Upcoming SlideShare
×

# F4 Maths Ppsmi 2007 P1

1,750
-1

Published on

2 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total Views
1,750
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
123
0
Likes
2
Embeds 0
No embeds

No notes for slide

### F4 Maths Ppsmi 2007 P1

2. 2. 1449/1 2 Form Four MATHEMATICAL FORMULAE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1 am × an = am + n 12 Pythagoras Theorem c2 = a2 + b2 2 am ÷ an = am − n 13 y2 − y1 m= x2 − x1 3 (am )n = am n 14 y − intercept m=− x − intercept 4 1 ⎛ d − b⎞ A−1 = ⎜ ⎟ ad − bc ⎜ − c a ⎟ ⎝ ⎠ 5 n( A) P ( A) = n( S ) 6 P ( A' ) = 1 − P( A) 7 Distance = ( x2 − x1 ) 2 + ( y2 − y1 ) 2 8 ⎛ x + x y + y2 ⎞ Midpoint, ( x, y ) = ⎜ 1 2 , 1 ⎟ ⎝ 2 2 ⎠ 9 distance travelled Average speed = time taken 10 sum of data Mean = number of data 11 sum of (class marks × frequency) Mean = sum of frequencies 1449/1 Form Four PPSMI/Maths/F4/P1/2007
3. 3. 1449/1 3 Form Four SHAPES AND SPACE 1 1 Area of trapezium = × sum of parallel sides × height 2 2 Circumference of circle = π d = 2 π r 3 Area of circle = π r 2 4 Curved surface area of cylinder = 2 π r h 5 Surface area of sphere = 4 π r 2 6 Volume of right prism = cross sectional area × length 7 Volume of cylinder = π r 2 h 8 1 Volume of cone = π r 2 h 3 9 4 Volume of sphere = π r 3 3 10 1 Volume of right pyramid = × base area × height 3 11 Sum of interior angles of polygon = (n −2)×180° 12 arc length angle subtended at centre = circumference of circle 360o 13 area of sector angle subtended at centre = area of circle 360o 14 PA' Scale factor, k = PA 15 Area of image = k2 × area of object 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
4. 4. 1449/1 4 Form Four 1. Round off 0⋅0459 correct to two significant figures. A 0⋅04 B 0⋅045 C 0⋅046 D 0⋅05 2. Express 0⋅00205 in standard form. A 2⋅05 × 103 B 2⋅05 × 102 C 2⋅05 × 10−3 D 2⋅05 × 10−2 3. 2⋅38 × 104 − 8⋅41 × 103 = A 1⋅539 × 104 B 1⋅539 × 103 C 6⋅03 × 104 D 6⋅03 × 103 5.2 × 10 −7 4. = (4 ×10 ) −2 2 A 3⋅25 × 10−4 B 1⋅3 × 10−3 C 3⋅25 × 10−12 D 1⋅3 × 10−11 1449/1 Form Four PPSMI/Maths/F4/P1/2007
5. 5. 1449/1 5 Form Four 5. The volume of a bottle of mineral water is 512 ml. The total volume, in litres, of 6 similar bottles of mineral water, correct to three significant figures is A 3⋅07 B 30⋅7 C 307 D 3070 6. ( r − 2s )( 5r + s ) = A 5r2 − 9rs − 2s2 B 5r2 − 9rs + 2s2 C 5r2 + 11rs − 2s2 D 5r2 + 11rs + 2s2 7. 5g ( g − h ) − ( 2g − h )2 = A g2 − gh − h2 B g2 − 5gh − h2 C g2 − 5gh + h2 D g2 − 9gh + h2 8. It is given that the universal set ξ = { 1 , 2 , 3 , 4 , 5 , 6 , 7 }, set P = { 1 , 3 , 5 , 7 } and set P ∩ Q = { 5 , 7 }. If ξ = P ∪ Q , list all the elements of set Q’. A 1,3 B 2,4,6 C 1,2,3,4,6 D 2,4,5,6,7 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
6. 6. 1449/1 6 Form Four 9. Diagram 1 shows a Venn diagram which shows the number of elements of sets J , K and L. J K L 5 3 1 4 2 DIAGRAM 1 If the universal set ξ = J ∪ K ∪ L , find n( J’ ∩ L ). A 3 B 4 C 6 D 7 10. The Venn diagram in Diagram 2 shows the universal set ξ, the elements of sets P , Q and R. ξ P Q •7 R •1 •2 •8 •4 •5 •6 •3 DIAGRAM 2 State all the elements of set P’ ∩ R’. A 2,6 B 2,3,6 C 2,6,8 D 2,3,6,8 1449/1 Form Four PPSMI/Maths/F4/P1/2007
7. 7. 1449/1 7 Form Four 11. Find the y-intercept of the straight line 5x − 3y = 15. A 5 B 3 C −3 D −5 x y 12. Find the x-intercept of the straight line + = 1. 3 4 1 A 4 1 B 3 C 3 D 4 13. Diagram 3 shows the straight line PQ on a Cartesian plane. DO GRIDS without coords. y P(−3,3) x O Q(1,−5) DIAGRAM 3 Find the gradient of PQ. A −2 1 B − 2 C 1 D 2 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
8. 8. 1449/1 8 Form Four 14. Diagram 4 is a bar chart which shows the score of a Mathematics quiz in class 4 Alpha Number of students 10 8 6 4 2 Score 1 2 3 4 5 DIAGRAM 4 Find the median score. A 4 B 3 C 2 D 1 15. Diagram 5 is a pictograph showing the number of books sold in January and March. The number of books sold in February are not shown. Month Number of books sold January February March represents 30 books DIAGRAM 5 The mean number of books sold for the three months is 150. Calculate the number of books sold in February. A 60 B 90 C 142 D 210 1449/1 Form Four PPSMI/Maths/F4/P1/2007
9. 9. 1449/1 9 Form Four 16. Diagram 6 is a pie chart which shows four uniform groups in a certain school. Police Cadets Red Crescent Society 150° 75° School Youth Cadets Scouts DIAGRAM 6 Calculate the ratio of the number of students in the Red Crescent Society to the number of students in the Police Cadets. A 3 : 10 B 10 : 3 C 1:5 D 5:1 17. A box contains similar white balls and green balls. A ball is picked at random from the box. 5 The probability of picking a green ball is . 9 If there are 36 balls in the box, calculate the number of white balls. A 16 B 18 C 20 D 32 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
10. 10. 1449/1 10 Form Four 18. Diagram 7 shows eight numbered cards. 1 2 3 4 5 6 7 8 DIAGRAM 7 A card is picked at random. Find the probability that the number shown is a factor of 8. 1 A 8 1 B 4 3 C 8 1 D 2 19. Ameen keeps his 15 blue marbles and 7 red marbles in a box. Later Ameen adds 3 blue marbles and 5 red marbles into the same box. A marble is chosen at random from the box. Find the probability of choosing a red marble. 2 A 5 7 B 22 4 C 9 6 D 11 1449/1 Form Four PPSMI/Maths/F4/P1/2007
11. 11. 1449/1 11 Form Four 20. Diagram 8 shows some letter cards. P L E A S E B E Q U I E T DIAGRAM 8 A card is picked at random. Find the probability that a card with letter E is picked? 1 A 13 1 B 4 2 C 5 4 D 13 21. In Diagram 9, LMN is a tangent to the circle at the points M. N M O 56° P z° L 120° Q DIAGRAM 9 Find the value of z. A 28 B 38 C 68 D 72 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
12. 12. 1449/1 12 Form Four 22. In Diagram 10, PQR is a tangent to the circle QTS at Q. S P x° Q 105° 65° T U R DIAGRAM 10 Find the value of x. A 30 B 40 C 50 D 60 23. In Diagram 11, EFG is a tangent to the circle at F. JOK is the diameter of the circle. HJF is a straight line. H y° O K J 30° E F G DIAGRAM 11 Find the value of y. A 105 B 120 C 135 D 150 1449/1 Form Four PPSMI/Maths/F4/P1/2007
13. 13. 1449/1 13 Form Four 24. It is given that cos y°= −0⋅8251 and 90°≤ y°≤ 270°. Find the value of y. A 124⋅40 B 145⋅60 C 214⋅40 D 235⋅60 25. In Diagram 12, O is the centre of the unit circle. y 1 P(0⋅6231,0⋅8816) −1 θ° 1 x O −1 DIAGRAM 12 The value of θ is A 28⋅16 B 38⋅54 C 51⋅46 D 61⋅83 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
14. 14. 1449/1 14 Form Four 26. In Diagram 13, QRS is a straight line. P 4 y° Q R S DIAGRAM 13 4 Given that cos ∠QPR = , find the value of cos y°. 5 3 A 5 4 B 5 3 C − 5 4 D − 5 27. In Diagram 14, LMN and PQ are two vertical poles standing on a horizontal ground. L M P N Q DIAGRAM 14 The angle of elevation of peak L from peak P is A ∠LPN B ∠LQN C ∠MPL D ∠MLP 1449/1 Form Four PPSMI/Maths/F4/P1/2007
15. 15. 1449/1 15 Form Four 28. In Diagram 15, EF is a vertical flag pole. GF is horizontal. E G 20 m F DIAGRAM 15 The angle of depression of G from E is 35°. Calculate the height, in m, of the flag pole EF. A B C D 29. Diagram 16 shows a right prism with a rectangular base EFGH. The trapezium EFQP is the uniform cross section of the prism. S P R Q H E G F DIAGRAM 16 Identify the angle between the line PG and the base EFGH. A ∠PGE B ∠PGF C ∠PGH D ∠PGR 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
16. 16. 1449/1 16 Form Four 30. Diagram 17 shows a right pyramid with a square base JKLM. The vertex V is vertically above M. V M J L K DIAGRAM 17 Identify the angle between the plane VKL and the base JKLM. A ∠VKM B ∠VML C ∠VLM D ∠VMK 31. In Diagram 18, PQRST are 5 consecutive vertices of a regular polygon. P Q T 30° R S DIAGRAM 18 Find the number of sides of the polygon. A 5 B 6 C 10 D 12 1449/1 Form Four PPSMI/Maths/F4/P1/2007
17. 17. 1449/1 17 Form Four 32. In Diagram 19, PQRSTU is a regular hexagon. UQV and SRV are straight lines. V n° P Q m° U R T S DIAGRAM 19 Find the value of m + n. A 108 B 120 C 144 D 180 33. Diagram 20 shows two quadrilaterals, KLMN and EFGH drawn on a square grid. E K P• N Q• S• H R• L M F G DIAGRAM 20 Quadrilateral EFGH is the image of quadrilateral KLMN under an enlargement. State the centre of enlargement. A P B Q C R D S 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
18. 18. 1449/1 18 Form Four 34. Diagram 21 shows two triangles PQR and RST drawn on a square grid. P T Q S R DIAGRAM 21 The triangle RST is the image of the triangle PQR under a clockwise rotation. State the centre of rotation and the corresponding angle of rotation. Centre Angle of rotation A R 90° B T 90° C R 270° D T 270° 35. It is given that 5 − 3(2k + 1) = 2k + 4. Find the value of k. 5 A − 2 3 B − 2 1 C 5 3 D 4 1449/1 Form Four PPSMI/Maths/F4/P1/2007
19. 19. 1449/1 19 Form Four h 36. Given that h − r = , express h in terms of r. r 2r A r −1 2r B r +1 r2 C r −1 − r2 D r +1 3 5 37. Which of the following is equivalent to w ? 5 A w3 3 B w5 C (w) 3 5 D (w) 5 3 (27m n ) × n 1 3 9 3 9 38. Simplify (m n ) 1 −2 4 2 A B C D 39. List all the integers x which satisfy both the inequalities 8 − x ≤ 6 and 3(x − 6) ≤ 12 − 2x. A 2,3,4,5 B 2,3,4,5,6 C 3,4,5 D 3,4,5,6 1449/1 [Turn Over PPSMI/Maths F4/P1/2007
20. 20. 1449/1 20 Form Four 5n 40. The solution for n − 1 ≤ = 4 is 2 A n ≥ −2 B n≥2 C n ≤ −2 D n≤2 END OF QUESTION PAPER 1449/1 Form Four PPSMI/Maths/F4/P1/2007