*p46228a01624*mrcheung.weebly.com/uploads/5/5/8/9/55894599/abridged... · 2019-05-14 · 16...
TRANSCRIPT
16
*P46228A01624*
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13 (a) Write 250 000 in standard form.
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(1)
The radius of the planet Jupiter is 6.99 × 107 metres. The radius of the Earth is 6.37 × 106 metres.
The volume of Jupiter is k times the volume of the Earth.
(b) Assuming that both planets are spheres, calculate the value of k. Give your answer correct to 3 significant figures.
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(3)
(Total for Question 13 is 4 marks)
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*P44614A0720* Turn over
6 E = {positive whole numbers less than 19} A = {odd numbers} B = {multiples of 5} C = {multiples of 4}
(a) List the members of the set
(i) A B
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(ii) B C
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(2)
D = {prime numbers}
(b) Is it true that B D = ?
Tick ( ) the appropriate box. Yes No
Explain your answer.
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(1)
(Total for Question 6 is 3 marks)
7 Lisa, Max and Punita share £240 in the ratio 3 : 4 : 8
How much more money than Lisa does Punita get?
£.. . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 is 3 marks)
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*P44614A01320* Turn over
15 Here is the graph of y = x2 – 2x – 1
(a) Use the graph to solve the equation x2 – 2x – 1 = 2
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(2)
The equation x2 + 5x – 7 = 0 can be solved by finding the points of intersection of the line y = ax + b with the graph of y = x2 – 2x – 1
(b) Find the value of a and the value of b.
a = .. . . . . . . . . . . . . . . . . . . . . . . . . . .
b = .. . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 15 is 4 marks)
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1
–1
–2
–3
–2 –1 1 2 3 4
y
x
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*P44614A01620*
18 An athlete runs 400 metres, correct to the nearest metre. The athlete takes 50.2 seconds, correct to the nearest 0.1 of a second.
Work out the upper bound of the athlete’s average speed. Give your answer correct to 3 significant figures.
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(Total for Question 18 is 3 marks)
19 a = 52−
⎛
⎝⎜
⎞
⎠⎟ b =
17
⎛
⎝⎜
⎞
⎠⎟ c =
−⎛
⎝⎜
⎞
⎠⎟70
(a) Write, as a column vector, 2a
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(1)
(b) Write, as a column vector, 3b – c
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(2)
(c) Work out the magnitude of a Give your answer as a surd.
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(2)
(Total for Question 19 is 5 marks)
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
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*P44614A01720* Turn over
20 The histogram shows information about the heights of some tomato plants.
26 plants have a height of less than 20 cm.
Work out the total number of tomato plants.
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(Total for Question 20 is 3 marks)
O 20 40 60 80Height (cm)
Frequency density
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*P44614A01920* Turn over
22 (a) Write 132
as a power of 2
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(2)
(b) Show that ( )( )4 12 5 3 14 6 3+ − = + Show each stage of your working clearly.
(3)
(Total for Question 22 is 5 marks)
23 Write 5 – (x + 2) ÷ xx
2 43
−−
⎛
⎝⎜
⎞
⎠⎟ as a single fraction.
Simplify your answer fully.
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(Total for Question 23 is 4 marks)
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*P44614A02020*
24 The diagram shows a sector OAPB of a circle, centre O.
AB is a chord of the circle. OA = OB = 6 cm.
The area of sector OAPB 2
Calculate the perimeter of the shaded segment. Give your answer correct to 3 significant figures.
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(Total for Question 24 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
P
BA
O
6 cm 6 cm
Diagram NOT accurately drawn
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*P44620A0824*
5 Here are some rows of a number pattern.
Row number Column 1 Column 2 Column 3
1 1 × 3 + 1 4 22
2 2 × 4 + 1 9 32
3 3 × 5 + 1 16 42
.
.
.
676
.
.
.
n
(a) Write down the Row number of the row that has 676 in Column 2
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(1)
(b) For Row number n,
(i) write down an expression, in terms of n, that should go in Column 1
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(ii) write down an expression, in terms of n, that should go in Column 3
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(2)
(Total for Question 5 is 3 marks)
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*P44620A0924* Turn over
6 The table gives information about the number of vehicles passing a point on a road in each of 70 intervals of equal length.
Number of vehicles Frequency
1 to 5 8
6 to 10 10
11 to 15 18
16 to 20 20
21 to 25 10
26 to 30 4
(a) Write down the modal class interval.
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(1)
(b) Calculate an estimate for the mean.
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(4)
(Total for Question 6 is 5 marks)
Do NOT write in this space.
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*P44620A01224*
9 E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {even numbers}
B = {multiples of 3}
(a) List the members of set B.
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(1)
(b) Find A ∪ B
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(1)
(c) Find A ∩ B
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(1)
x is a member of E
x B
x A
(d) What are the possible values of x?
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(2)
(Total for Question 9 is 5 marks)
Do NOT write in this space.
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*P44620A01324* Turn over
10
B
C
E
D
A10 cm
9 cm
13.5 cm
17 cm
Diagram NOT accurately drawn
In the diagram ABC and ADE are straight lines. BD is parallel to CE.
AB = 9 cm, BC = 13.5 cm, AD = 10 cm, BD = 17 cm
(a) Calculate the length of CE.
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(b) Calculate the length of DE.
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The area of triangle ABD is 36 cm2
(c) Calculate the area of quadrilateral BDEC.
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(3)
(Total for Question 10 is 7 marks)
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*P44620A01724* Turn over
14 (a) Solve x2 – 4x – 1 = 0
Show your working clearly. Give your solutions correct to 3 significant figures.
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(3)
Hence, or otherwise,
(b) solve (x + 3)2 – 4(x + 3) – 1 = 0
giving your solutions correct to 3 significant figures.
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(1)
(Total for Question 14 is 4 marks)
Do NOT write in this space.
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*P44620A01824*
15 Here is the parallelogram ABCD.
y
xO
D
C
B
A
Diagram NOT accurately drawn
AD→
= 12
⎛
⎝⎜
⎞
⎠⎟ , AB
→ =
53
⎛
⎝⎜
⎞
⎠⎟
(a) Find the magnitude of AD→
.
Give your answer correct to 3 significant figures.
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(2)
The point A has coordinates (4, 2)
(b) Work out the coordinates of the point C.
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(3)
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*P44620A01924* Turn over
The diagonals of the parallelogram ABCD cross at the point E.
(c) Find as a column vector, OE→
.
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(3)
(Total for Question 15 is 8 marks)
Do NOT write in this space.
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*P44620A02124* Turn over
17 (a) Show that ( )( )3 2 2 4 2 8 5 2+ − = +
Show your working clearly.
(2)
(b) Rationalise the denominator and simplify fully 10 3 22
+
Show your working clearly.
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(2)
(Total for Question 17 is 4 marks)
Do NOT write in this space.
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*P44620A02224*
18
O 4
–
8
–
12
–
16
–
20–
24–
28
–
32
–
36
–
40
–
Height (cm)
Frequency density
The histogram gives information about the heights of some plants.
There are 360 plants with a height of 20 cm or less.
Work out the number of plants with a height of more than 20 cm.
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(Total for Question 18 is 3 marks)
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*P44620A02424*
20 (a) Factorise 4x2 – 1
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(2)
(b) Solve 4
2 11
4 132x x+
+−
=
Show clear algebraic working.
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(4)
(Total for Question 20 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
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*P44389A0424*
3 Lia left home at 1100 to drive to a shopping centre. On her way, she stopped at a friend’s house. Here is the distance-time graph for her journey to the shopping centre.
50
45
40
35
30
25
20
15
10
5
01100 1200 1300 1400 1500 1600 1700
Time
Distance from home (km)
(a) (i) For how many minutes did Lia stay at her friend’s house?
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(ii) How far is it from her friend’s house to the shopping centre?
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Lia stayed at the shopping centre for 112
hours.
She then drove back home. She arrived home at 16 30
(b) Show all this information on the distance-time graph.
(2)
(Total for Question 3 is 4 marks)
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*P44389A0524* Turn over
4 Becky has a biased 6-sided spinner. She spins the spinner 25 times. She records the score for each spin. The table shows information about her scores.
Score Frequency1 92 63 34 25 16 4
(a) Find her median score.
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(2)
(b) Work out her mean score.
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(3)
(Total for Question 4 is 5 marks)
1
6
54
3
2
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*P44389A0924* Turn over
8 Diagram NOT accurately drawn
11.3 cm
x cm
39°
Work out the value of x. Give your answer correct to 2 decimal places.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 is 3 marks)
9 (a) Solve the inequalities –5 x + 4 3
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(2)
(b) n is an integer. Write down all the values of n that satisfy –3 n 2
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(2)
(Total for Question 9 is 4 marks)
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*P44389A01124* Turn over
(b) Find an estimate for the percentage of the 80 films that lasted more than 125 minutes.
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(Total for Question 10 is 5 marks)
11 x is an integer. The Lowest Common Multiple (LCM) of x and 12 is 120 The Highest Common Factor (HCF) of x and 12 is 4
Work out the value of x.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 11 is 2 marks)
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*P44389A01324* Turn over
14 L and M are two mathematically similar prisms.
3cm 20cm8cm
ML
Diagram NOT accurately drawn
Prism L has length 8 cm. Prism M has length 20 cm.
Prism L has height 3 cm.
(a) Work out the height of prism M.
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Prism M has a volume of 1875 cm3
(b) Work out the volume of prism L.
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(2)
(Total for Question 14 is 4 marks)
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*P44389A01524* Turn over
16 Diagram NOT accurately drawn
105°
14.6 cm
62°
x cm
Work out the value of x. Give your answer correct to 1 decimal place.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 is 3 marks)
17 ABCD is a parallelogram.
BC = 51−
⎛⎝⎜
⎞⎠⎟
DC = −⎛
⎝⎜⎞⎠⎟23
Find BD as a column vector.
⎛⎝⎜
⎞⎠⎟
(Total for Question 17 is 2 marks)
B
xO
AD
C
yDiagram NOT accurately drawn
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*P44393A01324* Turn over
12 The straight line L is shown on the grid.
5 x
L
O
3
y
Find an equation of L.
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(Total for Question 12 is 3 marks)
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*P44393A01924* Turn over
17 J, K, L and M are points on the circumference of a circle. GJH is the tangent to the circle at J. MK and JL intersect at the point P. GML is a straight line.
Angle HJK = 62°, angle JKM = 21° and angle JGL = 78°
Diagram NOT accurately drawn
L
62°
21°
K
HJG
M
P
78°
(a) Write down the size of angle MLJ.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(1)
(b) Write down the size of angle JLK.
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(1)
(c) Work out the size of angle KPL.
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(3)
(Total for Question 17 is 5 marks)
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*P44393A02024*
18 400 people are asked to guess the weight of a large cake. The table shows information about the weights they guess.
Weight (w kg) Number of guesses 0 w 1 50 1 w 1.6 901.6 w 2 120 2 w 2.5 952.5 w 4 45
Use the information in the table to complete the histogram.
O
Frequency density
1
–
2
–
3
–
4
–
Weight (w kg)
(Total for Question 18 is 3 marks)
21
*P44393A02124* Turn over
19 153
= 5p 1 = 5q 53 = 5r
(a) Write down the value of
(i) p
p = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) q
q = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) r
r = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(b) Show that 14245
= 2 55
You must write down each stage of your working.
(2)
e −( )2 32 = f – 20 3 where e and f are integers.
(c) Find the value of e and the value of f
e = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
f = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 19 is 8 marks)
3
*P46917A0324* Turn over
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Answer ALL TWENTY FOUR questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1 Here is a list of ingredients needed to make 16 cookies.
Ingredients for 16 cookies120 g butter150 g sugar240 g flour170 g chocolate1 egg
Max wants to make 40 cookies.
(a) How much flour does Max need?
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g(2)
Abby made cookies to sell at a school fair. She used 600 g of butter.
(b) How many cookies did she make?
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
(c) Find the ratio of the weight of sugar to the weight of flour in the list of ingredients. Give your answer in the form 1: n
1 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
(Total for Question 1 is 6 marks)
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*P46917A01424*
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14 (a) Complete the table of values for y = x3 x + 2
x 0 1 2 3
y 4 14
(2)
(b) On the grid, draw the graph of y = x3 x x 3
15
10
5
O
–5
–10
–2 –1 1 2 3 x
y
–3
(2)
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*P46917A01524* Turn over
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The equation x3 x + m = 0, where m is an integer, has one negative solution and two positive solutions.
(c) Given that x = 1 is one of the positive solutions, show that m = 5
(1)
(d) By drawing a suitable straight line on the grid, find an estimate for the negative solution of x3 x + 5 = 0
Give your estimate to 1 decimal place.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
(Total for Question 14 is 7 marks)
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15 Use algebra to show that the recurring decimal 0.26 = 415
(Total for Question 15 is 2 marks)
16 Q is inversely proportional to t2
Q = 320 when t = 0.5
Find a formula for Q in terms of t
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(Total for Question 16 is 3 marks)
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18 The incomplete histogram and the incomplete table show information about the ages of people watching a film in a cinema.
Age (a years) Number of people
10 a 20 38
20 a 25 24
25 a 40 63
40 a 50
50 a 80 24
(a) Use the histogram to complete the table.(2)
(b) Use the table to complete the histogram.(2)
(Total for Question 18 is 4 marks)
Frequency density
10
–
20
–
30
–
40
–
50
–
60–
70
–
80
–
Age in years
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21 ABCDE is a square-based pyramid.
Diagram NOT accurately drawn
A
E
C
D
15 cm
12 cm
B
AE = BE = CE = DE = 12 cm AB = 15 cm
Calculate the size of angle DEB. Give your answer to the nearest degree.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°
(Total for Question 21 is 4 marks)
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22 (a + b )2 = 49 + 12 b where a and b are integers, and b is prime.
Find the value of a and the value of b
a = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 3 marks)
23 ABC is a triangle.
AB = 12 cm AC = 14 cm The area of triangle ABC is 72 cm2
Find, in degrees, the two possible sizes of angle BAC. Give your answers correct to the nearest degree.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 23 is 4 marks)
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10 The highest common factor (HCF) of 140 and x is 20
The lowest common multiple (LCM) of 140 and x is 420
Find the value of x.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 2 marks)
14
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13 M is directly proportional to p3
M = 128 when p = 8
(a) Find a formula for M in terms of p.
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(3)
(b) Find the value of M when p = 5
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(1)
(Total for Question 13 is 4 marks)
14 Simplify x
x x
2
225
2 9 5−
− −
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(Total for Question 14 is 3 marks)
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15 (a) Write x x+ + −35
23
as a single fraction in its simplest form.
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(3)
(b) Simplify (8a9e6)13
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(2)
(c) Solve 23
y + 38
y = 5
Show clear algebraic working.
y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 15 is 8 marks)
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17 f is the function such that f (x) = 2x – 5
g is the function such that g(x) = x2 – 10
(a) Find f(4)
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(1)
(b) Find fg(–4)
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(2)
(c) Express the inverse function f –1 in the form f –1(x) = ...
f –1(x) = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(d) Solve gf(x) = –1
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(Total for Question 17 is 9 marks)
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21 Each student in a group of 32 students was asked the following question.
“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”
Their answers showed that
19 students have a desktop computer 17 students have a laptop 16 students have a tablet 9 students have both a desktop computer and a laptop 11 students have both a desktop computer and a tablet 7 students have both a laptop and a tablet 5 students have all three.
(a) Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
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D
T
L
(3)
One of the students with both a desktop computer and a laptop is chosen at random.
(b) Find the probability that this student also has a tablet.
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(1)
(Total for Question 21 is 4 marks)
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22
PR
Q
O
N
M
Diagram NOT accurately drawn
OMN is a triangle.
P is the point on OM such that OP = 14 OM
Q is the midpoint of ON R is the midpoint of PN
OP→
= p OQ→
= q
(a) Find, in terms of p and q,
(i) MN→
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(ii) PR→
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(2)
(b) Use a vector method to prove that QR is parallel to OP
(2)
(Total for Question 22 is 4 marks)
TOTAL FOR PAPER IS 100 MARKS
10
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11
R and T are points on a circle, centre O. ROP is a straight line. PT is a tangent to the circle. Angle TPO = 46°
(a) Explain why angle OTP = 90°
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(1)
(b) Work out the size of angle y.
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(3)
(Total for Question 11 is 4 marks)
Do NOT write in this space.
46°P
T
OyR
Diagram NOT accurately drawn
12
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13 (a) Write 0.000076 in standard form.
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(1)
The area covered by the Pacific Ocean is 1.6 × 108 km2
The area covered by the Arctic Ocean is 1.4 × 107 km2
(b) Write 1.6 × 108 as an ordinary number.
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(1)
The area covered by the Pacific Ocean is k times the area covered by the Arctic Ocean.
(c) Find, correct to the nearest integer, the value of k.
k= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 13 is 4 marks)
14 Kwo invests HK$ 40000 for 3 years at 2.5% per year compound interest. Work out the value of the investment at the end of 3 years.
HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 is 3 marks)
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17 The diagram shows a prism.
M
N
R
Q
P12cm
20cm
30°
L
Diagram NOTaccurately drawn
Triangle PQR is a cross section of the prism.
PR MP = 12cm Angle PRQ Angle PQR
Calculate the size of the angle that the line MR makes with the plane RQLN. Give your answer correct to 1 decimal place.
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(Total for Question 17 is 5 marks)
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18 The Venn diagram shows a universal setE and three sets X, Y and Z.
X
Z
30
43
Y
E
7
2
The numbers shown represent numbers of elements.
n(X´ n(Z
(a) Complete the Venn diagram.
(2)
(b) Find the value of
(i) n(X Z )
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(ii) n(X Y´ )
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(2)
(Total for Question 18 is 4 marks)
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5 Abri walks along a path from her home to a local village. Here is the distance-time graph for her journey from her home to the village.
4
3
2
1
012 00 12 30 13 00 13 30
Time
Distance from Abri’s home (km)
Village
Home
Benito leaves the village at 12 30 and walks at a constant speed along the same path to Abri’s home.
He arrives at Abri’s home at 13 15
(a) Show the information about Benito’s journey on the grid.(2)
(b) How far from the village were Abri and Benito when they passed each other?
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(Total for Question 5 is 3 marks)
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6 A has coordinates (11, 3e) B has coordinates (1, 7e) The midpoint of AB has coordinates (x, y)
(a) Find the value of x.
x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Find an expression for y in terms of e. Simplify your answer.
y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 6 is 3 marks)
7
P QP Q
P Q P Q
∪ = { }∩ = { }∈ ∈ ∉ { } ∩ = ∅
a ,b,c,d ,e,f
e
a c f b,d, , ,
(a) List the members of the set P.
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(2)
(b) List the members of the set Q.
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(1)
(Total for Question 7 is 3 marks)
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9 The diagram shows a ladder, EF, leaning against a vertical wall. The foot, E, of the ladder is on horizontal ground.
3.5 m
E
F
G2.1 m
Diagram NOT accurately drawn
EG = 2.1 m FG = 3.5 m angle EGF = 90°
(a) Work out the length of the ladder. Give your answer correct to 1 decimal place.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m(3)
(b) Work out the size of angle EFG. Give your answer correct to the nearest degree.
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(3)
(Total for Question 9 is 6 marks)
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12 The straight line L x y = 15
(a) Find the gradient of L.
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(3)
(b) Find the coordinates of the point where L crosses the y-axis.
( .. . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)
(c) Find an equation of the line that is parallel to L and crosses the x
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(2)
(Total for Question 12 is 6 marks)
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13Diagram NOT accurately drawn
79° 41°A
BC
D
E
O
B, D and E are points on a circle, centre O. ABC is a tangent to the circle. DEC is a straight line. Angle ABD = 79° and angle ECB = 41°
(a) Write down the size of angle BED.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(1)
(b) Work out the size of angle BOE.
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(2)
(Total for Question 13 is 3 marks)
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15 y
x
A
B
C
D
O
Diagram NOT accurately drawnE
AB→
= 32
⎛⎝⎜
⎞⎠⎟
and AC→
= 41−
⎛⎝⎜
⎞⎠⎟
(a) Find, as a column vector, BC→
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(2)
BCDE is a parallelogram.
CD→
= AC→
(b) Find the length of CE. Give your answer correct to 2 decimal places.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 15 is 5 marks)
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19
343
= n
(d) Work out the exact value of n.
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(3)
(Total for Question 16 is 9 marks)
17 A particle moves along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds is s metres where
s t
t= −4 92
Find the velocity of the particle at time 5 seconds.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s
(Total for Question 17 is 3 marks)
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18 The function f is such that f (x) = 2
3 5x
x +
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
The function g is such that g (x) = 34x +
(b) Find g (6)
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(2)
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(2)
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(d) Solve the equation f (x) = g (x) Show clear algebraic working.
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(4)
(Total for Question 18 is 9 marks)
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19 Here is the graph of y = h (x)
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(a) Use the graph to find an estimate for the gradient of the curve y = h (x
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(3)
(b) By drawing a suitable straight line on the grid, find an estimate for the solution of the equation h (x) = x
Give your answer correct to 1 decimal place.
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(2)
The equation h (x) = k has 3 different solutions for a < k < b
(c) Use the graph to find an estimate for the value of a and the value of b.
a = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 19 is 7 marks)
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21 The diagram shows a cuboid ABCDEFGH.
A B
CD
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FG
HK
21 cm
9 cm
Diagram NOT accurately drawn
AB = 21 cm and CH = 9 cm. K is the point on EH such that angle AKB = 68° and BK = 16.5 cm.
(a) Calculate the size of angle BAK. Give your answer correct to 1 decimal place.
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(3)
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(b) Calculate the size of the angle between the line BK and the plane ABCD. Give your answer correct to 1 decimal place.
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(2)
(Total for Question 21 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
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9 The diagram shows the positions of two towns, A and B.
Diagram NOT accurately drawn
North
North
A 60 km
x
110 km
B
The distance from A to B is 110 km. B is 60 km east of A.
(a) Work out the size of angle x. Give your answer correct to 1 decimal place.
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(3)
(b) Work out the bearing of B from A. Give your answer correct to the nearest degree.
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(2)
The distance from A to B is 110 km correct to 2 significant figures.
(c) (i) Write down the lower bound for the distance from A to B.
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(ii) Write down the upper bound for the distance from A to B.
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(Total for Question 9 is 7 marks)
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10 m = 34 × 53
n = 33 × 52 × 11
(a) Find the Lowest Common Multiple (LCM) of m and n.
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(2)
(b) Find the Highest Common Factor (HCF) of 5m and 3n.
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(2)
(Total for Question 10 is 4 marks)
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20 ( )( )3 2 3 1+ − = +c c k c where c and k are prime numbers.
(a) Find the value of c and the value of k.
c = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
p
p pm =
×1
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(b) Find the value of m.
m = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 20 is 6 marks)