3RD YEAR MATH (SPECIAL CLASS)

INSTRUCTIONS (FOLLOW CAREFULLY!): Below is a set exercise that you should submit upon resumption of classes. Copy&paste everything found below the series of en dashes and print a copy of this set exercise which should serve as your test paper. Follow this format: Times New Roman 12pts; single spacing; Narrow margin (0.5 each side). You will be submitting this test paper to me; as such, put all necessary answers & solutions in there as prescribed. Should you have questions or comments, email me at sigridgayangos@gmail.com or message me on Facebook. Have fun solving! :)

For your self-study: Download the pdf file found here http://www.mathdb.org/basic_calculus/BasicCalculus.pdf Read Chapters 0, 1, 2, 7 and 8 and answer the exercises found in each section. Correct answers can be found on pages 255 and above for your reference. For now, ignore the calculus parts first (there's no stopping you if you really do want to learn it now, though) but I promise you that soon as Metrobank season is over, we will do a bit of Calculus in class as well...among many others.


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NAME: _____________________________________                                                                     SCORE: _________

I. Solve each problem and write the answer on the blank before the number. Leave simplified radicals in answers. Use base ten when none is indicated and express areas of circles in terms of τ. (2 pts each)

___________1. L is a point on segment JG such that JL:LG=7:8. If JL=35, find LG.

___________2. If 8^x=4⁵, what is x?

___________3. Find all values of x that make log₃(x²-9)=3.

___________4. A diagonal of rectangle ABCD forms a 30˚ angle with the longer side of ABCD. If the diagonal is 20 cm long, find the area of ABCD.

___________5. If A is 80% of B, and B is 75% of C, then A is what percent of C?

___________6. If there are 888 terms in the addition of 888+888+…+888 and the sum is equal to 888^8x, find x.

___________7. Evaluate [(3/4)^-1 – (2/3]^-1

___________8. Find the value of cos(240˚)+sin(120˚).

___________9. Find all values of x that satisfy 2x²-x-10 > 0.

___________10. A particular radioactive substance has a half-life of 25 years. Of an initial 80 grams, how many grams would be left after 75 years?

___________11. If an interior angle of a regular pentagon is 160˚, how many sides has it?

___________12. One leg of a right triangle is 4 more than twice the other. If the area is 120cm², find the other leg.

___________13. Factor completely: 4x²(y²-x²)(x²-y²)

___________14. If z varies directly as x and inversely as y, find the percentage change in z if x increases by 20% and y increases by 25%.

___________15. Give one pair of consecutive integral values of x between which the graph of P(x)=2x⁴+5x³-3x²+x+2 crosses the x-axis.

II. Solve the following on a scratch paper, then write a neat and complete solution on the space provided. Give details and necessary reason/explanation or justify your answer to get full marks as partial credit will be given otherwise. (3 pts each)

1. Draw the figure: RSTU is a rectangle. X lies on side RS while Y lies on side TU. Segments RT, SU and XY meet in the interior of the rectangle at point O. What percent of the area of rectangle RSTU is the area of the region covered by triangles RXO and YOU? (In other news, typing this problem made me realize how I’ve always been typing literary stuff, that I find it mind-boggling to even just “draw” a rectangle with segments in it using Word. So yay, I’ll let you manually draw it instead.)

2. In circle O, chord AB is produced to C so that BC has the same length as one of the radii of the circle. CO is drawn and extended to meet the circle at D. AO is drawn. Express angle AOD in terms of angle C.

3. If (a+b)²=81 and ab=18, find the value of (1/a^2)+(1/b^2) .

4. A rhombus has a side of 12cm and one angle of 60˚. It is to be tiled with small equilateral triangles of side 1 cm. How many small tiles are needed?

5. A circle is tangent to the y-axis at (0,2) and the larger of its x-intercept is 8 units. Find the radius of the circle.

III. Solve the following on a scratch paper, then write a neat and complete solution on the space provided after #3 and at the back of this paper. Give details and necessary reason/explanation or justify your answer to get full marks as partial credit will be given otherwise. (5 pts each)

1. What is the area of the triangle formed by the coordinate axes and the line that passes through (2,3) and makes equal x and y intercepts?

2. Two ships leave the same pier at the same time. One ship sails on a course of 110˚ at 34mi/h. The other sails on a course of 230˚ at 40mi/h. Find the distance between them after 3 hours.

3. Inside square ABCD with sides of length 12 cm, AE is drawn, where E is the point on DC which is 5 cm from D. The perpendicular bisector of AE is drawn and intersects AE, AD and BC at points M, P and Q respectively. Find the ratio of PM to MQ.