5B · Original cumulative assessment

5B Cumulative Review 3 — Decimals, Geometry and Data

35 original questions across Chapters 9–12.

Attempt each question before opening its worked answer. When printing, solutions are hidden. Show reasoning and label physical units as asked.

Review and practice

Question 1

2 points

A measuring strip marks 23 tiny portions out of 1,000 equal portions. Give a fraction and a decimal for the marked part.

Check worked answer

Answer: 23/1000 = 0.023

23 equal thousandths equals 0.023 of one whole.

Question 2

2 points

Write 6.302 as words and as a sum of whole-number and decimal place values.

Check worked answer

Answer: Six and three hundred two thousandths; 6 + 3/10 + 2/1000

The hundredths position is a placeholder zero.

Question 3

2 points

Compare 5.041 and 5.014 with a place-value reason.

Check worked answer

Answer: 5.041 > 5.014

Both have five ones and zero tenths; hundredths 4 >1.

Question 4

2 points

Round 8.349 to the nearest tenth. Give its neighboring tenths to explain.

Check worked answer

Answer: 8.3

8.349 lies between 8.3 and 8.4, below 8.35 midpoint.

Question 5

2 points

Multiply 0.009 by 100, explaining how many thousandths make the answer.

Check worked answer

Answer: 0.9

9 thousandths ×100=900 thousandths=0.9.

Question 6

2 points

Calculate 52.5 ÷ 100 and explain the change in magnitude.

Check worked answer

Answer: 0.525

Dividing by 100 creates one hundredth of the original number.

Question 7

2 points

Convert 3.25 liters to milliliters; show the metric relationship.

Check worked answer

Answer: 3,250 mL

One liter is 1,000 mL, so 3.25×1000=3250.

Question 8

2 points

Find 15.02 − 6.99 using a compensation strategy; explain each adjustment.

Check worked answer

Answer: 8.03

Subtract 7.00, then return 0.01: 15.02−7+0.01=8.03.

Question 9

2 points

Find 0.305 + 2.097, showing the regrouping of the thousandths.

Check worked answer

Answer: 2.402

Thousandths: 5+7=12, write 2 and carry 1 hundredth. Hundredths: 0+9+1=10, write 0 and carry 1 tenth. Tenths: 3+0+1=4. Including 2 ones gives 2.402.

Question 10

2 points

Compute 6.000 − 2.875 and use addition to verify.

Check worked answer

Answer: 3.125

6−2.875=3.125; check 3.125+2.875=6.

Question 11

2 points

What is 4.6 × 0.1? Explain with fractional scaling.

Check worked answer

Answer: 0.46

Multiplication by 0.1 makes one tenth: 4.6÷10=0.46.

Question 12

2 points

Evaluate 0.75 × 0.16 by decomposing the second factor.

Check worked answer

Answer: 0.12

0.75×(0.10+0.06)=0.075+0.045=0.120.

Question 13

2 points

Share 9.45 L equally into three containers. Find the amount per container and check.

Check worked answer

Answer: 3.15 L

9.45÷3=3.15; 3×3.15=9.45.

Question 14

2 points

Seven parcels share 0.728 kg equally. Find the mass per parcel with the correct zero in its quotient.

Check worked answer

Answer: 0.104 kg

0.728÷7=0.104 kg; multiply by seven to check.

Question 15

2 points

How many groups of 0.01 fit in 1.2? Demonstrate the hundredth-unit count.

Check worked answer

Answer: 120

1.2=120 hundredths, so 1.2÷0.01=120.

Question 16

2 points

How many 0.5-liter cups can be filled from 8 liters? Explain the grouping interpretation.

Check worked answer

Answer: 16 cups

There are two half-liter groups in each liter, so 8×2=16.

Question 17

2 points

Construct a 35° angle with a ruler and protractor. Mark the vertex and describe its type.

Draw and label your construction here.

Check worked answer

Answer: 35°, acute angle

A correct construction has rays meeting at 35°; 35° is less than 90°.

Question 18

2 points

One angle where two straight lines cross is 128°. Find an adjacent angle and the opposite angle, explaining both.

Check worked answer

Answer: 52° adjacent, 128° opposite

180−128=52; vertically opposite angles are equal.

Question 19

2 points

A triangle has interior angles 40°,70°,70°. Classify it by sides and by angles and give a reason.

Check worked answer

Answer: Isosceles and acute

Two 70° angles imply two equal opposing sides; all corners are <90°.

Question 20

2 points

A triangle has two angles of 48° and 72°. Find the third angle, justifying the total.

Check worked answer

Answer: 60°

180−48−72=60°.

Question 21

2 points

A pupil draws a triangle with angles 42°, 59°, and 79°. They claim the exterior angle adjacent to the 79° interior angle is also 79°. Explain the error and calculate the correct exterior angle.

Check worked answer

Answer: 101°; the student confused the exterior angle with the adjacent interior angle

The adjacent interior and exterior angles form 180°, so exterior =180°−79°=101°. The remote interiors also total 42°+59°=101°.

Question 22

2 points

Explain why every square is a rhombus. Give one property that a rhombus need not share with a square.

Check worked answer

Answer: Both have four equal sides; a rhombus need not have right angles

Square is a special rhombus with four right angles.

Question 23

2 points

Find the fourth angle of a quadrilateral with other interior angles 96°,73°,121°. Explain the sum.

Check worked answer

Answer: 70°

360−(96+73+121)=70°; quadrilateral angles total 360°.

Question 24

2 points

One angle of a parallelogram is 105°. Find its adjacent and opposite angles.

Check worked answer

Answer: 75° adjacent, 105° opposite

Supplementary consecutive angles give 75°; opposite angles match.

Question 25

2 points

Construct a right triangle whose two perpendicular sides measure 3.5 cm and 4.5 cm. Explain how you verify its included angle.

Draw and label your construction here.

Check worked answer

Answer: 3.5 cm and 4.5 cm legs meeting at 90°

Use a protractor or set square to draw the perpendicular rays, measure legs and join ends.

Question 26

2 points

For the dataset 6,7,9,10, calculate the mean and show what total is shared.

Check worked answer

Answer: 8

Total=32, count=4, mean=8.

Question 27

2 points

Three numbers have mean 14. Two numbers are 12 and 15. Find the missing value and show the target total.

Check worked answer

Answer: 15

Target total 3×14=42; known sum27, missing15.

Question 28

2 points

Draw a line plot for 3,3,3,4,4,5. State the mode and explain how it appears on the plot.

Check worked answer

Answer: Mode 3

Plot three marks at 3, two at 4, one at 5; 3 is most common.

Question 29

2 points

Plot P(2,1), Q(2,4), R(6,4) on a first-quadrant grid. Explain which angle is right.

Check worked answer

Answer: Angle PQR at Q

PQ is vertical and QR is horizontal; perpendicular at Q.

Question 30

2 points

A graph has points (0,1),(1,3),(2,5). Write a simple linear rule and explain the pattern.

Check worked answer

Answer: y = 2x + 1

Starts at 1 and rises by 2 for each unit of x.

Question 31

2 points

0.085 m is scaled by 100. Compare the scaled length with 8 m and calculate the difference.

Check worked answer

Answer: 8.5 m, which is 0.5 m more than 8 m

0.085×100=8.5; 8.5−8=0.5.

Question 32

2 points

A 4.8-unit measure is divided into groups of 0.2, then the count is multiplied by 0.01. Find the final number and show both steps.

Check worked answer

Answer: 0.24

4.8÷0.2=24; 24×0.01=0.24.

Question 33

2 points

A triangle has interior angles 50° and 65°. A student claims that the exterior angle at the third vertex is 65°. Determine the third interior angle, correct the exterior angle, and explain the mistake.

Check worked answer

Answer: 65° third interior; 115° exterior; student confused interior and exterior

The third interior =180°−50°−65°=65°. Its adjacent exterior =180°−65°=115°, which also equals the sum of the two remote interiors 50°+65°.

Question 34

2 points

Plot the data 2,4,4,6 on a line plot. State the mean and mode, explaining why they match.

Check worked answer

Answer: Mean 4; mode 4

Total16 /4=4; 4 appears twice, most frequent.

Question 35

2 points

A chart follows y=1.5x+2 for x=0,2,4. Calculate the three y-values and their mean; give the units as general graph units.

Check worked answer

Answer: 2, 5, 8; mean 5

Substitute: x0→2, x2→5, x4→8; average15/3=5.