MCR 3U – Grade 11 University Preparation
Discrete Functions
23 K
14A
10T
Com. Level
KNOWLEDGE AND UNDERSTANDING [23 Marks]
Multiple Choice
Enter the letter of the correct answer for questions 1 - 8 into the table
below:
1
2
3
4
5
6
7
8
8K
1. What is the sum of terms in 14th row of Pascal's Triangle?
a) 32 768 b)16 384
c) 8 192
d)169
2. Finding the next term(s) in the Fibonacci sequence is considered a(n)
procedure.
a) Explicit b) Arithmetic
c) Geometric
d) Recursive
3. tn = n3 (6 – n) is an example of what type of formula?
a) Explicit b) Geometric c) Cubic d) Recursive
4. An auditorium has 13 rows of seats. Each row has 10 more seats than
the previous row and the first row has 8 seats. How many people does
the auditorium seat? - This question could be solved using:
a) An arithmetic series
c) A geometric series
b) An arithmetic sequence
d) A geometric sequence
5. How many terms are there in the expansion of the binomial power
(4x + 3)34?
a) 33
b) 34
c) 35
d) 43
6. In relation to Pascal's triangle: t9, 7 + t9, 6 is equal to ... ?
a) t10, 8
b) t10, 7 c) t10, 6
d) t9, 7
7. The domain of a function representing a sequence is the set (or subset)
of the ____________ numbers.
a) Real
b) Rational
c) Integer
d) Natural
8. In an arithmetic sequence a = 4 and d = -3. The first three terms of the
sequence are:
a) –3, –12, – 48 b) 4, 1, –2 c) –3, 1, 5 d) 4, –12, 36
Full Solution
Show all your work for the following questions. Use formulas instead of
listing terms.
9. Given the sequence: 4, –24, 144, –864, ..., determine: [2K, 1K, 1K,
2K]
a) The explicit formula
b) The recursive formula
b) The value of the 8-th term.
d) The sum of the first 8 terms.
10. Given the sequence: 45, 38, 31, 24, ..., determine: [2K, 1K, 1K, 2K]
a) The explicit formula
b) The recursive formula
c) The value of the 28-th term.
d) The sum of the first 15 terms.
11. Find the values of terms 3 and 4 in a sequence using the following
recursive formula: [3K]
𝑡𝑛 = 3𝑡𝑛−1 − 5𝑡𝑛−2 and 𝑡1 = 1,
𝑡2 = −2
APPLICATION [14 Marks]
12. Determine the explicit formula for the following sequence: [5A]
13. Use Pascal's Triangle to expand and simplify the following binomial
power: (5x3 – x) 4. [4A]
14. At a fish hatchery, fish hatch at different times even though the eggs
were all fertilized at the same time. On the first day, 2 fish hatch. Every
day thereafter, the number of fish hatching is triple the number from the
previous day. On the last day, 4 374 fish hatch. Calculate the total
number of fish that were hatched. [5A]
15. In a geometric sequence, the first three terms are 5x – 8, 3x, 2x + 2.
Find the value(s) of x and then calculate the sum of the first 5 terms
(using the formula). [6T]
16. How many ways are there to go from X to Y in the diagram below?
Rules: You can ONLY travel along the lines to the right or down. Try to
explain your thinking by labelling certain sections (which you believe
require clarification) in the diagram and refer to them in your
explanation. [4T]