Year 8 Maths

1. 1.2/3 × 9/8 = ? Write your answer as a fraction in its simplest form.

2. 2.Write the rational number that lies exactly halfway between 1/3 and 1/2.

3. 3.4/9 × 7/5 + 4/9 × 3/5 = ? Write your answer as a fraction.

4. 4.Sort each statement by whether it is true for every choice of rational numbers a, b and c.

   Groups: Always true · Not always true

   • a - b = b - a
   • a ÷ b = b ÷ a
   • a × b = b × a
   • a + b = b + a
   • (a + b) + c = a + (b + c)
   • (a - b) - c = a - (b - c)

5. 5.Put these rational numbers in order, smallest first.

   • 0
   • -1/4
   • 3/8
   • 7/6
   • -5/3
   • -1/2

6. 6.Tap where -7/4 sits.

   Mark the line with an X.

7. 7.What is the reciprocal of -7/9? Write your answer as a fraction.

8. 8.Match each rational number to its additive inverse — the number you add to it to get zero.

   • 2/7
   • -5/9
   • 3/4
   • -11/6
   • 8/3

   • 5/9
   • 11/6
   • -3/4
   • -2/7
   • -8/3

Properties of rational numbers · Year 8 Maths · www.arenapublications.com/learn

1. 1.Simplify (2³)².

   • a) 2¹
   • b) 2⁶
   • c) 2⁵
   • d) 2⁹

2. 2.What is 10⁴?

3. 3.What is 3⁰?

4. 4.Simplify a⁵ × a³.

   • a) 2a⁸
   • b) a¹⁵
   • c) a⁸
   • d) a²

5. 5.What is 5²?

6. 6.64 can be written as 2 to some power. What is that power?

7. 7.What is 2³ (two to the power 3)?

8. 8.Work out 2⁵ ÷ 2³ as an ordinary number.

Exponents and powers · Year 8 Maths · www.arenapublications.com/learn

1. 1.A journey takes 4 hours at 60 km per hour. How many hours would it take at 80 km per hour?

2. 2.If 5 pens cost $60, what do 8 pens cost? Give just the number.

3. 3.y is in inverse proportion to x. When x is 4, y is 15. What is y when x is 10?

4. 4.6 workers take 12 days to finish a job. Match each number of workers to the days they would take at the same rate.

   • 4 workers
   • 8 workers
   • 9 workers
   • 12 workers
   • 18 workers

   • 8 days
   • 4 days
   • 9 days
   • 6 days
   • 18 days

5. 5.12 pipes fill a tank in 20 minutes. How many minutes would 15 pipes take?

6. 6.If 4 kg of rice costs $200, what do 7 kg cost? Give just the number.

7. 7.6 workers build a wall in 12 days. How many days would 8 workers take, working at the same rate?

8. 8.A job takes 6 people 12 days. Put these teams in order by how long they would take, shortest first.

   • 12 people
   • 6 people
   • 9 people
   • 4 people
   • 18 people

Direct and inverse proportion · Year 8 Maths · www.arenapublications.com/learn

1. 1.The product of two integers is -48. One of them is 6. What is the other?

2. 2.Match each calculation to its answer.

   • -6 × 5
   • -6 × (-5)
   • -42 ÷ 7
   • -42 ÷ (-6)
   • 9 × (-2)

   • 7
   • -30
   • -6
   • 30
   • -18

3. 3.-15 + 3 × (-4) = ?

4. 4.-3 × (-4) × (-2) = ?

5. 5.56 ÷ (-7) = ?

6. 6.Tap the integer that is exactly halfway between -8 and 2.

   Mark the line with an X.

7. 7.-6 × 4 = ?

8. 8.-36 ÷ 9 = ?

Multiplying and dividing integers · Year 8 Maths · www.arenapublications.com/learn

1. 1.In a simple interest question, what does the rate tell you?

   • a) The total interest over the whole time
   • b) The interest earned on every 100 of the principal in one year
   • c) The amount borrowed at the start
   • d) The number of years the money is kept for

2. 2.Each of these is left for 2 years. Sort them by whether the simple interest comes to less or more than $500.

   Groups: Less than $500 · More than $500

   • $4000 at 8% per year
   • $2000 at 10% per year
   • $1000 at 20% per year
   • $5000 at 8% per year
   • $5000 at 6% per year
   • $3000 at 5% per year

3. 3.Find the simple interest on $600 at 12% per year for 5 years. Give just the number.

4. 4.The principal and the rate stay the same, but the money is left for twice as long. What happens to the simple interest?

   • a) It stays the same
   • b) It is multiplied by itself
   • c) It halves
   • d) It doubles

5. 5.Find the simple interest on $5000 at 8% per year for 2 years. Give just the number.

6. 6.Find the simple interest on $2000 at 5% per year for 3 years. Give just the number.

7. 7.The simple interest on $800 at 5% per year is $200. For how many years was the money invested?

8. 8.In every row the principal is $1000 and the rate is 10% per year. Match each length of time to the simple interest it earns.

   • 1 year
   • 2 years
   • 3 years
   • 5 years

   • 500
   • 300
   • 100
   • 200

Simple interest · Year 8 Maths · www.arenapublications.com/learn

1. 1.5*7 is divisible by 3. What is the largest digit that can replace the star?

2. 2.Put these numbers in order by how many of 2, 3, 5 and 9 divide into them exactly, fewest first.

   • 15
   • 7
   • 18
   • 90
   • 4

3. 3.A two-digit number is 27 more than the number you get by reversing its digits, and its two digits add to 11. What is the number?

4. 4.Match each divisibility test to the number it tests for.

   • The last digit is 0 or 5
   • The digits add to a multiple of 3
   • The last two digits make a multiple of 4
   • The digits add to a multiple of 9
   • The last digit is even

   • 3
   • 4
   • 2
   • 9
   • 5

5. 5.In the sum A7 + 4A = 113, the letter A stands for one digit. What digit is A?

6. 6.What is the smallest digit that can replace the star so that 3*5 is divisible by 3?

7. 7.How can you tell that 4832 is divisible by 8 without dividing the whole number?

   • a) Its digits add to a multiple of 8
   • b) Its first digit is divisible by 8
   • c) It ends in an even digit
   • d) Its last three digits, 832, make a multiple of 8

8. 8.What digit must replace the star so that 21*8 is divisible by 9?

Playing with numbers · Year 8 Maths · www.arenapublications.com/learn

1. 1.Solve x/5 + 2 = 5. x = ?

2. 2.Solve 7 - 2x = x + 1. x = ?

3. 3.Match each equation to its solution.

   • 2x + 3 = 11
   • 3x - 1 = 14
   • 5x + 4 = 4x + 10
   • 7x = 4x + 21
   • 2x - 9 = x - 1

   • 8
   • 4
   • 5
   • 6
   • 7

4. 4.Sort each equation by whether its solution is positive or negative.

   Groups: x is positive · x is negative

   • x + 6 = 2x
   • 4x + 7 = 2x + 1
   • 6x + 5 = 4x - 1
   • 5x - 2 = 3x + 6
   • 3x = x + 8
   • 2x + 9 = x + 4

5. 5.Which value of x makes 6x - 5 = 4x + 3 true?

   • a) 4
   • b) 1
   • c) 2
   • d) -4

6. 6.The sum of two consecutive whole numbers is 45. Write the smaller number.

7. 7.Solve 4(x - 3) = 2x + 6. x = ?

8. 8.A rectangle is 3 cm longer than it is wide, and its perimeter is 26 cm. How wide is it, in cm? Give just the number.

Linear equations with the unknown on both sides · Year 8 Maths · www.arenapublications.com/learn

1. 1.Which of these is x² + 10x + 25 written in factorised form?

   • a) (x + 5)²
   • b) (x + 10)²
   • c) (x + 25)(x + 1)
   • d) (x + 5)(x - 5)

2. 2.Divide x² + 5x + 6 by x + 2. Write the answer.

3. 3.Take a out of a² + ab as a common factor. What is left inside the bracket?

4. 4.Put these expressions in order by the highest common factor of their terms, smallest first.

   • 14x + 21
   • 4x + 8
   • 10x + 25
   • 6x + 18
   • 3x + 9

5. 5.Which of these is 4x² - 9 written in factorised form?

   • a) (2x - 3)(2x - 3)
   • b) (2x - 9)(2x + 1)
   • c) (2x - 3)(2x + 3)
   • d) (4x - 3)(x + 3)

6. 6.Take 5 out of 5y - 20 as a common factor. What is left inside the bracket?

7. 7.Divide 24y³ - 16y² by 8y². Write the answer.

8. 8.Match each expression to its factorised form.

   • x² - 16
   • x² + 8x + 16
   • 3x + 12
   • x² - 4x
   • 2x² - 32

   • 2(x - 4)(x + 4)
   • (x - 4)(x + 4)
   • x(x - 4)
   • (x + 4)²
   • 3(x + 4)

Factorisation · Year 8 Maths · www.arenapublications.com/learn

1. 1.A line graph shows a plant 4 cm tall on day 1 and 16 cm tall on day 7. How much did it grow over those six days, in cm? Give just the number.

2. 2.On a distance-time graph, what does a flat horizontal part of the line mean?

   • a) The object is going backwards
   • b) The graph has been drawn wrongly
   • c) The object is speeding up
   • d) The object is not moving

3. 3.Sort each point by where it sits on the grid.

   Groups: On the x-axis · On the y-axis · On neither axis

   • (0, -1)
   • (2, 7)
   • (-4, 0)
   • (0, 5)
   • (6, 6)
   • (3, 0)

4. 4.A car travels at a steady 50 km per hour. On a distance-time graph, how far has it gone after 3 hours, in km? Give just the number.

5. 5.A shop sells notebooks at $20 each. On a graph of cost against number bought, what is the cost of 7 notebooks? Give just the number.

6. 6.This distance-time graph shows one journey in three parts. Tap the part where the car was not moving.

   Write the number of the part.

7. 7.A point sits 4 units to the right of the origin and 7 units up. Write its y-coordinate.

8. 8.For the relation y = 3x, what is y when x is 6?

Introduction to graphs · Year 8 Maths · www.arenapublications.com/learn

1. 1.A cube has edges of 5 cm. What is its total surface area, in square centimetres?

2. 2.A circle has a radius of 14 cm. Take π = 22/7. What is its area, in square centimetres?

3. 3.A cylinder has a radius of 7 cm and a height of 10 cm. Take π = 22/7. What is its curved surface area, in square centimetres?

4. 4.A cube has edges of 5 cm. What is its volume, in cubic centimetres?

5. 5.A trapezium has parallel sides of 10 cm and 6 cm, and a height of 4 cm. What is its area, in square centimetres?

6. 6.A cylinder has a radius of 7 cm and a height of 10 cm. Take π = 22/7. What is its total surface area, in square centimetres?

7. 7.Sort each formula by what it measures.

   Groups: Measures area · Measures volume

   • π × r × r
   • length × width × height
   • edge × edge × edge
   • π × r × r × h
   • length × width
   • 2 × π × r × h

8. 8.Which of these gives the volume of a cylinder?

   • a) π × r × r
   • b) 2 × π × r × h
   • c) 2 × π × r
   • d) π × r × r × h

Mensuration · Year 8 Maths · www.arenapublications.com/learn

1. 1.Three angles of a quadrilateral are 80, 100 and 65 degrees. What is the fourth, in degrees? Give just the number.

2. 2.What do the interior angles of a hexagon add up to, in degrees? Give just the number.

3. 3.Which of these is true of every rhombus but not of every rectangle?

   • a) Opposite sides are parallel
   • b) Opposite angles are equal
   • c) The angles add up to 360 degrees
   • d) All four sides are the same length

4. 4.What do the interior angles of a pentagon add up to, in degrees? Give just the number.

5. 5.Sort each property by whether it is true of every parallelogram.

   Groups: True of every parallelogram · Not true of every parallelogram

   • Every angle is a right angle
   • The diagonals cut each other in half
   • All four sides are equal
   • Opposite angles are equal
   • The diagonals are equal in length
   • Opposite sides are equal

6. 6.Each exterior angle of a regular polygon is 45 degrees. How many sides has it?

7. 7.In which quadrilateral do the diagonals always cross at right angles and always come out the same length?

   • a) A parallelogram
   • b) A square
   • c) A rectangle
   • d) A rhombus

8. 8.Put these polygons in order by what their interior angles add up to, smallest first.

   • Octagon
   • Hexagon
   • Quadrilateral
   • Pentagon
   • Triangle

Understanding quadrilaterals · Year 8 Maths · www.arenapublications.com/learn

1. 1.Two triangles have two pairs of angles equal, and the side between those angles is equal too. Which rule proves they are congruent?

   • a) SAS
   • b) RHS
   • c) SSS
   • d) ASA

2. 2.Is knowing that all three pairs of angles are equal enough to prove two triangles congruent?

   • a) No — that only makes them the same shape, not the same size
   • b) Only for isosceles triangles
   • c) Only for right-angled triangles
   • d) Yes, always

3. 3.Sort each set of matching parts by whether it is enough to prove congruence.

   Groups: Proves congruence · Does not prove congruence

   • AAA
   • RHS
   • SAS
   • ASA
   • SSA
   • SSS

4. 4.In an isosceles triangle, the line from the apex to the midpoint of the base splits it into two triangles that are...

   • a) not related to each other
   • b) congruent, by SSS
   • c) the same shape but different sizes
   • d) congruent, by AAA

5. 5.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?

   • a) RHS
   • b) SSS
   • c) SAS
   • d) ASA

6. 6.Triangle ABC is congruent to triangle PQR. Angle A is 55°. How big is angle P, in degrees?

7. 7.Triangle ABC is congruent to triangle PQR. AB is 7 cm long. How long is PQ, in centimetres?

8. 8.Two triangles have two pairs of sides equal, and the angle between those sides is equal too. Which rule proves they are congruent?

   • a) ASA
   • b) SSS
   • c) RHS
   • d) SAS

Congruent triangles · Year 8 Maths · www.arenapublications.com/learn

1. 1.One side of a parallelogram is 8 cm long. How long is the side opposite it, in centimetres?

2. 2.In triangle PQR, the segment joining the mid-points of PQ and PR is 9 cm long. How long is QR, in centimetres?

3. 3.Match each quadrilateral to the property that sets it apart.

   • Parallelogram
   • Rectangle
   • Rhombus
   • Square
   • Kite

   • All four angles are right angles
   • All four sides are equal
   • Both pairs of opposite sides are parallel
   • Two pairs of equal sides, next to each other rather than opposite
   • All four sides equal and all four angles right angles

4. 4.In triangle ABC, D is the mid-point of AB and E is the mid-point of AC. BC is 12 cm long. How long is DE, in centimetres?

5. 5.Sort each property by whether every parallelogram has it.

   Groups: Every parallelogram · Not every parallelogram

   • The diagonals are equal in length
   • Every angle is a right angle
   • The diagonals cut each other in half
   • Opposite sides are equal
   • Opposite angles are equal
   • All four sides are equal

6. 6.Which of these is true of every rhombus but not of every parallelogram?

   • a) Opposite angles are equal
   • b) Opposite sides are parallel
   • c) The diagonals cut each other in half
   • d) All four sides are equal

7. 7.The mid-point theorem says the segment joining the mid-points of two sides of a triangle is...

   • a) twice the length of the third side
   • b) perpendicular to the third side
   • c) equal in length to the third side
   • d) parallel to the third side and half its length

8. 8.One angle of a parallelogram is 65°. How big is the angle opposite it, in degrees?

Quadrilaterals · Year 8 Maths · www.arenapublications.com/learn

1. 1.Sort each pair of figures by whether they have to be congruent.

   Groups: Must be congruent · Need not be congruent

   • Two equilateral triangles with sides of 5 cm
   • Two squares with sides of 4 cm
   • Two triangles with the same three angles
   • Two line segments 7 cm long
   • Two rectangles with the same area
   • Two rectangles with the same perimeter

2. 2.Two figures are congruent when they...

   • a) have the same shape, but may be different sizes
   • b) have exactly the same shape and exactly the same size
   • c) have the same area as each other
   • d) have the same number of sides as each other

3. 3.Triangle ABC is congruent to triangle PQR. The perimeter of ABC is 26 cm. What is the perimeter of PQR, in centimetres?

4. 4.Triangle ABC is congruent to triangle DEF. Angle C is 72°. How big is angle F, in degrees?

5. 5.Two line segments are congruent when...

   • a) they meet at a point
   • b) they are both perfectly straight
   • c) they are the same length
   • d) they point in the same direction

6. 6.Triangle ABC is congruent to triangle PQR, with A matching P, B matching Q and C matching R. Tap the side of triangle PQR that matches side AB.

   Write the number of the part.

7. 7.Triangle ABC is congruent to triangle DEF. BC is 9 cm long. How long is EF, in centimetres?

8. 8.A square tile is lifted up and put back down turned a quarter turn. Is it congruent to the way it was before?

   • a) Yes — turning a shape changes neither its shape nor its size
   • b) Only if it was the right way up to begin with
   • c) Only if it is turned back first
   • d) No, because it is facing a different way

Congruence · Year 8 Maths · www.arenapublications.com/learn