PRECALCULUS SUPPLEMENTARY IV

PRECALCULUS SUPPLEMENTARY IV - AP CALCULUS PRECALCULUS...

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AP CALCULUS PRECALCULUS SUPPLEMENTARY IV Problems : 1) Solve the following linear system: abcd bcde cdea deab eabc + + + = ++ += +++= 10 9 8 7 6 Hint : Add all the equations simultaneously and back substitute the result into each respective equation. 2) Let ABCD be a square and let point E be on AB such that the area of Δ ADE is 1 3 of the area of square ABCD . Find the value of AE AB . 3) a) Factor into a product of two quadratic factors with real integer coefficients. () fx x x x =−+− 42 69 Hint : Think difference of squares. A B C D E b) Are the roots of real or imaginary? Justify your answer. fx 4) In Δ ABC , D is the foot of the altitude to AC and E is the midpoint of the same side (see diagram to the right). Prove that ( )( ) AB BC ED AC 22 2 −= . 5) Consider Δ ABC with sides a , b and c . If a bca 2 333 = +− , then what is the value of ? CAB Hints: a) You will need the sum of cubes formula: ( ) xy x y xx y y 33 2 2 +=+ −+ b) You will need to use the Cosine Law.
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PRECALCULUS SUPPLEMENTARY IV - AP CALCULUS PRECALCULUS...

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