For the solutions and the explanations refer to the notes. Bellow some solutions are repeated. Section A 1. 10, 30, 60, 61, 63, 65, 69 Using only numbers from the list above, write down a) a multiple of 7, 63 b) a prime number, 61 c) the lowest common multiple of 20 and 30. 60 Refer to the notes for the solutions. 2. Ahmed earns $2500 in May. In June, he earns 2% more. Work out how much he earns in June. Refer to the notes for the solutions. 3. A box of chocolates contains 4 milk chocolates (M) and 6 plain chocolates (P). One chocolate is chosen at random and is not replaced. A second chocolate is chosen at random. a) Find the probability that the first chocolate chosen is a milk chocolate. b) Find the probability that both of the chocolates chosen are milk chocolates. Refer to the notes for the solutions. 4. a. Simplify. 5 + 3d – 1 + 4d =7d+4 b. Expand the brackets. 8(4 – 3n) = 32 – 24n Refer to the notes for the solutions. 5. Solve the following equation. 7q – 5 = 6 – 3q; q = 1.1 Refer to the notes for the solutions.
Transcript
For the solutions and the explanations refer to the notes.
Bellow some solutions are repeated.
Section A
1. 10, 30, 60, 61, 63, 65, 69Using only numbers from the list above, write downa) a multiple of 7, 63b) a prime number, 61c) the lowest common multiple of 20 and 30. 60
Refer to the notes for the solutions.
2. Ahmed earns $2500 in May. In June, he earns 2% more. Work out how much he earns in June.Refer to the notes for the solutions.
3. A box of chocolates contains 4 milk chocolates (M) and 6 plain chocolates (P). One chocolate is chosen at random and is not replaced. A second chocolate is chosen at random.a) Find the probability that the first chocolate chosen is a milk chocolate.b) Find the probability that both of the chocolates chosen are milk chocolates.
Refer to the notes for the solutions.
4. a. Simplify. 5 + 3d – 1 + 4d =7d+4b. Expand the brackets. 8(4 – 3n) = 32 – 24nRefer to the notes for the solutions.
5. Solve the following equation. 7q – 5 = 6 – 3q; q = 1.1Refer to the notes for the solutions.
6. Write 5392 correct toa. the nearest 100, 5400b. the nearest 10 . 5390
7. Here is a list of numbers. 4, 5, 11, 20, 27, 39, 43. Use the list to write downa. a square number, 4b. a factor of 20, 4, 5, 20c. a multiple of 5, 5, 20d. a prime number. 5, 11, 43
8. (a) The cost, in $, of hiring a machine is worked out using the formulacost = 50 + 25 × number of days hired.Work out the cost of hiring the machine for
i. 2 daysii. 1 week
Refer to the notes for the solutions.
(b) Simplify.5x + 4y + 2x – y = 7x + 3y
(c) Solve the following equation.3x + 5 = 23; x = 6
(d) Solve the simultaneous equations.3x + y = 19x + y = −5
x=12
y=-17
9. The population of India in 2011 was 1.21 × 109. The population of Pakistan in 2011 was 1.77 × 108. Calculate the total population of India and Pakistan in 2011. Give your answer in standard form.Refer to the notes for the solutions.
11. (a) Write down the value of(i) log 1000 = 3(ii) log 0.01 = -2
(b) Find E when 2log 5 – log 2 = log E .Refer to the notes for the solutions.
12. (a) Write 2log(x + 1) – log(x – 1) as a single logarithm.(b) log3 E = 4 where E is an integer. Find the value of E.Refer to the notes for the solutions.
13. Rearrange this equation to make x the subject.ax – 3y = b(x + 2y)Refer to the notes for the solutions.
14. (a) Find the value of ax3 when a = 1200 and x = 5.Give your answer in standard form.
(b) Make x the subject of the formula y = ax3.
Refer to the notes for the solutions.
15. These are the first five terms of a sequence.2, 6, 12, 20, 30(a) Find the next term.(b) Find an expression for the nth term.Refer to the notes for the solutions.
16. f(x) = 3 + 2xFind: (a) f(f(– 4)), (b) f -1(x) .Refer to the notes for the solutions.
17. y varies inversely as x2.When x = 2, y = 24.Find a formula for y in terms of x.Refer to the notes for the solutions.
18. Work out (1.6 × 103) ÷ (4 × 105).Give your answer in standard form.Refer to the notes for the solutions.
19. Jimmi’s pencil case only contains 3 pens and 12 pencils.(a) He chooses an object at random from his pencil case.
Find the probability that the object is a pencil.(b) Jimmi chooses an object at random from his pencil case and then replaces it.
He repeats this 100 times.How many times do you expect Jimmi to choose a pen?
23. Tiago buys a concert ticket and then sells it for $15.He makes a profit of 20%.Calculate how much Tiago paid for the ticket.Refer to the notes for the solutions.
24. (a) Find the amplitude and period of the function f(x) = 4cos(4x).(b) g(x) = 4cos(4x) – 4Describe fully the single transformation that maps the graph of y = f(x) onto the graph ofy = g(x).Refer to the notes for the solutions.
25. f(x) = 3x – 1 g(x) = 12 – xFind:
a. f(g(8)),b. f(g(x)), in its simplest form,c. g-1(x).
Refer to the notes for the solutions.
26. Three sisters, Meg, Jo and Pat, share $1400. Meg is 15 years old, Jo is 17 and Pat is 18. They divide the money in the ratio of their ages.a) Show that Jo receives $476 .b) Find the amount that Pat receives.c) Work out how many more dollars Pat receives than Jo.d) Write your answer to part (c) as a percentage of the $1400.
Refer to the notes for the solutions.
27. On any one night, the probability that José plays a computer game is 0.6. When José plays a computer game, the probability that he does his homework is 0.1. When he does not play a computer game, the probability that he does his homework is 0.8 .a) Complete the tree diagram.b) Find the probability that José plays a computer game and does his homework.c) Find the probability that José does not do his homework.
Refer to the notes for the solutions.
28. A pizza box has a height of 5 cm and a square base of side 30 cm.
a) (i) Find the area of the base of the box.
(ii) Calculate the volume of the box.
b) The radius of the circular pizza is 15 cm.
(i) Find the area of the base of this pizza.
(ii) The pizza is cut into 16 equal slices as shown in the diagram.Find the size of the angle of each slice.
(iii) Calculate the area of one slice of pizza.
c) A mathematically similar pizza box has height 4 cm.Calculate the length of the sides of the base of this pizza box.
Refer to the notes for the solutions.
29. Hugo, Ana and Bella all leave home at 07:45 to travel to school.(a) Hugo lives 3 km from school. He takes 20 minutes to skateboard to school.
(i) Find the time that Hugo arrives at school.
(ii) Find his average speed in kilometres per hour.
(b) Ana lives 1 km from school. She walks to school at 4 km/h. Find the time that Ana arrives at school.
(c) Bella travels to school by car at an average speed of 30 km/h. She arrives at school at 0810. Find the distance Bella travels to school.
(d) Which of these three students arrives at school first?
Refer to the notes for the solutions.
30. a. Here are the first four terms of a sequence. 28, 25, 22, 19(i) Write down the next two terms of this sequence.
(ii) Find the nth term of the sequence.
b. Find the nth term of each of the following sequences.(i) 21, 17, 13, 9, 5, ………
(ii) 3, 6, 12, 24, 48, ………
(iii) 0, 6, 24, 60, 120, ………
Refer to the notes for the solutions.
Section D
31. Simplify the following expression.2x – 1 + 2(x + 2) = 4x +3
Make s the subject of the formula.r = 2pm + ns; s =(r-2pm)/n
32. Manuel buys a car for $8000.(a) Each year the value of the car decreases by 8% of its value at the start of the year.
(i) Calculate the value of the car after 5 years.
(ii) Calculate how many more years it takes for the value of the car to be less than $4000.
(b) Manuel has a journey of 235 km. The journey takes 3 h 15 min and the car uses 19.7 litres of fuel.
(i) Calculate the average speed of the journey in kilometres per hour.
(ii) Find the rate at which the car uses fuel.Give your answer in litres per 100 km.Refer to the notes for the solutions.
38. B, C, D and E lie on a circle, centre O.CE is a diameter, angle DAC = 30° and angle BOE = 70°.Find the values of x, y and z.
Refer to the notes for the solutions.
39. P is the point (–2, 5) and Q is the point (4, 1).(a) Find the co-ordinates of the midpoint of PQ.(b) Find the gradient of PQ.(c) (i) Find the equation of the line perpendicular to PQ which passes
through the point (0, 4).(ii) Find the x co-ordinate of the point where this line cuts the x-axis.
Refer to the notes for the solutions.
40. The points A (1, 9) and B (7, 1) are shown on the diagram below.
(a) Calculate the length AB.
(b) (i) Find the co-ordinates of the midpoint of the line AB.
(ii) Find the equation of the perpendicular bisector of the line AB.
Refer to the notes for the solutions.
Section E
41.
Refer to the notes for the solutions.
42. Paulo goes to a supermarket.The probability that he buys orange juice is 0.65 .The probability that he does not buy milk is 0.30 .The probability that he buys milk but does not buy orange juice is 0.15 .(a) Complete the table of probabilities.
(b) Find the probability that Paulo buys either orange juice or milk but not both.
Refer to the notes for the solutions.
43. The bar chart shows the grades obtained by a group of students in an examination.
(a) How many students achieved an A grade?
(b) Write down the modal grade.
(c) How many students were there altogether?
(d) How many more students achieved a B grade than a D grade?
Refer to the notes for the solutions.
44. (a) Find the perimeter of this shape. 16 units
(b) Work out the area of this shape. 12 square units.
45. Describe fully the single transformation which maps triangle P onto triangle Q.
Rotation about the origin 90 degrees counterclockwise.
46. ABC is a sector of a circle with circumference 300 cm.Angle ACB is 120°.Find the length of the arc AB.
100 cm
47.
48.
Refer to the notes for the solutions.
49. A badge is in the shape of a square with four congruent triangles attached.The square has side 3 cm.The triangles each have a perpendicular height of 2 cm.Work out the area of the badge. 21 squared cm
