°).
Related competency: MATH-3B-C12-L04
3B-EXAM-031 · Those two angles are equal
In a triangle, equal sides face equal interior angles. This property is independent of the triangle’s orientation.
Related competency: MATH-3B-C12-L05
3B-EXAM-032 · Rhombus yes; square no
A rhombus has four equal sides. A square also requires four right angles, which this quadrilateral lacks.
Related competency: MATH-3B-C12-L06
3B-EXAM-033 · Two circles drawn around one center O; radii correctly labeled 2 cm and 4 cm
Mark O and keep the compass point fixed at O. Draw the first circle with a 2 cm opening, then draw the second with a 4 cm opening. Label radii from O to both boundaries. Both circles must share O.
Related competency: MATH-3B-C12-L07
3B-EXAM-034 · No; tiles must cover the region without gaps or overlaps
An overlapping tile double-counts some area, while an uncovered corner is not measured at all. Arrange equal square tiles to cover the region exactly once, without gaps or overlaps, before counting.
Related competency: MATH-3B-C13-L01
3B-EXAM-035 · 24 cm²
The child counted two-dimensional squares, so the unit must be square centimeters (cm²), not a length unit.
Related competency: MATH-3B-C13-L02
3B-EXAM-036 · 8 m
Rectangle area = length × width. Divide 48 m² by 6 m to get 8 m.
Related competency: MATH-3B-C13-L03
3B-EXAM-037 · 38 m²
First region 5×4=20 m²; second 3×6=18 m². They do not overlap, so sum 20+18=38 m².
Related competency: MATH-3B-C13-L04
3B-EXAM-038 · No; perimeter is 22 cm
4×7=28 cm² is area. Perimeter = 4+7+4+7 = 22 cm around the boundary.
Related competency: MATH-3B-C13-L06
3B-EXAM-039 · 9 cm
Half the perimeter is length + width = 15 cm; subtract width 6 cm to get length 9 cm.
Related competency: MATH-3B-C13-L07
3B-EXAM-040 · 16 and 24 square units
Both perimeters equal 2(2+8)=20 and 2(4+6)=20. Areas differ: 2×8=16 and 4×6=24. Equal perimeter need not give equal area.
Related competency: MATH-3B-C13-L08
3B-EXAM-041 · 17 days
Two weeks equals 2×7=14 days; 14+3=17 days.
Related competency: MATH-3B-C14-L01
3B-EXAM-042 · 47 minutes
2:35→3:00 takes 25 min; 3:00→3:22 takes 22 min; total 47 min.
Related competency: MATH-3B-C14-L02
3B-EXAM-043 · 10:15 a.m.
Count backward 10 minutes to 11:00 a.m. and another 45 minutes to 10:15 a.m.
Related competency: MATH-3B-C14-L04
3B-EXAM-044 · 45 minutes
11:35 p.m.→midnight takes 25 min; midnight→12:20 a.m. takes 20 min; total 45 min.
Related competency: MATH-3B-C14-L05
3B-EXAM-045 · 3:15 p.m.
Total duration = 40+15+35 = 90 min (1 h 30 min); 1:45 p.m. + 90 min = 3:15 p.m.
Related competency: MATH-3B-C14-L06
3B-EXAM-046 · $6.35
Six groups of 100 cents make $6, and 35 cents remain: $6.35.
Related competency: MATH-3B-C15-L01
3B-EXAM-047 · $5.24
$10.00−$4.76=$5.24; check $4.76+$5.24=$10.00.
Related competency: MATH-3B-C15-L02
3B-EXAM-048 · $15.63
Align dollars and cents: 8.95+6.68=15.63. The cents total $1.63, so regroup one dollar.
Related competency: MATH-3B-C15-L03
3B-EXAM-049 · $12.27
In cents: 1,505−278 = 1,227 cents = $12.27. Exchange one dollar to handle the cents.
Related competency: MATH-3B-C15-L04
3B-EXAM-050 · $12.50
Cost = $18.75+$18.75=$37.50; $50.00−$37.50=$12.50 change.
Related competency: MATH-3B-C15-L05
3B-EXAM-051 · 6 complete rows and 6 extra
6×9=54 students; 54 ÷ 8 = 6 remainder 6. The remainder cannot fill another complete row.
Related competency: MATH-3B-C08-L01, MATH-3B-C08-L09
3B-EXAM-052 · 5/6
With five pieces, sixth-pieces are larger than eighth-pieces; 5/6 > 5/8.
Related competency: MATH-3B-C09-L04
3B-EXAM-053 · 7/8 L
1/2 = 4/8. Add 4/8+3/8=7/8 L. The denominators represent consistent equal units.
Related competency: MATH-3B-C10-L02, MATH-3B-C10-L08
3B-EXAM-054 · 1 kg 375 g
4,000 g−1,650 g−975 g=1,375 g=1 kg 375 g.
Related competency: MATH-3B-C11-L06, MATH-3B-C11-L07
3B-EXAM-055 · They are the same size
The circle with 10 cm diameter has radius 5 cm, so both have the same radius. For circles, equal radius means equal size.
Related competency: MATH-3B-C12-L01
3B-EXAM-056 · Same grass area; first needs more fencing
Areas 36 m² for both. Perimeters 2(4+9)=26 m and 2(6+6)=24 m; first uses 2 more meters of fence.
Related competency: MATH-3B-C13-L03, MATH-3B-C13-L07, MATH-3B-C13-L08
3B-EXAM-057 · 32 minutes
Total elapsed 12 minutes to midnight + 27 minutes after midnight =39 minutes; subtract 7 minutes stationary =32 minutes moving.
Related competency: MATH-3B-C14-L05, MATH-3B-C14-L06
3B-EXAM-058 · $11.95
Start with $25.00; subtract $8.85 and $7.70 to get $8.45; add $3.50 to get $11.95.
Related competency: MATH-3B-C15-L03, MATH-3B-C15-L04, MATH-3B-C15-L05