2009 Practice Calc Part 2
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- Words: 545
- Pages: 8
18.
(a) Reflect triangle Q in the line y = x. Label the triangle R. (2) (b) Enlarge triangle Q, scale factor 2, from the origin. (2) 19. The graph shows the speed of a car in kilometres per hour (km/h).
(a) What is the speed of the car after 10 seconds? ……………..km/h (1) (b) After 30 seconds, the car travels at a steady speed of 60 km/h for 1 minute. Continue the t graph by drawing a line AB to show this. (1) (c) Draw a straight line from B to the point C (110,0). (1) (d) What does the graph between B and C tell you about what the car is doing? ……………………………… ………………………………………………… ……………… ……………………………… ………………………………………………… ………………. (1)
20.
Solve the simultaneous equations below. 6 + = 1 3 + 2 = −4
x = ……………. y = ……………. (4)
21.
Over a six month period in 2008, the average monthly value of FTSE on the London stock exchange changed as shown below. May 6200
June 6000
July 5550
August 5300
September October 5600 4000
Calculate the three point moving averages for this information.
……..………. ……..………. ……..………. ……..………. (4)
22.
A 10 dirham note is a 143 × 70 mm. A 100 dirham note is 153 × 75 mm.
Show working to prove the two notes are NOT mathematically similar.
(2) 23.
BE is parallel to CD. AB = 9 cm, AE = 6 cm, BC = 3 cm, CD = 7 cm. (a) Calculate the length of BE.
…………cm (2) (b) Calculate the length of ED.
…………cm (2)
24.
(a) Show that 12 75 − 48 = 6
(b) Show that
(3) = 3 2
(2)
25.
Express the recurring decimal 2.06 as a fraction, give your answer in its simplest form.
………………. (3)
26.
The diagram shows to vectors a and b. RS = a + 2b On the grid draw the vector RS RS. (2) 27.
X
A
B
a O
c
C
OABC is a trapezium. OC is parallel to AB. OA = a, OC = c, AB = 2 OC,, X is on point AB so that AX:XB = 3:1 Express XC in terms of a and c.
XC = ……………… (3)
28.
The diagram shows a pyramid. The apex of the pyramid is V. Each of the sloping edges is of length 6 cm. The base of the pyramid is a regular hexagon with sides of length 2 cm. O is the centre of the base.
(a) Calculate the height of V above the base of the pyramid, correct to 3 significant figures.
……………. cm (2) (b) Calculate the size of angle DVA, correct to 3 significant figure figures.
……………. ° (3)
(c) Calculate the size of angle AVC, correct to 3 significant figures.
……………. ° (4)
The diagram shows a tetrahedron. AD is perpendicular to both AB and AC. AB = 10 29. cm, AC = 8 cm, AD = 5 cm, Angle BAC = 90°.
(a) Calculate the size of BDC, correct to one decimal place.
……………..° (6)
(b) Work out the surface area of the tetrahedron.
……………cm3 (5)
30.
Make b the subject of the formula: =
. ( )
b= …………………… (4) _____________________________________________________________________ TOTAL FOR PAPER: 117 MARKS E D
(a) Reflect triangle Q in the line y = x. Label the triangle R. (2) (b) Enlarge triangle Q, scale factor 2, from the origin. (2) 19. The graph shows the speed of a car in kilometres per hour (km/h).
(a) What is the speed of the car after 10 seconds? ……………..km/h (1) (b) After 30 seconds, the car travels at a steady speed of 60 km/h for 1 minute. Continue the t graph by drawing a line AB to show this. (1) (c) Draw a straight line from B to the point C (110,0). (1) (d) What does the graph between B and C tell you about what the car is doing? ……………………………… ………………………………………………… ……………… ……………………………… ………………………………………………… ………………. (1)
20.
Solve the simultaneous equations below. 6 + = 1 3 + 2 = −4
x = ……………. y = ……………. (4)
21.
Over a six month period in 2008, the average monthly value of FTSE on the London stock exchange changed as shown below. May 6200
June 6000
July 5550
August 5300
September October 5600 4000
Calculate the three point moving averages for this information.
……..………. ……..………. ……..………. ……..………. (4)
22.
A 10 dirham note is a 143 × 70 mm. A 100 dirham note is 153 × 75 mm.
Show working to prove the two notes are NOT mathematically similar.
(2) 23.
BE is parallel to CD. AB = 9 cm, AE = 6 cm, BC = 3 cm, CD = 7 cm. (a) Calculate the length of BE.
…………cm (2) (b) Calculate the length of ED.
…………cm (2)
24.
(a) Show that 12 75 − 48 = 6
(b) Show that
(3) = 3 2
(2)
25.
Express the recurring decimal 2.06 as a fraction, give your answer in its simplest form.
………………. (3)
26.
The diagram shows to vectors a and b. RS = a + 2b On the grid draw the vector RS RS. (2) 27.
X
A
B
a O
c
C
OABC is a trapezium. OC is parallel to AB. OA = a, OC = c, AB = 2 OC,, X is on point AB so that AX:XB = 3:1 Express XC in terms of a and c.
XC = ……………… (3)
28.
The diagram shows a pyramid. The apex of the pyramid is V. Each of the sloping edges is of length 6 cm. The base of the pyramid is a regular hexagon with sides of length 2 cm. O is the centre of the base.
(a) Calculate the height of V above the base of the pyramid, correct to 3 significant figures.
……………. cm (2) (b) Calculate the size of angle DVA, correct to 3 significant figure figures.
……………. ° (3)
(c) Calculate the size of angle AVC, correct to 3 significant figures.
……………. ° (4)
The diagram shows a tetrahedron. AD is perpendicular to both AB and AC. AB = 10 29. cm, AC = 8 cm, AD = 5 cm, Angle BAC = 90°.
(a) Calculate the size of BDC, correct to one decimal place.
……………..° (6)
(b) Work out the surface area of the tetrahedron.
……………cm3 (5)
30.
Make b the subject of the formula: =
. ( )
b= …………………… (4) _____________________________________________________________________ TOTAL FOR PAPER: 117 MARKS E D
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