Section 1 Indices and Logarithms

1) Solve Ln(e6x−4+7)=7 for x.

The answer (correct to 3 decimal places) is x =

Section 2 Functions

2) Let f(x) = −4x+72x−2, find f-1(x).

Answer: (Correct to 3 decimal places) f-1(x) = (-2 x + ) / (x + ).

Section 3 Roots of Equations

3) Solve 3x30x2−124x−96=0.

The roots in ascending order (correct to 3 decimal places) are , and .

Section 4 Inequalities

4) Solve x3 -9 x2 +26 x -24< 0.

Answer: (Correct to 3 decimal places). If there is no upper bound, enter 999 as the value, i.e. x < 999. If there is no lower bound, enter -999 as the value, i.e. -999 < x or x > -999. List your inequalities from the lowest range to the highest range.

x < , < x < , x > ,

Section 5 Simultaneous Equations

5) Solve {3x+4y=4−8x+y=−8

Correct your answers to 3 decimal places. x = , y = .

Section 6 Coordinate Geometry

6) Given point A = (4, 9) and point B = (9, 14). A point C divides the line joining AB in the ratio of 3:8, i.e point C is nearer to point A. What is the equation of the line perpendicular to line AB and passes through point C, in the form of y = mx + c?

Answer: (Correct to 3 decimal places) The equation of the line is y = x +

Section 7 Differentiation 1

7) Given y = Ln(5x+8)+ex25+9x+3−−−−−√. Find dy/dx. Find the gradient of the tangent that touches the graph at x = 2.

Answer: (Correct to 3 decimal places) The gradient of the tangent is m =

Section 8 Differentiation 2

Given y = (2x−7)3e3x−8. When x = 4, dx/dt = 4. What is the dy/dt?

Answer: (Correct to 3 decimal places). dy/dt =

Section 9 Differentiation Optimization

9) Let y = 2 x3 -30 x2 +54 x. Find the maximum point.

Answer: (Correct to 3 decimal places) the maximum point is ( , ).

Section 10 Differentiation Estimation

10) Given y = 2 x3 +7 x2 -2 x -1. Find y when x = 1. Suppose x increases by 0.3, find the first order estimate for y, and second order estimate for y.

Answer: Correct to 3 decimal places.

First order estimate for y = .

Second order estimate for y = .

Section 11 Integration

11) Find ∫10(5x2+8+e9x−3+1−5x+6)dx.

Answer: (Correct to 3 decimal places) the answer is

Section 12 Sequences and Series

12) An Arithmetic Progression has the following terms: 2900, 3400, ... . Which term in this sequence would first exceed or equal 75,000? What is the sum from the 1st term to this term?

Answer: It would exceed or equal at the

th term.

(Correct to 3 decial places) The sum from the 1st term to this term =

Section 13 Probability 1

13) Given P(A) = 0.6, P(B) = 0.5, P(A ∪ B) = 0.72. Find P(A | B) and P(B | A).

Answer: (correct to 3 decimal places) P(A | B) =

and P(B | A) =

Section 14 Probability 2

14) A salesman has a success rate of 0.35, i.e. the probability that a passerby will buy the product after his salespitch is 0.35. What is the probability that there are 3 or more passersby out of 4 buying the product after his salespitch? Assume the 4 passersby's decisions are independent of each other.

Answer: P(3 or more passersby out of 4 buying the product after his salespitch) =

Section 15 Statistics

15) Given the following corresponding set of data values for x and y:

x 37 60 80 82

y 38 42 62 90

The population covariance (to 1 decimal place) =

The correlation (to 3 decimal places) =