R001 — Chapter 10
Answer: 4,085 m; 3 L 250 mL
Reasoning: Each kilometer is 1,000 meters: 4,000+85=4,085. One liter is 1,000 mL, so 3,250 mL is 3 L plus 250 mL.
Semester 4B — Worked Solutions
All 64 cumulative-review and 60 practice-exam items · complete answer explanations · exam marking criteria
Review solutions
R002 — Chapter 10
Answer: 8 ft; 96 in
Reasoning: Two yards is 6 ft; add 2 ft to make 8 ft; multiply by 12 to obtain 96 inches.
R003 — Chapter 10
Answer: 55 oz; the first bag, by 12 oz
Reasoning: 3×16+7=55 oz, and 55−43=12 oz.
R004 — Chapter 10
Answer: 10 cups
Reasoning: Each quart is 4 cups and each pint is 2 cups; 2×4+2=10 cups.
R005 — Chapter 10
Answer: 4 min 10 s
Reasoning: 2 min 35 s =155 s; 155+95=250 s =4 min 10 s.
R006 — Chapter 10
Answer: 75 cm; the whole is one meter
Reasoning: One whole meter is 100 cm. Three of its four equal quarters are 75 cm.
R007 — Chapter 10
Answer: 3,750 mL
Reasoning: A quarter of 6,000 mL is 1,500 mL. Subtract 1,500+750 from 6,000 to get 3,750 mL.
R008 — Chapter 11
Answer: 28 square units
Reasoning: There are four rows of seven equal unit squares (or seven columns of four). 7×4=28.
R009 — Chapter 11
Answer: 9 cm
Reasoning: Area = length×width; 54÷6=9 cm.
R010 — Chapter 11
Answer: 48 m²
Reasoning: The full rectangle is 54 m²; subtract the missing 6 m²: 48 m².
R011 — Chapter 11
Answer: 30 cm
Reasoning: 11+4+11+4=30 centimeters, not square centimeters.
R012 — Chapter 11
Answer: 26 m
Reasoning: Add all six exterior edges: 8+2+5+3+3+5=26 m.
R013 — Chapter 12
Answer: 7/10; 0.7
Reasoning: Seven of ten equal parts represent 7/10 of one whole, written 0.7.
R014 — Chapter 12
Answer: 0.9
Reasoning: Divide the whole interval into ten equal steps; 0.9 is nine steps from 0, farther right.
R015 — Chapter 12
Answer: 0.34; three tenths and four hundredths
Reasoning: 34 hundredths can be grouped as 30 hundredths and 4 hundredths.
R016 — Chapter 12
Answer: Both represent 6 tenths or 60 hundredths
Reasoning: Every tenth is 10 hundredths, so 6×10 = 60 hundredths. Appending zero does not change the value.
R017 — Chapter 12
Answer: 9/20
Reasoning: 0.45=45/100. Divide numerator and denominator by 5 to get 9/20.
R018 — Chapter 12
Answer: 0.75; 0.35
Reasoning: 3/4=75/100=0.75; 7/20=35/100=0.35.
R019 — Chapter 12
Answer: 0.68 < 0.7 < 0.75 < 0.8
Reasoning: Rename as hundredths: 68, 70, 75, 80 hundredths.
R020 — Chapter 12
Answer: 6.5; it lies between 6.4 and 6.5
Reasoning: 6.47 is 0.07 above 6.4 and 0.03 below 6.5; therefore it rounds to 6.5.
R021 — Chapter 13
Answer: 6.9; 3.5
Reasoning: Add or subtract ones and tenths: 46 tenths +23 tenths =69 tenths; 87−52 tenths=35 tenths.
R022 — Chapter 13
Answer: 9.5; 15 tenths regroup as 1 whole 5 tenths
Reasoning: 8 tenths+7 tenths=15 tenths; regroup 10 tenths as 1, then add the ones.
R023 — Chapter 13
Answer: 4.6
Reasoning: Rename 8.2 as 7 ones and 12 tenths; 12−6=6 tenths and 7−3=4 ones.
R024 — Chapter 13
Answer: 11.15
Reasoning: Hundredths 8+7=15; tenths 4+6+1=11; ones 7+3+1=11, giving 11.15.
R025 — Chapter 13
Answer: 0.33; 0.06
Reasoning: Rewrite as 1.00−0.67 and 0.10−0.04 to align place values.
R026 — Chapter 13
Answer: 4.17
Reasoning: Regroup 9.02 as 8 ones, 9 tenths, and 12 hundredths; subtract 4.85 to get 4.17.
R027 — Chapter 13
Answer: $4.36
Reasoning: Total is $5.64; subtract from $10.00 to get $4.36.
R028 — Chapter 14
Answer: 0.56
Reasoning: Eight hundredths taken seven times gives 56 hundredths, 0.56.
R029 — Chapter 14
Answer: 14.4
Reasoning: Six groups of 2 ones 4 tenths =12 ones+24 tenths=14.4.
R030 — Chapter 14
Answer: 30 m; about 24 to 36 m is reasonable
Reasoning: 1.25×(20+4)=25+5=30 m. An estimate such as 1.2×25≈30 checks the result.
R031 — Chapter 14
Answer: 0.09
Reasoning: 72 hundredths ÷8 =9 hundredths in each group.
R032 — Chapter 14
Answer: 2.4 L
Reasoning: 9.6 L ÷4 =2.4 L. Multiply 2.4×4 to check 9.6.
R033 — Chapter 14
Answer: 1.72
Reasoning: Divide 5 ones among 3; regroup remaining 2 ones into tenths, then regroup tenths as needed: 1.72.
R034 — Chapter 14
Answer: $3.90
Reasoning: 2,340 cents divided by 6 is 390 cents, or $3.90.
R035 — Chapter 15
Answer: No; ray length does not determine angle magnitude
Reasoning: The turning amount between the rays stays unchanged when a ray is lengthened.
R036 — Chapter 15
Answer: 65°
Reasoning: Center the protractor on the vertex, align 0° with the baseline, and read the matching scale at the slanted ray.
R037 — Chapter 15
Answer: A correctly constructed and labeled 115° angle
Reasoning: Position the protractor at the vertex, mark 115° from the baseline and draw the ray; examiner checks within an agreed tolerance.
R038 — Chapter 15
Answer: 107°
Reasoning: Angles on a straight line sum to 180°. Compute 180−73=107°.
R039 — Chapter 15
Answer: 235°
Reasoning: A full rotation is 360°; 360−125=235°.
R040 — Chapter 16
Answer: Yes, they meet at 90°
Reasoning: Their intersection forms a right angle; perpendicular lines meet at right angles.
R041 — Chapter 16
Answer: Two separated horizontal lines; same direction and constant separation
Reasoning: Parallel lines in a plane never intersect; these have constant distance apart.
R042 — Chapter 16
Answer: A valid perpendicular horizontal line and a second parallel horizontal line
Reasoning: Use the grid or a set square; the horizontal lines meet the vertical at 90° and remain parallel.
R043 — Chapter 16
Answer: Both have four right angles; a nonsquare rectangle has unequal adjacent side lengths
Reasoning: A square is a rectangle with all four sides equal; a general rectangle can have unequal adjacent sides.
R044 — Chapter 16
Answer: 2; the horizontal and vertical midlines
Reasoning: Folding along either midline matches the halves; diagonals are not symmetry axes unless it is a square.
R045 — Chapter 16
Answer: Partner 3 squares right of the mirror line at the same height
Reasoning: Reflect across the vertical axis by keeping equal perpendicular distances.
R046 — Chapter 17
Answer: 6 faces, 12 edges, 8 vertices
Reasoning: There are three pairs of opposite rectangular faces, 12 edges, and eight corners.
R047 — Chapter 17
Answer: Two 2×3, two 2×4, and two 3×4 rectangular faces in a foldable arrangement
Reasoning: Opposite faces match, and the six rectangles join along matching lengths with no overlap when folded.
R048 — Chapter 17
Answer: 40 cm², 24 cm², and 15 cm² (each twice)
Reasoning: The face dimensions are 8×5, 8×3, and 5×3, with two of each.
R049 — Chapter 10
Answer: 2,650 mL
Reasoning: Half of 4,000 mL is 2,000; add 650 to get 2,650.
R050 — Chapter 11
Answer: 81 m²
Reasoning: 12×8=96; 5×3=15; 96−15=81 m².
R051 — Chapter 11
Answer: 44 m
Reasoning: Perimeter=2(13+9)=44 m.
R052 — Chapter 12
Answer: Incorrect; 0.4=4/10=40/100
Reasoning: The 4 occupies the tenths place, not the hundredths place.
R053 — Chapter 12
Answer: 0.72 > 0.7
Reasoning: 0.7=0.70, and 72 hundredths >70 hundredths.
R054 — Chapter 13
Answer: 2.45
Reasoning: 1.60+0.85=2.45; the tenths and hundredths must remain aligned.
R055 — Chapter 13
Answer: $4.73
Reasoning: 6.48+3.79=10.27; 15.00−10.27=4.73.
R056 — Chapter 14
Answer: 4.5
Reasoning: Multiplication by 10 makes each digit worth ten times as much: 0.45×10=4.5.
R057 — Chapter 14
Answer: 6.2 L
Reasoning: 18.6÷3=6.2 L; 6.2×3=18.6.
R058 — Chapter 15
Answer: 90° is larger by 45°
Reasoning: 90−45=45; ray lengths do not affect the angle size.
R059 — Chapter 15
Answer: 62°
Reasoning: 180−118=62°.
R060 — Chapter 16
Answer: A finite drawing does not show the infinite lines; their extensions could intersect
Reasoning: Parallel requires the complete extended lines to never meet, not just the visible segments.
R061 — Chapter 16
Answer: Correct labeled parallel and perpendicular arrangement
Reasoning: Perpendicular pair forms 90°; parallel pair have same direction.
R062 — Chapter 16
Answer: 4 squares right at the same height
Reasoning: A reflection preserves perpendicular distance to the axis.
R063 — Chapter 17
Answer: No; faces are rectangles, and only in a cube must they all be squares
Reasoning: A 2×3×4 box has rectangular faces of three different shapes.
R064 — Chapter 17
Answer: They may be connected in a layout that overlaps or leaves an opening when folded
Reasoning: Face count and dimensions are necessary, but a foldable arrangement is also required.
Practice examination — 185-point marking guide
E001 · 3 points · Metric Units of Measurement
Answer: 7,048 mL; 5 kg 306 g
Worked reasoning: 7×1,000+48=7,048 mL. 5,306 g is five thousands plus 306 g.
Marking criteria — one point for each fulfilled criterion:
- Converts seven liters to 7,000 mL
- Adds 48 mL to give 7,048 mL
- Expresses 5,306 g as 5 kg 306 g
E002 · 3 points · Customary Units of Length
Answer: 120 in
Worked reasoning: 3 yd=9 ft, plus 1 ft=10 ft. 10×12=120 inches.
Marking criteria — one point for each fulfilled criterion:
- Converts three yards to nine feet
- Adds one foot to obtain ten feet
- Converts ten feet to 120 inches
E003 · 3 points · Customary Units of Weight
Answer: First is 45 oz; second is heavier by 6 oz
Worked reasoning: 2×16+13=45 oz; 51−45=6 oz.
Marking criteria — one point for each fulfilled criterion:
- Converts 2 lb 13 oz to 45 oz
- Correctly identifies the second crate as heavier
- Finds a difference of 6 oz
E004 · 3 points · Customary Units of Capacity
Answer: 12 pt
Worked reasoning: A gallon is 8 pints and 2 quarts are 4 pints: 8+4=12.
Marking criteria — one point for each fulfilled criterion:
- Converts one gallon to eight pints
- Converts two quarts to four pints
- Adds the converted quantities to obtain a total of 12 pints
E005 · 3 points · Units of Time
Answer: 2 h 15 min
Worked reasoning: 47+28=75 min=1 h 15 min; plus 1 h gives 2 h 15 min.
Marking criteria — one point for each fulfilled criterion:
- Adds the 47-minute and 28-minute intervals to 75 minutes
- Regroups 75 minutes as one hour 15 minutes
- Gives the combined duration as 2 h 15 min
E006 · 3 points · Fractions and Measurement — Part 1
Answer: 75 cm
Worked reasoning: Two meters =200 cm. One eighth is 25 cm; three eighths are 75 cm.
Marking criteria — one point for each fulfilled criterion:
- Identifies 2 m as 200 cm
- Calculates three eighths of 200
- States 75 cm decorated
E007 · 3 points · Fractions and Measurement — Part 2
Answer: 4,500 mL
Worked reasoning: 3/8 of 8,000=3,000 mL, then subtract 3,000 and 500 from 8,000.
Marking criteria — one point for each fulfilled criterion:
- Calculates three eighths of 8 L as 3 L
- Accounts for the additional 500 mL used
- Gives 4,500 mL remaining
E008 · 4 points · Area of Rectangles — Part 1
Answer: 45 square units
Worked reasoning: 9 columns of five unit squares give 9×5=45 square units.
Marking criteria — one point for each fulfilled criterion:
- Draws nine equal columns or nine equal unit rows correctly
- Shows five equal unit squares in the other direction
- Computes 9 × 5 = 45
- States area in square units
E009 · 3 points · Area of Rectangles — Part 2
Answer: 6 m
Worked reasoning: 72÷12=6 m.
Marking criteria — one point for each fulfilled criterion:
- Uses length times width equals area
- Divides 72 by 12
- States a width of 6 m
E010 · 3 points · Area of Composite Figures
Answer: 68 cm²
Worked reasoning: 10×8−4×3=80−12=68 cm².
Marking criteria — one point for each fulfilled criterion:
- Computes full rectangle area 80 cm²
- Computes removed corner area 12 cm²
- Subtracts to obtain 68 cm²
E011 · 3 points · Perimeter — Part 1
Answer: 25 cm
Worked reasoning: Sum all five outside edges: 3+6+4+7+5=25 cm.
Marking criteria — one point for each fulfilled criterion:
- Recognizes all five sides contribute to the boundary
- Adds the five lengths accurately
- States a perimeter of 25 centimeters
E012 · 3 points · Perimeter — Part 2
Answer: 36 cm
Worked reasoning: 11+3+5+4+6+7=36 cm.
Marking criteria — one point for each fulfilled criterion:
- Identifies all six external boundary lengths
- Adds 11 + 3 + 5 + 4 + 6 + 7
- States a perimeter of 36 centimeters
E013 · 3 points · Tenths — Part 1
Answer: 3/10
Worked reasoning: Three of ten equal parts represent three tenths, written 0.3.
Marking criteria — one point for each fulfilled criterion:
- Shades three out of ten equal sections
- Preserves the equal-sized whole
- Writes the fraction 3/10
E014 · 3 points · Tenths — Part 2
Answer: 0.4
Worked reasoning: Six tenths minus two tenths =four tenths.
Marking criteria — one point for each fulfilled criterion:
- Positions 0.2 at the second tenth
- Positions 0.6 at the sixth tenth
- Calculates their difference as 0.4
E015 · 3 points · Hundredths — Part 1
Answer: 0.58; tenths digit 5
Worked reasoning: Fifty-eight hundredths is five tenths and eight hundredths.
Marking criteria — one point for each fulfilled criterion:
- Writes 58/100 = 0.58
- Identifies 5 as the tenths digit
- Explains that 0.58 is 5 tenths and 8 hundredths
E016 · 3 points · Hundredths — Part 2
Answer: 0.5 by 0.01
Worked reasoning: 0.5=0.50=50 hundredths, which exceeds 49 hundredths by one.
Marking criteria — one point for each fulfilled criterion:
- Rewrites 0.5 as 0.50
- Compares 50 hundredths and 49 hundredths correctly
- States the difference is 0.01
E017 · 3 points · Expressing Decimals as Fractions in Simplest Form
Answer: 9/25
Worked reasoning: 36/100 simplifies by dividing numerator and denominator by four.
Marking criteria — one point for each fulfilled criterion:
- Writes 0.36 as 36/100
- Simplifies numerator and denominator by 4
- Gives 9/25 in simplest form
E018 · 3 points · Expressing Fractions as Decimals
Answer: 0.45; 0.6
Worked reasoning: 9/20=45/100=0.45; 3/5=6/10=0.6.
Marking criteria — one point for each fulfilled criterion:
- Computes 9/20 = 0.45
- Computes 3/5 = 0.6
- Explains at least one conversion by equivalent tenths/hundredths
E019 · 3 points · Comparing and Ordering Decimals
Answer: 0.6 > 0.54 > 0.5 > 0.47
Worked reasoning: Compare them as 60, 54, 50, 47 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Places 0.6 before the other numbers
- Places 0.54 before 0.5
- Places 0.47 last to give correct descending order
E020 · 3 points · Rounding Decimals
Answer: 9.7
Worked reasoning: 9.65 is exactly midway between 9.6 and 9.7; under the usual school midpoint rule round the tenths up.
Marking criteria — one point for each fulfilled criterion:
- Identifies 9.6 and 9.7 as adjacent tenths
- Recognizes 9.65 as exactly halfway
- Rounds up to 9.7 using stated school rule
E021 · 3 points · Adding and Subtracting Tenths
Answer: 7.6; 6.3
Worked reasoning: 62+14=76 tenths, and 95−32=63 tenths.
Marking criteria — one point for each fulfilled criterion:
- Computes 6.2 + 1.4 = 7.6
- Computes 9.5 − 3.2 = 6.3
- Correctly aligns tenths in both operations
E022 · 3 points · Adding Tenths with Regrouping
Answer: 12.4
Worked reasoning: 6+8 tenths=14 tenths=1 whole+4 tenths; 7+4+1=12.
Marking criteria — one point for each fulfilled criterion:
- Adds 6 tenths and 8 tenths to make 14 tenths
- Regroups ten tenths as one whole
- States the correct sum of 12.4
E023 · 3 points · Subtracting Tenths with Regrouping
Answer: 3.5
Worked reasoning: Rename 10.3 as 9 ones 13 tenths; subtract 6 ones 8 tenths to get 3.5.
Marking criteria — one point for each fulfilled criterion:
- Renames 10.3 as 9 ones and 13 tenths
- Subtracts corresponding units correctly
- States the correct answer of 3.5
E024 · 3 points · Adding Hundredths
Answer: 11.35
Worked reasoning: 6+9 hundredths=15 hundredths; regroup one tenth, then tenths regroup as necessary.
Marking criteria — one point for each fulfilled criterion:
- Adds hundredths 6+9=15 and exchanges 10 hundredths
- Correctly handles regrouped tenths
- States the correct sum 11.35
E025 · 3 points · Subtracting from 1 and 0.1
Answer: 0.42; 0.03
Worked reasoning: Use 1.00−0.58 and 0.10−0.07.
Marking criteria — one point for each fulfilled criterion:
- Calculates 1.00−0.58=0.42
- Calculates 0.10−0.07=0.03
- Shows appropriate hundredths place alignment
E026 · 3 points · Subtracting Hundredths
Answer: 4.16
Worked reasoning: 12.05−7.89=4.16. Check 7.89+4.16=12.05.
Marking criteria — one point for each fulfilled criterion:
- Computes 12.05−7.89=4.16
- Checks 7.89+4.16=12.05
- Shows the regrouping/place-value reasoning
E027 · 3 points · Money, Decimals, and Fractions
Answer: $10.36
Worked reasoning: Costs total $9.64. 20.00−9.64=$10.36.
Marking criteria — one point for each fulfilled criterion:
- Totals the purchases to $9.64
- Subtracts $9.64 from $20.00
- States exact change $10.36
E028 · 3 points · Multiplying Tenths and Hundredths
Answer: 0.72
Worked reasoning: Nine hundredths in each of eight groups makes 72 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Represents 0.09 as nine hundredths
- Multiplies nine hundredths by eight
- States the resulting product 0.72
E029 · 3 points · Multiplying Decimals by a Whole Number — Part 1
Answer: 22.4
Worked reasoning: 3×7=21 and 0.2×7=1.4, total 22.4.
Marking criteria — one point for each fulfilled criterion:
- Computes the whole-number partial product 3×7=21
- Computes 0.2×7=1.4
- Adds partial products to obtain 22.4
E030 · 3 points · Multiplying Decimals by a Whole Number — Part 2
Answer: 21.6 L; approximately 20–24 L
Worked reasoning: 1.35×(10+6)=13.5+8.1=21.6. 1.4×16≈22.4 is a useful check.
Marking criteria — one point for each fulfilled criterion:
- Multiplies 1.35×16 to obtain 21.6 L
- Gives a reasonable estimate of approximately 20–24 L
- Shows an appropriate place-value multiplication method
E031 · 3 points · Dividing Tenths and Hundredths
Answer: 0.08
Worked reasoning: 96 hundredths ÷12 =8 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Recognizes 0.96 as 96 hundredths
- Divides 96 hundredths into 12 shares
- States 0.08 per share
E032 · 3 points · Dividing Decimals by a Whole Number — Part 1
Answer: 2.5 kg
Worked reasoning: 12.5÷5=2.5 kg.
Marking criteria — one point for each fulfilled criterion:
- Uses division of the total by five equal packs
- Computes 12.5÷5=2.5
- States 2.5 kg per pack
E033 · 3 points · Dividing Decimals by a Whole Number — Part 2
Answer: 1.82
Worked reasoning: 7 ones divided by 4 gives 1 each, remainder 3 ones. Rename to 32 tenths; 8 tenths each; 8 hundredths ÷4=2 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Divides 7 ones by 4 and converts remainder to tenths
- Divides resulting tenths and hundredths correctly
- States the resulting quotient 1.82
E034 · 3 points · Dividing Decimals by a Whole Number — Part 3
Answer: $3.90
Worked reasoning: 2,730 cents divided by 7=390 cents.
Marking criteria — one point for each fulfilled criterion:
- Expresses the total as 2,730 cents or $27.30
- Divides total accurately among seven people
- States $3.90 per person
E035 · 3 points · The Size of Angles
Answer: It remains 48°
Worked reasoning: Angle measure describes turning between directions, not ray lengths.
Marking criteria — one point for each fulfilled criterion:
- States the angle remains 48°
- Identifies the false claim that doubling ray lengths doubles the angle
- Explains that angle measures change in direction, not ray length
E036 · 3 points · Measuring Angles
Answer: 125°
Worked reasoning: Align the center at the vertex, zero baseline to the horizontal ray, and read 125° on the correct scale.
Marking criteria — one point for each fulfilled criterion:
- Places the protractor center at the vertex
- Aligns the zero reference with the baseline and uses correct scale
- Reports approximately 125° within agreed protractor tolerance
E037 · 4 points · Drawing Angles
Answer: A labeled 70° angle
Worked reasoning: Use a baseline, measure 70° at the vertex, draw the second ray; human checks reasonable protractor tolerance.
Marking criteria — one point for each fulfilled criterion:
- Draws a clear baseline and marks a vertex
- Uses protractor to construct approximately 70°
- Draws second ray to the mark
- Labels the vertex correctly
E038 · 3 points · Adding and Subtracting Angles
Answer: 34°
Worked reasoning: 180°−146°=34°.
Marking criteria — one point for each fulfilled criterion:
- Uses 180° as the straight-angle total
- Subtracts the given 146°
- Reports the missing angle as 34 degrees
E039 · 3 points · Reflex Angles
Answer: 278°
Worked reasoning: 360°−82°=278°.
Marking criteria — one point for each fulfilled criterion:
- Recognizes a complete turn equals 360°
- Subtracts the interior 82°
- Reports reflex angle 278°
E040 · 3 points · Perpendicular Lines
Answer: A vertical line, meeting at a right angle
Worked reasoning: Horizontal and vertical directions meet at 90°.
Marking criteria — one point for each fulfilled criterion:
- Identifies a vertical line as perpendicular to horizontal
- States that perpendicular lines meet
- States that they meet at 90°
E041 · 3 points · Parallel Lines
Answer: Parallel
Worked reasoning: Parallel lines stay a constant distance apart in a plane.
Marking criteria — one point for each fulfilled criterion:
- Identifies the lines as parallel
- Explains they stay the same distance apart in a plane
- Explains that they do not meet when extended
E042 · 4 points · Drawing Perpendicular and Parallel Lines
Answer: A valid set of lines with the required perpendicular and parallel relationships
Worked reasoning: Examiner checks that m and p do not meet and n meets m at 90°.
Marking criteria — one point for each fulfilled criterion:
- Draws and labels a straight line m
- Draws and labels line n perpendicular to m
- Draws distinct line p parallel to m
- Marks a 90° angle at the m–n intersection
E043 · 3 points · Quadrilaterals
Answer: No; a rhombus may lack right angles
Worked reasoning: A square has four equal sides and four right angles. A nonsquare rhombus has equal sides but oblique angles.
Marking criteria — one point for each fulfilled criterion:
- States that not every rhombus is a square
- Explains that rhombuses have four equal sides
- Gives a nonright-angle rhombus as a counterexample
E044 · 3 points · Lines of Symmetry
Answer: Two
Worked reasoning: Horizontal and vertical midlines reflect the rectangle onto itself; the diagonals of a nonsquare rectangle do not.
Marking criteria — one point for each fulfilled criterion:
- States two axes of symmetry
- Identifies horizontal and vertical midlines through its center
- Explains why diagonals do not reflect a nonsquare rectangle onto itself
E045 · 4 points · Symmetrical Figures and Patterns
Answer: Matching triangle, each vertex equally far from the mirror line
Worked reasoning: Reflect each vertex to the same height at the same perpendicular distance.
Marking criteria — one point for each fulfilled criterion:
- Draws a recognizable triangle entirely on the left
- Draws the reflected triangle entirely on the right
- Corresponding vertices have equal perpendicular distances to axis
- Maintains equal corresponding vertical positions and joined edges
E046 · 3 points · Cuboids
Answer: 6 faces, 12 edges, 8 vertices
Worked reasoning: Three pairs of opposite faces, 12 edges, eight vertices.
Marking criteria — one point for each fulfilled criterion:
- States six faces
- States twelve edges
- States eight vertices
E047 · 4 points · Nets of Cuboids
Answer: Two 2×4, two 2×5, two 4×5 faces in a valid connected net
Worked reasoning: A valid net contains exactly the three matching pairs and folds without face overlap.
Marking criteria — one point for each fulfilled criterion:
- Draws a connected six-rectangle net
- Contains exactly two 2×4, two 2×5, two 4×5 faces
- Faces are joined along matching-length edges in foldable layout
- Labels all six rectangle dimensions clearly
E048 · 3 points · Faces and Edges of Cuboids
Answer: 42, 54, and 63 cm²
Worked reasoning: Multiply each pair: 6×7=42, 6×9=54, 7×9=63. Two faces of each size.
Marking criteria — one point for each fulfilled criterion:
- Calculates 6×7=42 cm²
- Calculates 6×9=54 cm²
- Calculates 7×9=63 cm²
E049 · 3 points · Customary Units of Capacity
Answer: 6 cups
Worked reasoning: 3 quarts are 12 cups plus 2 cups in a pint =14 cups; 14−8=6 cups.
Marking criteria — one point for each fulfilled criterion:
- Converts 3 qt and 1 pt to 14 cups
- Subtracts the eight cups poured out
- Reports 6 cups remaining
E050 · 3 points · Fractions and Measurement — Part 2
Answer: 8 L 250 mL
Worked reasoning: 12,000−3,000−750=8,250 mL=8 L 250 mL.
Marking criteria — one point for each fulfilled criterion:
- Calculates one quarter of 12 L as 3 L
- Subtracts additional 750 mL from nine remaining liters
- Reports 8 L 250 mL
E051 · 3 points · Area of Composite Figures
Answer: 50 m²
Worked reasoning: 8×7−2×3=56−6=50 m².
Marking criteria — one point for each fulfilled criterion:
- Calculates classroom area 8×7=56 m²
- Calculates cabinet region area 2×3=6 m²
- Gives carpeted area 50 m²
E052 · 3 points · Hundredths — Part 2
Answer: 30 hundredths equals 3 tenths
Worked reasoning: Each tenth consists of ten hundredths; 3 tenths =30 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Identifies 0.30 as 30 hundredths
- Identifies 0.3 as 3 tenths
- Explains why 3 tenths is equal to 30 hundredths
E053 · 3 points · Rounding Decimals
Answer: $4.40
Worked reasoning: 4.36 is 6 hundredths past 4.30, so to the nearest tenth it rounds to 4.4.
Marking criteria — one point for each fulfilled criterion:
- Recognizes the two nearest tenth-dollar amounts $4.30 and $4.40
- Uses the hundredths digit 6 to round upward
- States $4.40, equivalent to $4.4
E054 · 3 points · Subtracting Tenths with Regrouping
Answer: 3.5
Worked reasoning: Regroup 6.4 as 5 ones and 14 tenths; subtract 2 ones 9 tenths to get 3.5.
Marking criteria — one point for each fulfilled criterion:
- Identifies the error in taking 9−4 without regrouping
- Correctly renames 6.4 as 5 ones 14 tenths
- States the correct answer of 3.5
E055 · 3 points · Subtracting from 1 and 0.1
Answer: 0.02
Worked reasoning: One tenth is 10 hundredths; 10−8 hundredths =2 hundredths.
Marking criteria — one point for each fulfilled criterion:
- Explains that 0.1 is ten hundredths
- Subtracts eight hundredths from ten
- States the corrected difference as 0.02
E056 · 3 points · Multiplying Decimals by a Whole Number — Part 2
Answer: 22.5 kg
Worked reasoning: 1.25×(20−2)=25−2.5=22.5 kg.
Marking criteria — one point for each fulfilled criterion:
- Uses 18 groups of 1.25 kg
- Multiplies correctly using distribution or equivalent strategy
- States the total mass as 22.5 kg
E057 · 3 points · Dividing Decimals by a Whole Number — Part 1
Answer: $2.70
Worked reasoning: 1,620 cents÷6=270 cents per team.
Marking criteria — one point for each fulfilled criterion:
- Represents $16.20 as 1,620 cents or equivalent
- Divides the total by six equal teams
- States $2.70 per team
E058 · 3 points · Reflex Angles
Answer: 322°
Worked reasoning: 360°−38°=322°.
Marking criteria — one point for each fulfilled criterion:
- Uses 360° for complete turn
- Subtracts given 38°
- Reports the reflex angle as 322 degrees
E059 · 3 points · Lines of Symmetry
Answer: Its adjacent side lengths are unequal
Worked reasoning: A square must have four equal sides, while this rectangle has two lengths.
Marking criteria — one point for each fulfilled criterion:
- States the square requires four equal sides
- Identifies adjacent sides of lengths 4 cm and 7 cm as unequal
- Explains why the figure therefore is not a square
E060 · 3 points · Faces and Edges of Cuboids
Answer: A 2×4×5 cuboid needs two faces each of 2×4, 2×5, and 4×5
Worked reasoning: Four 2×5 rectangles omit the necessary pair of 4×5 faces.
Marking criteria — one point for each fulfilled criterion:
- States that 2×4, 2×5 and 4×5 pairs are required
- Recognizes the proposed design omits 4×5 faces
- Explains that the extra 2×5 faces cannot replace the missing pair