Moderator Note: We have received multiple reports that this set of test questions has been posted at four different sites (so far). This thread has been closed. We are waiting for your response to our private message.
1) Solve [FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]7[/FONT]Ln(e6x−4+7)=7 for x.
The answer (correct to 3 decimal places) is x =
2) Let f(x) = [FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT]−4x+72x−2, find f-1(x).
Answer: (Correct to 3 decimal places) f-1(x) = (-2 x + ) / ( x + ).
3) Solve [FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]124[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]96[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0[/FONT]3x30x2−124x−96=0.
The roots in ascending order (correct to 3 decimal places) are, and .
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 > ,
5) Solve [FONT=MathJax_Size3]{[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT]{3x+4y=4−8x+y=−8
Correct your answers to 3 decimal places. x =, y = .
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 + .
7) Given y = [FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]9[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]√[/FONT]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 = .
8) Given y = [FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT](2x−7)3e3x−8. When x = 4, dx/dt = 4. What is the dy/dt?
Answer: (Correct to 3 decimal places). dy/dt =
9) Let y = 2 x3 -30 x2 +54 x. Find the maximum point.
Answer: (Correct to 3 decimal places) the maximum point is (, ).
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 = .
11) Find [FONT=MathJax_Size1]∫[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Size2]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]9[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Size2])[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]x[/FONT]∫01(5x2+8+e9x−3+1−5x+6)dx.
Answer: (Correct to 3 decimal places) the answer is.
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 = .
13) Given P(A) = 0.6, P(B) = 0.5, P(A [FONT=MathJax_Main]∪[/FONT]∪ B) = 0.72. Find P(A | B) and P(B | A).
Answer: (correct to 3 decimal places) P(A | B) = and P(B | A) = .
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) =
15) Given the following corresponding set of data values for x and y:
The population covariance (to 1 decimal place) =
The correlation (to 3 decimal places) =
1) Solve [FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]7[/FONT]Ln(e6x−4+7)=7 for x.
The answer (correct to 3 decimal places) is x =
2) Let f(x) = [FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT]−4x+72x−2, find f-1(x).
Answer: (Correct to 3 decimal places) f-1(x) = (-2 x + ) / ( x + ).
3) Solve [FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]124[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]96[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0[/FONT]3x30x2−124x−96=0.
The roots in ascending order (correct to 3 decimal places) are, and .
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 > ,
5) Solve [FONT=MathJax_Size3]{[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT]{3x+4y=4−8x+y=−8
Correct your answers to 3 decimal places. x =, y = .
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 + .
7) Given y = [FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]9[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]√[/FONT]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 = .
8) Given y = [FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT](2x−7)3e3x−8. When x = 4, dx/dt = 4. What is the dy/dt?
Answer: (Correct to 3 decimal places). dy/dt =
9) Let y = 2 x3 -30 x2 +54 x. Find the maximum point.
Answer: (Correct to 3 decimal places) the maximum point is (, ).
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 = .
11) Find [FONT=MathJax_Size1]∫[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Size2]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]9[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Size2])[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]x[/FONT]∫01(5x2+8+e9x−3+1−5x+6)dx.
Answer: (Correct to 3 decimal places) the answer is.
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 = .
13) Given P(A) = 0.6, P(B) = 0.5, P(A [FONT=MathJax_Main]∪[/FONT]∪ B) = 0.72. Find P(A | B) and P(B | A).
Answer: (correct to 3 decimal places) P(A | B) = and P(B | A) = .
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) =
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) =
Last edited by a moderator: