C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?

Ans to Prelim revision Question 1 (i)Rearrange into the form y = mx + c (ii)read off gradient = m

C Prelim revision Question 2 What is the equation of a horizontal line passing through the point (a,b) ?

Ans to Prelim revision Question 2 y = b x y (a,b)

C Prelim revision Question 3 How do you remember the exact trig ratio values of 30 o, 45 o and 60 o ?

Ans to Prelim revision Question 3 Draw reference triangles Use SOH CAH TOA 30 o 60 o 12 √3√3 45 o 1 1 √2√2

C Prelim revision Question 4 How do you find the length of a line joining two points ?

Ans to Prelim revision Question 4 √(x 2 – x 1 ) 2 + (y 2 –y 1 ) 2 A(x 1,y 1 ) B(x 2,y 2 ) x y

C Prelim revision Question 5 What are the two formulae used to find the area of a triangle ?

Ans to Prelim revision Question 5 Area = ½base x height Area = ½bcsinA A BC a b c B a s e height

1.1 Prelim revision Question 6 What is a median of a triangle ?

Ans to Prelim revision Question 6 A line from a vertex to the middle of the opposite side

1.1 Prelim revision Question 7 What is the equation of a vertical line passing through (a,b) ?

Ans to Prelim revision Question 7 x = a x y (a,b)

1.1 Prelim revision Question 8 What do you know about the gradient of two perpendicular lines ?

Ans to Prelim revision Question 8 They multiply together to give -1 i.e. m 1 xm 2 = -1 x y m1m1 m2m2

1.2 Prelim revision Question 9 How do you draw the graph of 3-f(x) given the graph of f(x) ?

Ans to Prelim revision Question 9 Reflect the graph in the x-axis, then move it up 3

1.2 Prelim revision Question 10 How do you draw the graph of f(x+1) given the graph of f(x) ?

Ans to Prelim revision Question 10 Move the graph 1 unit to the left

1.2 Prelim revision Question 11 How do you draw the graph of f(x-1) given the graph of f(x) ?

Ans to Prelim revision Question 11 Move the graph 1 unit to the right

C Prelim revision Question 12 What is the Converse of Pythagoras’ Theorem ?

Ans to Prelim revision Question 12 If a 2 = b 2 + c 2 then ΔABC is right-angled at A A B C a c b

1.2 Prelim revision Question 13 How do you change from radians to degrees ?

Ans to Prelim revision Question 13 Divide by π and multiply by 180

1.2 Prelim revision Question 14 How do you find f(g(x)) for given functions f(x) and g(x) ?

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)

1.2 Prelim revision Question 15 Which two points does the graph y = a x always pass through ?

Ans to Prelim revision Question 15 (0,1) and (1,a)

1.2 Prelim revision Question 16 How do you draw a graph of the form y = cos bx or y = sin bx ?

Ans to Prelim revision Question 16 Draw the normal graph but fit in b cycles between 0 and 2 π

1.2 Prelim revision Question 17 What is the turning point of y = b-3(x-a) 2 ? and is it max or min ?

Ans to Prelim revision Question 17 (a,b) Maximum (a,b)

1.2 Prelim revision Question 18 For what values of a function is the function said to be undefined ?

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.

1.2 Prelim revision Question 19 How do you write functions like 2x x + 3 ? in the form a(x+b) 2 +c

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

1.2 Prelim revision Question 20 For what values is the function f(x) = √(x-a) undefined?

Ans to Prelim revision Question 20 x < a

1.2 Prelim revision Question 21 How do you draw a graph of the form y = acosx or y = asinx ?

Ans to Prelim revision Question 21 Draw y = cosx or y = sinx graph shape with a maximum of a and a minimum of -a

1.3 Prelim revision Question 22 How do you show that a curve is always increasing ?

Ans to Prelim revision Question 22 (i)Differentiate (ii)show that f ’ (x) is always > 0

2.2 Prelim revision Question 23 How do you find x √ x ∫ dx ?

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

1.3 Prelim revision Question 24 How do you find where a curve is decreasing ?

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

1.4 Prelim revision Question 25 How do you find the limit of a recurrence relation from its formula ?

Ans to Prelim revision Question 25 (i) let u n+1 = u n = L givingL=aL+b (ii) solve equation Remember: For u n+1 =au n +b, a limit only exists if -1<a<1

2.1 Prelim revision Question 26 How do you show that the root of a function lies between two given values ?

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

2.2 Prelim revision Question 27 How do you calculate the area between two curves ?

Ans to Prelim revision Question 27 (i) let equations equal each other (ii) solve to find limits (iii) integrate (upper - lower) functions between limits

1.2 Prelim revision Question 28 How do you solve equations of the form sin 2 x o = 0.25 ? (0≤x≤360)

Ans to Prelim revision Question 28 (i)rearrange to get sinx o = ± … (ii)find answers in all 4 quadrants

2.3 Prelim revision Question 29 How do you find exact values of sin2x and cos2x given cosx = 3 / 5 ?

Ans to Prelim revision Question 29 (i)draw a right-angled triangle (ii)find the missing side (iii)expand the double angle formula (iv)substitute in values from Δ A 3 5

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 ?

Ans to Prelim revision Question 30 (i)find the centre (ii)find gradient from centre to the point(a,b) (iii)find perpendicular gradient (iv)use y-b=m(x-a) x y (a,b) C