C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5...
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![Page 1: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/1.jpg)
C
Prelim revision Question 1
•How do you get the gradient of a line with an equation like3x + 2y = 5 ?
![Page 2: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/2.jpg)
Ans to Prelim revision Question 1
•(i) Rearrange into the formy = mx + c
(ii) read offgradient = m
![Page 3: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/3.jpg)
C
Prelim revision Question 2
•What is the equation of a horizontal line passing through the point (a,b) ?
![Page 4: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/4.jpg)
Ans to Prelim revision Question 2
•y = b
x
y
(a,b)
![Page 5: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/5.jpg)
C
Prelim revision Question 3
•How do you remember the exact trig ratio values of 30o, 45o and 60o ?
![Page 6: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/6.jpg)
Ans to Prelim revision Question 3
•Draw reference triangles•Use SOH CAH TOA
30o
60o
1 2
√3
45o
45o
1
1 √2
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C
Prelim revision Question 4
•How do you find the length of a line joining two points ?
![Page 8: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/8.jpg)
Ans to Prelim revision Question 4
•√(x2 – x1)2 + (y2 –y1)2
A(x1,y1)
B(x2,y2)
x
y
![Page 9: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/9.jpg)
C
Prelim revision Question 5
•What are the two formulae used to find the area of a triangle ?
![Page 10: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/10.jpg)
Ans to Prelim revision Question 5
•Area = ½base x height
•Area = ½bcsinAA
BCa
bc
B a s e
height
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1.1
Prelim revision Question 6
•What is a median of a triangle ?
![Page 12: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/12.jpg)
Ans to Prelim revision Question 6
•A line from a vertex to the middle of the opposite side
![Page 13: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/13.jpg)
1.1
Prelim revision Question 7
•What is the equation of a vertical line passing through (a,b) ?
![Page 14: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/14.jpg)
Ans to Prelim revision Question 7
•x = a
x
y
(a,b)
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1.1
Prelim revision Question 8
•What do you know about the gradient of two perpendicular lines ?
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Ans to Prelim revision Question 8
•They multiply together togive -1
i.e. m1xm2 = -1x
y
m1
m2
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1.2
Prelim revision Question 9
•How do you draw the graph of 3-f(x) given the graph of f(x) ?
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Ans to Prelim revision Question 9
•Reflect the graph in the x-axis, then move it up 3
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1.2
Prelim revision Question 10
•How do you draw the graph of f(x+1) given the graph of f(x) ?
![Page 20: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/20.jpg)
Ans to Prelim revision Question 10
•Move the graph 1 unit to the left
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1.2
Prelim revision Question 11
•How do you draw the graph of f(x-1) given the graph of f(x) ?
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Ans to Prelim revision Question 11
•Move the graph 1 unit to the right
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C
Prelim revision Question 12
•What is the Converse of Pythagoras’
Theorem ?
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Ans to Prelim revision Question 12
•If a2 = b2 + c2
then ΔABC isright-angled at A
AB
C
a
c
b
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1.2
Prelim revision Question 13
•How do you change from radians to degrees ?
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Ans to Prelim revision Question 13
• Divide by π and multiply by 180
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1.2
Prelim revision Question 14
•How do you find f(g(x)) for given functions f(x) and g(x) ?
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Ans to Prelim revision Question 14
•Substitute g(x) into f(x)i.e. each x in f(x) is replaced by the entire function g(x)
![Page 29: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/29.jpg)
1.2
Prelim revision Question 15
•Which two points does the graphy = ax always pass through ?
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Ans to Prelim revision Question 15
•(0,1) and (1,a)
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1.2
Prelim revision Question 16
•How do you draw a graph of the form
• y = cos bx• or y = sin bx ?
![Page 32: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/32.jpg)
Ans to Prelim revision Question 16
•Draw the normal graph but fit in b cycles between 0 and 2 π
•Draw the normal graph but fit in b cycles between 0 and 2 π
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1.2
Prelim revision Question 17
•What is the turning point of y = b-3(x-a)2 ?
• and is it max or min ?
![Page 34: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/34.jpg)
Ans to Prelim revision Question 17
•(a,b)
•Maximum
(a,b)
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1.2
Prelim revision Question 18
•For what values of a function is the function said to be undefined ?
![Page 36: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/36.jpg)
Ans to Prelim revision Question 18
•When you fit in a value of x and you cannot get an answer
•Remember you can’t divide by zero, or square root a negative number.
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1.2
Prelim revision Question 19
•How do you write functions like 2x2 + 12x + 3 ?
in the form a(x+b)2+c
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Ans to Prelim revision Question 19
• (i) multiply out a(x+b)2+c
•(ii) compare with given function
•(iii) find a, b and c
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1.2
Prelim revision Question 20
•For what values is the functionf(x) = √(x-a) undefined?
![Page 40: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/40.jpg)
Ans to Prelim revision Question 20
•x < a
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1.2
Prelim revision Question 21
•How do you draw a graph of the form
y = acosxor y = asinx ?
![Page 42: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/42.jpg)
Ans to Prelim revision Question 21
• Draw y = cosx
or y = sinx graph shape
with a maximum of a and a minimum of -a
![Page 43: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/43.jpg)
1.3
Prelim revision Question 22
•How do you show that a curve is always increasing ?
![Page 44: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/44.jpg)
Ans to Prelim revision Question 22
•(i) Differentiate•(ii) show that f’(x) is
always > 0
![Page 45: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/45.jpg)
2.2
Prelim revision Question 23
•How do you find x2 + 1√x
∫ dx ?
![Page 46: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/46.jpg)
Ans to Prelim revision Question 23
(i) change root to power
(ii) split up into fractions(iii) simplify each term(iv) integrate each term
(v) REMEMBER +C
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1.3
Prelim revision Question 24
•How do you find where a curve is decreasing ?
![Page 48: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/48.jpg)
Ans to Prelim revision Question 24
(i) differentiate(ii) let f’(x) = 0(iii)solve to find st pts(iv) draw nature table(v) read values where
graph is decreasing
![Page 49: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/49.jpg)
1.4
Prelim revision Question 25
•How do you find the limit of a recurrence relation from its formula ?
![Page 50: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/50.jpg)
Ans to Prelim revision Question 25
•(i) let un+1 = un = Lgiving L=aL+b
•(ii) solve equationRemember:For un+1=aun+b,a limit only exists if -1<a<1
![Page 51: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/51.jpg)
2.1
Prelim revision Question 26
•How do you show that the root of a function lies between two given values ?
![Page 52: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/52.jpg)
Ans to Prelim revision Question 26
•substitute in the two values and show that for one, the answer is positive, but for the other the answer is negative
x
+ve
-ve
![Page 53: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/53.jpg)
2.2
Prelim revision Question 27
•How do you calculate the area between two curves ?
![Page 54: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/54.jpg)
Ans to Prelim revision Question 27
•(i) let equations equal each other
•(ii) solve to find limits•(iii) integrate
(upper - lower) functions
between limits
![Page 55: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/55.jpg)
1.2
Prelim revision Question 28
•How do you solve equations of the form
sin2xo = 0.25 ?(0≤x≤360)
![Page 56: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/56.jpg)
Ans to Prelim revision Question 28
•(i)rearrange to get sinxo = ± …
•(ii) find answers in all 4 quadrants
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2.3
Prelim revision Question 29
•How do you find exact values of sin2x and cos2x given cosx =3/5 ?
![Page 58: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/58.jpg)
Ans to Prelim revision Question 29
• (i) draw aright-angledtriangle
• (ii) find the missing side
• (iii) expand the double angle formula
• (iv) substitute in values from Δ
A3
5
![Page 59: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/59.jpg)
2.4
Prelim revision Question 30
•How do you find the equation of the tangent to a circle at a particular point on the circumference ?
![Page 60: C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649ced5503460f949b987e/html5/thumbnails/60.jpg)
Ans to Prelim revision Question 30
(i) find thecentre
(ii) find gradientfrom centreto the point(a,b)
(iii) find perpendicular gradient(iv) use y-b=m(x-a)
x
y
(a,b)
C