PC 11
MIDTERM REVIEW
1. Given the arithmetic sequence 32, 38, 44, ..., determine
a. t11
b. t 24
c. t n
2. How many terms are in the following arithmetic sequences?
a. 29, 22, 15,...., -55
b. 3.2, 4.7, 6.2, ..., 34.7
c. -12x - 10, -9x - 8, -6x – 6, ... , 57x + 36
3. In the following arithmetic sequences, determine which term the bold number is in the sequence.
a. 31, 22, 13,..., -356
b. 43, 55, 67, ..., 463
c. 4, ... -73, -80, -87, ...
4. Insert two numbers between 5 and 44 so the four numbers form an arithmetic sequence.
5. Insert 3 numbers between 99 and 167 so the five numbers form an arithmetic sequence.
6. Copy and complete the arithmetic sequences: a. 3,___,___,___,23
b. 3,___,___,___,303
7. Write the formula for the general term of a sequence. a. 1, 3, 5, …
b. 11, 9, 7, …
8. A car salesperson receives a base salary of $275 per week, plus $250 for every car sold. What is the weekly
salary if
a. 6 cars are sold
b. 14 cars are sold.
9. Determine the sum of the first 10 terms of each arithmetic series.
a. 1 + 2 + 3 + …
b. 6 + 12 + 18 + …
c. -10 – 25 – 40 – ...
10. Determine the sum of each of the following arithmetic series
a. 6 + 10 + 14 + ... + 50
b. 1 + 2 +3 + ... + 999 c. 3 + 5.5 + 8 + ... + 133
11. If a = -5, tn = 22, and Sn = 85, determine n.
12. A pile of bricks is arranged in rows. The number of bricks in the rows forms an arithmetic sequence. There
are 35 bricks in the 4th row and 20 bricks in the 9th row. Assuming there are 9 rows,
a. How many bricks are there in the first row?
b. How many bricks are there in the pile?
13. Determine the indicated term of each geometric sequence.
a. 2, 6, 18, …, t9
b. 16, -8, 4, …, t11
c. -64, 48, -36, …, tn
14. In a geometric sequence, the 2nd term is 6 and the 5th term is 384. Determine the value of the first term.
15. A population grows by 3% a year. If the current population is 1,000,000, what will the population be in 5
years?
16. A battery loses 5% of its charge a day. If the battery is fully charged today, how much charge will be left in 8
days?
17. For the following geometric series, find the indicated sum.
a. 120 + 60 + 30 +... S10
b. 5 – 12.5 + 31.25 - ...S15
c. 10, 50, 250,...Sn
18. The sum of the geometric series 1 – 3 + 9 ... is --182. How many terms are in the series? (Hint: Change
powers so both sides of the equation have the same base)
19. Determine the infinite sum of each of the following geometric series.
a. 81 + 27 + 9 + ...
b. 140 + 35 + 8.75 + ...
c. 50 – 25 + 12.5 - ...
20. If S =90 and a = 54, determine the value of r.
21. A ball is dropped from a height of 4.0 m to a floor. After each bounce, the ball rises to 55% of its previous
height.
a. What is the total vertical distance the ball has travelled after it hits the ground on the 6th bounce?
b. What is the total vertical distance the ball travels before it comes to rest?
22. Draw each of the following angles in standard position. For each angle, determine the reference angle as
well.
a. 48˚
b. 115˚
c. 220˚
d. 37˚ after being reflected in the x-axis
23. Determine the exact values of each of the following angles.
a. cos 45˚
b. sin 60˚
c. tan 30˚
d. cos 90˚
e. sin 270˚
f. tan 180˚
24. Determine the exact values of each of the following angles.
a. cos 120˚
b. sin 150˚
c. tan 330˚
d. cos 225˚
e. sin 300˚
f. tan 225˚
25. Point P (-28, -45) lies on the terminal arm of angle θ, in standard position. Determine the exact values of sin
θ, cos θ, and tan θ
26. If the terminal arm of θ is in quadrant 4, and sin θ = 
5
, determine the exact values of cos θ and tan θ.
13
27. Determine θ for each of the following questions, if 0˚≤ θ < 360˚
a. tan θ =  1
b. sin θ =
28. Solve the following triangles.
a.
3
2
c. cos θ = -1
b.
c.
29. Solve ABC if b = 43 cm, c = 49 cm, B = 41˚
30. How does the graph of a quadratic function in the form y  a( x  p) 2  q change when
a. The value of p is increase by 4 and the value of q increased by 9.
b. The value of a is multiplied by a factor -2 and the value of p is decreased by 7
31. Graph y  2( x  1) 2  8 . State the vertex, equation of axis of symmetry, x-and y- intercepts, domain and
range, and the maximum or minimum value.
32. Determine the equation of the parabola that has a vertex of (-3, 12) and a y intercept of 39.
33. Convert the following equations to standard form ( y  ax 2  bx  c ).
a.
y  2 x  3x  7  14
b. y  3( x  4) 2  5
34. If the point (4, 8) is on the graph y  2( x  1) 2  26 , where will the point be on y  2( x  3) 2  18 ?
35. Complete the square.
a. y  x 2  4 x  2
b. y  3x 2  9 x  7
c. 3x 2  4 x  3  y   x 2  2 x  4
36. Solve the following.
a. The difference of two numbers is 40. Their product is a minimum. Determine the numbers.
b. The sum of two numbers is 28. The sum of their squares is a minimum. Determine the numbers.
c. A lifeguard marks off a rectangular swimming area at a beach with 200 metres of rope. What is the
maximum area of water she can enclose (assuming the rope is used for three sides of the rectangle)?
d. A theatre company is selling tickets to a show for $6. At this price, 400 people attend. For every $2
increase in price, 20 fewer people will go. What is the best ticket price to maximize revenue?
e. Two numbers have a difference of 20. When the squares of the numbers are added together, the
result is a minimum. What are the two numbers?
37. Solve 0  x 2  4 x  4 graphically.
38. Factor the following.
2
a. x  36
2
b. 49  x
2
c. 16 x  81
d. 7 x 2  7 y 2
2
e. 4 x  4 x  1
f. 9 x 2  18 xy  9 y 2
2
g. 6 x  21x  9
2
h. 7 x  28 x  21
2
i. 3x  11x  20
2
j. 2 x  5 x  2
2
k. 15  2x  x
2
l. 8 x  10 x  3
m. 10( x  3) 2  21( x  3)  10
n.
2 x  12  4 x  7 2
39. Solve the following.
2
2
2
2
a. x  20 x  51  0
b. x  12 x  28  0 c. x  16 x  48  0 d. 25 x  36  0
2
2
2
2
e. 49 x  144  0
f. x  18 x  81  0 g. 16 x  9 x  0
h. 8 x  15 x
2
2
2
2
i. 36 x  75 x  25  0 j. 10 x  x  3  0
k. 15 x  7 x  2  0 l. 10 x  17 x  6  0
40. Solve using the quadratic formula. Leave answers in exact form. Also, determine the nature of the roots.
2
2
2
2
a. 3x  11x  5  0
b. x  9 x  7  0
c. 3x  x  1  0
f. 9 x  24 x  16  0
41. Solve.
a. Find two consecutive numbers whose product is 30.
b. Find two consecutive integers, the sum of whose squares is 41.
c. One side of a square is increase by 6 cm and another side is increased by 12 cm, thereby forming a
rectangle whose area is 432 𝑐𝑚2 . What are the dimensions of the sides of the square?
d. Find the dimensions of a rectangle whose area is 48 and whose perimeter is 28.
e. The dimensions of a picture inside the frame are 8 and 12, and the area of the frame is 44. Find the
dimensions of the frame.
MIDTERM REVIEW ANSWERS
1a. 92 b. 170 c. tn = 6n + 26
2a. 13 b. 22 c. 24
3a. 44 b. 36 c. 13
6a. 8, 13, 18 b. 78, 153, 228
7a. tn = 2n - 1 b. tn = -2n + 13
15. ~1,159,274
3
22a
23a.
1
2
25. sin    45
53
b.
c.
 R  48
 R  65
29 C = 48.4˚ A = 90.6˚ a = 65.5
OR C = 131.6˚ A = 7.4˚ a = 8.4
 R  37
 R  40
24. -0.5 b. 0.5 c.  1
x-int: -1 or 3 ; y-int = 6
Domain: ARN ; Range: y ≤ 8 ; max of 8
33a. y  2 x 2  11x  7 b y  3x 2  24 x  53
32. y  3( x  3) 2  12
b. y  3( x  1.5) 2  0.25
c. y  4( x  0.25) 2  6.75
36a. 20 and -20
d. $23
34. (0, 0)
b. 14 and 14
c. 5000 m2
e 10 and -10
38a. x  6x  6
b. 7  x 7  x 
c. 4 x  94 x  9
d. 7 y  1 y  1 e. 2 x  12
f. 9x  y 2
g. 32 x  1x  3 h. 7x  1x  3 i. 3x  4x  5
j. 2 x  1x  2 k. 5  x 3  x 
l. 2 x  34 x  1
m. 2 x  115x  13
n.  12x  1x  4
37.
39a. x = 3, 17
d.
30a. It is moved 4 to the right and 9 up
b. It is reflected on the x-axis, expanded vertically 2 times, and moved left 7
31. Vertex (1, 8) ; Axis of Symmetry: x = 1 ;
35a y  ( x  2) 2  6
9
d.  1 e.  3 f. 1
2
3
2
26. cos   12 tan    5
12
13
28a. x = 37m θ = 70˚ y = 37m
b. B = 63.5˚ R = 79.9˚ H = 36.6˚
c. x = 54.4 km a = 43.9˚ b = 87˚
1 d. 0 e. -1 f. 0
3
28
45
cos   
tan  
53
28
27a. θ = 135˚ or 315˚ b. θ = 60˚ or 120˚
c. θ = 180˚
b. 330 c. -775
21a. 13.29m b. 13 7 m
20. 0.4
3
3
c.
2
b.
8a. $1775 b. $3775 9a. 55
17a. 239.77 b. 1,330,462.25 c. Sn  2.55n  1
16. ~66.3%
19a. 121.5 b. 186 2 c. 33 1
18. 6
5. 116, 133, 150
13a. 13,122 b. 0.015625 c. tn = -64(-0.75)n-1
10a. 336 b. 499,500 c. 3604 11. n = 10 12a. 44 b. 288
14. 1.5
4. 18, 31
b. x = 2, -14
c. x = 4, 12
d. x=  6
5
e.  12
7
1 2
k.  ,
5 3
f. x = 9
5
, 5
j.  1 , 3
l.  3 , 2
12
3
10
2 5
16
40a. x= 11  181 ; 2 diff. r.r.
b. x= 9  109 ; 2 diff. r.r
c. No Solution ; no r.r.
d. x = 4 ; two equal r.r
3
2
6
41a. 5,6 or -5, -6 b. 4, 5, or -4, -5 c. 12 cm by 12 cm d. 6 by 8 e. 10 cm by 14 cm
g. 0, 9
h. x = 0, 15
8
i. 