11H Homework booklet

Maths - Autumn 1

Name: _____________

Teacher: _____________

Week 3 1) Simplifying and evaluating using index laws

a) Simplify 𝑦𝑦5 𝑥𝑥 𝑦𝑦7

b) Simplify 2𝑎𝑎3𝑦𝑦5 𝑥𝑥 5𝑎𝑎𝑎𝑎7

c) Simplify 9𝑥𝑥5

3𝑥𝑥2

d) Simplify (3𝑛𝑛𝑛𝑛6)³

e) Evaluate 6412

f) Evaluate 6413

g) 5−3

h) (27125

)23

2) Calculating with numbers in standard form a) Write 0.00034 in standard form

b) Write 4.56 x 105 as an integer

c) Calculate (3 x 105) + (2.4 x 104)

d) Calculate (3 x 106) x (4 x 1010)

e) Calculate (1.6 x 107) ÷ (4 x 103)

3) To use the rule for the nth term in linear sequences a) Here are the first 5 terms in a sequence 10, 14, 18, 22, 26… i) Find an expression, in terms of n, for the nth term of this sequence.

ii) What is the 100th term of this sequence?

iii) Is 204 a term in this sequence? Explain your answer.

b) Here are the first 5 terms in a sequence 30, 27, 24, 21, 18… i) Find an expression, in terms of n, for the nth term of this sequence.

ii) What is the 50th term of this sequence?

iii) Is -34 a term in this sequence? Explain your answer.

4) Calculating volume and surface area Calculate the volume and surface area of the following shapes a)

b)

c)

5) Re-arranging equations

Re-arrange the following equations to make ‘m’ the subject

a) 3m + n = 8

b) 5m² = t

c) (am)² = fc

d) 3m + r = am + g

e) 2𝑚𝑚−𝑡𝑡𝑎𝑎𝑚𝑚

= w

6) Interpreting information from a scatter graph.

The average daytime temperature for 10 days is recorded. A shop also records its ice cream sales for each of the 10 days. The scatter graph shows this information.

a) Draw a line of best fit and state the correlation. b) Describe what the correlation shows. c) On another day, the temperature was 12°C. Estimate the amount of sales made on this day. d) Why would it not be appropriate to use this scatter graph to estimate the amount of sales if the temperature was -2°C. e) One of the points is an outlier. Identify the co-ordinates of the point.

7) Constructing and interpreting two-way tables 100 students attended a revision lesson at the weekend. Each student went to Maths or English or Science. 55 of these students attended on Saturday. Over the weekend a total of 40 students went to Maths. 12 of the 27 students that went to Science went on Sunday. 10 students went to English on Saturday. How many students went to the Maths revision lesson on Saturday?

8) Co-ordinate geometry

a) The line, L, passes through two points A (1, 1) and (5, 13) i) What is the gradient of this line

ii) What is the equation of this line iii) What is the midpoint of AB iv) What is the length of the line segment AB

b) Identify the equation of the following lines

________________ ________________ _______________

Week 4 1) Calculating percentage change

a) Increase £60 by 35% b) Decrease £240 by 0.5% c) Emma buys a house for £201 500. She sells the house for £213 590 Calculate the percentage profit Emma makes. d) Darren bakes 420 cakes. 1

3 of the cakes are vanilla. 35% of the cakes are chocolate. The

remaining cakes are banana. How many banana cakes did Darren bake? e) An adult ticket for the cinema costs £13.40. A child ticket is half the price of an adult ticket. Mr and Mrs Henderson and their six children go to see a movie. Mrs Henderson has a voucher for 18% off. Work out how much Mrs Henderson pays for the tickets.

2) Problem solving with averages a) The mean of five numbers, 3, 4, 5, 5, x is 5. Calculate the value of x.

b) The mean of 5 numbers is 8. Another number is added. The mean is now 6. What number was added?

c) The mean age of a team of 25 players is 26. One of the players, age 20, is sold. What is now the mean age of the team?

d) 50 students each did a mathematics test. The mean score for these 50 students was 8.4

There were 30 boys. The mean score for these 30 boys was 8.25

Work out the mean score for the girls.

3) Calculating missing angles a) Calculate the value of x. b) Calculate the value of x. Give reasons for your answer.

Give reasons for your answer.

c) ABD and BCD are both isosceles triangles. ABC is a straight line. Is ADC a right angle?

4) Calculating missing sides in similar shapes a) Shapes ABCD and EFGH are mathematically similar.

i) Calculate the length of BC ii) Calculate the length of EF

b) The diagram shows two similar shapes

i) i) Calculate the length of PR ii) Calculate the length of BC

c) Calculate the length of ED

5) To perform and identify transformations

Triangle P is drawn on a coordinate grid. The triangle P is reflected in the line x = –1 and then reflected in the line y = 1 to give triangle Q. Describe fully the single transformation which maps triangle P onto triangle Q. a) Rotate the triangle Q 180° about the point (-1, 1). Label the

new triangle A. b) Translate the triangles A by the vector � 3

−5�. Label the new triangle B.

6) Forming expressions

a) Dave is x years old. Angus is three years older than Dave. Peter is twice as old as Angus. Write an expression for their combined age.

b) The length of a rectangles is 3 times longer than the width. i) Write an expression for the perimeter of the rectangle

ii) Write an expression for the area of the rectangle

c) A Tv costs £x. A DVD player is £35 cheaper than a TV. Write an expression for the cost of 3TV’s and 2 DVD players.

7) HCF and LCM a) i) Express 70 as a product of its prime factors.

ii) Express 56 as a product of its prime factors. iii) Hence, calculate the HCF and LCM of 70 and 56.

b) Calculate the HCF and LCM of 12, 15 and 18.

8) Solving linear equations a) 5x – 2 = 13 b) 2(3x + 4) = 20 c) 5x – 2 = 3x + 17 d) 3x + 5 = 5 7

Week 5 1) Calculating repeated percentage change

a) Anil invests £3000 into a savings account. He earns 2% compound interest per annum. How much money will he have in his account after 4 years. b) The value of a car depreciated by 8% every year. If you bought the car 5 years ago for £24,000. How much is it worth now? c) Alex invests some money for 3 years in a savings account. She gets 4% per annum compound interest. Alex has £5680.56 at the end of 3 years, work how much she invested d) Sandra invests £2500 into a savings account for three years. She gets 3% compound interest for the first year and than x% for the next two years. Sandra has £2705.36 in her account after three years, work out the value of x.

2) Calculations with fraction

a) 213 + 52

5

b) 6 27 x 34

9

c) 4 15 ÷ 13

8

d) Simplify 2𝑥𝑥3

+ 5𝑥𝑥5

e) Simplify 2𝑥𝑥+35

- 𝑥𝑥−24

3) Calculating missing sides and angles in right-angled triangles a) Calculate the area and perimeter of the triangle

c) Calculate the length of AD. Give your answer to 3 siginificatn figures.

c) Calculate the size of angle BAC. d) Calculate the size of angle BAD.

e) Calculate the size of angle BCD.

4) Expanding double brackets and factorising quadratics a) Expand and simplify (2x + 3) (x + 5) b) Expand and simplify (3x – 5) (5x – 3) c) Factorise x² + 11x + 24 d) Factorise x² - x – 20

5) To form and solve equations

a) Adnan is x years. Pheobe is three times as old as Adnan. Adam is 5 years older than Pheobe. Their combined age is 145. How old is each person.

b) The length of a rectangles is 5cm longer than the width. The perimeter of the rectangle is 42cm. Calculate the area of the rectangle.

c) Calculate the size of each angle

d) The perimeter of the parallelogram is 24cm. Calculate the value of x.

6) Solving quadratic equations

a) x² + 13x + 30 = 0

b) x² + x – 20 = 0

c) x² + 8x = 20

d) x² + 5x + 3 = 0. Give your answer to 2dp.

e) 3x² - 11x = 13. Give your answer to 2dp.

7) Calculating HCF and LCM

e) i) Express 84 as a product of its prime factors.

ii) Express 120 as a product of its prime factors. iii) Hence, calculate the HCF and LCM of 84 and 120.

f) Calculate the HCF and LCM of 72, 90 and 126.

g) A meteor shower happens every 120 years. A different meteor shower happens every 150 years. The last time they happened in the same year was 1950. What is the next year that both meteor showers will happen together?

Week 6

1) (a) (i)Write x² + 8x + 5 in the form (x + a)² + b where a and b are integers. (ii) Hence, or otherwise, write down the coordinates of the turning point of the graph of y = x² + 8x + 5 (b) By completing the square, find the coordinates of the turning point of the curve with the equation y = x² + 3x – 7 You must show all your working.

2) (a) Solve the simultaneous equations x² + y² = 34 x – y = 2 (b) Solve the simultaneous equations x² + y² = 20 3x = 2 – y

(c ) Solve the simultaneous equations y – 2x – 4 = 0 4 x2 + y2 + 20x = 0

3)

4) Solve 2x² + 13x + 7 = 0 Give your solutions correct to 2 decimal places.

5)

Two solid shapes, A and B, are mathematically similar. The base of shape A is a circle with radius 4 cm. The base of shape B is a circle with radius 8 cm. The surface area of shape A is 80 cm2

(a) Work out the surface area of shape B.

The volume of shape B is 600 cm 3 . (b) Work out the volume of shape A.

6) Dana invests £5000 for 4 years in a savings account. She gets 2% per annum compound interest in the first year, then x% for 3 years. Dana has £5508.23 at the end of 4 years, work out the value of x .

7)

8) A garage sells cars. It offers a discount of 20% off the normal price for cash. Dave pays £5200 cash for a car. Calculate the normal price of the car.

Week 7

1) (a)

The diagram shows a sector of a circle, centre O. The radius of the circle is 13 cm. The angle of the sector is 150°. Calculate the area of the sector. Give your answer correct to 3 significant figures. (b)

The diagram shows a sector of a circle, centre O. The radius of the circle is 6 cm. Angle AOB = 120°. Work out the perimeter of the sector. Give your answer in terms of π in its simplest form.

2) (a) There are 17 boys and 14 girls in a choir. One boy and one girl will be selected to sing a duet. Work out the total number of ways of choosing a boy and a girl.

(b) There are 5 starters, 6 main course and x desserts in a restaurant. Riley says there are 130 different ways of a starter, a main course and a dessert. Could Riley be correct? You must show your working.

3) c is inversely proportional to d When c = 3, d = 8 Find the value of c when d = 2

4)

5) Jon plays a game where he can win, draw or lose. The probability Jon wins any game 0.5. The probability Jon draws any game is 0.3 Jon plays two games.

(a) Construct a tree diagram to represent this information

(b) Calculate P(Jon wins both games)

6) The line L1 has equation 4x + 2y – 3 = 0.

(a) Find the gradient of L1.

The line L2 is perpendicular to L1 and passes through the point (2, 5). (b) Find the equation of L2 in the form y = mx+ c, where m and c are constants.

7) Expand and Simplify

(a) (x + 4)(x + 5)(x – 4)

(b) (x + 3)(x – 1)2

8)

The line y = x + 2 meets the curve x2 + 4y2 – 2x = 35 at the points A and B as shown in Figure 2. (a) Find the coordinates of A and the coordinates of B.

(b) Find the distance AB to 2.d.p

Week 8

1)

2)

3) (a)

(b)

4) (a) Write 9.516 × 106 as an ordinary number. (b) Write 0.0724 in standard form. (c) Calculate (8.694 × 102) ÷ (6.21 × 10-3) Give your answer in standard form.

(c) Work out (6.7 × 104) × (3.4 × 10-8) Give your answer in standard form.

5) In a bag there are blue sweets and red sweets. The ratio of blue sweets to red sweets is 2:7 What fraction of the sweets are red?

6) The line l1 has equation 4y − 3x = 10.

The line l2 passes through the points (5, −1) and (−1, 8). Determine, giving full reasons for your answer, whether lines l1 and l2 are parallel, perpendicular or neither.

7) A shop decreases prices by 10% and then by a further 20%. Rachel says: “Prices have now decreased by 30%”. Is Rachel correct? You must show your working.

8) a + b = 7 ab = 9 Calculate the sum of the reciprocals of a and b