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Term pack

Year 10 Maths

Name: ________________________

Skills in this pack

  • Real numbers
  • Pair of linear equations
  • Quadratic equations
  • Arithmetic progressions
  • Distance and section formulas
  • Introduction to trigonometry
  • Heights and distances
  • Areas related to circles
  • Combined solids
  • Similar triangles
  • Circles and tangents
  • Statistics of grouped data
  • Probability

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Year 10 Maths · 1 of 13

Real numbers

Use Euclid's division lemma and prime factorisation to find HCF and LCM, and tell a rational number from an irrational one.

Before you start

Move along this line between 1 and 2, a tenth at a time. Every tick you land on is a fraction — a whole number over a whole number.

1.01.11.21.31.41.51.61.71.81.92.0

√2 is about 1.414, so it hides between two of these ticks. Make the steps ten times finer and it hides between two of those instead. It never lands on one, and that is exactly what irrational means.

  1. 1.For any two numbers, HCF × LCM equals the product of the numbers. The HCF of two numbers is 9 and their LCM is 360. One of the numbers is 45. What is the other?

  2. 2.Find the HCF of 96 and 404 using Euclid's algorithm.

  3. 3.Euclid's division lemma says that for whole numbers a and b there are whole numbers q and r with a = bq + r, where r is smaller than b. Divide 455 by 42. What is the remainder?

  4. 4.What is the largest prime factor of 156?

  5. 5.Sort each number by whether it is rational or irrational.

    Groups: Rational · Irrational

    • 22/7
    • √3
    • √5
    • 0.75
    • √7
    • √9

  6. 6.√2 is neither a whole number nor a fraction, so it sits between two ticks on this line. Tap the tick just below it.

    Mark the line with an X.

    1.01.11.21.31.41.51.61.71.81.92.0

  7. 7.Find the HCF of 616 and 32 using Euclid's algorithm.

  8. 8.13/125 has a decimal expansion that stops. After how many decimal places does it stop?

    • a) 1
    • b) 4
    • c) 2
    • d) 3

Real numbers · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 2 of 13

Pair of linear equations

Solve a pair of linear equations in two variables by substitution and elimination, and say how many solutions a pair has.

Before you start

One scale, and every box on it hides the same weight. Move things about and find out what a single scale can and cannot tell you.

113

A scale can pin down one unknown, never two at once — which is exactly why a pair of equations is needed. Elimination is the step that turns the pair into a single scale like this one.

  1. 1.The sum of two numbers is 25 and their difference is 7. What is the larger number?

  2. 2.How many solutions does the pair x + 2y = 4 and 2x + 4y = 12 have?

    • a) Exactly one
    • b) None
    • c) Exactly two
    • d) Infinitely many

  3. 3.Two adult tickets and one child ticket cost 900 $. One adult ticket and one child ticket cost 500 $. What does one adult ticket cost? Give just the number.

  4. 4.Solve the pair 3x + 2y = 12 and x = 2. What is y?

  5. 5.For which of these pairs do the two lines cross at exactly one point?

    • a) x + y = 5 and x + y = 8
    • b) 2x + 3y = 6 and 4x + 6y = 5
    • c) x + 2y = 5 and 2x + y = 4
    • d) x + y = 5 and 2x + 2y = 10

  6. 6.Solve the pair x + y = 10 and x - y = 4. What is y?

  7. 7.Sort each pair of equations by whether its two lines ever meet.

    Groups: They meet · They never meet

    • 2x + y = 7 and x + 3y = 6
    • 2x - y = 1 and x + 2y = 8
    • x + y = 4 and 2x + 2y = 9
    • 3x + 2y = 6 and 6x + 4y = 5
    • x + y = 4 and x - y = 2
    • x + 5y = 2 and 2x + 10y = 9

  8. 8.The sum of two numbers is 25 and their difference is 7. What is the smaller number?

Pair of linear equations · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 3 of 13

Quadratic equations

Solve quadratic equations by factorising, and use the discriminant to describe the roots.

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

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

  2. 2.Solve x² - 5x + 6 = 0. Give the smaller root.

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

  4. 4.A quadratic equation whose discriminant is 0 has...

    • a) three real roots
    • b) two different real roots
    • c) two equal real roots
    • d) no real roots

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

    • x² + 5x + 6
    • x² - 5x + 6
    • x² - 4
    • x² + 4x + 4
    • (x + 2)(x - 2)
    • (x - 2)(x - 3)
    • (x + 2)(x + 3)
    • (x + 2)(x + 2)

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

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

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

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

Year 10 Maths · 4 of 13

Arithmetic progressions

Find the common difference, the nth term and the sum of an arithmetic progression.

Before you start

This line is the progression 5, 10, 15, 20 and onwards. Move from one term to the next and count the steps you have taken.

510152025303540

The first term takes no steps at all, so the 8th term is 5 with seven steps of 5 added on: 5 + 7 × 5 = 40. That is a + (n - 1)d, read straight off the line.

  1. 1.In the AP 3, 7, 11, 15, ... what is the common difference?

  2. 2.Sort each list by whether it is an arithmetic progression.

    Groups: Is an AP · Is not an AP

    • 9, 6, 3, 0
    • 10, 20, 30, 40
    • 2, 3, 5, 7
    • 1, 2, 4, 8
    • 1, 4, 9, 16
    • 1, 3, 5, 7

  3. 3.Find the sum of the first 10 terms of 2, 4, 6, 8, ...

  4. 4.Match each progression to its common difference.

    • 2, 5, 8, 11
    • 1, 3, 5, 7
    • 10, 6, 2, -2
    • 7, 8, 9, 10
    • 0, 10, 20, 30
    • 3
    • 10
    • 2
    • -4
    • 1

  5. 5.Find the sum 1 + 2 + 3 + ... + 100.

  6. 6.In the AP 5, 8, 11, ... what is the 20th term?

  7. 7.In the AP 3, 7, 11, 15, ... what is the 10th term?

  8. 8.Find the sum of the first 15 terms of 1, 3, 5, 7, ...

Arithmetic progressions · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 5 of 13

Distance and section formulas

Find the distance between two points, the point that divides a segment in a given ratio, and the area of a triangle from its vertices.

  1. 1.Which of these points is the same distance from the origin as (3, 4)?

    • a) (1, 6)
    • b) (4, 4)
    • c) (5, 0)
    • d) (2, 3)

  2. 2.Find the distance between the points (1, 2) and (4, 6). Give the answer in units.

  3. 3.How far is the point (7, 24) from the origin? Give the answer in units.

  4. 4.Find the midpoint of the segment joining (2, 3) and (8, 11). What is its y-coordinate?

  5. 5.What is the area of the triangle whose vertices are (1, 2), (2, 4) and (3, 6)? Give the answer in square units.

    • a) 2
    • b) 0
    • c) 3
    • d) 1

  6. 6.This line runs from 0 to 10. Tap the point that divides it in the ratio 2 : 3, measured from 0.

    Mark the line with an X.

    012345678910

  7. 7.The point P divides the segment joining (1, 2) and (7, 11) in the ratio 2 : 1, measured from (1, 2). What is the x-coordinate of P?

  8. 8.Match each pair of points to the distance between them, in units.

    • (0, 0) and (5, 12)
    • (0, 0) and (9, 12)
    • (0, 0) and (8, 6)
    • (1, 1) and (4, 5)
    • 5
    • 13
    • 10
    • 15

Distance and section formulas · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 6 of 13

Introduction to trigonometry

Find sine, cosine and tangent in a right-angled triangle and recall the standard angles.

Before you start

One angle of this right-angled triangle has been marked. Find out what that angle and each of the three sides are called.

1234
  1. 1. Opposite
  2. 2. Adjacent
  3. 3. Hypotenuse
  4. 4. The marked angle

Mark the other corner instead and opposite and adjacent swap over. The hypotenuse never moves, because it is fixed by the right angle rather than by the angle you chose.

  1. 1.What is sin 30°? Give your answer as a fraction.

  2. 2.In a right-angled triangle the side opposite an angle is 3 cm and the side next to it is 4 cm. What is the tangent of that angle? Give your answer as a fraction.

  3. 3.What is tan 45°?

  4. 4.What is tan 30°?

    • a) 1/2
    • b) 1/√3
    • c) √3
    • d) √3/2

  5. 5.What is sin 60°?

    • a) 1/√3
    • b) 1/2
    • c) √3
    • d) √3/2

  6. 6.What is sin 90°?

  7. 7.What is cos 0°?

  8. 8.Sort each ratio by its value.

    Groups: Equals 0 · Equals 1

    • tan 0°
    • cos 90°
    • cos 0°
    • sin 90°
    • sin 0°
    • tan 45°

Introduction to trigonometry · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 7 of 13

Heights and distances

Use angles of elevation and depression with the standard angles to find a height or a distance you cannot measure directly.

  1. 1.A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. Take √3 = 1.73. How far up the wall does it reach, in metres?

  2. 2.From a window you look down at a car, and from the car someone looks up at the window. How do the angle of depression and the angle of elevation compare?

    • a) They add up to 90°
    • b) The angle of elevation is larger
    • c) They are equal
    • d) The angle of depression is larger

  3. 3.From the top of a cliff, the angle of depression of a boat is 30°. As the boat sails straight towards the base of the cliff, what happens to the angle of depression?

    • a) It increases
    • b) It stays the same
    • c) It becomes an angle of elevation
    • d) It decreases

  4. 4.A pole stands upright on level ground. From a point 10 m from its base, the angle of elevation of the top of the pole is 45°. How tall is the pole, in metres?

  5. 5.The angle of elevation of the top of a tower from a point on level ground is 60°, and the point is 45 m from the base of the tower. Take √3 = 1.73. How tall is the tower, in metres?

  6. 6.An upright pole casts a shadow. Put these angles of elevation of the Sun in order, shortest shadow first.

    • 45°
    • 75°
    • 30°
    • 60°

  7. 7.From the top of a cliff 40 m high, the angle of depression of a boat at sea is 45°. How far is the boat from the base of the cliff, in metres?

  8. 8.Someone at the top of a cliff is looking down at a boat. Tap the angle of depression.

    Write the number of the part.

    123

Heights and distances · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 8 of 13

Areas related to circles

Find the arc length, area and perimeter of a sector, and the area of a segment.

  1. 1.Doubling a sector's radius while keeping its angle at the centre the same multiplies its area by what?

    • a) 2
    • b) 3
    • c) 8
    • d) 4

  2. 2.A sector of a circle of radius 6 cm has an angle of 60° at the centre. Take π = 3.14. What is its area, in square centimetres?

  3. 3.In a circle of radius 10 cm a sector has an angle of 90° at the centre. Take π = 3.14. The triangle made by the two radii and the chord joining their ends has an area of 50 square centimetres. What is the area of the minor segment cut off by that chord, in square centimetres?

  4. 4.A quadrant is a sector with an angle of 90° at the centre. Take π = 22/7. What is the area of a quadrant of a circle of radius 14 cm, in square centimetres?

  5. 5.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. What is its area, in square centimetres?

  6. 6.A sector of a circle of radius 7 cm has an angle of 90° at the centre. Take π = 22/7. How long is its arc, in centimetres?

  7. 7.The minute hand of a clock is 21 cm long. Take π = 22/7. What area does it sweep in 5 minutes, in square centimetres?

  8. 8.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. How long is its arc, in centimetres?

Areas related to circles · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 9 of 13

Combined solids

Find the surface area and volume of a solid made by joining a cylinder, a cone or a hemisphere.

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

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

    Groups: A surface area · A volume

    • πrl
    • 4/3 πr³
    • 1/3 πr²h
    • 2πrh
    • 3πr²
    • πr²h

  3. 3.A toy is a cone standing on a hemisphere, both of radius 7 cm. The cone is 24 cm tall. What is the cone's slant height, in centimetres?

  4. 4.A cone, a hemisphere and a cylinder all have a radius of 7 cm, and the cone and the cylinder are both 7 cm tall. Which holds the most?

    • a) The hemisphere
    • b) The cone
    • c) The cylinder
    • d) They all hold the same

  5. 5.Match each solid to the formula for its curved surface area.

    • A sphere
    • A hemisphere
    • A cone
    • A cylinder
    • 2πrh
    • πrl
    • 2πr²
    • 4πr²

  6. 6.A sphere of radius 7 cm is cut exactly in half. Take π = 22/7. What is the total surface area of one hemisphere, counting its flat face, in square centimetres?

  7. 7.A cylinder of radius 7 cm and height 10 cm has a cone of radius 7 cm and slant height 25 cm standing on top of it. Its outside is the cone's curved surface, the cylinder's curved surface and the circular base. Take π = 22/7. What is the total surface area, in square centimetres?

  8. 8.A solid is a cylinder of radius 7 cm and height 10 cm with a cone of radius 7 cm and height 12 cm standing on top of it. Take π = 22/7. What is the volume of the cylinder part, in cubic centimetres?

Combined solids · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 10 of 13

Similar triangles

Use equal angles and side ratios in similar triangles, including the ratio of their areas.

  1. 1.Which of these is true of two similar triangles?

    • a) Matching sides are equal
    • b) They must be right-angled
    • c) Matching sides are in the same ratio
    • d) They must be the same size

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

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

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

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

  4. 4.Two similar triangles have sides in the ratio 2:3. The area of the smaller is 16 square centimetres. What is the area of the larger, in square centimetres?

  5. 5.In triangle ABC, DE is parallel to BC. AD is 2 cm, DB is 4 cm and AE is 3 cm. How long is EC, in centimetres?

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

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

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

    Groups: Always similar · Not always similar

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

  8. 8.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?

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

Year 10 Maths · 11 of 13

Circles and tangents

Use the two tangent properties of a circle: a tangent meets the radius at a right angle, and the two tangents from an outside point are equal.

Before you start

Three straight lines have been drawn on this circle. Find out what each one is called.

123
  1. 1. Diameter
  2. 2. Chord
  3. 3. Tangent

The tangent is the only one of the three that never gets inside the circle. And a diameter is not a separate kind of thing at all — it is simply a chord that happens to pass through the centre.

  1. 1.A tangent from a point P touches a circle with centre O at A. The radius OA is 8 cm and the hypotenuse OP is 17 cm. How long is the tangent PA, in centimetres?

  2. 2.Two tangents are drawn from a point P to a circle, touching it at A and B. How does PB compare with PA?

    • a) PB is twice PA
    • b) PB is half of PA
    • c) It depends on the radius
    • d) PB is the same length as PA

  3. 3.A tangent from a point P touches a circle with centre O at A. The radius OA is 5 cm and the hypotenuse OP is 13 cm. How long is the tangent PA, in centimetres?

  4. 4.PA and PB are the two tangents drawn from a point P, and PA is 12 cm long. What is the total length of PA and PB, in centimetres?

  5. 5.A tangent PA is 24 cm long and the hypotenuse OP of triangle OAP is 25 cm. How long is the radius OA, in centimetres?

  6. 6.In triangle OAP the angle at A is a right angle and the angle at P is 30°. What is the angle at O, in degrees?

  7. 7.Match each circle and outside point to the length of the tangent from that point, in centimetres.

    • radius 3 cm, point 5 cm from the centre
    • radius 8 cm, point 10 cm from the centre
    • radius 12 cm, point 13 cm from the centre
    • radius 6 cm, point 10 cm from the centre
    • 4
    • 6
    • 5
    • 8

  8. 8.OAPB is a quadrilateral with right angles at A and B, and its angle at P is 70°. What is its angle at O, in degrees?

Circles and tangents · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 12 of 13

Statistics of grouped data

Find the mean, median and mode of grouped data, and read a cumulative frequency curve.

  1. 1.A grouped table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 2, 4, 3 and 1. Which class has the highest frequency? Give its lower limit.

  2. 2.A grouped table has the classes 0–10, 10–20 and 20–30 with frequencies 3, 5 and 2. What is the mean, using class marks?

  3. 3.In a grouped table the modal class is 30–40 with a frequency of 20. The class before it has a frequency of 10 and the class after it has a frequency of 5, and every class is 10 wide. The mode is l + ((f₁ - f₀) ÷ (2f₁ - f₀ - f₂)) × h. What is the mode?

  4. 4.A grouped table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 2, 4, 3 and 1. What is the mean, using class marks?

  5. 5.Match each class to its class mark.

    • 0–10
    • 20–40
    • 25–45
    • 50–70
    • 5
    • 60
    • 35
    • 30

  6. 6.A less-than ogive is drawn for 50 observations. At what cumulative frequency do you read across the curve to find the median?

  7. 7.This histogram shows a grouped frequency table. Tap the modal class.

    Write the number of the part.

    1234

  8. 8.What is the class mark of the class 40–70?

Statistics of grouped data · Year 10 Maths · www.arenapublications.com/learn

Year 10 Maths · 13 of 13

Probability

Work out the probability of a simple event and of it not happening.

  1. 1.A card is drawn from a full pack of 52. What is the probability it is red? Give your answer as a fraction.

  2. 2.A fair die is rolled. What is the probability of getting a number greater than 4? Give your answer as a fraction.

  3. 3.A card is drawn from a full pack of 52. What is the probability it is a king? Give your answer as a fraction.

  4. 4.Which of these could never be a probability?

    • a) 0
    • b) 0.25
    • c) 1
    • d) 1.5

  5. 5.The probability that it rains tomorrow is 0.3. What is the probability that it does not rain?

  6. 6.A fair die is rolled. What is the probability of getting a 4? Give your answer as a fraction.

  7. 7.What is the probability of an event that is certain to happen?

    • a) It depends on the event
    • b) 0.5
    • c) 1
    • d) 0

  8. 8.A fair die is rolled. What is the probability of getting an even number? Give your answer as a fraction.

Probability · Year 10 Maths · www.arenapublications.com/learn

Answer keys — Year 10 Maths

In the same order as the worksheets.

Real numbers

  1. 1. 72
  2. 2. 4
  3. 3. 35
  4. 4. 13
  5. 5. √9 → Rational; 0.75 → Rational; 22/7 → Rational; √5 → Irrational; √7 → Irrational; √3 → Irrational
  6. 6. 1.4
  7. 7. 8
  8. 8. d) 3

Pair of linear equations

  1. 1. 16
  2. 2. b) None
  3. 3. 400
  4. 4. 3
  5. 5. c) x + 2y = 5 and 2x + y = 4
  6. 6. 3
  7. 7. x + y = 4 and x - y = 2 → They meet; x + y = 4 and 2x + 2y = 9 → They never meet; 2x + y = 7 and x + 3y = 6 → They meet; 3x + 2y = 6 and 6x + 4y = 5 → They never meet; 2x - y = 1 and x + 2y = 8 → They meet; x + 5y = 2 and 2x + 10y = 9 → They never meet
  8. 8. 9

Quadratic equations

  1. 1. b) x² - 4x + 3 = 0
  2. 2. 2
  3. 3. 3
  4. 4. c) two equal real roots
  5. 5. x² + 5x + 6 → (x + 2)(x + 3); x² - 5x + 6 → (x - 2)(x - 3); x² - 4 → (x + 2)(x - 2); x² + 4x + 4 → (x + 2)(x + 2)
  6. 6. -4
  7. 7. 6
  8. 8. -11

Arithmetic progressions

  1. 1. 4
  2. 2. 1, 3, 5, 7 → Is an AP; 10, 20, 30, 40 → Is an AP; 9, 6, 3, 0 → Is an AP; 1, 2, 4, 8 → Is not an AP; 2, 3, 5, 7 → Is not an AP; 1, 4, 9, 16 → Is not an AP
  3. 3. 110
  4. 4. 2, 5, 8, 11 → 3; 1, 3, 5, 7 → 2; 10, 6, 2, -2 → -4; 7, 8, 9, 10 → 1; 0, 10, 20, 30 → 10
  5. 5. 5050
  6. 6. 62
  7. 7. 39
  8. 8. 225

Distance and section formulas

  1. 1. c) (5, 0)
  2. 2. 5
  3. 3. 25
  4. 4. 7
  5. 5. b) 0
  6. 6. 4
  7. 7. 5
  8. 8. (0, 0) and (5, 12) → 13; (0, 0) and (9, 12) → 15; (0, 0) and (8, 6) → 10; (1, 1) and (4, 5) → 5

Introduction to trigonometry

  1. 1. 1/2
  2. 2. 3/4
  3. 3. 1
  4. 4. b) 1/√3
  5. 5. d) √3/2
  6. 6. 1
  7. 7. 1
  8. 8. sin 0° → Equals 0; cos 90° → Equals 0; tan 0° → Equals 0; cos 0° → Equals 1; sin 90° → Equals 1; tan 45° → Equals 1

Heights and distances

  1. 1.
    • 8.65
    • 8.66
  2. 2. c) They are equal
  3. 3. a) It increases
  4. 4. 10
  5. 5.
    • 77.85
    • 77.94
  6. 6. 1. 75° 2. 60° 3. 45° 4. 30°
  7. 7. 40
  8. 8. 1 — The angle of depression at the cliff top

Areas related to circles

  1. 1. d) 4
  2. 2. 18.84
  3. 3. 28.5
  4. 4. 154
  5. 5. 231
  6. 6. 11
  7. 7. 115.5
  8. 8. 22

Combined solids

  1. 1. 308
  2. 2. 2πrh → A surface area; πr²h → A volume; 4/3 πr³ → A volume; πrl → A surface area; 3πr² → A surface area; 1/3 πr²h → A volume
  3. 3. 25
  4. 4. c) The cylinder
  5. 5. A sphere → 4πr²; A hemisphere → 2πr²; A cone → πrl; A cylinder → 2πrh
  6. 6. 462
  7. 7. 1144
  8. 8. 1540

Similar triangles

  1. 1. c) Matching sides are in the same ratio
  2. 2. c) Yes, always
  3. 3. c) divides the other two sides in the same ratio
  4. 4. 36
  5. 5. 6
  6. 6. c) similar
  7. 7. Two squares → Always similar; Two circles → Always similar; Two equilateral triangles → Always similar; Two rectangles → Not always similar; Two isosceles triangles → Not always similar; Two rhombuses → Not always similar
  8. 8. 30

Circles and tangents

  1. 1. 15
  2. 2. d) PB is the same length as PA
  3. 3. 12
  4. 4. 24
  5. 5. 7
  6. 6. 60
  7. 7. radius 3 cm, point 5 cm from the centre → 4; radius 8 cm, point 10 cm from the centre → 6; radius 12 cm, point 13 cm from the centre → 5; radius 6 cm, point 10 cm from the centre → 8
  8. 8. 110

Statistics of grouped data

  1. 1. 10
  2. 2. 14
  3. 3. 34
  4. 4. 18
  5. 5. 0–10 → 5; 20–40 → 30; 25–45 → 35; 50–70 → 60
  6. 6. 25
  7. 7. 2 — 10–20
  8. 8. 55

Probability

  1. 1. 1/2
  2. 2. 1/3
  3. 3. 1/13
  4. 4. d) 1.5
  5. 5. 0.7
  6. 6. 1/6
  7. 7. c) 1
  8. 8. 1/2

Year 10 Maths · www.arenapublications.com/learn