Microsoft Word - Revision 1
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MATHEMATICS FORM 5 – REVISION 1
1.
Calculate the value of 0.8 × 0.31 + 1.26 ÷ 700 and express the answer in standard form. [3 marks]
2.
Find the value for each of the following and express your answer in standard form. (a) 106 × 101 100 [4 marks] (b) = 104
3.
The width and length of a rectangle are (6x − 5) cm and (x + 10) cm respectively. Form a quadratic expression for the area, in cm2, of the rectangle, in term of [4 marks] x.
4.
Sketch the graph for the cubic function y = x3.
[5 marks]
5. The following graph shows that y = -2x + 2. Please describe the shaded region.
6.
[3 marks]
-9 Given that transformation T is the translation and transformation R is a 2 reflection in the line y = -x, state the coordinates of the image of point (4, 5) under combined transformation (a) RT, (b) TR. [4 marks]
(
)
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
7.
If a + 1001002 = 10111102, find a in base two.
8.
Find the value of the following and express your answer in standard form. 870000 84000 (a) = (b) = 6 3 × 10 6 × 108
9.
[5 marks]
[6 marks]
Complete the following sequence. 18, _____, 138, _____, _____
[6 marks]
10. Complete the following sequence. 25, 45, _____, _____, _____
[6 marks]
11. Complete the following sequence. 228, 258, _____, _____, _____
[6 marks]
12.
The diagram above show a quadrilateral ABCD on a Cartesian plane. Given that A'B'C'D' 3 is the image of ABCD under the translation -3 followed by a clockwise rotation of 90° about the origin, find the coordinates of A', B', C' and D'. [12 marks]
( )
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
13.
In the Venn diagram above, ξ = P ∪ Q ∪ R (a) State the value of (i) n(Q), (ii) n(P' ∩ R' ). (b) Given that n(P) = n(Q), find the value of (i) m, (ii) n, if n(P ∪ Q) = n(Q' ). (c) Hence, find the value of n(ξ).
[12 marks]
14. (a)
The table below shows the values of x and y which satisfy the equation y = 2x2 − 2x − 15. Calculate the values of k and m. -3 -2.2 -1 0 1 2 2.5 x 9 k -11 -15 -15 m -7.5 y (b) Draw the graph of y = 2x2 − 2x − 15 for −4 ≤ x ≤ 4. (c) From your graph, find (i) the value of y when x = 1.8, (ii) the value of x when y = -12. (d) Draw a suitable straight line on your graph to find a values of x which satisfy the equation 2x2 + x − 18 = 0 for −4 ≤ x ≤ 4. State the values of x. [12 marks]
15. (a) Complete the table in the answer space for the equation y = 6 – x3 by writing down the values of y when x = –1 and x = 2. [2 marks] (b) By using a scale of 1 cm to 1 unit on the x-axis and 1 cm to 10 units on the y-axis, draw the graph of y = 6 – x3 for –3 ≤ x ≤ 2.5. [4 marks] (c) From your graph, find
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(i) the value of y when x = 1.2, (ii) the value of x when y = 20.
[2 marks]
(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3 – 8x – 6 = 0 for –3 ≤ x ≤ 2.5. State these values of x. [4 marks] Answer: (a) x y
–3 33
–2.5 21.63
–2 14
–1
0 6
1 5
2
2.5 -9.63
(b)
(c) (i) y = __________ (ii) x = __________ (d) x = __________, __________
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
Answers: 1. 0.2498, 2.498 × 10-1 2. (a) 1 × 107 (b) 1 × 10-4 3. 6x2 + 55x -50 cm2 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
y ≥ -2x + 2 (a) (-7, 5) (b) (-14, -2) 1110102 (a) 2.9 × 10-1 (b) 1.4 × 10-4 68, 208, 258 115, 135, 205 308, 338, 368 A'(4, 4) B'(4, 1) C'(2, 1) (a) (i) 15 (ii) 8 (b) (i) 11 (ii) 15 (c) 41 14. (a) k = -0.92, m = -11 (b)
D'(2, 4)
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(c) (i) y = -12.1, (ii) x = -0.8, 1.8 (d) y = -3x + 3, x = -3.3, 2.8 15. (a) (i) 10, (ii) 7 (b) (i) 3, (ii) 7 16. (a)
x y x = –1,
–3 –2.5 33 21.63 y = 6 – (–1)3 = 7
x = 2,
y = 6 – (2)3 = -2
–2 14
–1 7
0 6
1 5
2 -2
2.5 -9.63
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(b)
(c) (i) When x = y= (ii)When y = x=
1.2, 4.27 20, –2.41
(d) y = 6 – x3 x3 – 8x – 6 = 0
....... (1) ....... (2)
Equation (1) + Equation (2) y = –8x From the graph, x = –0.8, –2.3
DES : CHAPTER 1,2,3 FORM 4 & 5
1.
Calculate the value of 0.8 × 0.31 + 1.26 ÷ 700 and express the answer in standard form. [3 marks]
2.
Find the value for each of the following and express your answer in standard form. (a) 106 × 101 100 [4 marks] (b) = 104
3.
The width and length of a rectangle are (6x − 5) cm and (x + 10) cm respectively. Form a quadratic expression for the area, in cm2, of the rectangle, in term of [4 marks] x.
4.
Sketch the graph for the cubic function y = x3.
[5 marks]
5. The following graph shows that y = -2x + 2. Please describe the shaded region.
6.
[3 marks]
-9 Given that transformation T is the translation and transformation R is a 2 reflection in the line y = -x, state the coordinates of the image of point (4, 5) under combined transformation (a) RT, (b) TR. [4 marks]
(
)
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
7.
If a + 1001002 = 10111102, find a in base two.
8.
Find the value of the following and express your answer in standard form. 870000 84000 (a) = (b) = 6 3 × 10 6 × 108
9.
[5 marks]
[6 marks]
Complete the following sequence. 18, _____, 138, _____, _____
[6 marks]
10. Complete the following sequence. 25, 45, _____, _____, _____
[6 marks]
11. Complete the following sequence. 228, 258, _____, _____, _____
[6 marks]
12.
The diagram above show a quadrilateral ABCD on a Cartesian plane. Given that A'B'C'D' 3 is the image of ABCD under the translation -3 followed by a clockwise rotation of 90° about the origin, find the coordinates of A', B', C' and D'. [12 marks]
( )
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
13.
In the Venn diagram above, ξ = P ∪ Q ∪ R (a) State the value of (i) n(Q), (ii) n(P' ∩ R' ). (b) Given that n(P) = n(Q), find the value of (i) m, (ii) n, if n(P ∪ Q) = n(Q' ). (c) Hence, find the value of n(ξ).
[12 marks]
14. (a)
The table below shows the values of x and y which satisfy the equation y = 2x2 − 2x − 15. Calculate the values of k and m. -3 -2.2 -1 0 1 2 2.5 x 9 k -11 -15 -15 m -7.5 y (b) Draw the graph of y = 2x2 − 2x − 15 for −4 ≤ x ≤ 4. (c) From your graph, find (i) the value of y when x = 1.8, (ii) the value of x when y = -12. (d) Draw a suitable straight line on your graph to find a values of x which satisfy the equation 2x2 + x − 18 = 0 for −4 ≤ x ≤ 4. State the values of x. [12 marks]
15. (a) Complete the table in the answer space for the equation y = 6 – x3 by writing down the values of y when x = –1 and x = 2. [2 marks] (b) By using a scale of 1 cm to 1 unit on the x-axis and 1 cm to 10 units on the y-axis, draw the graph of y = 6 – x3 for –3 ≤ x ≤ 2.5. [4 marks] (c) From your graph, find
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(i) the value of y when x = 1.2, (ii) the value of x when y = 20.
[2 marks]
(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3 – 8x – 6 = 0 for –3 ≤ x ≤ 2.5. State these values of x. [4 marks] Answer: (a) x y
–3 33
–2.5 21.63
–2 14
–1
0 6
1 5
2
2.5 -9.63
(b)
(c) (i) y = __________ (ii) x = __________ (d) x = __________, __________
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
Answers: 1. 0.2498, 2.498 × 10-1 2. (a) 1 × 107 (b) 1 × 10-4 3. 6x2 + 55x -50 cm2 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
y ≥ -2x + 2 (a) (-7, 5) (b) (-14, -2) 1110102 (a) 2.9 × 10-1 (b) 1.4 × 10-4 68, 208, 258 115, 135, 205 308, 338, 368 A'(4, 4) B'(4, 1) C'(2, 1) (a) (i) 15 (ii) 8 (b) (i) 11 (ii) 15 (c) 41 14. (a) k = -0.92, m = -11 (b)
D'(2, 4)
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(c) (i) y = -12.1, (ii) x = -0.8, 1.8 (d) y = -3x + 3, x = -3.3, 2.8 15. (a) (i) 10, (ii) 7 (b) (i) 3, (ii) 7 16. (a)
x y x = –1,
–3 –2.5 33 21.63 y = 6 – (–1)3 = 7
x = 2,
y = 6 – (2)3 = -2
–2 14
–1 7
0 6
1 5
2 -2
2.5 -9.63
DES : CHAPTER 1,2,3 FORM 4 & 5
MATHEMATICS FORM 5 – REVISION 1
(b)
(c) (i) When x = y= (ii)When y = x=
1.2, 4.27 20, –2.41
(d) y = 6 – x3 x3 – 8x – 6 = 0
....... (1) ....... (2)
Equation (1) + Equation (2) y = –8x From the graph, x = –0.8, –2.3
DES : CHAPTER 1,2,3 FORM 4 & 5
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