9 Maths questions high school/a level

Question 1

Find the gradient, -intercept and -intercept of the line

.

Give your answers exactly, as integers or single fractions.

The gradient is

The -intercept is

The -intercept is

Question 2

giving your answers exactly, as integers or single fractions.

The solutions are q =

Question 3

Suppose that and
Find the rule of the composite function  

[Remember that, for example, you can input by typing sqrt(x) ]

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Question 4 

Find the rule of the inverse of the function .

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Question 5

Simplify the expression .

Expand brackets and gather like terms in your answer, but do not take out any common factors.

=

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Question 6

Solve the equation .

Give your answer as a decimal number to three significant figures.

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Question 7

The  triangle  has angle , angle  and side of length  .

Find the length of side . Give your answer as a decimal number to one decimal place.

 =

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Question 8

The angle in triangle is  ,  and the lengths of two sides are and .

Find  the length of side . Give your answer as a decimal number to one decimal place.

 =

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Question 9

Use an appropriate half-angle identity to find the exact value of .

Give your answer exactly, as a numerical expression involving surds and fractions.

To enter, for example,  type sqrt(x)