1. The document contains 50 math problems involving calculations, factorizing expressions, solving equations and inequalities, working with fractions and percentages, and other math topics. 2. Many problems require setting up and solving multi-step calculations and expressions. 3. Questions cover a wide range of math skills including fractions, percentages, exponents, standard form, factorizing, simplifying expressions, solving equations, graphing, proportions, and more.

1. 1
1 (a) Work out 80 ÷ 0.02 4024/12
Oct/Nov 2022
……………………………… [1]
(b) Evaluate √1000
3
……………………………… [1]
2 (a) Put one pair of brackets into this calculation 4024/12
to make it correct. Oct/Nov 2022
4 + 4 × 4 − 4 = 4
[1]
(b) Work out −6 × (−3 + 7)
................................................. [1]
3. Write 7.54 × 10−4
as an ordinary number 4024/12
Oct/Nov 2022
.......................

2. 2
4 (a) Work out
11
15
−
2
3
................................................. [1]
(b) Work out
3
10
÷ 6
Write your answer as a fraction in its simplest form.
................................................. [2]
5 By writing each number correct to 1 significant figure,
estimate the value of
47.5+36.1
64.9÷17.7
..................................... [2]

3. 3
6 (a) Write 420 as the product of its prime factors
................................................. [2]
(b) Given that 1512 = 23
× 33
× 7,find the highest common factor of
420 and 1512.
................................................. [1]
7 (a) Represent the inequality −4 ≤ 𝑥 < 2 on the
number line below
(b) Solve the inequality [2]
10 − 𝑛 < 2𝑛 − 5
................................................. [2]

4. 4
8 (a) Simplify (𝑥2)3
................................................. [1]
(b) 𝑡2
= 9
Find the value of t
................................................. [1]
(c) √5 × 50
= 5𝑘
Find the value of k
k =................................................. [1]
9 Factorise.
(a) 9𝑝2
− 𝑞2
................................................. [1]
(b) 𝑎𝑐 − 3𝑏𝑐 + 𝑎 − 3𝑏
................................................. [2]

5. 5
10 (a) The temperature was −2 ℃.The temperature decreased
by 8℃.Find the temperature after this change.
............................................ °C [1]
(b) On another day, the temperature increases from −5℃ 𝑡𝑜 3℃
Workout the increase in temperature.
............................................ °C [1]
11 Find 45% of $1.20
$ ................................................. [2]
12 Write these fractions in order of size, stating with the smallest
11
12
4
5
27
30
13
15

6. 6
13 (a) Write 306.248
(i) Correct to 2 decimal places,
................................................. [1]
(ii) Correct to 2 significant figures.
................................................. [1]
(b) By writing each number correct to 1 significant figure, estimate the value of
9.372
− √1046
3
................................................. [2]
14 (a) Work out
7
8
-
3
4
............................................... [2]
(b) Work out 1
3
5
÷
4
7
Give your answer as a mixed number in its lowest terms.
............................................... [2]

7. 7
15 Factorise 3𝑎2
+ 12𝑎
............................................... [2]
16 (a) Write the number 320 000 000 inn standard form.
................................................ [1]
(b) Evaluate
2×10−3
4×109
Give your answer in standard form
............................................... [2]
17 (a) Write 120 as a product of its factors
……………….......................... [2]

8. 8
(b) 315 = 32
× 5 × 7
Use this information to find the smallest integer value of n, such that
315𝑛 is a square number.
................................................. [1]
18 (a) Expand and simplify
3(2𝑥 + 1) − 2(4𝑥 + 3)
............................................... [2]
(b) (𝑥 + 5)(𝑥 − 3)
............................................... [2]
19 (a) The nth term of a sequence is 3𝑛2
− 1.
Find the first three terms of the sequence.
............, ................, ................... [2]

9. 9
(b) These are the first five terms of a different sequence
1 3 9 27 81
Find an expression, in terms of n, for the nth term of this sequence
............................................... [2]
20 b is directly proportional to the square of a.
When 𝑎 = 3, 𝑏 = 18.Find b when 𝑎 = 5.
𝑏 =............................................... [2]
21 Kabir invest $250 in a saving account. 4024/12
The account pays simple interest at a rate May/June 2022
of 1.5% per year.
Calculate the total amount of interest he will receive at
The end of 4 years.
$ ................................................ [2]

10. 10
4024/12
22
May/June 2022
The diagram shows a pentagon.
Find the value of a.
a = ……………………………… [3]
23 A bag contains red ball, blue balls and green balls. 4024/12
The ratio red: blue=3:8. May/June 2022
The ratio green: blue=2:5
Work out the fraction of the balls that are blue.
……………………………… [3]
24 (a) Write 0.00203561 correct to 3 significant figures. 4024/12
May/June 2022
................................................. [1]
(b) By writing each number correct to 1 significant figure,
estimate the value of
√3.93×63.7
0.425
................................................. [2]

11. 11
25 (a) Evaluate (√9 × √64
3
)
2
4024/12
May/June 2022
................................................. [2]
(b) Write down an irrational value of n that satisfies
this inequality
4.5 ≤ 𝑛 ≤ 5.5
................................................. [2]
26 (a) Write these numbers in order of size, 4024/12
starting with the smallest. May/June 2022
2000 0.002 2 × 10−4
2 × 10−2
……………….. ,…………….….. ,……..................... ,.................................... [1]
Smallest
(b) This is a calculation using numbers in standard form.
a × 10−7
÷ 5 × 10b
= 4 × 10−16
Find the value of a and the value of b.
𝑎 =...............................................
𝑏 =...............................................

12. 12
27 y is directly proportional to (𝑥 − 1)2
4024/12
When 𝑥 = 5, 𝑦 = 32.Find the value of y when 𝑥 = −2 May/June 2022
................................................. [2]
28 (a) Factorise 4𝑥2
+ 5𝑥 − 6
................................................. [2]
(b) Simplify (
16
𝑥6)
−
1
2
................................................. [2]
29 (a) Solve
2−5𝑥
3𝑥+10
= 3
𝑥 =................................................. [3]

13. 13
(b) Express as a single fraction in its simplest form
3
𝑥−2
−
5
2𝑥+1
𝑥 =................................................. [2]
30 Write down
(a) a prime number between 10 and 15
………….................. [1]
(b) an irrational number between 10 and 15
................................................. [1]
31 20 students were asked how many pets they owned.
The responses are shown in the table.
Name of pets 0 1 2 3 4 5
Frequency 3 8 3 4 0 2
(a) Find the median number of pets.
................................................. [1]

14. 14
(b) Calculate the mean number of pets.
................................................. [2]
32 Write these lengths in order of size with the smallest.
32000 cm 3300 mm 3.1 Km 34m
……………….. ,…………….….. ,……..................... ,.................................... [2]
Smallest
32 (a) 100 adults were asked the colour of their car.
The results are shown in the table.
Write down the relative frequency that one of these cars in blue.
................................................. [1]
(b) A different group of 1200 adults were asked the colour of their car.
The relative frequency of one of these adults owning a while car is 0.3.
Find the number of these adults who own a white car.
................................................. [1]
Colour of car Red Black Blue Silver
Frequency 36 11 23 30

15. 15
33 By writing each number correct to 1 significant figure,
estimate the value of
0.28×37.4
77.8
................................................. [2]
34 (a) Evaluate 7−3
÷ 7−4
................................................. [1]
(b) Find the value of k when (36)𝑘
= 32
k................................................. [1]
(c) Simplify 3(22
× 32
× 54)2
Give your answer in the form 2𝑎
× 3𝑏
× 5𝑏
.
................................................. [2]

16. 16
35 The scale of a map is 2 cm to 1 km
The area of a wood on the map is 6 𝑐𝑚2
Calculate the actual area of the wood in Km2
Km2................................................ [2]
36 𝑦 is inversely proportional to(𝑥 + 1)2
.
Given that 𝑦 = 2 when 𝑥 = 3,find y when 𝑥 = 9.
𝑦 =................................................ [2]
37 Factorise.
(a) 5𝑎𝑥 − 3𝑎𝑦 − 10𝑐𝑥 + 6𝑐𝑦
............................................... [2]
(b) 15𝑥2
− 7𝑥 − 4.
............................................... [2]

17. 17
38 𝑦 =
3𝑥+2
2𝑥−1
Rearrange the formula to make 𝑥 the subject.
𝑥 =............................................... [4]
39 The perimeter of a regular hexagon is equal to the perimeter 4024/12
of a regular octagon. Each edge of the octagon is 9 cm long. Oct/Nov- 2022
Find the length of one edge of the hexagon
.........................................cm [2]

18. 18
40
In the diagram, AD, AB and BC are three sides of a regular pentagon
and DC is a diagonal of the pentagon.
AB is parallel to DC.
(a) Find the value of x.
x =................................................. [2]
(b) Find the value of y.
y =................................................. [1]
41 Sophie cycles 2600 meters in 12 minutes.
Work out Sophie’s average speed in kilometers per hour.
......................................... Km/h [3]

19. 19
42
ABC is an isosceles triangle with AB=BC.The ratio 𝐴𝐵
̂𝐶: 𝐵𝐴
̂𝐶 = 2: 5
Find 𝐴𝐵
̂𝐶.
𝐴𝐵
̂𝐶 = ................................................. [2]
43 Azra has a spinner.
The sections are colored red, blue, yellow or green.
The relative frequency of the spinner landing on red,
blue or yellow is shown in the table.
Coloured on spinner Red Blue Yellow Green
Relative frequency 0.15 0.3 0.2
(a) Find the relative frequency of the spinner landing on green.
................................................. [2]
(b) Azra spins the spinner 150 times.
How many times would she expect the spinner to land on blue?
................................................. [1]

20. 20
44
NOT TO
SCALE
The diagram shows the points A (0, 6), B (p, 0) and C (p, 6).
The equation of the line AB is 3𝑦 + 4𝑥 = 18.
(a) Find the value of p.
p =................................................. [1]
(b) Write down the three inequalities that define the region inside triangle ABC.
................................................
................................................
................................................. [2]
45 P is the point (-2, 1) and Q is the point (6, 13).
M is the midpoint of the line PQ.
(a) Find the coordinates of M.
( ...................... , ...................... ) [1]

21. 21
(b) (i) Find the gradient of the line PQ.
................................................. [2]
(ii) Write down the gradient of a line that is perpendicular to the line PQ.
................................................. [1]
46 Solve.
3𝑥−1
6
+
𝑥+2
4
=
5
3
x = ................................................. [4]
47 𝑓(𝑥) = 1 +
3𝑥
2
𝑔(𝑥) =
2
1−𝑥
(a) Find 𝑓−1
(𝑥)
𝑓−1
(𝑥)= ................................................. [3]

22. 22
(b) Solve 𝑔(𝑥) = 𝑓(−4)
x =................................................. [3]
48 sinx°= sin50° and 90 < 𝑥 < 180.
Find the value of x.
x =................................................. [1]
49 Simplify
𝑥2−4𝑥
𝑥2−𝑥−12
................................................. [3]

23. 23
50 NOT TO
SCALE
OAC is a triangle and B is a point on AC such that AB: BC = 3: 2.
𝑂𝐴
⃗⃗⃗⃗⃗ = a and 𝑂𝐵
⃗⃗⃗⃗⃗ = b.
(a) Find 𝑂𝐶
⃗⃗⃗⃗⃗ in terms of a and b, giving your answer in its simplest form.
𝑂𝐶
⃗⃗⃗⃗⃗ = ................................................. [3]
(b) D is a point on OC such that 𝑂𝐷
⃗⃗⃗⃗⃗⃗ = 𝑏 −
2
5
𝑎
Show that OABD is a trapezium.
[2]

24. 24
51 (a) In the Venn diagram, shade the region 4024/11
Oct/Nov 2022
[1]
(b) This Venn diagram shows information about the number of students who
study English (E), Spanish (S) and German (G).
................................................. [1]
(i) Find the number of students who study English and German but not Spanish.
................................................. [1]
(ii) Find n (G∪S)/ .
................................................. [1]

25. 25
52 4024/11
Oct/Nov 2022
B, C and D are points on the circumference of a circle, centre O.
AB is a tangent to the circle at B. BD is a diameter and OCA is
a straight line.𝐶𝐷
̂𝐵 = 𝑥0
.
Find an expression, in terms of x, for each of the following.
Write each expression in its simplest form.
(a) C𝑂
̂B
C𝑂
̂B =................................................ [1]
(b) O𝐴𝐵
̂
O𝐴𝐵
̂ =................................................ [1]
(c) 𝐶𝐵
̂𝑂
𝐶𝐵
̂𝑂 = ................................................ [2]

26. 26
53
(a) Find the gradient of the line L.
................................................. [1]
(b) The shaded region on the diagram is defined by three inequalities.
Write down these three inequalities
.................................................
.................................................
................................................. [3]

27. 27
54
.
Triangle ABC is mathematically similar to triangle DEC.
AB = 12cm, BC = 27cm, CD = 7 cm and DE = 3 cm.
(a) Calculate AC.
.......................................... cm
(b) Given that the area of triangle ABC is 160 cm2, calculate the area of triangle DEC.
............................................ cm2 [2]

28. 28
55 The diagram shows the speed–time graph of Sam’s journey from home to work.
(a) Calculate the acceleration, in m/s2 , for the first 2 minutes of Sam’s journey.
........................................m/s2 [1]
(b) Calculate Sam’s average speed, in m/s, for the whole journey.
................................m/s [3]

29. 29
56
ABD is an equilateral triangle.
C lies on DB and AC is perpendicular to DB.
Show that triangle ADC is congruent to triangle ABC.
Give a reason for each statement you make
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………..[3]
57 A farmer records the mass of each of his sheep. 4024/11
Some of the results are summarized in the table Oct/Nov 2022
and illustrated in the histogram.
(a) Use the histogram to find the value of a.
a =................................................. [1]
(b) Complete the histogram. [2]

30. 30
58 A=(
3 1
−3 2
) A+2B=(
1 5
10 12
)
(a) Find B
( ) [2]
(b) Find 𝐴−1
( ) [2]
59 (a) 𝑥2
− 6𝑥 − 7 = (𝑥 + 𝑎)2
+ 𝑏 4024/11
Find the value of a and the value of b. Oct/Nov 2022
a=…………………………………..
b=……………………………….. [2]

31. 31
(b) Hence solve the equation 𝑥2
− 6𝑥 − 7 = 0
Show your working.
x = .................. or x =.................. [2]
60 A solid cone has radius y cm. 4024/11
The slant height of the cone is 25% larger Oct/Nov 2022
than the radius of the cone.
A solid sphere has radius R cm.
The surface area of the sphere is equal to the
total surface area of the cone.
(a) Show that 𝑦 =
4𝑅
3
[3]
(b) Find the volume of the cone in terms of R.
Give your answer as simply as possible.
cm3......................................... cm

32. 32
61
4024/12
May/June 2022
The area of the rectangle is 9 cm2.The area of the
triangle is 85 mm2.
Calculate the shaded area. Give your answer in cm2.
......................................... cm2 [2]
62 Shani makes a sequence of patterns using counters. 4024/12
May/June 2022
(a) Complete the table.
Pattern number 1 2 3 4 5
Number of counters 5 8 11
[1]
(b) Find an expression, in terms of n, for the number of counters in Pattern n.
................................................. [2]

33. 33
(c) Shani has 100 counters.
She uses some of the counters to make Pattern 20.
She uses all the remaining counters to make Pattern k.
Find the value of k.
k =................................................ [3]
63 𝑓(𝑥) = 3𝑥 − 7 4024/12
May/June 2022
𝑓−1
(𝑥)
𝑓−1(𝑥) =. . . . . . . . . . . . . . . . . . . . . . . . . . . [2]
64 (a) 𝜀= {a, b, c, d, e, f, g, h, i, j} 4024/12
P = {a, e, i} May/June 2022
Q = {f, g, h, i, j}
R = {c, d, e, f, g}
(i) Find 𝑃 ∪ 𝑄,
................................................. [1]

34. 34
(ii) Find n (𝑃′
∩ (𝑄 ∪ 𝑃))
................................................. [1]
(b)
Use set notation to describe the shaded subset in the Venn diagram.
................................................. [1]
65 4024/12
May/June 2022
A, B, C and D are points on the circle, centre O.
(a) Find ADB
A𝐷
̂B =................................................ [1]
(b) Find BCD
.
B𝐶
̂D =................................................ [2]

35. 35
66 A bag contains these 9 letter tiles. 4024/12
May/June 2022
(a) Nur takes one tile from the bag at random.
She notes the letter and then puts the tile back in the bag.
Find the probability that she does not take a letter E.
................................................. [1]
(b) Nur now takes two of the 9 letter tiles at random without replacement.
Find the probability that both tiles show the same letter.
................................................. [3]
67 4024/12
May/June 2022
The diagram shows the major sector of a circle with centre O and radius 3 cm.
Calculate the area of this sector.
Give your answer in the form𝑘𝜋, where k is an integer.
......................................... cm2 [2]

36. 36
68 4024/12
May/June 2022
OABC and OPQR are parallelograms.
A is a point on OP and C is a point on OR.
OA = a and OC = c.
OA: OP = 1: 4 and OC: CR = 2: 3.
(a) Find OR in terms of c.
OR =................................................ [1]
CQ =................................................ [2]
(b) Find CQ, as simply as possible, in terms of a and c.
𝐶𝑄
⃗⃗⃗⃗⃗ = ................................................ [2]
(c) Find the ratio area OABC: area OPQR.
....................... : ....................... [1]

37. 37
69 (a) Write down the value of the 5 in the number 253 624. 4024/11
May/June 2022
................................................. [1]
(b) The crowd at a sports event is exactly 35 687.
Write this number correct to the nearest ten.
................................................. [1]
70 4024/11
May/June 2022
Write down the number of lines of symmetry of this diagram.
................................................ [1]

38. 38
Write down the order of rotational symmetry of this diagram.
................................................. [1]
71 The table shows the average monthly temperatures, in °C, in Vladivostok.
4024/11
May/June 2022
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
−12 −8 −2 5 10 14 18 20 16 9 −1 −9
(a) Find the difference between the highest and lowest of these temperatures.
............................................. °C [1]
(b) In February, the average temperature in Yakutsk is 37°C below
that in Vladivostok.
Find the average temperature in Yakutsk in February.
............................................. °C [1]

39. 39
72 Two cubes have a total volume of 152 cm3.
One cube has an edge of length 5 cm.
(a) Calculate the length of the edge of the other cube.
............................................ cm [2]
(b) Work out the total length of all of the edges of the larger cube.
............................................ cm [1]
73 The diagram shows the net of a solid drawn on a 1 cm grid. 4024/11
May/June 2022
Name the solid formed by this net and describe fully the dimensions of this solid.
Name of solid........................................................
Dimensions........................................................................................................ [3]

40. 40
74 The table below shows the monthly rent for nine apartments 4024/11
and the distance of these apartments from the city centre. May/June 2022
(a) Complete the scatter diagram.
The first four points have been plotted for you. [2]
(b) What type of correlation is shown on the scatter diagram?
................................................. [1]
(c) On the scatter diagram, draw a line of best fit. [1]
(d) Use your line of best fit to estimate the monthly rent for an apartment
which is 4 km from the city centre.
$ ................................................. [1]

41. 41
75 (a) Write 0.000 863 in standard form. 4024/11
May/June 2022
................................................. [1]
(b) The table below shows the approximate area of some deserts.
(i) Write down the name of the desert with the largest area.
................................................. [1]
(ii) Calculate the total area of the Arabian and Kalahari deserts.
Give your answer in standard form.
.......................................... km2 [2]
Desert Area in Km2
Antarctica 1.4x107
Arabia 2.3x106
Gobi 1.3x106
Kalahari 9.0x105
Sahara 9.0x106

42. 42
76 p=(
2
3
) q=(
−3
2
) 4024/11
(a) On the unit grid below, draw and label vector p May/June 2022
.
[1]
(b) On the unit grid below, draw and label vector 2q.
(c) On the unit grid below, draw and label vector 𝑝 − 𝑞
[2]

43. 43
77 (a) In the Venn diagram, shade the region represented by 𝑃 ∩ 𝑄′
4024/11
May/June 2022
(b) A club has 32 members.
14 of the members are female and 18 of the members are male.
5 of the females have black hair.
6 of the males have black hair.
Complete the Venn diagram to show this information. [2]

44. 44
78 4024/11
May/June 2022
B, D, E, F and G are points on the circumference of a circle centre O.
AC is a tangent to the circle at B.
Angle DFG = 75° and angle ABG = 48°.
(a) Find angle DEG.
Angle DEG =................................................. [1]
(b) Find angle DOG.
Angle DOG =................................................. [1]
(c) Find angle DBC.
Angle DBC =................................................. [2]

45. 45
79 𝑓(𝑥) =
6𝑥+2
2
4024/11
May/June 2022
(a) Find 𝑓(3)
................................................ [1]
(b) Find 𝑓−1
(𝑥)
𝑓−1
(𝑥)= ................................................. [3]
80 𝑀 = (
1 0
4 3
) 𝑁 = (
𝑘 0
1 4
) 4024/11
Given that MN = NM, find the value of k May/June 2022
.
k =................................................. [3]

46. 46
81 4024/11
May/June 2022
In triangle ACD, B is the midpoint of AC and E is the midpoint of AD.
𝐴𝐵
⃗⃗⃗⃗⃗ =6a+3b and 𝐷𝐶
⃗⃗⃗⃗⃗ = 5a+2b.
(a) Express, as simply as possible, in terms of a and b.
(i) 𝐴𝐶
⃗⃗⃗⃗⃗
AC =................................................. [1]
(ii) 𝐴𝐷
⃗⃗⃗⃗⃗
AD =................................................. [2]
(b) Show that 𝐸𝐵
⃗⃗⃗⃗⃗ is parallel to𝐷𝐶
⃗⃗⃗⃗⃗ .
....................................................................................................................
.................................................................................................................................
.
.................................................................................................................................
. . ..
...............................................................................................................................
. ..........................................................................................................................
............................................................................................................................ [3]

47. 47
82 4024/11
Oct/Nov 2021
[1]
Shade one more small triangle so that the shape has rotational
symmetry of order 3.
83 Write down the name of the solid formed from each net.
[3]

48. 48
84
In the diagram, ABCD and EFGH are parallel lines.
The lines CF and BG intersect at X.
C𝐹
̂G = 53°, B𝐺
̂F = 46° and B𝑋
̂C = 81°.
(a) Find C𝑋
̂G
C𝑋
̂G =................................................ [1]
b) Find B𝐶
̂X
B𝐶
̂X =................................................ [1]
(c) Find A𝐵
̂X
A𝐵
̂X =................................................ [1]
85 (a) Workout 69 ÷ 0.3
.............................................. [1]

49. 49
(b) Workout 1
4
7
÷
3
5
Give your answer as a mixed number in its simplest form.
................................................. [2]
86 By writing each number correct to 1 significant figure,
estimate the value of
8230×0.64
18.7
................................................. [2]
87 (a) Write 0.06 km in meters.
............................................. m [1]
(b) Convert 7m2 to cm2
.......................................... cm2

50. 50
88 (a) Write 216 as a product of its prime factors.
................................................. [2]
(b) Two positive integers are each greater than 25.
Their lowest common multiple (LCM) is 216.
Their highest common factor (HCF) is 18.
Find the two integers.
..................... and..................... [2]
89 During one year the value of a bicycle decreased
from $200 to $160.
Calculate the percentage decrease in the value of the bicycle.
............................................. % [2]

51. 51
90 4024/12
Oct/Nov 2021
(a) Describe fully the single transformation that maps triangle A onto triangle B.
................................................................................................................
................................................................................................................ [2]
(b) Triangle A is mapped onto triangle C by a rotation, 90° anticlockwise,
centre (0, 0).Draw triangle C. [2]
(c) Triangle A is mapped onto triangle D by an enlargement, scale factor 3,
centre (5, -5).Draw triangle D. [2]
91 Solve the simultaneous equations. 4024/12
Show all your working. Oct/Nov 2021
2𝑥 − 𝑦 = 12
7𝑥 + 37 = 29
x=.................................................
y =................................................. [3]

52. 52
92
The diagram shows a rectangle ABCD.
E is a point on the diagonal AC such that D𝐸
̂C = 90°.
Prove that triangle ADC is similar to triangle DEC.
Give a reason for each statement you make.
............................................................................................................................................
............................................................................................................................................
...................................................................................................................................... [3]
93 The mean of five numbers is 17.
The numbers are listed in order of size,
starting with the smallest.
The three smallest numbers are equal.
The middle three numbers add to 35.
The largest number is four times the smallest number.
List the five numbers in order of size.
...................., ....................., ....................., ....................., ..................... [3]
smallest

53. 53
94 The diagram shows the speed-time graph for the start of a cyclist’s journey
(a) Find the acceleration during the first 20 seconds.
........................................ m/s2 [1]
(b) Describe the motion of the cyclist between t = 20 and t = 30.
............................................................................................................................ [1]
(c) Find the total distance travelled in the 50 seconds.
............................................. m [3]

54. 54
95 During one year the value of a bicycle decreased
from $200 to $160.
Calculate the percentage decrease in the value of the bicycle.
............................................. % [2]
96
The diagram shows a shaded region ABC.
The equation of the line AC is 𝑦 = −
1
2
𝑥 + 5
Write down the three inequalities that define the shaded region.
.................................................
..…………………………………
........................................... [2]

55. 55
97
A, B and C lie on a circle, centre O.
The line PBQ is a tangent to the circle at B.
OCQ is a straight line.
B𝑄
̂O=36o and B𝐴
̂C=xo
Find the value of x
x =................................................ [2]
98 The point A has position vector (
3
−7
)and 𝐴𝐵
⃗⃗⃗⃗⃗ = (
−5
12
) 4024/11
(a) Find the coordinates of point B. Oct/Nov 2021
( ...................... , ...................... ) [2]

56. 56
(b) Find |𝐴𝐵
⃗⃗⃗⃗⃗ |
|𝐴𝐵
⃗⃗⃗⃗⃗ |=…………………………………units [2]
99 (a) Solve
27𝑘
= 9
k =................................................ [2]
(b) Simplify
(
16
𝑥8)
−
1
4
................................................. [2]
100 Solve the inequality
23 + 2𝑛 > 5 − 6𝑎
................................................. [2]