Maths F5 Mid-Term Examination (E)

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PAPER 1 Time: One hour fifteen minutes This question paper consists of 40 questions. Answer all the questions. Each question is followed by four options A, B, C and D. For each question, choose only one answer. Non-programmable scientific calculator is allowed.

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MID-TERM EXAMINATION (Chapter 1 to Chapter 6)

1 What is the value of digit 4, in base

ten, in the number 3 4798?A 8 C 256B 32 D 400

2 Express 53 + 2 as a number in base five.A 75 C 1275

B 1255 D 10025

3 110012 – 11102 =A 10112

B 10012

C 11002

D 11012

4 Express 5.74 × 10–3 as a single number.A 0.000574 B 0.00574C 0.0574D 0.574

5 Express 111011012 as a number in base eight.A 3158

B 3508

C 3558

D 3658

6 Given k – 10112 = 1012, find the value of k.A 1102

B 10112

C 11112

D 100002

7 Find the value of x in the equation 110112 + x = 111102.A 102

B 112

C 1102

D 1112

8 Which of the following graphs represent the function y = (x – 4)(x + 2)?A

B

C

D

9 Which of the following graphs

represents y = ?

A

B

C

D

10 Diagram 1 shows the graph of a function.

Diagram 1 Which of the following is the equation for the function?A y = 2x3 + 3B y = –2x3 + 3C y = 2x3 – 3D y = –2x3 – 3

11 Diagram 2 shows GH is a straight

line with gradient – .

Diagram 2 Find the x-intercept of the straight line GH.A –25 C –5B –10 D –1

12 Which of the following graphs represents y = 16 – 5x3?A

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B

C

D

13 Diagram 3 shows a shaded region.

Diagram 3 The inequalities that define the shaded region areA y x; x O; y < 5B y x; x O; y 5C y x; x O; y < 5D y x; x O; y > 5

14 Diagram 4 shows the graph of the function y = –x2 + 8.

Diagram 4 Which of the following straight line is suitable to be drawn to find the value of x which satisfies the equation –x2 + x + 8 = 0?A y = –2x C y = xB y = –x D 2y = x

15 Diagram 5 shows five triangles are drawn on a grid of squares.

Diagram 5 Which of the triangles, A, B, C and D is the image of triangle K under an enlargement of scale factor Z?

16 Diagram 6 shows X is the image of point Y under a translation.

Diagram 6 What is the translation?

A C

B D

17 Diagram 7 shows 6 points are drawn on a grid of squares.

Diagram 7

Point K is the image of point L under a reflection. Which of the following straight lines is the axis of reflection?A PSB PQC RQD RS

18 Diagram 8 shows 5 triangles are drawn on a grid of squares.

Diagram 8 Which of the triangles A, B, C and D is not an image of triangle M under a rotation.

19 Diagram 9 shows N is the image of M under a rotation of 90° clockwise.

Diagram 9 Which of the points A, B, C and D is the centre of rotation?

20 Diagram 10 shows X is the image of Y under a rotation of 90° anticlockwise about point (t, u)

followed by a translation .




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Diagram 10 The values of t and u areA t = 1, u = 1 C t = 1, u = 2 B t = 2, u = 1 D t = 2, u = 2

21 Given (k 4) = (4 29), find

the value of k.A –5 C –3C –4 D 3

22 4 – 2 =

A C

B D

23 Given (4 x 1) = (1 28),

find the value of x.A –3 C –1B –2 D 2

24 –2 + – 2

=

A C

B D

25 Find the value of x in the following matrix equation:

3 – 2 =

A –2 C 3B 2 D 4

26 Given the matrix equation 5 –

2 = , find the value of x – y.A –2 C 4B 2 D 6

27 Given that G = and H = ,

find the value of k which satisties the

equation G + = H.

A 2 C 6B 4 D 8

28 Given that the inverse matrix of

is m , find the

value of m + n.

A C 2

B –3 D –5

29 Given that y varies directly as x3 and y = 32 when x = 2, express y in terms of x.A y = x3 C y = 4x

B y = 4x3 D y =

30 Given that f varies inversely as W and W = 5 when f = 3, express f in terms of W.

A f = C f =

B f = 15w D f =

31 Diagram 11 shows some values of the variables X, Y and Z such that X varies directly as Y and inversely as Z.

X Y Z5 3 2

7.5 h 4Diagram 11

Calculate the value of h.A 6 C 12B 9 D 15

32 Given p varies directly as the cube of q, and p = 54 when q = 3, find the value of p when q = 5.A 25B 50C 125 D 250

33 Given that G and G = 16

when m = 4 and n = 4, find the value of m when G = 27 and n = 16.A 6 C 10 B 8 D 12

34 Diagram 12 shows some values of the variables X, Y and Z such that X

.

X Y Z3 2 5

6 p

Diagram 12 Find the value of p.A 6 C 10 B 8 D 14

35 Given that M N and N = 5P – 3. M = 10 when P = 1, find the value of P when M = 60.A 3 C 6B 4 D 7

36 Given that P Q, Q = 3R + 1 and P = 14 when R = 2, the equation that relates P and Q isA P = QB P = 2Q

C P = Q

D P = Q + 2

37 Diagram 13 shows the graph of speed-time of a particle for a period of 20 seconds.

Diagram 13




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Find the total distance, in m, travelled by the particle.A 100 C 200B 160 D 260

38 Diagram 14 shows the graph of speed-time of a particle for a period of 18 seconds.

Diagram 14 The total distance travelled by the particle is 430 m. Find the value of U.

A 24 C 30B 28 D 34

39 Diagram 15 shows the speed-time graph of a car driver.

Diagram 15 Find the time, t, if the distance travelled at a uniform speed is 60 m.A 2 C 6B 5 D 8

40 Diagram 16 shows the speed-time graph of a trolley for a period of 10 seconds.

Diagram 16 Find the total distance, in m, travelled by the trolley.A 10 C 25B 20 D 30

PAPER 2 Time: Two hours and thirty minutes

This question paper consists of two sections: Section A and Section B. Answer all the questions in Section A and four questions from Section B. Write your answers in the spaces provided in the question paper. Show your working. It may help you to get mark. Non-programmable scientific calculator is allowed.

Section A [52 marks]

Answer all the questions in this section.

1 (a) Express 5 × 84 + 2 × 83 + 7 × 81 + 1 × 80 as a number in base eight.

(b) Express 578 as a number in base two.[2 marks]

2 Solve each of the following. (a) 1001112 + 1011012

(b) 101102 – 11012

[4 marks]

3 On the graph below, shade the region which satisfy the three inequalities y –x + 5, y 2x – 2 and x > 1.

[3 marks]

4 Diagram 1 shows a shaded region.

Diagram 1 State three inequalities which define the shaded region.

[3 marks]




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5 (a) Given that the inverse matrix of = p ,

find the values of p and q. (b) Using matries, calculate the values of x and y that

satisfy the following simultaneous linear equations.x + 4y = 10

2x + 5y = 11 [6 marks]

6 Given H = where H is a 2 × 2 matrix.

(a) Find the matrix H. (b) Write the following simultaneous equations as a matrix

equation.–3x – 5y = 13x + 4y = –2

Hence, calculate the value of x and of y by using the matrix method.

[6 marks]

7 It is given that matrix P = .

(a) Find the value of w for which p has no inverse. (b) Hence, using matrises, find the values of x and y that

satisfy the matrix equation,

= [6 marks]

8 (a) Given P = Qn, where n is an integer, state the value

of n if (i) P varies directly as Q, (ii)P varies inversely as the cube root of Q.

(b) Given E , F = 2G + 1 and E = when G = 3,

find the value of E when G = 2.[6 marks]

9 Diagram 2 shows the speed-time graphs for a particle X and particle Y. Both the particle move from the same place and time.

Diagram 2 (a) State the time, in s, that both particles move at the same

speed.(b) Find the distance, in m, travelled by particle X in the

first 8 seconds, (c) Find total difference of distance travelled, in m, by the

two particles for the first 8 seconds.[6 marks]




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10 Diagram 3 shows distance-time graph for a student to walk from his house to school.

Diagram 3 (a) Find the speed of the student in the first 4 minute. (b) Given the average speed for the whole journey is 25 m

min–1, find the value of s.[4 marks]

11 Diagram 4 shows speed-time graph of a movement of an object within 14 s.

Diagram 4 It is given that the distance travelled by the object within 14 s is 82 m. (a) State the length of time, in s, that the object moves at a

uniform speed. (b) Find the value of w. (c) Calculate average speed, in m s–1 for the whole journey

of the object.[6 marks]

Section B [48 marks]

Answer any four questions from this section.

12 (a) Complete Table 1 for the equation y = x3 – 13x – 12.x –4 –3 –2 –1 0 1 2 3

y –24 0 0 –12 –30

Table 1 [3 marks]

(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to

5 units on y-axis, draw the graph of y = x 3 – 13x – 12 for –4 x 3. [3 marks]

(c) From your graph, find the value of y when x = 0.5.

[1 mark](d) Draw a suitable straight line on your graph to find all

the values of x which satisfy the equation x 3 – 13x – 5 = 0 for –4 x 3. [5 marks]




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13 (a) Complete Table 2 for the equation y = x(x + 4).x –4 –3 –2.5 –2 –1.5 –1 0 1 2

y 0 –3 –4 –3.75 0 5 12

Table 2 [2 marks]

(b) Using a scale of 2 cm to 1 unit on x-axis and 1 cm to 1 unit an y-axis, draw the graph of y = x(x + 4) for –4 x

2. [4 marks](c) Draw a suitable straight line on your graph to find all

the values of x which satisfy the equation x2 + 4x + 2 = 0 for –4 x 2. State these values of x. [4 marks]

(d) Shade the region which satisfied the three inequalities y x(x + 4), x < 2 and x + y 2. [2 marks]

14 (a) Transformation A is a translation .

Transformation B is a rotation of 90° clockwise about the centre (1, 2).Transformation C is a reflection in the line y = k. (i) The point (3,7) is the image of point (3, –3) under

the transformation C. State the value of k. (ii) Find the coordinates of the image of point (–4, 4)

under the following combined transformations:(a) A2,(b) AB. [5 marks]

(b) Diagram 5 shows three quadrilaterals, ABCD, KLMN and PQRS, drawn on a Cartesian plane.

Diagram 5 (i) ABCD is the image of PQRS under a combined

transformation UT. Describe in full the transformations.(a) T,(b) U.

(ii) It is given that quadrilateral PQRS represents a region of area 20 m2. Calculate the area, in m2, of the region represented by the shaded region.

[7 marks]

15 Diagram 6 shows triangles ABC, DEF and JKL drawn on a Cartesian plane.

Diagram 6




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(a) Transformation R is a rotation of 90° anticlockwise about the centre (1, 1).

Transformation P is a translation .

State the coordinates of the image of point A under each of the following transformations: (i) R,(ii) RP. [3 marks]

(b) JKL is the image of ABC under the combined transformations MN.Describe in full (i) the transformation M, (ii) the transformation N,

[4 marks](c) DEF is the image of JKL under an enlargement at centre

(5, –3). (i) State the scale factor of the enlargement. (ii) Given that JKL represents a region of area 360 m2,

calculate the area, in m2, of the region represented by DEF.

[5 marks]16 (a) Table 3 shows two sets of values of p, q and which

satisfy r .

p q r

2 25 10

3 36 x

Table 3 (i) Express r in terms of q and p. (ii) Find the value of x.

(b) Given that A = , B = and C = ,

find the values of AB – 2C.

(c) Given that = , find the values of

(i) m,(ii) n. [4 marks]




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Maths F5 Mid-Term Examination (E)

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