BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL 4

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1 BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL

2 Rounding 1. Round these numbers to the nearest 10: a) 238 b) 719 c) Round these numbers to the nearest 100: a) 6783 b) c) Round these numbers to the nearest 1000: a) 1827 b) 8710 c) Round these numbers to the nearest : a) b) 9.82 c) Round these numbers to the nearest metre: a) 3m 65cm b) 6m 5cm c) 1m 5cm 3 6. Round these numbers to one decimal place: a) 5.8 b) c) Round these numbers to two decimal places: a) b).773 c) Round these numbers to one significant figure: a) 369 b) 721 c) 55 d) 0.52 e) 0.09 f) Sasha bought a new car for Round this to the nearest thousand The deepest point in the ocean is feet below sea level, This is the Mariana Trench in the western Pacific. Round this number to the nearest 100 feet. 1 (29)

3 Integers 1. Work out the answers to the following questions: 5 (a) 7 (b) 9 7 (c) 3 10 (d) 6 2 (e) Work out the answers to the following questions: 5 (a) 5 3 (b) 8 6 (c) 5 9 (d) 3 (e) Work out the answers to the following questions: 5 (a) 6 8 (b) 3 10 (c) 3 5 (d) 7 (e) In an experiment Rashid measures the temperature of two liquids The temperature of the first liquid is 11 Celsius. The temperature of the second liquid is 23 Celsius. Find the difference between these temperatures. The circle above contains seven numbers. Find the three numbers from the circle which add up to 10. You must show your working. 6. In July the average temperature in Anchorage, Alaska is 9 C. By January the average temperature has fallen by 26 C. What is the average temperature in Anchorage in January? 2 (21)

4 Brackets & Equations 1. Remove the brackets. a) (x + 1) b) 6(y - 7) c) 8(3 + 2b) d) 5(9c 6) 2. Multiply out the brackets and simplify. a) 3(7g + 9) - 7 b) 7c + 5(2 c) c) 3(m - 2) + 2(m + 1) d) 2(x + ) + 3(x - 2) Write two expressions for the perimeter of the rectangle, one with brackets and one without. All measurements are in centimetres. 3 3a. Remove the brackets and solve the equations. a) (x + 3) = 36 b) 8(2 + x) = 6 c) 3(3x 2) = 12 d) 28 = (5x - 3) 8 5. The stars are of equal length. All measurements are in centimetres. a) write an equation with brackets 1 b) solve the equation by first removing the brackets 2 c) if the total length of the lines is 5 cm, what is the length of one star? 2 (2x + ) 5cm 6. Cadberry sells bags of mini chocolate bars, each holding the same amount. The cost of chocolate has increased and rather than put the price up, there are less mini bars in each bag. To fill 50 bags they now need 800 mini bars. Let x be the original number of mini bars in a bag. Form an equation in x and solve it to find the original number of mini bars in each bag. 3 (33)

5 Pythagoras Theorem 1. Without performing the calculation, which of the following is most likely to be the length of the hypotenuse of the right angled triangle: A - 15cm B - 18cm C - 25cm D - 3cm Give a reason for your answer. 1 y y 2. Calculate the length of the missing side in the following triangles: a) b) A ship leaves port heading North and sails for 73miles. The captain then turns so the ship is heading East and sails for 5miles. He wants to calculate how far he is from the port. a) Why can we use Pythagoras Theorem for this calculation? 1 b) How far is the ship from the port?. Calculate the height of the frame for the swing shown in the diagram below. (16)

6 Factorisation Factorise the following expressions: 1. 2x w y x 2 5. x² + x 2 6. n² - 6n ab + 6a 2 8. xy + y² x - 15x² r - 6rs + 8rt 2 (20)

data to create a frequency table. 2 2. The ages of employees who work in a factory are given in the table below.

7 Statistics 1. Pupils in an S1 Maths class were questioned on what they normally do for. The results are shown below. Canteen Packed Home Canteen Packed Home Town Canteen Canteen Packed Packed Packed Canteen Packed Home Packed Packed Packed Canteen Canteen Packed Home Canteen Packed Packed Home Town Packed Use this data to create a frequency table The ages of employees who work in a factory are given in the table below Create a stem and leaf diagram and comment on the findings Calculate the mean, median, mode and range for the data below: A bag contains a selection of sweets. There are 12 toffees, 9 mints and 3 truffles. Sally chooses a sweet at random. Calculate the probability that she chooses a a) truffle b) toffee c) sweet that s not a mint 6 (18)

Distance, Speed and Time 1. Convert into hours: a) 180 minutes b) 90 minutes c) 105 minutes d) 135 minutes 2.

2 5. A train journey covers a distance of 20 miles. If the average speed of the train is 60 miles per hour how long will the train take to complete the journey? 2 6.

A greyhound can run at a top speed of 5 miles per hour. If a greyhound could maintain this speed how long would it take a greyhound to run 9 miles?

8 Distance, Speed and Time 1. Convert into hours: a) 180 minutes b) 90 minutes c) 105 minutes d) 135 minutes 2. Convert into minutes: a) hours b) 2 and a half hours c) 3 and a quarter hours d) 8 and three quarter hours 3. A car drives for hours at a speed of 60 miles per hour. Find the distance covered. 2. If an aeroplane flies 700 kilometres in 2 hours find its average speed A train journey covers a distance of 20 miles. If the average speed of the train is 60 miles per hour how long will the train take to complete the journey? 2 6. If a jogger runs at an average speed of miles per hour how long would it take him to complete a marathon? (A marathon is about 26 miles long) 2 7. A greyhound can run at a top speed of 5 miles per hour. If a greyhound could maintain this speed how long would it take a greyhound to run 9 miles? Give the answer in hours then convert it into minutes Jack and Jill travel from Edinburgh to Birmingham. Jack travels by train and Jill travels by aeroplane. The graph below shows their journeys. a) What is the distance between Edinburgh and Birmingham? 1 b) How much sooner than Jack does Jill arrive in Birmingham? 1 c) Calculate the average speed, in miles per hour, of Jack s journey. 3

Ratio 1. Write the ratio of circles to squares in its simplest form. 2 2.

$5 1 b) What fraction of the class is made up of boys?$ 1 c) If the class consists of 25 pupils, calculate the number of boys in the class.

100:350. a) Write this ratio in its simplest form.

This money will be divided between the tennis section and the golf section in the

9 Ratio 1. Write the ratio of circles to squares in its simplest form The ratio of boys to girls in a classroom is 3:2. a) How many parts are there in the ratio? 5 1 b) What fraction of the class is made up of boys? 1 c) If the class consists of 25 pupils, calculate the number of boys in the class At Dunmore Tennis and Golf club, the ratio of tennis players to golfers is 100:350. a) Write this ratio in its simplest form. 1 b) The club has been given 16,200.This money will be divided between the tennis section and the golf section in the same 5 ratio as above. How much money will be allocated to the tennis section? 3. John, Jim and Mary put money towards a Lottery Syndicate every week. John puts in 6, Jim puts in and Mary puts in 3. One week they win 83,200. How much money should each person get as their share of the winnings? (1)

10 Angles and Circles 1 Copy all the diagrams. Show your working. 1. Find the value of the letter in each diagram. Give a reason for your answer. 2. Find the size of each lettered angle Calculate the missing lengths in the triangles to 1 d.p. All measurements are in centimetres. 6 6 (25)

Angles and Circles 2 Copy all the diagrams. Show your working. 1. Find the size of each lettered angle. 7 2. The semicircular green house is supported by a metal frame.

11 Angles and Circles 2 Copy all the diagrams. Show your working. 1. Find the size of each lettered angle The semicircular green house is supported by a metal frame. 5 Calculate the length of AC to 1 d.p The arch of a tunnel is semicircular. Its diameter is XY. A light is fixed at point Z on the arch. A wire runs from the light at point Z to point Y. YZ = 2.9 m, XZ = 6.3 m a) What is the diameter of the arch? Give your answer 3 significant figures. 3 b) Y is 3.5 m from the ground. 5 How high is the top of the arch above the ground? Give your answer to 1 d.p. 3 (16)

12 TRIGONOMETRY - SOHCAHTOA 1. Three steel rods are welded together to make a shelf bracket. The sloping side makes an angle of 28 with the horizontal and is 2cm long. 28 2cm Calculate the size of the horizontal rod marked x, giving your answer to the nearest centimetre. 2. An access ramp is constructed in front of the main doors of a primary school. The ramp is 0 cm long and rises up to a point 65cm above ground level. y 0cm 65cm Disability legislation states that angle y, between the ramp and the ground, can be no more than 9. Does this ramp comply with these requirements? Justify your answer A radio mast AD is held in place by two cables DC and DB. AC = 15 metres and CB = 18 metres, and the angle of elevation of the top of the mast from C is 65. Calculate a) The height of the mast AD 3 b) The angle marked x. 3 (13)

13 Number Patterns & Relationships 1. What is a sequence? 1 2. Write down the next 3 terms of each sequence a), 7, 10, 13, 16 1 b) 5, 13, 21, 29, 37 1 c) 3, 6, 11, 18, 27 1 d) 1,, 9, 16, Below is a sequence of dot designs. The designs continue to be built up in the same way a) Copy and complete the following table 3 Design Number (n) No. of Dots (D) 5 8 b) Write down a formula for calculating the number of dots when you know the design number. 2 c) How many dots are needed for the 9 th design? 2 d) Which design number requires 191 dots? 2. Find (i) the nth term formula (ii) use this formula to find the indicated term a) 5, 7, 9, 11, 13 the 29 th term 2, 1 b) 3, 10, 17, 2, 31 the 17 th term 2, 1 (20)

BASICS OF TRIGONOMETRY

Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 09-10-015 Mathematics Revision