HIGHSCHOOL MATH REVIEWER

HIGHSCHOOL MATH REVIEWER

• 1.
  1 HIGHSCHOOL MATHEMATICS ASSESMENTEXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.)HIGHSCHOOL MATHEMATICS ASSESMENT EXAM (10 things before calculus) (90 min.) NAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORENAME: YEAR LEVEL: DATE: TOTAL SCORE:::: INSTRUCTIONS:INSTRUCTIONS:INSTRUCTIONS:INSTRUCTIONS: Read and solve each problem carefully. Choose the letter of the correct answer. Calculators are not allowed in this test, you are allowed to guess between the 4 choices available but make sure at the end of this exam you come up to the best solution. Good Luck! 1111----TRIGONOMETRYTRIGONOMETRYTRIGONOMETRYTRIGONOMETRY(9(9(9(9THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Find the solution set on [0, ߨ] for the equation: sin ‫ݔ‬ + tan ‫ݔ‬ − tan ‫ݔ‬ sin ‫ݔ‬ − 1 = 0 a) ߨ b) గ ଶ c) గ ଷ d) గ ସ 2. Solve the equation3 tan ߠ + sec ߠ + 1 = 0, for all non-negative θ less than 360⁰. a) 180⁰ b) 315⁰ c) 135⁰ d) 0⁰ 3. Below are the solutions included in the solution set of the equation 2 tan ߠ + √3 sin ߠ ‫ܿ݁ݏ‬ଶ ߠ = 0, ‫ݓ‬ℎ݁‫݁ݎ‬ 0 ≤ ߠ ≤ 2ߨ except a) 0 b) ଻గ ଺ c) ହగ ଺ d) గ ଺ 4. If sin(2ߙ) = ଶ ଷ , compute the numerical value of ‫݊݅ݏ‬଺ ܽ + ܿ‫ݏ݋‬଺ ܽ a) 1 b) ସ ଽ c) ଶ ଷ d) ଷ ସ 5. A flagpole, which is 34 ft. high, stands on top of a tower, which is 30 ft. high. From a certain point in the same horizontal plane with the base of the tower, the angle subtended by the pole is equal to the angle of elevation of the top of the tower. Find the distance from this point to the base of the tower. a) 60 ft. b) 90 ft. c) 120 ft. d) 64 ft. 2222----LOGARITHMSLOGARITHMSLOGARITHMSLOGARITHMS(8(8(8(8THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Suppose that logଶ(logଷ(logହ(log଻(logଵଵ ܰ)))) = 13. How many different prime numbers are factors of N? a) 2 b) 3 c) 5 d) 1 2. What are the positive numbers x which satisfy the equation: logଶ ‫ݔ‬ logଷ ‫ݔ‬ logହ ‫ݔ‬ = logଶ ‫ݔ‬ logଷ ‫ݔ‬ + logଶ ‫ݔ‬ logହ ‫ݔ‬ + logଷ ‫ݔ‬ logହ ‫ݔ‬ ? a) (1, 40) b) (1, 30) c) (1, 20) d) (1, 10) 3. Express as a single logarithm. 2 log௫ ܽ − 2 log௫ ܾ + 3 log௫ √ܾ − ଵ ଷ log௫ ܽ a) ଵ ଺ log௫ ቀ ௔భబ ௕య ቁ b) ଵ ଵ଴ log௫ ቀ ௔భబ ௕ల ቁ c) ଵ ଺ log௫ ቀ ௔ల ௕భబ ቁ d) ଵ ଵ଴ log௫ ቀ ௔భబ ଷ௕ ቁ 4. Solve for x: ln ‫ݔ‬ − 1 = ln(2‫ݔ‬ + 1) a) The equality never exist b) 0 c) ݁ d) 1 5. Solve for x satisfying ݁୪୭୥భబ ௫ − 10୪୬ ଶ௫ = 0. a) ‫ݔ‬ ≈ 2.546 b) ‫ݔ‬ ≈ 1.232 c) ‫ݔ‬ ≈ 4.915 d) ‫ݔ‬ ≈ 0.246
• 2.
  2 3333----GEOMETRY(7GEOMETRY(7GEOMETRY(7GEOMETRY(7THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Findthe area of the region enclosed by the graph |‫|ݔ‬ + |‫|ݕ‬ = 16. a) 648 b) 256 c) 768 d) 512 2. A barber pole is a revolving cylinder 25ߨ inches tall with a diameter of 12 inches. The red stripe make 5 complete turns around the cylinder as it goes from the bottom to the top. How long is the stripe? a) 25ߨ b) 60ߨ c) 65ߨ d) 100ߨ 3. A quadrilateral has vertices at A (-5,4), B (8,6), C (12,0) and D (-1,-2). What type of quadrilateral is ABCD? a) Parallelogram b) Trapezoid c) Square d) Kite 4. Given a 4 m by 4 m square, form a new square by connecting each vertex to the midpoint of the opposite side. What is the area of the new square? a) 4.5 sq. meters b) 3.2 sq. meters c) 2.8 sq. meters d) 16 sq. meters 5. The perimeter of a right triangle is 15 + 20√22 units. The sum of the squares of all its sides is 396. Find the area of the triangle. a) ‫ܣ‬ ≈ 3 448 ‫.ݍݏ‬ ‫ݏݐ݅݊ݑ‬ b) ‫ܣ‬ ≈ 2 392 ‫.ݍݏ‬ ‫ݏݐ݅݊ݑ‬ c) ‫ܣ‬ ≈ 6 385 ‫.ݍݏ‬ ‫ݏݐ݅݊ݑ‬ d) ‫ܣ‬ ≈ 2 194 ‫.ݍݏ‬ ‫ݏݐ݅݊ݑ‬ 6. What is the ratio of the area of a square that is inscribed in a regular octagon to tha area of the regular octagon? a) ඥଶା√ଶ ଶ b) √ଶ ଶ c) √ଶିଵ ଶ d) √ଶ ସ 7. Suppose we draw 200 horizontal lines and 200 vertical lines in a plane. How many “pieces” of the plane are formed by cutting among all of these lines? a) 40 401 b) 40 000 c) 48 400 d) 44 100 8. A 5 in by 6 in by 12 in box is to have an equal increase to each edge to increase its capacity by 1080cubic inches. Find the increase. a) 1 inch b) 2 inches c) 4 inches d) 8 inches 9. What is the area of the square whose diagonal is two units longer than the length of its side? a) 8√2 b) 2√2 c) √2 d) 4√2 10. A certain chord of a circle is 12 inches and is the perpendicular bisector of a radius of the circle. Determine the area of the circles in terms of pi. a) గ ଵ଺ sq. inches b) 4ߨ sq. inches c) 36ߨ sq. inches d) 27ߨ sq. inches 4444----COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8COORDINATE GEOMETRY(8THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Find the equation of the circle with a center at (2, -5) and is tangent to the line x=7. a) 10‫ݔ‬ଶ − ‫ݕ‬ଶ − 4‫ݔ‬ + 4‫ݕ‬ + 5 = 0 b) ‫ݔ‬ଶ + 2‫ݕ‬ଶ − 4‫ݔ‬ + 10‫ݕ‬ + 5 = 0 c) ‫ݔ‬ଶ + ‫ݕ‬ଶ − 4‫ݔ‬ + 10‫ݕ‬ + 4 = 0 d) ‫ݔ‬ଶ + ‫ݕ‬ଶ + 4‫ݔ‬ − 4‫ݕ‬ + 10 = 0
• 3.
  3 2. All orderedpairs below are positive integers (x,y) that can satisfy the equation: ‫ݕ‬௫మିଵଵ௫ାଶସ = 1, ‫ݔ‬ + ‫ݕ‬ = 11 ݁‫ݐ݌݁ܿݔ‬ a) (8,3) b) (3,8) c) (1, 8) d) (1,7) 3. Find the area bounded by 2‫ݔ‬ଶ + 4‫ݔ‬ + ‫ݕ‬ = 0 ܽ݊݀ ‫ݐ‬ℎ݁ ݈݅݊݁ ‫ݕ‬ = 2‫ݔ‬ a) 3√3 ‫.ݍݏ‬ ‫ݏݐ݅݊ݑ‬ b) 9 sq. units c) 12 sq. units d) 6 + 2√2 sq. units 5555----ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10ANALYTICAL GEOMETRY(10THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Find the equation of the hyperbola whose transverse axis is parallel to the y-axis, its y-intercepts are 3 and -1, and asymptotes having equations ‫ݕ‬ − ‫ݔ‬ − 1 = 0 ܽ݊݀ ‫ݕ‬ + ‫ݔ‬ − 1 = 0. a) (௬ିଵ)మ ସ − (௫ି଴)మ ଶ = 1 b) (௬ାଵ)మ ସ − (௫ିଵ)మ ସ = 1 c) (௬ିଵ)మ ସ + (௫ିଵ)మ ଶ = 1 d) (௬ିଵ)మ ଶ − (௫ା଴)మ ଶ = 1 2. Convert the polar equation of the cardioid ‫ݎ‬ = 2(1 − cos ߠ) into the equivalent equation in rectangular coordinates. a) (‫ݔ‬ଶ − ‫ݕ‬ଶ + 2‫ݔ‬)ଶ = 4(‫ݔ‬ଶ + ‫ݕ‬ଶ) b) (‫ݔ‬ଶ + 2‫ݕ‬ଶ + ‫ݔ‬)ଶ = (‫ݔ‬ଶ − ‫ݕ‬ଶ) c) (2‫ݔ‬ଶ + ‫ݕ‬ଶ + ‫ݔ‬)ଶ = 2(4‫ݔ‬ଶ + ‫ݕ‬ଶ) d) (‫ݔ‬ଶ + ‫ݕ‬ଶ + 2‫ݔ‬)ଶ = 4(‫ݔ‬ଶ + ‫ݕ‬ଶ) 6666----PROBABILITY(8PROBABILITY(8PROBABILITY(8PROBABILITY(8THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Two balls are picked randomly at a time from a jar containing 5 balls that are numbered 2, 3, 6, 9 and 10. What is the probability that the selected balls are both prime numbered balls? a) ଵ ଶ b) ଵ ଵ଴ c) ଶ ହ d) ଵ ଺ 2. Three sticks are chosen from a set of nine sticks whose lengths are 1 dm, 2 dm, 3 dm …, 9 dm. What is the probability that the three sticks, placed end to end will form a triangle? a) ଽ ଷସ b) ଷ ଶ଼ c) ଼ ଽ d) ଵ଻ ସଶ 7777----FUNCTIONFUNCTIONFUNCTIONFUNCTION (10(10(10(10THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. If ݂(‫)ݔ‬ = ଷ௫ି௔ ହ௫ି௕ for any real positive number a and b. If ݂(0) = 0 and ݂(1) ݅‫ݏ‬ ‫.݂݀݁݊݅݁݀݊ݑ‬ ܹℎܽ‫ݐ‬ ݅‫ݏ‬ ݂ ቀ ଷ ହ ቁ ? a) ଷ ହ b) − ଽ ଵ଴ c) − ଷ ହ d) ଽ ଵ଴ 2. For which values of x does ݂(‫ݔ‬ + 3) = ݂(‫ݔ‬) + 1 ? a) (0,1) b) (1,1) c) (1,-1) d) (0,-1) 3. If ݂(݊ + 1) = ௡ ௙(௡) for all positive integers n and ݂(1) = 2. ‫݀݊݅ܨ‬ ݂(8). a) ଵ଺ ଷ b) ଵହ ଵ଺ c) ଵହ ଷଶ d) ଷହ ଷଶ 8888----ARITHMETICARITHMETICARITHMETICARITHMETIC (7(7(7(7THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. Reversing the digits of Anna’s age gives her mother’s age with difference of eighteen years. If the sum of the digits of each are 6, how old is Anna? a) 15 y.o. b) 24 y.o. c) 42 y.o. d) 33 y.o.
• 4.
  4 2. Two brothersgo up the 60-step escalators. The older brother rides up the escalators, but can only take 20 steps up during the ride since it is quite crowded. His younger brother runs up the empty down escalator, arriving the top at the same time as his brother. How many steps does the younger brother take, assuming that both escalator have the same rate? a) 100 steps b) 60 steps c) 40 steps d) 150 steps 3. The positive integers 24, 56 and A have the property that the product of any two of them is divisible by the third. What is the smallest possible value of A ? a) 21 b) 24 c) 8 d) 18 4. Today is Monday, 1 July 2002. What day of the week will be 2ଽ଼ଷଷ days from now? a) Wednesday b) Sunday c) Tuesday d) Friday 5. Find the smallest positive integer that has exactly 15 positive integral divisors. a) 144 b) 36 c) 324 d) 81 6. Find the sum of 1ଷ + 2ଷ + 3ଷ + ⋯ + 100ଷ a) 25 205 050 b) 25 502 500 c) 25 520 500 d) 25 025 050 7. The sum of three geometric progression is 52. If 8 is added to the middle term, the other two are left unchanged, the progression becomes arithmetic. What is the original middle term? a) 20 b) 12 c) 16 d) 36 8. The sum of the squares of the digits in a three place number is 84. The square of the middle digit is equal to the product of the two numbers. If the digit are reversed in order, the number is decreased by 594. What is the number? a) 631 b) 284 c) 402 d) 842 9. My watch is 2 seconds fast each hour and my seatmate’s is 3 seconds slow each hour. Right now they show the same time. In how many days will they show the same time again? a) 200 days b) 360 days c) 640 days d) 400 days 10. Melissa’s credit card number consists of nine nonrepeated, nonzero digits. By examining the digits from left to right, she found that 1 divides the 1st digit, 2 divided the first 2 digits, 3 divides the first three, and so on, until 9 divides the entire number. If the number begins with 3816, what is her complete credit card number? a) 381 627 945 b) 381 692 574 c) 381 654 729 d) 381 697 542 9999----POLYNOMIALS (10POLYNOMIALS (10POLYNOMIALS (10POLYNOMIALS (10THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. What should be the value/s of k such that the expression ݇‫ݔ‬ଶ + 24‫ݔ‬ + 9݇ become a perfect square trinomial? a) ±2 b) ±6 c) ±4 d) ±1 2. The quadratic equation ‫ݔ‬ଶ + ܽ‫ݔ‬ + ܾ = 0, has roots c and d. The quadratic equation ‫ݔ‬ଶ + ܿ‫ݔ‬ + ݀ = 0 has roots a and b. Give all the possible values of the sum a+b+c+d. a) 1 and 0 b) -2 and 0
• 5.
  5 c) -2 and1 d) -1 and 1 3. Evaluate the following sum: ݅଴! + ݅ଵ! + ݅ଶ! + ݅ଷ! + ⋯ + ݅ଵ଴଴! a) 97 b) 90+i c) 95+2i d) 96+4i 4. Find the term in ൫3 + √‫ݔ‬൯ ଵଵ that has ‫ݔ‬ସ as its variable. a) 1 472 ‫ݔ‬ସ b) 2 591 ‫ݔ‬ସ c) 3 545 ‫ݔ‬ସ d) 4 455 ‫ݔ‬ସ 5. The quadratic polynomial has the following properties ܲ(‫)ݔ‬ ≥ 0 for all real numbers x, ܲ(6) = 0, ܽ݊݀ ܲ(10) = 10. What is the value of ௉(ଶ଺)ା௉ (ି଺) ଶ ? a) 125 b) 170 c) 45 d) 295 10101010----ALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIESALGEBRAIC EQUATIONS AND INEQUALITIES (9(9(9(9THTHTHTH GRADE)GRADE)GRADE)GRADE) 1. The numbers x, y and z satisfy the equation |‫ݔ‬ + 3| + |‫ݕ‬ + 5| + |‫ݖ‬ − 8| = 1. Which of the following could be the value of |‫ݔ‬ + ‫ݕ‬ + ‫?|ݖ‬ a) 8 b) 3 c) 5 d) 0 2. Find the value of ‫ݔ‬ − ଵ ௫ , given that √‫ݔ‬ + ଵ √௫ = 5 ‫ݓ‬ℎ݁‫݁ݎ‬ ‫ݔ‬ ≠ 0. a) 25 b) 21√5 c) 21 d) 5√21 3. Find the value of ‫ݔ‬ଶ + ‫ݕ‬ଶ , ݂݅ ଵ ௫ା௬ + ଵ ௫ି௬ = ଵ ସ for any positive integers x and y, where x > y ? 4. For which value of x satisfying ௫ |௫ିଵ| > 9 is true a) ‫ݔ‬ ≠ 0 b) ‫ݔ‬ > ଽ ଵ଴ c) ‫ݔ‬ > ଽ ଼ d) ‫ݔ‬ = 1 5. Solve the equation for x: ‫ݕ‬ = ଵି √௫మయ ଵା √௫మయ a) ‫ݔ‬ = ටቀ ଵି௬ ଵା௬ ቁ ଷ b) ‫ݔ‬ = ට1 − ௬ ௬ାଵ య c) ‫ݔ‬ = (1 − ‫)ݕ‬(ଵା௬) d) ‫ݔ‬ = ටቀ ଵି௬ ଵା௬ ቁ ଶయ THANK YOU FOR CONSIDERING YOUR TIME TAKING THIS TEST! ASSESMENT EVALUATIONASSESMENT EVALUATIONASSESMENT EVALUATIONASSESMENT EVALUATION TRIGONOMETRYTRIGONOMETRYTRIGONOMETRYTRIGONOMETRY 4/5 4/5 2/5 2/5 LOGARITHMSLOGARITHMSLOGARITHMSLOGARITHMS 4/5 4/5 2/5 2/5 GEOMETRYGEOMETRYGEOMETRYGEOMETRY 8/10 7/10 6/10 4/10 CORRDINATE GEOMETRYCORRDINATE GEOMETRYCORRDINATE GEOMETRYCORRDINATE GEOMETRY 3/3 2/3 2/3 1/3 ANALYTICAL GEOMETRYANALYTICAL GEOMETRYANALYTICAL GEOMETRYANALYTICAL GEOMETRY 2/2 1 /2 1 /2 1 /2 PROBABILITYPROBABILITYPROBABILITYPROBABILITY 2/2 1/2 1/2 1 /2 FUNCTIONSFUNCTIONSFUNCTIONSFUNCTIONS 3/3 2/3 2/3 1 / 3 ARITHMETICARITHMETICARITHMETICARITHMETIC 8/10 7/10 6/10 4/10 POLYNOMIALSPOLYNOMIALSPOLYNOMIALSPOLYNOMIALS 4/5 3/5 3/5 2/5 ALGEBRAALGEBRAALGEBRAALGEBRA 4/5 4/5 3/5 2/5 RATINGS:RATINGS:RATINGS:RATINGS: 42424242----50505050 EXCELLENTEXCELLENTEXCELLENTEXCELLENT 35353535----41414141 EFFICIENTEFFICIENTEFFICIENTEFFICIENT 28282828----34343434 SATISFACTORYSATISFACTORYSATISFACTORYSATISFACTORY 0000----28282828 PROFICIENTPROFICIENTPROFICIENTPROFICIENT
• 6.
  6 Excellence – Youexcel in different branch of Mathematics. Keep it going! Efficient – You are diligent in finding solutions and efficient in aiming high scores Satisfactory – You are a “middle-class” Math student that satisfies a good highschool math enthusiast Proficient – You are on your way to open some improvements! Math is hard but sure is fun ANSWER KEYANSWER KEYANSWER KEYANSWER KEY TRIGONOMETRY 1. D 2. A 3. D 4. C 5. C LOGARITHMS 1. D 2. B 3. A 4. A 5. D GEOMETRY 1. D 2. C 3. A 4. B 5. D 6. B 7. A 8. C 9. A 10. D COORDINATE GEOMETRY 1. C 2. C 3. B ANALYTICAL GEOMETRY 1. A 2. D PROBABILITY 1. B 2. D FUNCTIONS 1. B 2. C 3. D ARITHMETIC 1. B 2. A 3. A 4. D 5. A 6. B 7. C 8. D 9. B 10. C POLYNOMIALS 1. A 2. B 3. C 4. D 5. B ALGEBRA 1. D 2. D 3. C 4. B 5. A