Math 12 Exam Review

Math 12 – Exam Review

QUADRATICS:

1. What is the vertical stretch factor associated with this graph?

(a) -3 (b) (c) (d) 3

2. If the solutions of a quadratic equation are imaginary, which is true about the value of the discriminant?

(a) D < 0 (b) D = 0 (c) D > 0 (d) D is imaginary

3. Which graph best represents the function y = (x + 2)2 – 3 ?

4. What is the standard form of the function: ?

(a) (b) (c) (d)

5. Which maps the function y = x2 onto the image ?

(a) (b) (c) (d)

6. What is the value of the disriminant for 3x2 + 6x – 1 = 0?

(a) (b) (c) 24 (d) 48

7. What is the vertex of the parabola given by y = x2 + 4x + 1?

(a) (-2,3) (b) (-2,-3) (c) (2,3) (d) (4,1)

8. What type of function would best model this data?

(a) cubic (b) exponential (c) linear (d) quadratic

9. What are the roots of x2 = 5x + 14?

(a) x = -2 and x = -7 (b) x = -7 and x = 2 (c) x = 7 and x = -2 (d) x = 7 and x = 2

10. What are the x-intercepts for the graph of y = (x)(2x – 1)?

(a) (b) (c) (d)

11. What transformation of y = x2 results in the equation 3(y + 2) = (x – 6)2?

(a) VT 2, HT -6, VS 3 (b) VT -2, HT 6, VS

12. What is the range of the function shown?

(a) (b)

13. What is the value of t5 in the sequence defined by tn = -3n2 + 1?

(a) -78 (b) -76 (c) -74 (d) 5

14. What value of ‘c’ makes x2 + 7x + c a perfect square?

(a) (b) 7 (c) (d) 49

15. A quadratic equation f(x) = 0, has a negative discriminant. Which is the graph of f(x)?

16. The graph of a quadratic function intersects the x-axis at points (1,0) and (7,0), respectively. The equation of the axis of symmetry for the graph of this function is:

(a) x = 7 (b) x = 4 (c) y = 4 (d) y = 1

17. A dare-devil pilot was flying his plane along a certain path defined by , where ‘h’ represents the plane’s height at different times, ‘t’. From the equation, what indicates that the plane will have a minimum height?

(a) The y-intercept is 104 (b) The coefficient of ‘t2’ is positive

18. Determine the roots of .

19. Given the following quadratic equation:

(a) Write the equation in transformational form.

(b) State the transformations of y = x2. (c) Write the mapping rule.

20. The daily revenue (y) in dollars for Ski Wentworth can be modeled by the equation where x represents the temperature in degrees Celsius.

(revenue = income – expenses).

(a) What is the maximum daily revenue and at what temperature does this occur?

(b) For what temperatures is Ski Wentworth losing money?

21. The data in the table below was recorded at a football game. Richard kicked a football and the height of the football was recorded.

t (time in seconds) / 1 / 2 / 3 / 4
h (height in metres) / 15 / 21.5 / 17 / 1.5

(a) Using a graphing calculator, find the equation of the best fit for the table above.

(b) How long does it take the ball to hit the ground?

22. Given: x2 – x – 2 = 0

(a) Solve for ‘x’. (b) Solve for ‘x’ using a different method.

23. Find the zeros of y = 3x2 – 6x – 9.

24. Write two different quadratic functions such that each has x-intercepts at -5 and 4.

25. The function describes the height of a baseball ‘h’, in metres, as a function of time ‘t’, in seconds, from the instant the ball is hit.

(a) Express this function in transformational form.

(b) How long will it take the baseball to reach its maximum height?

26. An object is fired into the air and the function expresses the relationship between height, h, in metres, and time, t, in seconds.

(a) What is the maximum height reached by this object?

(b) When will the object be at a height of 30 m above the ground?

EXPONENTIALS AND LOGARITHMS:

1. Which function best represents this graph?

(a) y = (0.5)x (b) y = (0.5)x + 1

2. What is the equation of the horizontal asymptote for y = 3(4)x + 2?

(a) y = 2 (b) y = 3 (c) y = 4 (d) y = 5

3. What is the range of the function y = 3(2)x + 1?

(a) {y│y > 1, y ε R} (b) {y│y ≥ 1, y ε R} (c) {x│x > 4, x ε R} (d) {x│x ε R}

4. Ralph buys a new house valued at $90000. If the value of the house increases by 4% every 3 years, which equation best models the value of the house in terms of the number of years since it was purchased?

(a) (b) (c) (d)

5. Which sequence represents an exponential function?

(a) {1, 3, 5, 7, 9, ...} (b) {1, 4, 9, 16, 25, ...} (c) {1, 3, 9, 27, 81, ...} (d)

6. What is the value of (30 + 4-1)-2?

(a) (b) (c) (d) 4

7. What is the simplified form of: ?

(a) 2x3 (b) 2x4 (c) (d) 2x8

8. What is the value of x in the equation ?

(a) -2 (b) -1 (c) 0 (d) 1

9. Which function describes this data?

(a) (b) (c) y = 3(5)x (d)

10. What are the coordinates of the y-intercept of the function y = 20(1.8)x + 3.4?

(a) (0,1.8) (b) (0,3.4) (c) (0,20) (d) (0,23.4)

11. Evaluate

(a) (b) (c) (d)

12. What is the equation of the horizontal asymptote of the graph of the function y = -4(1.2)x + 2.5?

(a) y = -4 (b) y = -2.5 (c) y = 1.2 (d) y = 2.5

13. The value of is:

(a) -25 (b) -5 (c) (d)

14. The value of is

(a) -16 (b) (c) (d)

15. Write as a single logarithm.

(a) log 3 (b) log 2 (c) log36 (d) log63

16. If , determine an expression for log B.

(a) (b) (c) (d)

17. Given the function . It models

(a) $10000 invested at 108% yearly interest for t years.

(b) $10000 returned from an investment lasting t years with an interest rate of 8% per year.

(d) the amount owed after borrowing $10000 for 8 years.

18. Simplify .

(a) 2a3 (b) (c) (d)

19. Which of the following is FALSE?

(a) (b) (c) (d)

20. The expression simplifies to

(a) (b) (c) (d)

21. Which sequence is geometric?

(a) 2, 5 + , , … (b) 2, 4, 16, 128, … (c) 2, 4, 6, 8, … (d) , 6, , 12, …

22. The expression is equivalent to

(a) 2k (b) 2k (c) 25k (d) 25k

23. Evaluate the following expression:

24. Solve for ‘x’.

(a) (b) (c)

25. Mom invests $4000 when Billy is born. She is told that Billy will have $20000 in 18 years. Determine the doubling period for this investment.

26. Solve for ‘x’ in

27. The population of a newly discovered organism can be described by the function where ‘P’ is the number of organisms and ‘t’ is the time (in minutes).

(a) In the equation , what do the ‘3’ and the ‘10’ signify in the context of the problem?

(b) How long does it take the population to double?

28. Show that 2a, 2a+d, 2a+2d is a geometric sequence for all values of ‘a’ and ‘d’.

29. Using the laws of logarithms and the definition of an arithmetic sequence, show that

log(a), log(ab), log(ab2), log(ab3) is an arithmetic sequence.

30. Algebraically solve for ‘x’ in each of the following.

(a) (b) (c)

CIRCLES & COORDINATE GEOMETRY

1. If the coordinates of the midpoint M, of AB are (2,-3) and B is the point (-5,1), then A has the coordinates:

(a) (-1.5,-1) (b) (-9,7) (c) (3.5,-2) (d) (9,-7)

2. Which is the converse of the following statement?

“If two chords of a circle are congruent, then they are equidistant from the centre of the circle.”

(a) If two chords of a circle are not congruent, then they are not equidistant to the centre of the circle.

(b) Two chords that are equidistant from the centre of the circle must be congruent.

(d) Two chords of a circle are equidistant to the centre of a circle, if they are congruent.

3. If a chord in a circle measures 12 units and the radius of the circle measures 12 units, how far is the chord from the centre?

(a) 12 units (b) units (c) 6 units (d) units

4. PQ has a midpoint at (m,0) and the coordinates of P are (0,p). The coordinates of Q are

(a) (2m,2p) (b) (c) (-m,-p) (d) (2m,-p)

5. Given the statement: In a 4 sided figure, if the lengths of all four sides are equal, then the diagonals are perpendicular.

(a) Write the converse of this statement. (b) Is the converse true? Explain.

6. A chord 8 cm in length is drawn in a circle with a radius of 6.5 cm. How far is the chord from the centre of the circle?

7. Given A(-4,2) and B(10,6) are the endpoints of a segment. Find the coordinates of the points dividing the segment AB into 4 equal segments.

8. A quadrilateral has vertices P(-6,8), Q(0,-5), R(14,3), and S(8,16). Prove that the figure PQRS is a parallelogram.

9. Line segment AB has endpoints at A(2,11) and B(8.-7). Line segment CD has endpoints at C(9,8) and D(-1,-9). Determine whether or not the line segments AB and CD bisect each other.

10. A circle has its centre at the origin, (0,0). A chord of the circle has endpoints A(3,1) and B(-1,-3). Find the equation of the perpendicular bisector and show that it goes through the centre of the circle.

PROBABILITY

1. An experiment consists of tossing a fair coin and rolling a fair die. What is the probability of obtaining a head and a 5?

(a) (b) (c) (d)

2. A math club has 24 students. In how many ways can a president and vice-president be chosen?

(a) (b) (c) (d)

3. If event ‘X’ is randomly choosing an ace from a standard deck of 52 playing cards, then is

(a) (b) (c) (d)

4. Suppose event ‘X’ is “obtaining a 6” when rolling a die. Which of the following statements is FALSE?

(a) (b) (c) (d) and X are mutually exclusive

5. The exact value of is

(a) (b) 2 (c) 9900 (d) undefined

6. If the probability of winning game A is 0.20 and the probability of winning game B is 0.35, what is the probability of winning game A or game B?

(a) 0.07 (b) 0.15 (c) 0.48 (d) 0.55

7. There is a bag containing 10 marbles. Five marbles are white, two are blue and three are red. If you take one marble from the bay, what is the probability of it being white?

(a) (b) (c) (d)

8. One man and two women are seated randomly in a row. What is the probability that the two women are seated next to each other?

(a) (b) (c) (d)

9. Of 100 people surveyed, 42 people owned a dog, 53 people owned a cat and 17 people owned both a dog and a cat. Based on this information, the probability that one of the people surveyed will own neither a dog nor a cat is:

(a) (b) (c) (d)

10. Three cards are dealt from a standard deck of 52 cards. Determine the probability of getting at least one diamond.

(a) 0.41 (b) 0.44 (c) 0.59 (d) 0.75

11. An examination consists of 13 questions. A student must answer only one of the first two questions and only nine of the remaining ones. How could you calculate the number of choices of questions a student has?

(a) 13C10 (b) 11C8 (c) 2 x 11C9 (d) 2 x 11P2

12. Suppose one card is drawn from a standard deck of 52 cards. What is the probability of the card drawn being: (a) an ace (b) a queen or a jack?

13. Explain the meaning of 5Co = 1. Use an example in your explanation.

14. A box contains 6 white balls and 5 red balls. David randomly selects three balls at the same time. What is the probability that when he removes the three balls

(a) exactly two will be white? (b) all three will be white? (c) at least one will be white?

15. A toy box contains 4 different cars and 6 different trucks. What is the probability of choosing a collection which consists of 2 cars and 3 trucks?

16. Mathematics students were surveyed and asked whether they use a pencil or pen to write a math exam. The information obtained is given in the Venn diagram below.