Year 10 Maths

1. 1.What is the discriminant, b² - 4ac, of x² + 4x + 4 = 0?

2. 2.Solve x² + 7x + 12 = 0. Give the smaller root.

3. 3.Match each quadratic to its factorised form.

   • x² + 5x + 6
   • x² - 5x + 6
   • x² - 4
   • x² + 4x + 4

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

4. 4.Which of these is a quadratic equation?

   • a) x + 7 = 0
   • b) x³ - 1 = 0
   • c) x² - 4x + 3 = 0
   • d) 2x + 5 = 0

5. 5.Solve x² - 9 = 0. Give the positive root.

6. 6.The product of two consecutive whole numbers is 42. What is the smaller number?

7. 7.Solve x² - 5x + 6 = 0. Give the larger root.

8. 8.What is the discriminant, b² - 4ac, of x² - 3x + 5 = 0?

Quadratic equations · Year 10 Maths · www.arenapublications.com/learn

1. 1.£4000 is lent at 10 per cent per year, compounded half-yearly, for 1 year. What amount is owed at the end? Give just the number.

2. 2.Sort each description by which kind of interest it belongs to.

   Groups: Simple interest · Compound interest

   • Each year's interest is added on before the next year is worked out
   • A population rising by the same percentage every year
   • The interest is the same amount every year
   • Doubling the time doubles the interest exactly
   • Interest is always worked out on the original sum only
   • The amount grows faster and faster as the years go by

3. 3.Find the compound interest on £1000 at 20 per cent per year for 2 years. Give just the number.

4. 4.The simple interest on £4000 at 10 per cent for 2 years is £800. What is the compound interest on the same sum at the same rate and time? Give just the number.

5. 5.A town of 10000 people grows by 10 per cent every year. How many people live there after 2 years?

6. 6.Find the compound interest on £5000 at 10 per cent per year for 2 years. Give just the number.

7. 7.A machine worth £20000 loses 10 per cent of its value every year. What is it worth after 2 years? Give just the number.

8. 8.£2000 is invested at 10 per cent per year, compounded yearly, for 3 years. What amount does it grow to? Give just the number.

Compound interest · Year 10 Maths · www.arenapublications.com/learn

1. 1.Two similar triangles have sides in the ratio on the left. Match it to the ratio of their areas.

   • 1:2
   • 1:3
   • 2:3
   • 3:4
   • 1:5

   • 9:16
   • 1:25
   • 4:9
   • 1:9
   • 1:4

2. 2.Are any two squares similar to each other?

   • a) No, never
   • b) Only if they are the same size
   • c) Only if they are drawn on grid paper
   • d) Yes, always

3. 3.Two similar triangles have sides in the ratio 3:5. The perimeter of the smaller is 18 cm. What is the perimeter of the larger, in centimetres?

4. 4.Two triangles have all three pairs of angles equal. The triangles are...

   • a) unrelated
   • b) similar
   • c) always right-angled
   • d) congruent

5. 5.Triangle ABC is similar to triangle PQR. AB is 4 cm and PQ is 12 cm. BC is 5 cm. How long is QR, in centimetres?

6. 6.The Basic Proportionality Theorem says that a line drawn parallel to one side of a triangle...

   • a) divides the other two sides in the same ratio
   • b) cuts the other two sides exactly in half
   • c) makes the triangle isosceles
   • d) is equal in length to the side it is parallel to

7. 7.Two similar triangles have sides in the ratio 1:4. The area of the smaller is 5 square centimetres. What is the area of the larger, in square centimetres?

8. 8.Sort each pair of shapes by whether they must always be similar.

   Groups: Always similar · Not always similar

   • Two isosceles triangles
   • Two rectangles
   • Two rhombuses
   • Two squares
   • Two circles
   • Two equilateral triangles

Similar triangles · Year 10 Maths · www.arenapublications.com/learn

1. 1.A sphere has a radius of 7 cm. Take π = 22/7. What is its surface area, in square centimetres?

2. 2.Which of these gives the volume of a sphere?

   • a) (4/3) × π × r × r × r
   • b) (1/3) × π × r × r × h
   • c) 4 × π × r × r
   • d) 2 × π × r × r

3. 3.Which of these gives the volume of a cone?

   • a) π × r × l
   • b) π × r × r × h
   • c) (4/3) × π × r × r × r
   • d) (1/3) × π × r × r × h

4. 4.A sphere has a radius of 21 cm. Take π = 22/7. What is its volume, in cubic centimetres?

5. 5.Match each solid to the formula for its volume.

   • Cuboid
   • Cylinder
   • Cone
   • Sphere

   • π × r × r × h
   • (1/3) × π × r × r × h
   • length × width × height
   • (4/3) × π × r × r × r

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

7. 7.A cone has a radius of 7 cm and a slant height of 25 cm. Take π = 22/7. What is its curved surface area, in square centimetres?

8. 8.A cone has a radius of 7 cm and a height of 24 cm. What is its slant height, in centimetres?

Surface area and volume · Year 10 Maths · www.arenapublications.com/learn