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Quiz

Lesson 1: Integration Techniques (Substitution and By Parts) and Definite Integrals — Picture questions (exam style)

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  • Questions count: 38
  • Passing grade: 60%
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1.
If f″(x) = 6⋅x + 12, f′(0) = 2 and f(0) = -2, which option is correct?
If f″(x) = 6⋅x + 12, f′(0) = 2 and f(0) = -2, which option is correct?
f(2) = 34, f′(2) = 38
f(2) = 36, f′(2) = 39
f(2) = 36, f′(2) = 24
f(2) = 34, f′(2) = 2
2.
A curve y = F(x) passes through (1, 3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, 3) and its gradient is the expression shown. Find y when x = 2.
11.8
18.6
15.2
44
3.
If f″(x) = 12⋅x + 2, f′(0) = 1 and f(0) = 3, which option is correct?
If f″(x) = 12⋅x + 2, f′(0) = 1 and f(0) = 3, which option is correct?
f(2) = 22, f′(2) = 1
f(2) = 28, f′(2) = 26
f(2) = 26, f′(2) = 29
f(2) = 25, f′(2) = 29
4.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
16.5
6.325
14.05
11.61
5.
If f″(x) = 8 - 6⋅x, f′(0) = 2 and f(0) = 0, which option is correct?
If f″(x) = 8 - 6⋅x, f′(0) = 2 and f(0) = 0, which option is correct?
f(1) = 5, f′(1) = 8
f(1) = 7, f′(1) = 7
f(1) = 5, f′(1) = 7
f(1) = 7, f′(1) = 2
6.
If f″(x) = 8 - 6⋅x, f′(0) = -2 and f(0) = -1, which option is correct?
If f″(x) = 8 - 6⋅x, f′(0) = -2 and f(0) = -1, which option is correct?
f(2) = 4, f′(2) = 3
f(2) = 3, f′(2) = -2
f(2) = 3, f′(2) = 2
f(2) = 1, f′(2) = -2
7.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
11.19
5.695
0.1945
9.389
8.
If f″(x) = 4, f′(0) = 0 and f(0) = 2, which option is correct?
If f″(x) = 4, f′(0) = 0 and f(0) = 2, which option is correct?
f(2) = 10, f′(2) = 0
f(2) = 8, f′(2) = 0
f(2) = 10, f′(2) = 8
f(2) = 10, f′(2) = 9
9.
A curve y = F(x) passes through (0, 2) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 2) and its gradient is the expression shown. Find y when x = 1.
1.482
-2.99
0.7022
1.222
10.
If f″(x) = 4, f′(0) = 1 and f(0) = -1, which option is correct?
If f″(x) = 4, f′(0) = 1 and f(0) = -1, which option is correct?
f(2) = 9, f′(2) = 9
f(2) = 10, f′(2) = 1
f(2) = 8, f′(2) = 4
f(2) = 9, f′(2) = 10
11.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 1.
-5.406
-4.11
4.594
-0.4057
12.
A curve y = F(x) passes through (2, -1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, -1) and its gradient is the expression shown. Find y when x = 4.
3.837
-2.387
4.275
4.713
13.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 6) and its gradient is the expression shown. Find y when x = 2.
6.595
0.5945
-0.4286
-5.405
14.
A curve y = F(x) passes through (2, -5) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, -5) and its gradient is the expression shown. Find y when x = 4.
-0.3971
3.127
-1.484
6.651
15.
A curve y = F(x) passes through (0, -4) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, -4) and its gradient is the expression shown. Find y when x = 2.
3.976
1.479
2.976
4.976
16.
A curve y = F(x) passes through (0, 5) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 5) and its gradient is the expression shown. Find y when x = 1.
-3
2
4
7
17.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
164.8
144.6
191
167.8
18.
If f″(x) = 10, f′(0) = -3 and f(0) = 1, which option is correct?
If f″(x) = 10, f′(0) = -3 and f(0) = 1, which option is correct?
f(1) = 3, f′(1) = 8
f(1) = 0, f′(1) = -3
f(1) = 2, f′(1) = 8
f(1) = 3, f′(1) = 7
19.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 2.
1.325
0.4932
5.325
-2.675
20.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
A curve y = F(x) passes through (2, 1) and its gradient is the expression shown. Find y when x = 4.
6.273
11.73
3
9
21.
A curve y = F(x) passes through (1, -1) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, -1) and its gradient is the expression shown. Find y when x = 2.
-0.2621
5.379
9.506
1.252
22.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 2.
10.99
23.65
8.66
17.32
23.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 3) and its gradient is the expression shown. Find y when x = 1.
5.143
1.143
-2.857
1.922
24.
If f″(x) = 10 - 18⋅x, f′(0) = 1 and f(0) = -1, which option is correct?
If f″(x) = 10 - 18⋅x, f′(0) = 1 and f(0) = -1, which option is correct?
f(1) = 3, f′(1) = 2
f(1) = 2, f′(1) = -8
f(1) = 2, f′(1) = 2
f(1) = 3, f′(1) = -8
25.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 2.
0.7392
2.779
1.706
-0.2273
26.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, -2) and its gradient is the expression shown. Find y when x = 3.
15
18
21.33
14.67
27.
If f″(x) = 18⋅x + 10, f′(0) = -1 and f(0) = -4, which option is correct?
If f″(x) = 18⋅x + 10, f′(0) = -1 and f(0) = -4, which option is correct?
f(2) = 38, f′(2) = 55
f(2) = 38, f′(2) = 56
f(2) = 37, f′(2) = 55
f(2) = 56, f′(2) = -1
28.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 2.
-5.5
6.833
2
0.6667
29.
A curve y = F(x) passes through (1, -5) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, -5) and its gradient is the expression shown. Find y when x = 3.
14.22
1.385
6.206
-1.806
30.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, -3) and its gradient is the expression shown. Find y when x = 1.
-2.5
1
3.5
0.5
31.
A curve y = F(x) passes through (2, -4) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (2, -4) and its gradient is the expression shown. Find y when x = 3.
36.47
21.09
9.696
23.09
32.
If f″(x) = 12 - 12⋅x, f′(0) = 1 and f(0) = 0, which option is correct?
If f″(x) = 12 - 12⋅x, f′(0) = 1 and f(0) = 0, which option is correct?
f(1) = 5, f′(1) = 1
f(1) = 5, f′(1) = 8
f(1) = 6, f′(1) = 7
f(1) = 5, f′(1) = 7
33.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 2.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 2.
-1.01
1.99
4.99
2.291
34.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 0) and its gradient is the expression shown. Find y when x = 1.
4.718
5.718
6.47
3.718
35.
A curve y = F(x) passes through (2, 2) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (2, 2) and its gradient is the expression shown. Find y when x = 3.
-3
-4.5
-0.5
-8.5
36.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
A curve y = F(x) passes through (1, 6) and its gradient is the expression shown. Find y when x = 3.
-1.263
-1.004
-1.133
-6.222
37.
A curve y = F(x) passes through (0, 1) and its gradient is the expression shown. Find y when x = 1.
A curve y = F(x) passes through (0, 1) and its gradient is the expression shown. Find y when x = 1.
3.012
2
4.012
2.012
38.
If f″(x) = 12⋅x + 4, f′(0) = -4 and f(0) = -4, which option is correct?
If f″(x) = 12⋅x + 4, f′(0) = -4 and f(0) = -4, which option is correct?
f(2) = 32, f′(2) = 28
f(2) = 12, f′(2) = 28
f(2) = 8, f′(2) = -4
f(2) = 8, f′(2) = 28
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