Fourth Level Hwk Zeta Maths - LT Scotland · 2019-12-18 · !©Zeta!Maths!Ltd.! ©!ZETA!MATHSLTD....

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Fourth Level Mathematics

DEVELOPMENT AND CONSOLIDATION

Homework Exercises

© Zeta Maths Ltd.

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INTRODUCTION

The aim of this book is to support learners in their pursuit of excellence in Mathematics. Curriculum for Excellence offers learners breadth in learning; this resource is intended to assist learners in developing depth and consolidation of skills.

The resource can be used in a variety of ways: It may be used systematically as learners work through the book progressively doing each of the four exercises from each homework on consecutive days of the week, or it may be used in a more flexible way. The contents page is intended for learners and teachers to keep track of progress through the resource. Learners may use a traffic light system for each of the exercises to monitor progression through each of the experiences and outcomes.

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Homework Contents Ex 1 Ex 2 Ex 3 Ex 4

1 Mixed Third Level Review 2 Mixed Homework 1 3 Mixed Third Level Review 4 Mixed Homework 1 5 Mixed Homework 4 6 Mixed Homework 2 7 Mixed Homework 2 8 Mixed Homework 4 9 Speed, Distance, Time 10 Mixed Homework 1 11 Volume and Surface Area 1 12 Mixed Homework 4 13 Volume and Surface Area 2 14 Straight Line – Gradient 15 Straight Line – Equation from Graph 16 Straight Line – Mixed 17 Sequences, Fractions, Algebra 18 Expanding Brackets 19 Factorising 20 Solving Equations -‐ Brackets 21 Mixed Homework 1 22 Solving Equations -‐ Brackets 23 Solving Equations -‐ Fractions 24 Mixed Homework 2 25 Mixed Homework 3 26 Solving Inequations 27 Circles – Area and Perimeter 28 Mixed Homework 2 29 Mixed Homework 1 30 Mixed Homework 5 31 Mixed Homework 3 32 Mixed Homework 6 33 Pythagoras 1 34 Pythagoras 2 35 Mixed Homework 3 36 Trigonometry 1 37 Mixed Homework 1 38 Trigonometry 2 39 Similar Shapes 40 Angles, Pythagoras 41 Angles, Pythagoras 42 Mixed Homework 2 43 Mixed Homework 1 44 Coordinates 45 Mixed Homework 3

CONTENTS CONTENTS

1

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Homework Contents Ex 1 Ex 2 Ex 3 Ex 4 46 Mixed Homework 6 47 Mixed Homework 2 48 Mixed Homework 3

CONTENTS Contd. CONTENTS Contd.

Exercise 1 Exercise 2

Exercise 4

1 Homework Fourth Level Homework Booklet CALCULATOR

Exercise 3

© Zeta Maths Ltd.

1. Find 55 x 30

2. Solve 6a – 2 = a + 9

3. 3 + 9 x 2 - 82

4. Find 18 000 ÷ 60

5. Find 1675 x 8 (show working)

6. Find the HCF of 32 and 18

7. Change 5.5m into mm. 8. Find the LCM of 5 and 12

9. Change 65cm to km

1. Find 27 x 600 2. Solve 9a – 5 = 2a + 8 3. 2 x 42 – 3 x (8 + 7)

4. Find 6400 ÷ 400


6. Find the HCF of 57 and 24 7. Change 40.5m into mm 8. Find the LCM of 7 and 12

9. Change 80cm to km

1. Find 1452 x 200

2. Solve 12a – 17 = 9 –a

3. 3 + 12 x 2 - 72

4. Find 452 000 ÷ 400

5. Find 17 984 x 6 (show working)


7. Change 312mm to m 8. Find the LCM of 9 and 6

9. Change 142km to mm

1. Find 245 x 500 2. Solve 4 – 5a = 9a + 7 3. 5 + 62 – 3(3 + 9) 4. Find 49 000 ÷ 70



7. Change 670mm to m

8. Find the LCM of 3 and 13

9. Change 0.04km to mm

CfE Outcomes 3-03a, 3-03b 3-15a, 2-03c, 2-01a, 2-03a, 3-07a

NON-‐ MEARNS CASTLE HIGH SCHOOL

Licensed to staff and pupils of Mearns Castle High School only


Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Express 72 as a product of prime factors.

2. Solve 4a – 2 = 3a + 8

3. 42 – 2 x 3 + 9

4. Simplify: 3a + 2a x 4a – a

5. Round the following to 2 significant figures:

a. 0.000405 b. 45 214

6. Find 0.002 x 0.4

7. Find 31

43+

8. Find the supplement of 76º.

1. Express 96 as a product of prime factors. 2. Solve 6a – 2 = 8a + 8 3. 3 x 22 – 2 x (3 + 9) 4. Simplify 4a x 2a - 4a2 5. Round the following to 2 significant figures:

a. 0.007695 b. 785 415 6. Find 23 x 0.9

7. Find 31

52−

8. Find the supplement of 108º.


2. Solve 7a – 2 = 9 – 3a

3. 8 – 2 x 7

4. Simplify 3a + 2a – 17a


a. 0.09099 b. 147 015

6. Find 0.002 x -0.8

7. Find 43

61+

8. Find the complement of 56º.

1. Express 56 as a product of prime factors. 2. Solve 4 – 3a = 5a + 7 3. 2 + 52 – 2(3 + 9) 4. Simplify 5a x 3 – 4a + 9 5. Round the following to 2 significant figures:

a. 0.06709 b. 999 999 6. Find 0.002 x -0.0005

7. Find 51

65−

8. Find the complement of 76º.

CfE Outcomes 3-05a, 3-15a, 4-03b, 4-01a, 3-07a, 3-07b, 3-17a




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find 46 x 30

2. Solve 3a – 2 = a + 8

3. Find 52 – 6 x 3 + 9

4. Find 18 000 ÷ 900.


6. Find the HCF of 64 and 18.

7. Change 2m into mm. 8. Find the LCM of 4 and 6.

9. Change 45cm to km.

1. Find 27 x 40 2. Solve 6a – 2 = 2a + 8 3. Find 3 x 32 – 4 x (3 + 7)

4. Find 4200 ÷ 600.


6. Find the HCF of 36 and 24. 7. Change 3.5m into mm. 8. Find the LCM of 3 and 17.

9. Change 69cm to km.

1. Find 132 x 200.

2. Solve 7a – 2 = 9 –a

3. Find 8 – 2 x 7

4. Find 48 000 ÷ 600.



7. Change 3mm to m. 8. Find the LCM of 4 and 14.

9. Change 16km to mm.

1. Find 245 x 500. 2. Solve 4 – 3a = 8a + 7 3. Find 2 + 52 – 2(3 + 9) 4. Find 420 000 ÷ 7000.



7. Change 15mm to m.

8. Find the LCM of 8 and 15.

9. Change 41km to mm

CfE Outcomes 3-03a, 3-03b 3-15a, 2-03c, 2-01a, 2-03a, 3-07a




Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 5t – 3 = 2t + 12

3. 62 – 5 x 4 + 12

4. Simplify: 7y + y x 4y – 5y


a. 0.08715 b. 614,709

6. Find 0.012 x 0.3

7. Find 15+34

8. Find the supplement of 13º

1. Express 125 as a product of prime factors. 2. Solve 9g – 4 = 4g + 31 3. 8 x 32 – 2 x (5 + 6) 4. Simplify: 8p x 5p – 3p2 5. Round the following to 2 significant figures:

a. 0.10367 b. 3,791 6. Find 31 x 0.6

7. Find 57−18



2. Solve 8h – 4 = 20 – 2h

3. 102 – 5 x 8

4. Simplify: 7f + 4f – 15f


a. 0.006362 b. 535,193

6. Find 0.0006 x -0.03

7. Find 15+37

8. Find the complement of 19.5º

1. Express 200 as a product of prime factors. 2. Solve 3 – 2r = 5r + 16 3. 3 + 62 – 4(8 - 2) 4. Simplify: 7n x 2 – 3n + 10 5. Round the following to 2 significant figures:

a. 0.07610 b. 1,090,907 6. Find 0.005 x -0.0008

7. Find 1316

−38






Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Write the following in scientific notation: (a) 14,920 (b) 265,000 (c) 0.004572

2. Round the numbers above to 2 significant

figures.

3. Petrol prices increased from £1.28 to £1.35, calculate the % increase to 1 decimal place.

4. Four apples cost £1.32, how much do 7 cost?

5. Find the volume of the shape, give your answer

in litres:

1. Write the following in scientific notation:

(a) 26,420 (b) 1,365,000 (c) 0.0009472


figures.

3. Petrol prices increased from $3.30 to $4.00, calculate the % increase to 1 decimal place.

4. Five apples cost £1.25, how much do 7 cost?


in litres:

1. Write the following in scientific notation: (a) 89,520 (b) 1,999,000 (c) 0.00009872


figures.

3. Petrol prices increased from €1.15 to €1.30, calculate the % increase to 1 decimal place.



in litres:


(a) 65,920 (b) 26,000 (c) 0.004


figures.


4. Six apples cost £1.68, how much do 7 cost?


in litres:

CfE Outcomes 4-06b, 4-01a, 4-03a, 3-11a, 3-11b

5cm

15cm

12cm

16cm 6cm

12cm

18cm

15cm

9cm

12cm

10cm

15cm 7cm

8cm

12cm

10cm

5cm 5cm

6cm 4cm

MEARNS CASTLE HIGH SCHOOL



Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x = 4, y = -2 and z = 3 find:

a. 4x +3y −2z b. x 2 − 4y +6z

2. Solve 7x – 4 = 3x + 8

3. Evaluate: 62 – 2 x (5 - 6) showing working

4. Simplify 5a – 3 - 4a + 6


a. 0.0000936 b. 178,764

6. Find 0.0625 ÷ 0.005

7. Find 34×17

1. If x = 4, y = -2 and z = 2 find:

a. 5x +3y 2 −3z b. x 2 +2y +5z

2. Solve 4x – 2 = 6x + 3

3. Evaluate: 22 – 2 x (7 - 7) showing working 4. Simplify 4a + 8 – 10a – 5 5. Round the following to 3 significant figures:

a. 0.01064 b. 5,784,984 6. Find 180 ÷ 0.02

7. Find 27×45

1. If x = -5, y = -2 and z = 3 find:

a. zx +2y 2 b. 2x − 4y 2 + 4z

2. Solve 7x – 5 = 9 - 6x


4. Simplify 12a – 6 – 16a + 16


a. 0.004809 b. 606,486

6. Find 0.032 ÷ 0.0004

7. Find 16×34

1. If x = -5, y = -3 and z = 5 find:

a. 2xy +3z b. 3xyz

2. Solve 4 – 3x = 8x + 7 3. E valuate: 72 – 4 x (5 - 7) showing working 4. Simplify 8a + 16 – 10 – 2a 5. Round the following to 3 significant figures:

a. 6.5073 b. 1,086,483 6. Find 0.002 ÷ 0.00004

7. Find 56×15

CfE Outcomes 3-14a, 3-15a, 4-03b, 3-14a, 3-01a, 3-07a, 3-04a




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x = 5, y = -1 and z = 6 find:

a. x − y −2z b. 2x − y 2 +3z 2

2. Solve 2x – 1 = 5x + 8


4. Simplify a – 12 + 2a + 10


a. 0.0006032 b. 2,252,394

6. Find 0.0675 ÷ 0.005

7. Find 25×34

1. If x = -2, y = -3 and z = -4 find:

a. 2x +3y 2 −z b. x − 4x 2 −7z

2. Solve 8x – 2 = 6x + 14

3. Evaluate: 62 – 2 x (1 - 3) showing working 4. Simplify 4a – 8 – 6a – 3 5. Round the following to 3 significant figures:

a. 0.0001105 b. 799,901 6. Find 3600 ÷ 0.009

7. Find 47×512

1. If x = 10, y = -3 and z = 2 find:

a. zx +zy 2 b. 2x + y 2 −8z

2. Solve 4x – 7 = 14 - 3x


4. Simplify -2a – 9 + 15a - 16

5. Round the following to 1 significant figure:

a. 0.00804 b. 166,786

6. Find 0.042 ÷ 0.0006

7. Find 29×34

1. If x = -10, y = 2 and z = -5 find:

a. xy −2z 2 b. −xyz

2. Solve 4 – x = 8x + 22 3. E valuate: 112 – 3 x (1 - 6) showing working 4. Simplify 14a + 1 – 10a – 9 – 2a 5. Round the following to 4 significant figures:

a. 11.5076 b. 1,026,491 6. Find 0.00024 ÷ 0.0000004

7. Find 37×712

CfE Outcomes 3-14a, 3-15a, 4-03b, 3-14a, 3-01a, 3-07a, 3-04a




Exercise 4


Exercise 3

© Zeta Maths Ltd.



figures.

3. Diesel prices increased from £1.26 to £1.34, calculate the % increase to 1 decimal place.

4. Seven pears cost £2.03, how much do 5 cost?


in litres:


(a) 19,700,000 (b) 134 (c) 0.001883


figures.

3. Diesel prices increased from $4.20 to $4.80, calculate the % increase to 1 decimal place.



in litres:



figures.


4. Six peaches cost £2.52, how much do 9 cost?


in litres:


(a) 17,250 (b) 341,000 (c) 0.005111


figures.


4. Eight kiwis cost £3.84, how much do 4 cost?


in litres:


4cm

12cm

11cm

14cm 8cm

14cm

17cm

20cm

8cm

13cm

13cm

12cm 7cm

8cm8cm

11cm

9cm

4cm 9cm

7cm 7cm




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Convert each of these times to hours and minutes. (a) 2.3 hours (b) 3.6 hours

2. Convert each of these times to hours as a

decimal (a) 5 hours 42 minutes (b) 9 hours 18 minutes

3. A plane travels at 520mph for 2.2 hours.

Calculate the total distance travelled.

4. A car covers 220 miles in 4 hours 42 minutes. Calculate the average speed of the journey.

5. A boat travels 30miles at an average speed of

8mph. Calculate the time taken in hours and minutes.

1. Convert each of these times to hours and

minutes. (a) 8.7 hours (b) 1.5 hours






5. A boat travels 20.4miles at an average speed of


1. Convert each of these times to hours and minutes.

(a) 5.25 hours (b) 823

hours








1. Convert each of these times to hours and

minutes.

(a) 4 13

hours (b) 6.9 hours


decimal (a) 1 hour 9 minutes (b) 3 hours 12 minutes






CfE Outcomes 4-10b




Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 18t – 4 = 12t + 20

3. 92 – 2 x 3 - 13

4. Simplify: 20k + k x 3k – 5k


a. 0.0028634 b. 91,542

6. Find 0.012 x 0.3

7. Find 12+23+15


1. Express 400 as a product of prime factors. 2. Solve 50g – 7 = 44g + 35 3. 7 x 22 – 3 x (2 + 3) 4. Simplify: 7h x 5h x 2h 5. Round the following to 3 significant figures:

a. 6.0362 b. 158,342 6. Find 31 x 0.6

7. Find 89−38



2. Solve 15h – 9 = 51 – 5h

3. 202 – 5 x 10 + 102

4. Simplify: 7f + 4f – 15f


a. 0.028763 b. 1,987,862

6. Find 0.002 x 0.009

7. Find 25+49


1. Express 250 as a product of prime factors. 2. Solve 5 – 3v = 8v - 28 3. 7 + 32 – 6(5 - 2) 4. Simplify: 7n x 2 – 3n + 10 5. Round the following to 3 significant figures:

a. 0.49999 b. 14,810,109 6. Find 0.12 x 0.005

7. Find 1217

−334

8. Find the supplemplement of 120.6º





Exercise 4


Exercise 3

© Zeta Maths Ltd.

Find (i) the volume and (ii) the surface area of the following shapes: 1.

2. 3.


2. 3.


2. 3.


2. 3.

CfE Outcomes 4-11b, 4-11c, 4-16b

12cm

8cm

10cm

15cm

10cm

10cm

25cm

12cm

15cm

40cm

15cm

20cm

120mm

100mm

90mm

18mm

20mm

50mm

9m

8m

4m

50cm

9cm

11cm




Exercise 4


Exercise 3

© Zeta Maths Ltd.



figures.

3. Diesel prices decreased from £1.41 to £1.37, calculate the % increase to 1 decimal place.

4. Five pears cost £1.35, how much do 8 cost?


in litres:


(a) 12,600,000 (b) 225 (c) 0.003460


figures.

3. Diesel prices increased from $4.15 to $4.35, calculate the % increase to 1 decimal place.



in litres:



figures.


4. Six bananas cost £1.14, how much do 12 cost?


in litres:


(a) 18,650 (b) 918,000 (c) 0.006999


figures.


4. Seven plums cost £3.71, how much do 11 cost?


in litres:


4cm

7cm

6cm

5cm 17cm

13cm

30cm

30cm

50cm

70cm

80cm

90cm 30cm

42cm

54cm

50cm

3cm 14cm

22cm 40cm




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. The Khufu Pyramid has a square base of approximate length 230m and sloped height 186m as in the net below: (a) Calculate its surface

area

(b) Its vertical height is 140m. Calculate its volume to the nearest thousand.

2. An ice-cream cone has a radius of 5cm and a

height of 16cm, calculate the volume of the cone, give your answer to 2 significant figures.

1. An unused toilet roll has a

radius of 16cm and a height of 14cm. The empty roll has a radius of 6cm. Find the volume of toilet paper on the roll.

2. Find the volume of the composite shape below.

1. The glass pyramid at the Louvre has a square base of approximate length 35m and sloped height 28m as in the net below: (a) Calculate its surface

area

(b) Its vertical height is 22m. Calculate its volume to the nearest thousand.

2. An ice-cream cone has a radius of 8cm and a height of 18cm, calculate the volume of the cone, give your answer to 2 significant figures.

1. An unused kitchen roll has

a radius of 24cm and a height of 26cm. The empty roll has a radius of 6cm. Find the volume of kitchen paper on the roll.

2. Find the volume of the composite shape below.

CfE Outcomes 4-11b, 4-11c, 4-16b

25cm

22cm

30cm 38cm

230m

186m

35m

28m




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Plot the points on a Cartesian diagram (x and y graph) and determine the gradient of the line passing through them: (a) (0,4), (1,4), (3,4)

(b) (-1,-3), (1,1), (3,5)

(c) (5,-2), (5,3), (5,7)

(d) (-2,4), (0,-2), (2,-8)

2. For each of the following equations, make a table using three x-values, plot the points on a Cartesian diagram and write down the gradient of each line:

(a) y = 2x (b) y = ½x (c) y = -x (d) y = -4x

1. Plot the points on a Cartesian diagram (x and y

graph) and determine the gradient of the line passing through them: (a) (1,4), (2,7), (3,10)

(b) (-2,-3), (-2,0), (-2,3)

(c) (4,-2), (5,-2), (7,-2)

(d) (-3,7), (2,-3), (4,-7)


(a) y = 3x + 1 (b) y = ½x + 5 (c) y = -x - 5

1. Plot the points on a Cartesian diagram (x and y graph) and determine the gradient of the line passing through them: (a) (-1,3), (0,-1), (2,-9)

(b) (1,-3), (2,-1), (3,1)

(c) (3,-3), (5,-3), (6,-3)

(d) (-3,11), (0,2), (3,-7)


(a) y = 2x + 3 (b) y = -½x (c) y = -2x + 7

1. Plot the points on a Cartesian diagram (x and y

graph) and determine the gradient of the line passing through them: (a) (0,0), (0,4), (0,6)

(b) (-1,0), (1,0), (3,0)

(c) (6,-2), (7,-3), (8,-4)

(d) (-1,-4), (0,1), (1,6)


(a) y = -x - 1 (b) y = -½x + 4 (c) y = -6x + 5

CfE Outcomes 4-13c, 4-13d




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line:

1. Find (i) the gradient (ii) the y-intercept

(iii) the equation of each line:

1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line:

1. Find (i) the gradient (ii) the y-intercept

(iii) the equation of each line:

CfE Outcomes 4-13b, 4-13c

(a)

(b)

(c) (d)

(a)

(b) (c)

(d)

(a)

(b)

(c)

(d)

(a) (b)

(c)

(d)




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line (assume each square counts for 1 unit):

2. (a) What do you notice about the gradient? (b) What does this tell us about the lines?

1. From the following straight-line equations,

state which pair are parallel? (a) y = 4x – 3 (b) y = -2x (c) y = ⅔x (d) y = -⅔x (e) y = ¼x – 3 (f) y = -2x + 7

2. For each pair of coordinates, find (i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (-5,4), (0,12) (b) (0,4), (9,14) (c) (-3,10), (0, -5) (d) (0,0), (6,-6)

3. For each equation, state the gradient and y-intercept: (a) y = x – 5 (b) y = 3x + 22 (c) y = -x

1. From the following straight-line equations, state which pair are parallel? (a) y = 2x + 5 (b) y = -x (c) y = ¼x + 4 (d) y = ⅓x (e) y = ¼x – 3 (f) y = -2x

2. For each pair of coordinates, find

(i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (0,6), (8,12) (b) (1,4), (1,14) (c) (-4,-2), (0, -9) (d) (0,5), (4,5)

3. For each equation, state the gradient and y-intercept:

(a) y = ⅙x + 20 (b) y = 7x (c) y = -⅞x - 5

1. From the following straight-line equations,

state which pair are parallel? (a) y = 7x – 3 (b) y = 15x (c) y = -x - 8 (d) y = 9 - x (e) y = ¼x + 6 (f) y = -3x + 2

2. For each pair of coordinates, find (i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (-7,-2), (0,9) (b) (0,0), (6,-14) (c) (-2,-1), (0, -5) (d) (0,9), (6,0)

3. For each equation, state the gradient and y-intercept:

(a) y = 8 - x (b) y = 11 + 4x (c) y = 1 - ⅘x

CfE Outcomes 4-13b, 4-13c, 4-13d

(a)

(b)

(c)




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find the next three terms in each sequence (a) 8, 11, 14, 17 (b) 25, 35, 45, 55 (c) 72, 80, 88, 96 (d) 100, 98, 96, 94

2. For each of the questions above, find an

expression for the nth term. (Eg, 2n + 1)

3. Use the formula in question 2 to find the 20th

term in each sequence.

4. Find 23+15

5. Solve 7y + 2 = 4y + 20

6. Simplify: 5a + a x 2a - a

1. Find the next three terms in each sequence

(a) 5, 9, 13, 17 (b) 32, 37, 42, 47 (c) 51, 57, 63, 69 (d) 124, 121, 118, 115





4. Find 34+13

5. Solve 12y - 2 = 6y + 40

6. Simplify: 6r + r – 3r x 2r

1. Find the next three terms in each sequence (a) 2, 11, 20, 29 (b) 15, 26, 37, 48 (c) 73, 81, 89, 97 (d) 250, 245, 240, 235





4. Find 27+13

5. Solve 18y - 7 = 6y + 41

6. Simplify: 10p x p + p

1. Find the next three terms in each sequence

(a) 15, 19, 23, 27 (b) 400, 500, 600, 700 (c) 180, 170, 160, 150 (d) 118, 114, 110, 106





4. Find 89−13

5. Solve 5y + 5 = 10y - 20

6. Simplify: y + y + y x y

CfE Outcomes 4-13a, 4-07b, 3-15a, 3-14a




Exercise 4


Exercise 3

© Zeta Maths Ltd.

Multiply out and, when necessary, collect like terms:

1. 3(a −2b)

2. m(4 − n)

3. −x (x + y )

4. 3a(5a −2b)

5. 3(x − 4) +2(5 − x )

6. 3x (2x − 1) −8x (x − 4)


1. 5(x +2y )

2. t(3−u)

3. p(q − p)

4. a(5a −b)

5. 4(m − 4) −3(5 −m)

6. 3y (2z +5) +8y (y − 4z )


1. 3(x +7) − 15

2. 8−2(4 − n)

3. 3x −x (x +2)

4. 12a2 −3a(5a −2)

5. 4x (x −5) −2x (3+2x )

6. 3(2x 2 − 1) −5x (1− 4x )


1. 3(a −8) + 13

2. 5 − (x +2)

3. 17 − (x −5)

4. 8ab +3a(a −2b)

5. 3(x − 4) − (5 − x )

6. 3x (3x − 1) +x (4 −x )

CfE Outcomes 4-14a, 4-3b




Exercise 4


Exercise 3

© Zeta Maths Ltd.

Factorise the following expressions:

1. 3a + 12

2. 8a +24b

3. 12a − 16ab

4. ab +a2

5. 5a2 − 15a

6. 4ab +6a2


1. 4x + 12

2. 16x +24y

3. 15x − 18xy

4. 2xy − y 2

5. 7x 2 −21x

6. 12xy − 15x 2


1. 3m + 15

2. 28m +36n

3. −mn − 16n

4. mn2 +m2n

5. 5m2n − 10(mn)2

6. 21m2n +28mn2


1. ax +ay

2. 20px +24py

3. 12pq − 16q

4. pq + p2q

5. 5p2q2 −35p2q

6. −42p2q2 +6q2

CfE Outcomes 4-14b




Exercise 4


Exercise 3

© Zeta Maths Ltd.

Solve the following equations:

1. 4(x +2) = 2(x +3)

2. 5(x +2) = 3(x +2)

3. 6(x +3) = 3(x +2)

4. 3(x +2) = 2(x +3)

5. 4(x −2) = 3(x +3)

6. 4(2x −2) = 3(x − 4)


1. 5(x +2) = 3(x + 4)

2. 6(x +3) = 4(x +3)

3. 7(x +2) = 4(x +2)

4. 4(x +6) = 3(x +7)

5. 5(x −6) = 4(x +6)

6. 5(3x − 4) = 6(x −7)


1. 7(x −3) = 4(x −5)

2. 7(x −3) = 5(x +3)

3. 8(x +2) = 5(x −2)

4. 5(x +6) = 3(x +7)

5. 6(x +7) = 3(x +6)

6. 7(4x − 4) = 5(x +7)


1. 9(3x −3) = 7(x + 12)

2. 5(4x −3) = 7(8x −6)

3. 9(3x + 12) = 5(4x −9)

4. 3(2x −9) = 3(10x + 4)

5. 12(3x − 10) = 5(5x +3)

6. 7(2x + 12) = 10(2x +5)

CfE Outcomes 4-14a, 4-15a




Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 9(x – 2) = 3(x + 8)

3. Evaluate: 62 – 2 x (5 + 9) showing working.

4. Simplify a + a + a x a


a. 0.005999 b. 48 678

6. Find 0.00025 x 0.4

7. Find 51

43+

8. In a right-angled triangle, one of the angles is

26º, what is the unknown angle?

1. Express 96 as a product of prime factors. 2. Solve 6(x – 2) = 8(x + 8)

3. Evaluate: 52 – 2 x (5 - 7) showing working. 4. Simplify a x a – a + a + a x a 5. Round the following to 3 significant figures:

a. 0.007695 b. 785 415 6. Find 15 x 0.9

7. Find 31

72−




2. Solve 7(x – 2) = 2(9 - 3x)


4. Simplify 3a + a + a x a


a. 0.09099 b. 147 015

6. Find 0.002 x -0.8

7. Find 43

612 +


22º, what is the unknown angle

1. Express 88 as a product of prime factors. 2. Solve 2(4 – 3x) = 5x + 7 3. Evaluate: 82 – 4 x (12 - 7) showing working 4. Simplify a + a x a - a 5. Round the following to 3 significant figures:

a. 0.06709 b. 999 999 6. Find 0.002 x -0.00105

7. Find 511

651 −



CfE Outcomes 3-05a, 3-15a, 4-03b, 3-14a, 4-01a, 3-07a, 3-07a, 3-17a




Exercise 4


Exercise 3

© Zeta Maths Ltd.


1. 4(x −2) = 3(x +3)

2. 5(x +2) = 2(x −2)

3. 6(x − 4) = 3(x + 1)

4. 3(x +2) + 4 = 2(x +3)

5. 4(x −2) −5 = 2+3(x +3)

6. 4(2x −2) −8 = 3(x − 4)


1. 5(x + 4) = 3(x +5)

2. 5(2x −3) = 2(3x +2)

3. 3(2x −6) = 6(3x +2)

4. 2(2x +6) + 4 = 2(5x + 4)

5. 4(2x −6) −5 = 2−3(2x +3)

6. 6(2x −3) = 4 −5(x −5)


1. 7(x + 4) = 5x +2

2. 5x − 10 = 8(x −2)

3. 7(x − 4) = 6(x + 1)

4. 4(2x +2) − 10 = 5(2x +3)

5. 5(x −2) −5 = 8−3(2x +7)

6. 4(8x −2) −8 = 3(7x − 4) −20


1. 3(x +3) = 8(x + 10)

2. 6(3x −2) = 5(2x +6)

3. 9(2x − 12) = 6(6x +9)

4. 3(2x −5) − 12 = 2(8x + 4)

5. 9(3x −5) + 14 = 2−5(5x +3)

6. 7(2x + 12) = 4 − 10(x −5)





Exercise 4


Exercise 3

© Zeta Maths Ltd.


1. 12(x − 12) = 4(x −8)

2. 14(x −3) = 1

2(x −2)

3. 13(2x −3) = 1

6(x −2)

4. 14(x −5) = 1

8(x −2)

5. 13(x + 12) = 1

4(x −2)

6. 34(x +5) = 1

5(x − 4)


1. 13(x −9) = 5(x −3)

2. 14(x +2) = 1

2(x − 4)

3. 13(4x − 4) = 1

6(x −3)

4. 14(x −5) = 1

12(2x − 12)

5. 13(2x +3) = 1

4(3x −6)

6. 34(x −6) = 2

5(x −5)


1. 15(2x − 12) = 1

5(x −5)

2. 15(2x + 4) = 1

6(x −2)

3. 13(2x −3) = 2

7(2x −5)

4. 34(x −2) = 1

3(x −2)

5. (x + 12)3

=(x −2)

4

6. (x −3)5

=(x −2)

4


1. 18(x − 13) = 4(x −8)

2. 14(x −5) = 1

5(x −3)

3. 34(5x −3) = 5

6(x −2)

4. 34(x − 4) = 5

8(x −2)

5. (x +9)3

=(x +5)

7

6. (x + 10)4

=(x +8)

9


=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

= =

=

=

=

=

=




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x = 2 and y = -3 find:

a. 224 yx − b. yx 42 −

2. Solve 7(x – 4) = 3(x + 8)

3. Evaluate: 62 – 2 x (5 - 6) showing working.

4. Simplify 5(a – 3) -4a


a. 0.007594 b. 57,546

6. Find 0.025 ÷ 0.005

7. Find 51

43×

1. If x = -4 and y = -2 find:

a. 224 yx − b. yx 42 −

2. Solve 4(x – 2) = 6(x + 3)

3. Evaluate: 22 – 2 x (7 - 7) showing working. 4. Simplify 4(a + 2) – 5(2a – 5) 5. Round the following to 3 significant figures:

a. 0.00054897 b. 4,987,756 6. Find 18 ÷ 0.9

7. Find 31

72×

1. If x = -5 and y = -4 find:

a. 224 yx + b. 242 yx −

2. Solve 7(x – 5) = 2(9 - 6x)


4. Simplify 6(2a – 1) – 4(4a + 4)


a. 0.0045634 b. 759,987

6. Find 0.032 ÷ (-0.008)

7. Find 43

612 ×

1. If x = -5 and y = -4 find:

a. 224 yx + b. 242 yx −

2. Solve 3(4 – 3x) = 8x + 7 3. E valuate: 72 – 4 x (5 - 7) showing working 4. Simplify 8(a + 2) – 2(5 – a) 5. Round the following to 3 significant figures:

a. 1.048795 b. 489,999 6. Find 0.002 ÷ (-0.0005)

7. Find 511

651 ×





Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. (a) Find an expression for the perimeter of the rectangle.

(b) The perimeter is 54cm, find x.

2. Solve ½(x – 4) = ¼(x + 8)

3. Increase £2400 by 2.2%.

4. Find the percentage depreciation on a boat purchased for £45,000 and sold for £32,000.

5. Find how much interest was gained on an

investment of £3400 at 4% per annum for 3 years.

1. (a) Find an expression for the perimeter of the

rectangle.


2. Solve ½(x – 5) = ¼(x + 9)

3. Decrease £5500 by 4.3%.



investment of £12,000 at 3.5% per annum for 3 years.



2. Solve ½(x – 3) = ¼(x + 2)

3. Increase £6500 by 2.2%.





rectangle.


2. Solve ½(2x – 7) = ¼(x + 5)

3. Decrease £13500 by 7.6%.




CfE Outcomes 3-14a, 3-15a, 4-03a

x + 2

3x - 7

x + 8

2x - 7

2x + 2

4x - 2

3x + 1

5x - 7




Exercise 4


Exercise 3

© Zeta Maths Ltd.

Solve the following inequations:

1. 5x + 1 < 26

2. 2x + 6 > 30

3. 4x + 3 ≤ 23

4. 8x – 2 ≥ 38

5. 4(2x + 3) < 28

6. ½x + 6 > 14

7. 5(2x – 1) ≤ 2x + 19

8. 7x + 5 > 4(5x – 2)


1. 6x + 2 < 32

2. 7x + 8 > 50

3. 3x + 2 ≤ 25

4. 9x – 4 ≥ 32

5. 6(5x + 3) < 48

6. ⅓x + 3 > 33

7. 6(2x – 2) ≤ 2x + 8

8. 5x + 6 > 4(3x – 2)


1. 3x + 9 < 27

2. 2x + 10 > 40

3. 8x + 5 ≤ 45

4. 10x – 5 ≥ 60

5. 7(2x + 3) < 63

6. ¼x + 2 > 20

7. 8(x – 2) ≤ 2x + 18

8. x + 4 > 2(x – 2)


1. 8x + 7 < 71

2. 16x + 2 > 34

3. 4x + 1 ≤ 17

4. 20x – 20 ≥ 100

5. 9(x + 5) < 72

6. ⅕x + 6 > 8

7. 3(2x – 2) ≤ 2x + 5

8. x + 7 > 2(x – 2)

CfE Outcomes 4-15a




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find area and the perimeter of the following shape:

2. An athlete runs round a 400m running track in 54 seconds, calculate his speed in metres per second (ms-1).

1. Find area and the perimeter of the following

shape:

2. An plane flies 4500 miles at an average speed of 550mph, how long does the journey take (give your answer in hours and minutes)?

1. Find area and the perimeter of the following shape:

2. An athlete runs round a 400m running track in 51 seconds, calculate his speed in metres per second (ms-1).

1. Find area and the perimeter of the following

shape:

2. An plane flies 6800 miles at an average speed of 540mph, how long does the journey take (give your answer in hours and minutes)?

CfE Outcomes 4-16b, 4-10b

30cm

24cm

20cm

15cm

30cm

10cm

50cm

20cm




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x = -1 and y = -5 find:

a. 3x +2y 2 b. −x −2y

2. Solve 5(x – 2) = 2(x - 7)

3. Evaluate: 32 – 3 x (7 - 6) showing working.

4. Simplify 6(a + 3) - 5a


b. 0.007814 b. 97 346

6. Find 0.035 ÷ 0.005

7. Find 23×26

1. If x = -6 and y = -1 find:

a. x − y 2 b. 3x + 4y

2. Solve 7(x – 1) = 5(x + 8)

3. Evaluate: 32 – 3 x (9 - 7) showing working. 4. Simplify 8(a + 3) – (a – 5) 5. Round the following to 3 significant figures:

a. 0.0005897 b. 7 985 756 6. Find 18 ÷ 0.2

7. Find 26×17

1. If x = -8 and y = 4 find:

a. 3x +6y b. −2x + 4y 2

2. Solve 10(x – 2) = 2(6 - x)


4. Simplify 4(2a – 3) – 2(4a + 1)


a. 0.004569 b. 109 987

6. Find 0.04 ÷ (-0.008)

7. Find 1 14×23

1. If x = -3 and y = -6 find:

a. 4x + y 2 b. 2x + y 2

2. Solve 7(2 – x) = 6x + 9 3. E valuate: 32 – 2 x (-2 - 7) showing working 4. Simplify 6(a + 1) – 3(5 – a) 5. Round the following to 3 significant figures:

a. 1.098795 b. 89 999 6. Find 0.004 ÷ (-0.0005)

7. Find 1 12×1 3

4





Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 2(x – 1) = 5(x + 4)


4. Simplify: a + a – a + 2a –a + a x a


a. 0.005160 b. 48 632

6. Find 0.0020 x 0.4

7. Find 34+23




3. Evaluate: 52 – 3 x (4 - 7) showing working. 4. Simplify: a x a + a + a + a - a 5. Round the following to 3 significant figures:

a. 0.007632 b. 776 432 6. Find 0.002 x 0.9

7. Find 27−12




2. Solve 6(x – 2) = 2(2 + 2x)


4. Simplify: 3a + a + a + a x a


a. 0.09093 b. 144 123

6. Find 0.003 x -0.6

7. Find 2 16+22

6



1. Express 86 as a product of prime factors. 2. Solve 2(3 + 3x) = 5x + 7 3. Evaluate: 92 – 3 x (11 - 6) showing working 4. Simplify: a x a x a x a 5. Round the following to 3 significant figures:

a. 0.06707 b. 999 898 6. Find 0.003 x -0.00106

7. Find 156− 1 3

4







Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find the perimeter of the shape:

2. Solve ½(3x – 5) = ¼(x + 8)

3. A plane flies from Glasgow to New York in 5 hours 42 minutes, the distance is 3200miles, calculate the speed.

4. How long in hours and minutes does it take to

travel 400miles at a speed of 70mph?

5. Find how much interest was gained on an investment of £4500 at 4% per annum for 3 years.


2. Solve ½(x + 3) = ¼(8x + 6)




5. Find how much interest was gained on an investment of £1100 at 4.2% per annum for 3 years.


2. Solve ½(5x + 6) = ¼(3x + 9)




5. Find how much interest was gained on an investment of £12,800 at 6.5% per annum for 4 years.


2. Solve ½(4x – 10) = ¼(2x + 8)




5. Find how much interest was gained on an investment of £112,000 at 4.2% per annum for 5 years.

CfE Outcomes 3-14a, 3-15a, 4-15a, 4-03a, 4-10b

120m

60m

110m

70m

115m

56m

118m

66m




Exercise 4


Exercise 3

© Zeta Maths Ltd.



2. Solve ½(x – 2) = ¼(x + 10)

3. Increase £4800 by 2%.

4. Find the percentage depreciation on a car purchased for £24,000 and sold for £16,000.




rectangle.


2. Solve ½(x – 7) = ¼(x + 20)

3. Decrease £6200 by 8%.

4. Find the percentage depreciation on a caravan purchased for £24,000 and sold for £18000.


investment of £10,000 at 3% per annum for 3 years.



2. Solve ½(x – 6) = ¼(x + 4)






rectangle.


2. Solve ½(2x – 2) = ¼(x + 8)


4. Find the percentage depreciation on a house purchased for £800,000 and sold for £600,000.




x + 6

2x - 3

x + 7

4x - 2

5x + 1

9x - 1

4x + 5

7x - 3




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. For the number series below, find the next three terms and an expression for the nth term:

12, 15, 18, 21

2. For the series above, use the formula to find the 20th term in the sequence.

3. Simplify 3(a + 4) – 2(2a – 6)

4. Find 12% of £800

5. Factorise 4ab + 8a2


b. 0.000209 b. 64 089

7. Find 3 13÷2 1

4

1. For the number series below, find the next

three terms and an expression for the nth term: 21, 29, 37, 45


3. Simplify 5(2a + 9) – 3(a – 2)

4. Find 14% of £600 5. Factorise 12xy3 + 18xy2 6. Round the following to 2 significant figures:

a. 0.09921 b. 125 555

7. Find 825÷3 1

4


50, 90, 130, 170


3. Simplify 8(a + 1) – 5(3a – 7)

4. Find 17.5% of £1400

5. Factorise 14h2g3 – 21 hg2


a. 9.1362 b. 300 986

7. Find 9 47÷29


three terms and an expression for the nth term:

200, 196, 192, 188 2. For the series above, use the formula to find

the 16th term in the sequence.

3. Simplify 6(4a + 1) – 3(6a – 1) 8. Find 22.5% of £1600 4. Factorise 11p2j + 44p 5. Round the following to 2 significant figures:

a. 18.0003 b. 989 700

6. Find 356÷ 1 1

3





Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Using Pythagoras’ Theorem, calculate the

length of each missing side in these right angled triangles (2 decimal places):

1. Using Pythagoras’ Theorem, calculate the

length of each missing side in these right angled triangles (2 significant figures):

Copy the axes and use Pythagoras’ Theorem to calculate the length of each line (1 decimal place)

Copy the axes and use Pythagoras’ Theorem to calculate the length of each line (2 decimal places):

CfE Outcomes 4-16a

A cm 11 cm

14 cm

B mm

9 mm

11 mm

C m

7 m 13 m D km 120 km

115 km

P cm 17 cm

15 cm

Q mm

3 mm

8 mm

R m

19 m 22 m S km 185 km

135 km

(a)

(b)

(a)

(b)




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Draw a Cartesian diagram and use Pythagoras’

Theorem to find the length of the line joining the points (to 2.d.p): (a) A(-2,-6) & B(1,3) (b) P(0,7) & Q(9,-1)

2. The cross section of a pipe, with centre O, is filled with water as shown.

1. Draw a Cartesian diagram and use Pythagoras’

Theorem to find the length of the line joining the points (to 2.d.p): (a) A(-5,0) & B(4,-3) (b) P(0,-3) & Q(-3,9)

2. The cross section of a pipe, with centre O, is filled with water as shown.

1. Using the converse of Pythagoras’ Theorem,

determine whether the triangle is right angled:

2.

1. Using the converse of Pythagoras’ Theorem,

determine whether the triangle is right angled:

2.

CfE Outcomes 4-16a

O

Q

P R The distance from R to P is 9cm. Calculate (a) The distance from O, to the top of the water at S. (b) The total depth of the water.

5cm

S

Q

P R The distance from R to P is 11cm. Calculate (a) The distance from O, to the top of the water at S. (b) The total depth of the water.

6cm

S

10 cm

24 cm

26 cm

P m

9 m

The cross section of a tunnel is shown. The radius is given as 5m. Use the information to calculate the height P.

6 cm

The cross section of a tunnel is shown. The radius is given as 7m. Use the information to calculate the height L.

8 cm 11 cm

11 m

L m




Exercise 4


Exercise 3

© Zeta Maths Ltd.


25, 30, 35, 40


3. Simplify 6(a + 1) – 2(5a – 2)

4. Find 11% of £80

5. Factorise 12b - 18


a. 0.0002331 b. 28,092

7. Find 7 15÷3 1

9


three terms and an expression for the nth term: 32, 40, 48, 56


3. Simplify 7(7a + 2) – 5(a – 6)

4. Find 13% of £300 5. Factorise 25a2b5 + 30ab4 6. Round the following to 2 significant figures:

a. 0.08067 b. 271,682

7. Find 227÷9 1

10


20, 110, 200, 290


3. Simplify 5(4a + 2) – 3(2a – 9)

4. Find 17.5% of £280

5. Factorise 20abc3 – 30ac


b. 9.9999 b. 213,096

7. Find 6 411÷3 3

22


three terms and an expression for the nth term:



3. Simplify 8(a + 1) – 7(2a – 10) 4. Find 22.5% of £320 5. Factorise 15pr2d + 20pd2 6. Round the following to 2 significant figures:

a. 19.9999 b. 201,199

7. Find 4 716

÷3 132





Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Using the tan ratio, calculate the length of

each missing side in these right angled triangles (2 decimal places):

1. Using the sine ratio, calculate the length of


1. Using the cosine ratio, calculate the length

of each missing side in these right angled triangles (2 decimal places):

1. Using the tan ratio, calculate the size of the

angle in these right angled triangles (nearest whole number):

CfE Outcomes 4-16a

Acm

34° 14cm Bmm

29°

11mm

Cm

7m 20°

115km

57° Dkm

Acm

36°

16cm

Bm

25° 17m

Cmm

7mm 18°

215km

62°

Dkm

Acm 44° 27cm Bmm 18° 37mm

Cm 53m

24° 98km

67° Dkm

12cm

u° 14cm 9mm

x° 11mm

4 m

7m

y°

95 km

z°

85km




Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 7(a – 5) = 5(a + 5)


4. Simplify a - a + a x a + a2


b. 9.005003 b. 48 078

6. Find 0.00025 x 0.05

7. Find 31

94+



1. Express 98 as a product of prime factors. 2. Solve 3(a – 2) = 8(a + 7)

3. Evaluate: 42 – 2 x (5 - 3) showing working. 4. Simplify a x a – a + a x a + b x b – b2 5. Round the following to 3 significant figures:

a. 0.100695 b. 765 425 6. Find 15 x 0.003

7. Find 311

432 −

8. In an equilateral triangle, what is the size of

one of the angles?


2. Solve 4(a – 2) = 2(9 – 6a)


4. Simplify 9a + a2 + a x a

5. Round the following to 1 significant figure:

a. 0.0895 b. 184 715

6. Find 0.33 x 0.05

7. Find 32

95+



1. Express 148 as a product of prime factors. 2. Solve 4(4 – 3a) = 2a + 7 3. E valuate: 82 – 4 x (12 - 7) showing working 4. Simplify a + a x a – b + b2 5. Round the following to 4 significant figures:

a. 0.06801702 b. 819 909 6. Find 0.2 x 0.75

7. Find 542

321 −







Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Using the sine ratio in A and B, and cosine in C

and D to calculate the size of each angle in these right angled triangles (to the nearest whole number):

1. Using SOHCAHTOA, calculate the length of


1. Using SOHCAHTOA, calculate the size of

each missing angle in these right angled triangles (1 decimal place):

1. Using SOHCAHTOA, calculate the length of

each missing side or angle in these right angled triangles (2 significant figures):

CfE Outcomes 4-16a

15 cm

A°

19 cm 21 mm

B°

11 mm

13 m

7 m C°

176 km D°

184 km

A cm 38° 12 cm

B m

23° 19 m

C mm

79 mm 17°

D km

62°

215 km

30cm u°

38 cm

37 mm

v°

47 mm

14 m

9 m w°

144 km x°

155 km

A cm

33°

17 cm B mm 38°

53 mm

64 m

45 m

C°

D°

2100 km

3023 km




Exercise 4


Exercise 3

© Zeta Maths Ltd.

?

12cm

1. These two rectangles below are similar. Find

the length of the missing side.

2. The two trapeziums are similar. Calculate the area of the larger one.

3. Change these times to hours and minutes (a) 6.3 hours (b) 4.7 hours

4. Solve: 2(2x – 4) = 12

5. Find 34÷25



2. The two trapeziums are similar. Calculate the

area of the larger one.

3. Change these times to hours and minutes (a) 2.1 hours (b) 3.5 hours 4. Solve: 3(5x – 2) = 39

5. Find 23÷17



2. The two trapeziums are similar. Calculate the area of the larger one

3. Change these times to hours and minutes

(a) 9.6 hours (b) 2.8 hours 4. Solve: 4(6x – 1) = 20

5. Find 29÷14



2. The two trapeziums are similar. Calculate

the area of the larger one

3. Change these times to hours and minutes (a) 10.25 hours (b) 6.75 hours

4. Solve: 3(7x + 2) = 48

5. Find 35÷16

CfE Outcomes 4-17b, 4-15a, 4-10b, 4-07b

32cm 8cm 3cm ?

5cm 15cm

18cm 12cm

?

72cm 48cm ?

6cm

2cm

6cm 12cm

Area = 20cm2

3cm 9cm

Area = 10cm2

4cm 8cm

Area = 22cm2

16cm 32cm

Area = 120cm2




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. Find all the missing angles:

2. The diagram represents a tunnel. If the

diameter of the tunnel is 16m, find the height of the tunnel.


2. The diagram represents a water pipe. If the

diameter of the tunnel is 40mm and the surface of the water is 34mm across, find the depth of the water.


2. The diagram represents a tunnel. If the

diameter of the tunnel is 24m, find the height of the tunnel.


2. The diagram represents a water pipe. If the

diameter of the tunnel is 200mm and the surface of the water is 80mm across, find the depth of the water.


d

b a 45° 115° c

e

f

i

g

h

10m

d b

a 50°

c

e

34mm

d

b a 51° 121° c

e

f

i

g

h

16m

d b

a 47°

c

e

80mm




Exercise 4


Exercise 3

© Zeta Maths Ltd.

6. Find angles ‘a’ and ‘b’:

7. The diagram represents a design for a badge. If

the radius of the circle is 12cm, find the height ‘h’ of the badge.

3. Find angles ‘a’, ‘b’ and ‘c’:


the radius of the circle is 16cm, find the height ‘h’ of the badge.

1. Find angles ‘a’ and ‘b’:


the bottom of the badge is 14cm across, find the height ‘h’ of the badge.

1. Find angles ‘a’, ‘b’ and ‘c’:


the bottom of the badge is 20cm across, find the height ‘h’ of the badge.

CfE Outcomes 4-17a

b b

a

40°

c

34mm

16m 80mm

a

62°

62°

h

54°

h

b a

112°

60°

h

14cm

b a

25°

c

59°

h

20cm




Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x =7 and y = -2 find:

a. 224 yx − b. yx 42 −

2. Solve 5 (a + 7) = 4 (4a - 3)


4. Simplify 8(c – 11) - 4c


a. 0.078013 b. 82 105

6. Find 0.025 ÷ 0.0005

7. Find 51

43÷

1. If x = -7 and y = 4 find:

a. 226 yx − b. yx 49 −

2. Solve 2(x – 7) = 6(x + 3)

3. Evaluate: 52 – 2 x (9 - 7) showing working. 4. Simplify 7(z + 2) – 5(8z – 6) 5. Round the following to 3 significant figures:

a. 0.4065 b. 869 201 6. Find 16 ÷ 0.08

7. Find 31

72÷

1. If x = -3 and y = 4 find:

a. 248 yx + b. 237 yx −

2. Solve 5(x – 1) = 5(7 - 2x)


4. Simplify 3(3a – 7) + 4(a + 9)


a. 4.702845 b. 400 749

6. Find 0.040 ÷ (-0.008)

7. Find 43

65÷

1. If x = -5 and y = -4 find:

a. 224 yx + b. 242 yx −

2. Solve 3(4 – 3x) = 8x + 7 3. Evaluate: 52 – 4 x (9 - 7) showing working 4. Simplify 8(a + 2) – 2(5 – a) 5. Round the following to 3 significant figures:

a. 12.00004 b. 100 900 000 6. Find 0.002 ÷ (-0.0005)

7. Find 156÷ 1 1

5





Exercise 4


Exercise 3

© Zeta Maths Ltd.


2. Solve 4(x – 3) = 2(x -7)


4. Simplify a + a + a ÷ a


a. 0.008943 b. 35 596

6. Find 0.00075 x 0.5

7. Find 13+56




3. Evaluate: 42 – 5 x (3 - 6) showing working. 4. Simplify a x a – 2a ÷ a + a + 3a 5. Round the following to 3 significant figures:

a. 0.004856 b. 394 412 6. Find 12 x 0.7

7. Find 34−16




2. Solve 3(x – 3) = 4(4 - 4x)


4. Simplify 4a + a + a x a ÷ a2


a. 0.06065 b. 468 286

6. Find 0.052 x (-0.7)

7. Find 227+58

8. In a right angled triangle, one of the angles is


1. Express 55 as a product of prime factors. 2. Solve 4(4 – 7x) = 7x + 7 3. Evaluate: 92 – 8 x (16 - 8) showing working 4. Simplify a + a ÷ a – a2 5. Round the following to 3 significant figures:

a. 0.07765 b. 409 795 6. Find 0.072 x -0.05

7. Find 156− 1 1

5

8. In an isosceles triangle, the two equal angles

are 39º each, what is the unknown angle





Exercise 4


Exercise 3

© Zeta Maths Ltd.

6. Write down each of the coordinates from the

diagram below.

The coordinates (-3, 6), (-2, 1) and (2, 5) represent three vertices of a rhombus, the fourth vertex has coordinate (3, y), find y.

1. Write down each of the coordinates from the diagram below.

The coordinates (-6, -6), (2, -6) and (-3, -2) represent three vertices of a parallelogram, the fourth vertex has coordinate (x, -2), find x.

1. Write down each of the coordinates from the

diagram below.

The coordinates (1, 0), (-3, 4) and (-7, 0) represent three vertices of a square, the fourth vertex has coordinate (-3, x), find x.

1. Write down each of the coordinates from the diagram below.

The coordinates (-3, -3), (3, -3) and (0, 3) represent three vertices of a parallelogram, the fourth vertex has coordinate (x, 3), find x.

CfE Outcomes 4-18a

NON-‐

G

D

F

A

E B

C

G

D

F

A

E B

C

G

D

F

A

E

B

C

G

D

F

A E

B

C




Exercise 4


Exercise 3

© Zeta Maths Ltd.



2. Solve ½(6x – 6) = ¼(2x + 7)

3. Increase £1600 by 2.2%.





rectangle.


2. Solve ½(3x – 5) = ¼(5x + 9)

3. Decrease £5500 by 4.3%.



investment of £3000 at 3.5% per annum for 3 years.



2. Solve ½(5x – 2) = ¼(7x + 9)

3. Increase £12500 by 6.7%.





rectangle.


2. Solve ½(9x + 12) = ¼(3x + 3)

3. Decrease £80500 by 5.9%.





x + 4

5x - 2

x + 8

6x - 3

x + 12

8x - 4

x + 10

2x - 12




Exercise 4


Exercise 3

© Zeta Maths Ltd.


three terms and an expression for the nth term

40, 60, 80, 100


3. Simplify 2(y + 4) – 4(5y – 7)

4. Find 18% of £1200

5. Factorise 18tp + 20p


b. 0.15020 b. 31 028

7. Find 4 19÷2 1

3

1. For the number series below, find the next three terms and an expression for the nth term

21, 32, 43, 54


3. Simplify 6(5y + 3) – 2(3y – 1)

4. Find 15% of £640 5. Factorise 20abc + 50ac 6. Round the following to 2 significant figures:

a. 0.00235 b. 222 298

7. Find 1 215

÷ 1 130


three terms and an expression for the nth term

10, 140, 270, 400


3. Simplify 10(7y + 1) – 5(2y – 3)

4. Find 17.5% of £440

5. Factorise 27prt + 9p2t


a. 0.1029346 b. 629 748

7. Find 1 313

÷2 526

1. For the number series below, find the next three terms and an expression for the nth term



3. Simplify 8(y + 2) – 6(2y – 1) 4. Find 22.5% of £680 5. Factorise 8v2g – 12vg2 6. Round the following to 2 significant figures:

a. 134 b. 8953.02

7. Find 1 714

+ 1 328





Exercise 4


Exercise 3

© Zeta Maths Ltd.

1. If x = 9 and y = 6 find:

a. 5x 2 +2y 2 b. yx 42 −

2. Solve 4(x – 4) = 2(x + 8)


4. Simplify 5(a – 3) - 2a


a. 0.599453 b. 426 785

6. Find 0.625 ÷ 0.005

7. Find 52

43×

1. If x = -4 and y = 5 find:

a. 7x +3y 2 −x b. 6x + 4y 3

2. Solve 6(x – 2) = 9(x + 3)

3. Evaluate: 82 – 2 x (5 - 4) showing working. 4. Simplify 4(a + 3) – 5(2a – 2) 5. Round the following to 3 significant figures:

a. 0.007695 b. 785 415 6. Find 18 ÷ 0.9

7. Find 31

32×


b. 5x +2y 2 b. 2xy −5x

2. Solve 4(x – 5) = 8(9 - 6x)


4. Simplify 6(4a – 1) – 4(4a + 9)


a. 0.23455 b. 472 345

6. Find 0.072 ÷ (-0.008)

7. Find 43

652 ×


b. 7x + 4y 2 b. 2x 2 −6y 2 2. Solve 5(4 – 3x) = 8x + 9 3. E valuate: 52 – 4 x (12 - 2) showing working 4. Simplify 8(a + 6) – 2(5 – a) 5. Round the following to 3 significant figures:

a. 0.06709 b. 999 454 6. Find 0.64 ÷ (0.0008)

7. Find 761

541 ×





Exercise 4


Exercise 3

© Zeta Maths Ltd.



2. Solve ⅓(x – 2) = ⅙(x + 8)


4. Find the percentage depreciation on a watch purchased for £32,000 and sold for £16,000.




rectangle.


2. Solve ⅓(x + 12) = ⅙(x - 20)


4. Find the percentage depreciation on a boat purchased for £32,000 and sold for £24000.


investment of £12,000 at 4�3% per annum for 5 years.



2. Solve ⅓(x – 10) = ⅙(x - 4)






rectangle.


2. Solve ⅓(2x – 3) = ⅙(x + 9)


4. Find the percentage depreciation on a car purchased for £600,000 and sold for £120,000.




2x + 3

3x - 7

x + 3

3x + 5

2x + 5

3x + 4

5x - 9

7x - 9



Fourth Level Hwk Zeta Maths - LT Scotland · 2019-12-18 · !©Zeta!Maths!Ltd.! ©!ZETA!MATHSLTD....

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Transcript of Fourth Level Hwk Zeta Maths - LT Scotland · 2019-12-18 · !©Zeta!Maths!Ltd.! ©!ZETA!MATHSLTD....