Each worksheet starts with two easy questions and finishes with two hard ones, so most Year 7 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
Flowcharts
Flowcharts: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
Which number is divisible by 5?
- A52
- B65
- C76
- D98
- 2
Which number is even?
- A131
- B247
- C358
- D509
- 3
Is 204 divisible by 3?
- AYes, because 2 + 0 + 4 = 6
- BNo, because 2 + 0 + 4 = 7
- CNo, because 204 is even
- 4
Which number is divisible by 3?
- A142
- B251
- C312
- D430
- 5
Put 1236 through the flowchart. Is it divisible by 5? Is it divisible by 3?
- ANo, Yes
- BYes, No
- CYes, Yes
- DNo, No
- 6
Which number is divisible by both 3 and 5?
- A105
- B110
- C125
- D205
- 7
Follow the flowchart. What is the last number written down?
- 8
72 students are put into equal teams. Which team size does NOT work?
- A3
- B4
- C5
- D6
- 9
A number is divisible by 2, by 3 and by 5. Which of these must it also be divisible by?
- A10
- B15
- C30
- Dall of these
- 10
What is the smallest 3-digit number that is divisible by 2, by 3 and by 5?
Answers: Flowcharts: worksheet 1
- B: 65 Numbers divisible by 5 end in 0 or 5. 65 ends in 5.
- C: 358 Even numbers end in 0, 2, 4, 6 or 8. 358 ends in 8.
- A: Yes, because 2 + 0 + 4 = 6 2 + 0 + 4 = 6, and 6 is in the 3 times table, so 204 is divisible by 3. (204 = 3 × 68.)
- C: 312 3 + 1 + 2 = 6, which is in the 3 times table. The others: 142 gives 7, 251 gives 8, 430 gives 7.
- A: No, Yes 1236 ends in 6, so it is not divisible by 5. 1 + 2 + 3 + 6 = 12, which is in the 3 times table, so it is divisible by 3.
- A: 105 105 ends in 5, and 1 + 0 + 5 = 6 is in the 3 times table. 110 has digit sum 2, 125 has 8 and 205 has 7.
- 32 It writes 1, 2, 4, 8, 16, 32. Then n doubles to 64, which is more than 50, so it stops before writing 64.
- C: 5 72 doesn't end in 0 or 5, so it can't be split into 5s. 72 ÷ 3 = 24, 72 ÷ 4 = 18 and 72 ÷ 6 = 12.
- D: all of these Divisible by 2 and 5 means divisible by 10. Divisible by 3 and 5 means divisible by 15. Divisible by 2, 3 and 5 means divisible by 30. So all of them.
- 120 It must end in 0 (for 2 and 5) and have a digit sum in the 3 times table. 100 gives 1, 110 gives 2, 120 gives 3. So 120.
Formulas with letters
Formulas with letters: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
If b = 7, what is 4b?
- 2
If y = 9, what is y − 4?
- 3
If n = 4, what is n²?
- 4
If a = 2 and b = 9, what is ab?
- 5
If x = 5, what is 2x²?
- 6
The area of a triangle is A = bh ÷ 2. Find A when the base b is 10 cm and the height h is 7 cm.
cm² - 7
Use P = 2l + 2w. A rectangle has perimeter 36 cm and length 11 cm. What is its width w?
cm - 8
Use A = lw. A rectangle has area 54 cm² and width 6 cm. What is its length?
cm - 9
Plumber A charges C = 80 + 60h dollars and Plumber B charges C = 50 + 70h dollars for h hours. For a 2-hour job, how many dollars cheaper is the cheaper plumber?
dollars - 10
Use F = 1.8C + 32. Water boils at 212 °F. What is that in °C?
°C
Answers: Formulas with letters: worksheet 1
- 28 4b means 4 × b. 4 × 7 = 28.
- 5 Put 9 in place of y: 9 − 4 = 5.
- 16 n² means n × n. 4 × 4 = 16.
- 18 ab means a × b. 2 × 9 = 18.
- 50 Only x is squared: x² = 25. Then 2 × 25 = 50.
- 35 cm² A = 10 × 7 ÷ 2 = 70 ÷ 2 = 35 cm².
- 7 cm 36 = 2 × 11 + 2w, so 36 = 22 + 2w. Take away 22: 2w = 14. So w = 7 cm.
- 9 cm 54 = l × 6, so l = 54 ÷ 6 = 9 cm.
- $10 (Plumber B) A: 80 + 60 × 2 = $200. B: 50 + 70 × 2 = $190. B is cheaper by 200 − 190 = $10.
- 100 °C 212 = 1.8C + 32. Take away 32: 1.8C = 180. Divide by 1.8: C = 100 °C.
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.
Four quadrants
Four quadrants: worksheet 1
Name Date Score / 10
The questions get harder as you go. Show your working in the space beside each question.
- 1
In which quadrant is point A?
- Athe second quadrant
- Bthe fourth quadrant
- Cthe first quadrant
- Dthe third quadrant
- 2
In which quadrant is the point (−2, −5)?
- Athe first quadrant
- Bthe second quadrant
- Cthe third quadrant
- Dthe fourth quadrant
- 3
Which point is in the fourth quadrant?
- A(3, −4)
- B(3, 4)
- C(−3, −4)
- D(−3, 4)
- 4
What is the y-coordinate of the point (−5, −2)?
- 5
The point (4, 2) moves 7 units left. What are its new coordinates?
- A(11, 2)
- B(4, −5)
- C(3, 2)
- D(−3, 2)
- 6
The point (−2, −1) moves 3 units right and 5 units up. What are its new coordinates?
- A(1, −6)
- B(3, 4)
- C(1, 4)
- D(−5, 4)
- 7
A point moves 4 units left and 3 units down, and ends at (−1, −1). Where did it start?
- A(3, 2)
- B(3, −4)
- C(−5, −4)
- D(−5, 2)
- 8
A point starts at (−2, 5). It moves 7 units down, then 5 units right. Which quadrant is it in now?
- Athe second quadrant
- Bthe fourth quadrant
- Cthe third quadrant
- Dthe first quadrant
- 9
A rectangle ABCD has A (−4, 2), B (3, 2) and C (3, −3). What is its perimeter?
units - 10
A triangle has corners (−1, −2), (3, −2) and (3, 3). It is translated so that the corner (3, 3) lands on (−2, 0). Where does the corner (−1, −2) land?
- A(−6, −5)
- B(−6, 1)
- C(4, 1)
- D(−4, −5)
Answers: Four quadrants: worksheet 1
- C: the first quadrant A is to the right of the y-axis and above the x-axis: top right is the first quadrant.
- C: the third quadrant Both coordinates are negative: left of the y-axis and below the x-axis. Bottom left is the third quadrant.
- A: (3, −4) The fourth quadrant is bottom right: x positive, y negative. That is (3, −4).
- -2 The y-coordinate is the second number: −2.
- D: (−3, 2) 4 steps left reach 0 and 3 more reach −3. y stays 2. New point (−3, 2).
- C: (1, 4) x: 3 right from −2 is 2 steps to 0, then 1 more, so x is 1. y: 5 up from −1 is 1 step to 0, then 4 more, so y is 4. New point (1, 4).
- A: (3, 2) Undo each move: 4 right from −1 gives 3, and 3 up from −1 gives 2. It started at (3, 2).
- B: the fourth quadrant 7 down: y goes from 5 to −2. 5 right: x goes from −2 to 3. The point (3, −2) is bottom right, the fourth quadrant.
- 24 units AB: −4 to 3 is 7 units. BC: 2 to −3 is 5 units. Perimeter = 7 + 5 + 7 + 5 = 24 units.
- A: (−6, −5) (3, 3) to (−2, 0) is 5 units left and 3 units down. (−1, −2) moves 5 left to −6 and 3 down to −5: (−6, −5).
Averages and range
Averages and range: 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 how many books some students read in a month. What is the range?
- A3 books
- B5 books
- C6 books
- D8 books
- 2
Find the median of 2, 3, 8, 10 and 11.
- 3
Find the mean of 2.5, 3.5 and 6.
- A3.5
- B4
- C6
- D12
- 4
Seven students measured their hand spans in millimetres: 31, 47, 25, 52, 39, 44 and 28. What is the median?
- A27 mm
- B39 mm
- C44 mm
- D52 mm
- 5
Find the median of 14, 9, 21, 17, 10 and 12.
- A12
- B13
- C14
- D19
- 6
A shoe shop wants to know which shoe size to order the most of. Which average is the most useful?
- AMedian
- BMean
- CMode
- 7
Four friends have a mean height of 150 cm. A fifth friend, Zara, who is 160 cm tall, joins them. What is the new mean height?
- A152 cm
- B155 cm
- C160 cm
- D190 cm
- 8
This dot plot shows how many kilometres 8 people walked on Sunday. What is the median?
km - 9
Every value in a set of data has 3 added to it. Which statistic stays the same?
- ARange
- BMean
- CMedian
- DMode
- 10
Five whole numbers have a mode of 4, a median of 5 and a mean of 6. The largest number is 10. When the numbers are in order, what is the fourth one?
Answers: Averages and range: worksheet 1
- B: 5 books The biggest value is 6 and the smallest is 1, so the range is 6 − 1 = 5.
- 8 The numbers are already in order. The middle one of the five is 8.
- B: 4 2.5 + 3.5 + 6 = 12, and 12 ÷ 3 = 4.
- B: 39 mm In order: 25, 28, 31, 39, 44, 47, 52. The 4th value is in the middle, 39.
- B: 13 In order: 9, 10, 12, 14, 17, 21. The two middle values are 12 and 14, and halfway between them is 13.
- C: Mode The mode is the most common size, so it tells the shop which size sells most.
- A: 152 cm The four friends total 4 × 150 = 600 cm. Add Zara: 600 + 160 = 760 cm. 760 ÷ 5 = 152.
- 4.5 km In order: 2, 3, 3, 4, 5, 5, 6, 8. The two middle values (4th and 5th) are 4 and 5, so the median is 4.5.
- A: Range Every value moves up by 3, so the biggest and smallest both go up by 3 and their difference does not change. The mean, median and mode all go up by 3.
- 7 The mode 4 means two of them are 4, and the median is 5: 4, 4, 5, ?, 10. The total is 5 × 6 = 30, so ? = 30 − 4 − 4 − 5 − 10 = 7.
The full set for Year 7
With a subscription you can print five worksheets for each of the 26 Year 7 maths topics, 130 in all, from Grown-ups > Maths worksheets. Every sheet has its own answer page. These are the topics:
Number
- Flowcharts
- Factors and multiples
- Below zero
- Squares and square roots
- Powers and prime factors
- Fractions to percentages
- Rounding and estimating
- Fraction problems
- Percentages of amounts
- Best buys and discounts
Algebra
- Formulas with letters
- Simplifying expressions
- Solving equations
- Real-life graphs
- Patterns to graphs
Measurement
- Area of triangles
- Volume of prisms
- Angles and parallel lines
Space
- Four quadrants
- Drawing 3D objects in 2D
- Classifying shapes
- Transformations
Statistics
- Averages and range
- Data investigation
Probability
- Chance experiments
- Sample spaces