IB Math SL Year 2Name: ___________________________

Quarterly topical Review

Topic: Sequence/Series

Use formula booklet for this section

1. Arturo goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks).

(a) How far does Arturo swim in the final week?

(b) How far does he swim altogether?

2. Consider the geometric sequence −3, 6, −12, 24, ….

(i) Write down the common ratio.

(ii) Find the 15th term.

3. In an arithmetic sequence, the first term is 5 and the fourth term is 41. a) Find the common difference.

b) Find the value of n where un = 9005.

IB Math SL Year 2

4. Find the sum of the infinite geometric series ...

8116

278

94

32

a) For this series, find the common ratio, giving your answer as a fraction in its simplest form.

b) Find the seventh term of this series; leave your answer as a fraction.

c) Find the exact value of the sum of the infinite series.

5. In a geometric progression, u2=12and S∞=64. Find u1.

6. The first term of an infinite geometric sequence is 18, while the third term is 8. There are two possible sequences. Find the sum of each sequence.

IB Math SL Year 2Name: ___________________________

Quarterly topical Review

Topic: Binomial Expansion and Graphing

Use formula booklet for expansions

For graphing, INCLUDE LABELS for FULL CREDIT

1. Consider the expansion of (x2 – 2)5.

(a) Write down the number of terms in this expansion.

(b) The first four terms of the expansion in descending powers of x are

x10 – 10x8 + 40x6 + Ax4 + ...

Find the value of A.

2. Consider the expansion (x+ y )14. a) How many terms would there be in this expansion

b) Determine the coefficient of x3 y11

3. f ( x )= 2x−4 Sketch

vertical asymptote(s) _______________

horizontal asymptote _______________

y-intercept _____________

x-intercept(s) _____________

domain _______________

IB Math SL Year 2

4. Graph f ( x )=3x+2

a) State any asymptotes

b) State any intercepts

c) State an additional point

d) Sketch graph including labels of all details stated in a-c

5. Given function: g(x) =log2 x

i) Find the equation for the vertical asymptote

ii) Find the x-intercept

iii) Evaluate g(2) .

iv) Hence, sketch the graph for g(x )

IB Math SL Year 2

Name: ___________________________

Quarterly topical Review

Topic: Logarithms and Exponential Equations

1. Let ln a = p, ln b = q. Write the following expressions in terms of p and q.

(a) ln a3b (b) ln

ba

2. Let p = log10 x, q = log10 y and r = log10 z.

Write the expression log10

zyx

2 in terms of p, q and r.

3. Solve for x:

IB Math SL Year 2

4. Solve for x: i) 2×5x−1=250 ii) 3x2−2 x=27 iii)

18x

=32−x+2

5. Solve for x:

7. Solve the equation for x. log5(x+6)−log5(x+2)=log5 x

8. Solve for x: log3 (4 x−1 )=3

IB Math SL Year 2

Name: ___________________________

Quarterly topical Review

Topic: Probability

3. The mass of packets of a breakfast cereal is normally distributed with a mean of 750 g and standard deviation of 25 g.

(a) Find the probability that a packet chosen at random has mass

(i) less than 740 g;

(ii) at least 780 g;

(iii) between 740 g and 780 g.

4. Let A and B be events such that P(A) = 21

, P(B) = 43

and P(A B) = 87

.

(a) Calculate P(A B).

(b) Calculate P(AB).

(c) Are the events A and B independent? Give a reason for your answer.

5. The number of club members of each gender choosing each game in a particular year is shown in the table below. Billiards Snooker Darts

Male 39 16 10Female 21 14 18

IB Math SL Year 2

A club member is to be selected at random. What is the probability that the club member selecteda. Is female given they like darts? b. Is a male?

6.a) Let U = {2, 3, 4, 5, 7, 9}

X = {x : x ∈Z, 2≤x<6}Y = {x : x ∈ odd numbers}Z = {2, 4, 5, 7, 9}

a) What elements belong to X ∩Y ?

b) Is 5∈(X ∩Y )?

c) What is n(X∪Z)?

d) Is Y ⊆Z? Explain why or why not.

7.

IB Math SL Year 2

Name: ___________________________

Quarterly topical Review

Topic: Statistics

1. a) Find the Z-score corresponding to the given value of X with X~N(12,36), x = 11

b) Interpret this z score with respect to the mean.

2. Find the approximate standard deviation for the data set shown below.

3.

a) Determine the equation for the line of best fit.

b) Determine the correlation coefficient. What does this tell you about the relationship?

c) Predict my weight. I am 165.1cm tall. Why is using the linear regression equation to make a prediction is reliable in this situation?

IB Math SL Year 2

4. The random variable X has the following distribution. (a) Find c.

(b) Find E(X).

5. A fair six-sided dice has a ‘1’ on one face, a ‘2’ on two of its faces and a ‘3’ on the remaining three faces. The dice is thrown twice. T is the random variable ‘the total score thrown’

a) tabulate the sample space

b) find the probability that the total score is more than 4.

6. A family consists of 3 children. What is the probability that at most 2 of the children are boys?

7. A bag contains 6 red Bingo chips, 4 blue Bingo chips, and 7 white Bingo chips. What is the probability of drawing a red Bingo chip at least 3 out of 5 times? Round your answer to the nearest hundredth

x 1 2 3 4 5P(X=x) 7c 5c 4c 3c c

IB Math SL Year 2

Name: ___________________________

Quarterly topical Review

Topic: Transformations/Functions/Quadratics

1. If f ( x )=−x+7, find(a) f (2) (b) f (x)=3

2. Is the following relation a function? Why or why not?  { (1, 5), (6, 4), (4, 2), (3, 5), (0, 9) }

3. For each graph shown, determine the domain and range: a) (b)

4. If f ( x )=5−3 x and g ( x )=x2+4, (a) find ( f ∘ g)(3) (b) find ( f ∘ g)(x)

5. Determine the inverse function, f−1 (x ) of f ( x )=2x+3.

6. For the following, draw the line y=x and then sketch graph the inverse, f−1(x).

IB Math SL Year 2

7. The graph of the function y = f (x), 0 < x < 4, is shown below. On the diagram below,draw the graph of y = 3f (−x). (It might help to state the transformations that occurred!)

8. Consider the following function: y = -3f(2x-6) + 9. Order the following transformation in the correct sequence that they would be performed:

_____ reflect over x-axis_____ vertical stretch of 3_____ horizontal shrink of 2_____ shift right 6_____ shift up 9

9. Write each function in the form f(x) = a(x-h)2+ k. Then state the vertex and y-intercept.(a) f(x) = x2 + 10 x – 6 (b) f(x) = -2x2 + 8x – 3

10. Using the information provided in the graph, write the equation of the quadratic function. Write your final answer in the standard form y=a x2+bx+c.

IB Math SL Year 211. Write down the equation for the axis of symmetry of the following function: