Each worksheet starts with two easy questions and finishes with two hard ones, so most Year 8 children can begin on their own and will have to think by the end. The answers print on a separate page, with a worked solution for every question, so you can mark it together.
A good habit: ask your child to explain how they got two or three of the answers. If the explanation is shaky, the worked solution shows one clear way to think it through.
On this page
Powers and prime factors
Powers and prime factors: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
2³ = ?
- 2
10⁴ = ?
- 3
5³ = ?
- 4
2⁵ = ?
- 5
Which is 24 as a product of prime factors?
- A2³ × 3
- B2² × 6
- C2 × 3 × 4
- D3³ × 2
- 6
Which is 100 as a product of prime factors?
- A10²
- B2 × 5²
- C4 × 25
- D2² × 5²
- 7
A city has about 4 × 10⁵ people. How many is that?
- A20
- B40 000
- C400 000
- D4 000 000
- 8
A number's prime factor form is 2² × 3 × 7. What is the number?
- 9
√(2⁴ × 3²) = ?
- 10
A square number has an even index on every prime in its prime factor form. Which of these is a square number?
- A2 × 3
- B2³ × 3²
- C2² × 3² × 5
- D2⁴ × 5²
Answers: Powers and prime factors: worksheet 1
- 8 2³ = 2 × 2 × 2 = 8.
- 10 000 10⁴ = 10 × 10 × 10 × 10 = 10 000. Four zeros.
- 125 5³ = 5 × 5 × 5 = 25 × 5 = 125.
- 32 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. (2, 4, 8, 16, 32.)
- A: 2³ × 3 From the tree: 24 = 2 × 2 × 2 × 3 = 2³ × 3.
- D: 2² × 5² 100 = 10 × 10 = (2 × 5) × (2 × 5) = 2² × 5².
- C: 400 000 10⁵ = 100 000, and 4 × 100 000 = 400 000.
- 84 2² = 4. 4 × 3 = 12, and 12 × 7 = 84.
- 12 2⁴ × 3² = 16 × 9 = 144, and √144 = 12. (Or halve each index: 2² × 3 = 12.)
- D: 2⁴ × 5² 2⁴ × 5² has even indexes, so it is (2² × 5)² = 20² = 400. 2³ × 3² has an odd index on the 2, and 2² × 3² × 5 has 5¹.
Changing one variable
Changing one variable: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
In A = l × w, the width w triples and the length stays the same. What happens to A?
- AIt triples
- BIt goes up by 3
- CIt doubles
- DIt stays the same
- 2
The spreadsheet works out P = 4s for squares. What goes in the empty cell?
- 3
The spreadsheet works out A = l × w with w kept at 4. What happens to A each time l goes up by 1?
- AIt goes up by 4
- BIt doubles
- CIt goes up by 5
- DIt goes up by 1
- 4
Phone plan: C = 20 + 0.1m dollars. By how many dollars does C go up when m goes up by 50 minutes?
dollars - 5
A rectangle is 3 cm by 5 cm. Both sides are doubled. What is the new area?
cm² - 6
A rectangle has area A = l × w = 24 cm². The length is tripled and the width is halved. What is the new area?
- A36 cm²
- B12 cm²
- C72 cm²
- D24 cm²
- 7
In A = l × w, the length is doubled and the width is tripled. What happens to the area?
- AIt is 3 times as big
- BIt is 5 times as big
- CIt is 6 times as big
- DIt is 9 times as big
- 8
A square's area is A = s². The side grows from 3 cm to 6 cm. How many times bigger is the area?
times - 9
A rectangle has area 40 cm². Its length is multiplied by 3 and its width is divided by 2. What is the new area?
cm² - 10
In A = l × w, the length goes up by 10% and the width goes down by 10%. What happens to the area?
- AIt gets slightly bigger
- BIt gets slightly smaller
- CIt drops by 10%
- DIt stays the same
Answers: Changing one variable: worksheet 1
- A: It triples Try l = 5, w = 2: A = 10. Triple w to 6: A = 30, which is 3 times 10.
- 16 s = 4, so P = 4 × 4 = 16. P goes up by 4 each row.
- A: It goes up by 4 4, 8, 12, 16: each extra 1 cm of length adds a strip of 4 cm².
- $5 Each minute adds $0.10. 50 × 0.1 = $5.
- 60 cm² New sides 6 cm and 10 cm: 6 × 10 = 60 cm², which is 4 times the old 15 cm².
- A: 36 cm² Tripling makes it 3 times as big; halving makes it half. 24 × 3 ÷ 2 = 36. Example: 6 × 4 = 24 becomes 18 × 2 = 36.
- C: It is 6 times as big 2 × 3 = 6. Example: 2 × 1 = 2 becomes 4 × 3 = 12, 6 times as big.
- 4 times 3² = 9 and 6² = 36. 36 ÷ 9 = 4, so 4 times as big.
- 60 cm² The area is multiplied by 3 and divided by 2: 40 × 3 ÷ 2 = 60 cm². Example: 10 × 4 becomes 30 × 2.
- B: It gets slightly smaller Try 10 by 10 = 100. Then 11 by 9 = 99. The area drops a little (by 1%).
Area of triangles
Area of triangles: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
What is the area of this parallelogram?
- A10 cm²
- B10.5 cm²
- C21 cm²
- 2
What is the area of this triangle?
cm² - 3
A tile shaped like a parallelogram measures 11 cm along its base and stands 5 cm tall, measured straight up from the base. What is the area of the tile?
- A55 cm²
- B16 cm²
- C27.5 cm²
- 4
The base of this triangle is its upright side. What is the area of the triangle?
cm² - 5
The dashed height of this triangle falls outside the shape. What is the area of the triangle?
- A30 cm²
- B50 cm²
- C15 cm²
- D25 cm²
- 6
A triangle has an area of 36 cm² and a perpendicular height of 9 cm. How long is its base?
cm - 7
This arrow is a 6 cm by 4 cm rectangle with a triangle on the end. The triangle sticks out 3 cm, as the dashed line shows. What is the area of the arrow?
- A36 cm²
- B27 cm²
- C24 cm²
- D30 cm²
- 8
A garden bed shaped like a parallelogram has a base of 2 m and a perpendicular height of 50 cm. What is its area in square metres?
- A10 m²
- B0.1 m²
- C1 m²
- D100 m²
- 9
A triangle and a parallelogram both have an area of 48 cm² and a base of 8 cm. How much taller is the triangle than the parallelogram?
cm - 10
Noah is painting the front of this shed: a rectangle with a triangle on top. The door, 1 m wide and 2 m tall, is not painted. What area does he paint?
m²
Answers: Area of triangles: worksheet 1
- C: 21 cm² Base × perpendicular height = 7 × 3 = 21 cm².
- 20 cm² 8 × 5 = 40, and half of 40 is 20 cm².
- A: 55 cm² Measured straight up means the perpendicular height, so 11 × 5 = 55 cm².
- 20 cm² The base is 8 cm and the height at a right angle to it is 5 cm: ½ × 8 × 5 = 20 cm².
- C: 15 cm² Base 5 cm, perpendicular height 6 cm: 5 × 6 = 30, and half of 30 is 15 cm².
- 8 cm ½ × base × 9 = 36, so base × 9 = 72 and base = 72 ÷ 9 = 8 cm.
- D: 30 cm² Rectangle: 6 × 4 = 24 cm². Triangle: base 4 cm, height 3 cm, so ½ × 4 × 3 = 6 cm². Total 30 cm².
- C: 1 m² Change 50 cm to 0.5 m first. 2 × 0.5 = 1 m².
- 6 cm Parallelogram: 48 ÷ 8 = 6 cm. Triangle: 2 × 48 ÷ 8 = 12 cm. 12 − 6 = 6 cm taller.
- 22 m² Rectangle 6 × 3 = 18 m², triangle ½ × 6 × 2 = 6 m², total 24 m². Take away the door, 1 × 2 = 2 m²: 22 m².
Parts of a circle
Parts of a circle: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
The middle point of a circle is called the...
- Aradius
- Bcentre
- Ccircumference
- Ddiameter
- 2
Which part of a circle goes right across, through the centre?
- Acircumference
- Bradius
- Cdiameter
- Dcentre
- 3
A netball hoop has a diameter of 38 cm. What is its radius?
cm - 4
A car wheel has a radius of 35 cm. What is its diameter?
cm - 5
A hāngī pit cover has a diameter of 1.2 m. What is its radius, in metres?
m - 6
A round table at a Napier café has a radius of 75 cm. What is its diameter?
cm - 7
A round clock has a radius of 14 cm. Tama's square frame must be 4 cm wider than the clock's diameter. How wide is the frame?
cm - 8
Three round plates, each with a radius of 12 cm, sit in a straight row touching each other. How long is the row?
cm - 9
Five round coasters, each with a radius of 4.5 cm, sit in a straight row touching each other. How long is the row?
cm - 10
A round café table in Queenstown has a diameter of 1.5 m. It is pushed right up against a wall. How far is the centre of the table from the wall, in centimetres?
cm
Answers: Parts of a circle: worksheet 1
- B: centre The centre is the middle point. Every point on the circle is the same distance from it.
- C: diameter A diameter goes all the way across the circle and passes through the centre.
- 19 cm The radius is half the diameter: 38 ÷ 2 = 19 cm.
- 70 cm The diameter is 2 × the radius: 2 × 35 = 70 cm.
- 0.6 m The radius is half the diameter: 1.2 ÷ 2 = 0.6 m.
- 150 cm The diameter is 2 × the radius: 2 × 75 = 150 cm.
- 32 cm The diameter is 2 × 14 = 28 cm. Add 4 cm: 28 + 4 = 32 cm.
- 72 cm Each plate is 2 × 12 = 24 cm across. Three plates: 3 × 24 = 72 cm.
- 45 cm Each coaster is 2 × 4.5 = 9 cm across. Five coasters: 5 × 9 = 45 cm.
- 75 cm The centre to the wall is a radius: 1.5 ÷ 2 = 0.75 m. 0.75 m = 75 cm.
Stem-and-leaf plots
Stem-and-leaf plots: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
This dot plot shows the hours of sleep some students had. How many students had 9 hours?
students - 2
This dot plot shows the hours of sleep some students had. What is the mode?
hours - 3
This dot plot shows how many goals a futsal team scored in each game. What is the mode?
goals - 4
This dot plot shows how many pets the students in a group own. How many students are in the group?
students - 5
This dot plot shows how many pets the students own. Which value is an outlier?
- A0
- B1
- C2
- D9
- 6
This dot plot shows the hours of sleep some students had. What is the mean?
hours - 7
These dot plots show the number of push-ups two groups did. What is the difference between their medians?
push-ups - 8
This plot shows the boys' 400 m times. The girls had a median of 65 seconds and a range of 16 seconds. Which statement is true? (A smaller time is faster.)
- AThe boys' times are faster on average and more spread out.
- BThe girls' times are more spread out.
- CThe girls are faster on average.
- DBoth groups have the same median.
- 9
The pets dot plot shows 10 students, with a median of 1 pet. Some new students join, and each of them owns 3 pets. What is the least number of new students needed to make the median 2 pets?
students - 10
These plots show two classes' test scores. Class A wants the class with the more consistent results. Which class, and which statistic shows it?
- AClass A, because its range is smaller
- BClass B, because its range is larger
- CClass B, because its median is higher
- DClass A, because its median is higher
Answers: Stem-and-leaf plots: worksheet 1
- 4 students There are 4 dots above 9.
- 9 hours 9 has the most dots (4), so the mode is 9 hours.
- 2 goals The tallest column of dots is above 2, with 4 dots. That is the most common value.
- 10 students Each dot is one student. There are 10 dots.
- D: 9 Most students have 0 to 2 pets. 9 is far away from the rest of the data, so it is an outlier.
- 8.8 hours Add every value: 7 + 8 + 8 + 8 + 9 + 9 + 9 + 9 + 10 + 11 = 88. Divide by 10 students: 8.8.
- 3 push-ups Group P has 9 values; its 5th is 6. Group Q has 9 values; its 5th is 9. 9 − 6 = 3.
- A: The boys' times are faster on average and more spread out. Boys: median 63, range 23. Girls: median 65, range 16. The boys' median time is smaller (faster) and their range is bigger.
- 5 students There are 7 values of 0 or 1 and two 2s. With 4 new students (14 values) the middle two are the 7th and 8th: 1 and 2, median 1.5. With 5 new students (15 values) the median is the 8th value, which is 2. So 5 is the least.
- A: Class A, because its range is smaller Consistent means the scores are close together. Class A's range is 4; Class B's is 9. Class A is more consistent.
The full set for Year 8
With a subscription you can print five worksheets for each of the 21 Year 8 maths topics, 105 in all, from Grown-ups > Maths worksheets. Every sheet has its own answer page. These are the topics:
Number
- Powers and prime factors
- Fractions to percentages
- Multiplying fractions
- Integers
- Ratios
- Negative powers of 10
- Cube roots
- Integers and order of operations
- Budgets and discounts
Algebra
- Changing one variable
- Equations and inequalities
- Expanding and factorising
- Triangular, square and cube numbers
Measurement
- Area of triangles
- Angle sums
- Scale drawings
- Trapeziums, triangular prisms and composite volume
- Converting area and volume units
Space
- Parts of a circle
Statistics
- Stem-and-leaf plots
Probability
- Simulations